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Perfusion culture : investigation of temperature distribution in an acoustic separator Drouin, Hans 2004

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PERFUSION  CULTURE:  INVESTIGATION OF TEMPERATURE DISTRIBUTION IN AN ACOUSTIC SEPARATOR  by  HANS DROUIN B . A . S c , University of Sherbrooke, 2001  A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S FOR T H E D E G R E E OF MASTERS OF A P P L I E D S C I E N C E in T H E F A C U L T Y OF G R A D U A T E STUDIES Department of Chemical and Biological Engineering and  The Biotechnology Laboratory  We accept this thesis as conforming to the required standard  The University of British Columbia May 2004 © Hans Drouin, 2004  Library Authorization  In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  IICIY)^  Pro,, ; ^  13/dT/ZOOH  Name of Author (please print)  Title of Thesis:  S)^  p^H  Degree:  fo,  ^  Date (dd/mm/yyyy)  Cutk„*  !  f ^^Lv^ „„ t  C<3v  Year:  Jj^  Department of £ h * r n ^ J a » r i The University of British Columbia Vancouver, B C C a n a d a  r W o O, j  y  w J )  2&c3q  2?nc,W/,W /  / j  /  r  n„J 4 f  Abstract Mammalian cell perfusion cultures require practical and efficient cell retention devices that maintain high performance while minimizing negative influences on the culture. The acoustic separator is a mechanically simple device that provides high separation efficiency for months of continuous operation. The cells are retained in the chamber by acoustic forces whose magnitude is limited because the acoustic energy is ultimately dissipated as heat. On the other hand, the cell suspension, pumped into the acoustic separator through a recirculation line, is cooled somewhat by heat transfer to the ambient environment. Thus, the thermal control of the acoustic filter is essential to avoid negative effects on the cell culture while maximizing efficient separation.  The purpose of this work was to investigate the thermal aspects of acoustic separations. Cell culture experiments demonstrated that C H O cells could be exposed to a cyclic temperature variation from 31.5 to 38.5°C, in a simulated acoustic separator environment, without significant effects on their growth rate, glucose consumption or t-PA production. Following an investigation of the acoustic separator recommended settings, a minimal recirculation flow rate of 15 L day" , at an ambient temperature of 22°C with a 45 s run 1  time was found to provide efficient operation with limited environmental influences on the cells. Nonetheless, for a reactor cell concentration of 10 cells mL" and a 5 L day" 7  1  1  harvest flow rate, the separation efficiency was greater than 95% for ambient temperatures from 19 to 26°C.  A i r cooling flow rates from 0 to 16 L min" did not 1  perturb the separation efficiency of the system though air cooling was required to limit the temperature increase. A central composite factorial design experiment was used to ii  obtain surface response models of the inlet and outlet temperatures as well as the inlet to outlet temperature change. These empirical models provided a tool to help optimize acoustic separator operation (i.e., selecting conditions that ensure temperatures are maintained in the acceptable range). Also, a theoretical model of the acoustic separator was developed, based on energy conservation, which provided an estimate of the 3dimensional temperature distribution in the device. Once all of the unknown parameters had been determined by fitting the model to measured temperature data, it was able to predict the outlet temperatures to within 1°C. It was estimated that 56% of the power input was transformed into heat in the liquid compared with 6.5% in the transducer wall and 2% in the reflector wall. It was assumed that the remainder was lost due to the conversion of electric to acoustic energy and to conduction and eventual dissipation to the surroundings through the other solid components of the separator.  Temperature  profiles generated by the model as well as experimental measurements confirmed that the air cooling device was essential to control the temperature in the acceptable range.  iii  Table of Contents  ABSTRACT TABLE OF CONTENTS  II IV  LIST OF TABLES  Vlll  LIST OF FIGURES  IX  NOMENCLATURE  XIII  ACKNOWLEDGEMENTS  XV  1  INTRODUCTION  1  1.1  Overview  1  1.2  Production Methods  1  1.3  Types of Cell Retention Devices  2  1.4  Acoustic Separators  3  2  THESIS MOTIVATION  4  3  LITERATURE REVIEW  5  3.1 Effect of Temperature on Cell Cycle and Metabolism 3.1.1 Effect of Low Temperatures in Batch Systems 3.1.2 Effect of Low Temperatures in Perfusion Systems 3.1.3 Effect of High Temperatures and Heat-Shock.... 3.1.4 Range of Temperature for CHO Cells 3.2 Types of Cell Retention Devices 3.2.1 Gravity Settlers 3.2.2 Centrifuges 3.2.3 Spin Filters 3.2.4 Cross-Flow Membrane Filters 3.2.5 Controlled Shear Filters 3.2.6 Acoustic Filters 3.2.7 Summary  5 5 7 8 8 9 9 11 12 14 15 16 18  iv  3.3 Acoustic Filters 3.3.1 Basic Principle  19 19  4  22  4.1  MATERIALS AND METHODS Cell Line and Medium  22  4.2 Cell Culture Experiments 4.2.1 Batch Operation  23 23  4.3 Temperature Measurements in Perfusion Cultures 4.3.1 Bioreactor Operation 4.3.2 Acoustic Separator Operation 4.3.3 Design of Temperature Measurement Equipment 4.3.3.1 Thermocouple Positions 4.3.3.2 Modified Acoustic Separator 4.3.4 Convection Test 4.3.5 Optical System 4.3.6 Design of Experiments.....  26 26 28 30 30 32 33 34 35  4.4  36  Modeling  4.5 Analytical Methods 4.5.1 Cell Concentration and Viability 4.5.2 t-PA Analysis  37 37 38  4.6 Calculations 4.6.1 Cell Culture Experiment 4.6.2 Temperature Measurements in Perfusion Culture 4.6.3 Modeling  39 39 41 42  4.7 Error Analysis 4.7.1 Cell Culture Experiment 4.7.2 Temperature Measurements in Perfusion Culture 4.7.3 Modeling  44 44 44 45  5  46  CELL CULTURE EXPERIMENTS  5.1  Introduction  46  5.2  Validation of Experimental System  47  5.3  Cell Culture Results  49  5.4  Discussion and Conclusions  51  v  6 6.1  TEMPERATURE MEASUREMENT IN PERFUSION CULTURE  53  Introduction  6.2 Influence of System Variables 6.2.1 Power Input 6.2.2 A i r Cooling 6.2.3 Flow Rate 6.2.4 Ambient Temperature 6.2.5 Duty Cycle 6.2.6 Cell Concentration 6.2.7 Discussion and Conclusions  53  .'.  53 53 55 56 59 60 62 63  6.3 Investigation of Recommended Settings 6.3.1 Introduction 6.3.2 Temperature Results 6.3.3 Separation Efficiency Analysis 6.3.4 Recommendations  64 64 65 67 69  6.4 System Efficiency 6.4.1 Natural Convection 6.4.2 Ambient Temperature 6.4.3 Air Cooling 6.4.4 Frequency 6.4.5 Discussion and Conclusions  69 69 71 72 73 75  6.5 Design of Experiment 6.5.1 Description 6.5.2 Full Models Analysis 6.5.3 Optimized Models Analysis 6.5.3.1 Optimized Inlet Temperature Model 6.5.3.2 Optimized Outlet Temperature Model 6.5.3.3 Optimized Delta T Temperature Model 6.5.4 Process Optimization 6.5.5 Discussion and Conclusions  76 76 77 82 82 84 86 88 91  ,  vi  7  MODELING  93  7.1  Introduction  93  7.2  Mathematical Model  94  7.2.1 Model Description 7.2.2 Velocity Distribution 7.2.3 Model Refinement 7.2.3.1 Manual Refinement 7.2.3.2 Computer Optimization 7.2.4 Temperature Profiles 7.2.5 Discussion and Conclusions  7.3  Comparison of Models  94 97 98 99 101 106 109  112  8  CONCLUSIONS AND RECOMMENDATIONS  114  9  REFERENCES  119  APPENDIX 1: PERFUSION SYSTEM  123  APPENDIX 2: RAW DATA  130  APPENDIX 3: MATLAB CODE  152  List of Tables Table 5-1: Average temperatures measured in the tube side of the exchanger for different shell-side inlet temperatures 48 Table 5-2: Temperatures inside spinners with and without pumping  49  Table 6-1: Averaged values and standard deviations of the temperatures recorded in Figure 6.6  62  Table 6-2: Suggested power settings and duty cycle times at selected cell concentrations and perfusion rates 65 Table 6-3: Inlet, outlet temperatures and their difference for two different recirculation flow rates for the setting " A " in Table 6-2 66 Table 6-4: Factorial analysis of the full inlet temperature model  78  Table 6-5: Factorial analysis of the full inlet temperature model without runs # 53 & 54. 82 Table 6-6: Factorial analysis of the optimized inlet temperature model  83  Table 6-7: Factorial analysis of the optimized outlet temperature model  85  Table 6-8: Factorial analysis of the optimized delta T model  87  Table 7-1: Best-fit parameters determined using the manual refinement method  101  Table 7-2: Compilation of the best-fit volumetric source terms (Si) and heat transfer coefficients (h,) obtained for the liquid (Liq.), transducer (Trans.), reflector (Refl.) and side wall (side) 103 Table 7-3: Sum of squared errors between predicted and measured delta T for the four different models listed in Table 7-1 104  viii  List of Figures Figure 3.1: Schematic drawing and photograph of an industrial inclined settler (Lamella Gravity Settler, Parkson Corporation) 10 Figure 3.2: Schematic drawing and photograph of a centrifuge; G E A Westfalia centrifuged separator  11  Figure 3.3: Schematic drawing and photograph of a spin filter (New Brunswick Scientific)  13  Figure 3.4: Schematic drawing and photograph of a Millipore cross-flow  14  filter  Figure 3.5: Schematic drawing of a laboratory-scale controlled shear filter (Vogel et al., 1999) 15 Figure 3.6: Schematic drawing and photograph of acoustic filter (Applikon Biotechnology) Figure 3.7: Action of the forces on particles inside the acoustic standing wave field  17 21  Figure 4.1: Photograph of the spinners and heat exchangers used for cell culture experiments  24  Figure 4.2: Schematic drawing of the apparatus for cell culture experiments  24  Figure 4.3: Dimensions of heat exchanger used for cell culture experiment  25  Figure 4.4: Schematic of perfusion system  27  Figure 4.5: Flow diagrams for recirculation and backflush modes  30  Figure 4.6: Picture showing the cuvette of the acoustic separator  31  Figure 4.7: Picture showing the modified acoustic separator and the positions of the inlet and outlet thermocouples Figure 4.8: Photograph of the connection that allows aseptic sealing of each thermocouple in the modified acoustic separator  32  Figure 4.9: Optical system set up  34  33  Figure 5.1: Temperature profile during the cyclic pumping of water to the tube side of the heat exchanger and at the entrance of the shell side 47 Figure 5.2: Effect on the specific growth rate and on the specific glucose consumption for CHO cells exposed to different average temperature 50  ix  Figure 5.3: Effect on the cell specific t-PA production rate and on t-PA concentration for CHO cells exposed to different average temperature 51 Figure 6.1: Effect of power input on inlet and outlet temperatures  55  Figure 6.2: Effect of air cooling on the difference in temperature between the inlet and outlet 56 Figure 6.3: Effect of harvest flow rate on the inlet and outlet temperatures for a relatively constant ambient temperature 57 Figure 6.4: Effect of recirculation flow rate on inlet and outlet temperatures for a relatively constant ambient temperature  59  Figure 6.5: Effect of ambient temperature on the fluid inlet and outlet temperatures  60  Figure 6.6: Effect of duty cycle on the inlet and outlet temperatures  61  Figure 6.7: Photograph of cell planes in the acoustic chamber  62  Figure 6.8: Effect of cell concentration on the inlet and outlet temperatures  63  Figure 6.9: Inlet, outlet and ambient temperatures for the investigated settings of Table 6-2 66 Figure 6.10: Separation efficiency and cell concentration for the investigated settings of Table 6-2 67 Figure 6.11: Effect of variation of the duty cycle on separation efficiency  68  Figure 6.12: Effect of natural convection during the operation of an acoustic separator with the ambient temperature at A) 19.0°C and B) 26.0°C 70 Figure 6.13: Effect of variation of ambient temperature on the inlet and outlet temperatures and on the separation efficiency  71  Figure 6.14: Effect of variation of ambient temperature on the separation efficiency for different separation efficiency ranges 72 Figure 6.15: Effect of the air cooling flow rate on the separation efficiency for different separation efficiency ranges 73 Figure 6.16: Effect of frequency shift on the temperature of the acoustic separator  74  Figure 6.17: Effect of frequency shift on separation efficiency  75  Figure 6.18: Distribution and variation of the replicate runs of the factorial design  80  Figure 6.19: Example of differences in temperature between the air used in the cooling device and the ambient temperature provided by the air conditioner for a 22-minute time interval 81 Figure 6.20: Residuals versus run number for the preliminary refinement of the delta T model 81 Figure 6.21: Predicted versus experimental inlet temperatures  84  Figure 6.22: Predicted versus experimental outlet temperatures  85  Figure 6.23: Predicted versus experimental delta T  87  Figure 6.24: Response of inlet temperature to variations in power input (PI) and net harvest flow rate (PR)  89  Figure 6.25: Response of outlet temperature to variations in power input (PI) and net harvest flow rate (PR) 89 Figure 6.26: Response of inlet temperature to variations in power input (PI) and net harvest flow rate (PR)  90  Figure 6.27: Response of outlet temperature to variations in power input (PI) and net harvest flow rate (PR) 91 Figure 7.1: Geometry used in developing a thermal model of the acoustic separator  94  Figure 7.2: Schematic of one cuvette wall used for deriving the boundary condition.... 96 Figure 7.3: Experimentally measured data for the outside temperatures of the reflector and side wall of the acoustic separator 100 Figure 7.4: Comparison of delta T predicted by the model using parameters obtained by the manual refinement method and delta T measured 101 Figure 7.5: Comparison of predicted and measured temperature differences using best-fit parameters obtained for four different optimized models 104 Figure 7.6: Residual plot of the final mathematical model  105  Figure 7.7: Predicted temperature distribution in the acoustic separator at the vertical midplane and at the outlet cross-section in absence (left) and presence (right) of air cooling 107 Figure 7.8: Comparison of temperature profiles obtained using the manual + computer parameters versus the Computer Model 01 parameters 108 Figure 7.9: Predicted temperature distribution at the vertical midplane and the outlet cross-section of the acoustic separator for different harvest flow rates 109 xi  Figure 7.10: Comparison of measured outlet temperatures with those predicted from the mathematical model and the factorial design model 113  Nomenclature Abbreviations ACF BUN BX [cell] [ceiljaverage  CHO CI D.C. DO HF Fab Liq. NF PI PR Refl. RF rpm RR SS ST std. dev. Trans. TA ts v/v  air cooling flow rate (L min") blood urea nitrogen bioreactor viable cell concentration (cells mL" ) viable cell concentration (cells mL" ) average viable cell concentration (cells mL" ) Chinese ovary cell confidence interval duty cycle dissolved oxygen harvest flow rate (L day" ) fragment antigen binding liquid net harvest flow rate (L day" ) power input (W) net harvest flow rate (L day" ) reflector recirculation flow rate (L day" ) rotation per minute ratio of recirculation flow rate to harvest flow rate sum of squared errors stop time (s) standard deviation transducer ambient temperature (°C) temperature sensitive volume / volume 1  1  1  1  1  1  1  Symbols A Charvest Cbioreactor C ,l p  G  ki k s  L  •  m P q 9P  cross-sectional area of the duct (m ) viable cell concentration in the harvest flow (cells mL" ) viable cell concentration in the bioreactor (cells mL" ) heat capacity of the liquid (J kg^-K" ) glucose concentration (mM thermal conductivity of the liquid (W nf'-K" ) thermal conductivity of the solid (Wnf'-K" ) characteristic dimension of the flow channel (m) 1  1  1  1  1  mass flow rate (kg s" ) t-PA concentration (mg L" ) heat transfer rate (W) specific t-PA production rate (mg L" cell" ) 1  1  1  1  qc QG S, S, S, S SE t T T T b, Too  specific glucose consumption rate (mM h" cell") glucose consumption rate m M h" ) volumetric heat generation source term (W m" ) separation efficiency (%) time (h) temperature ( K o r ° C ) local temperature of the solid (K or °C) ambient temperature (K or °C)  T AT v, v , v , v wp X XM  average temperature (K or °C) difference between inlet and outlet temperatures (K or velocity (m s" ) wetted perimeter (m) viable cell concentration (cells mL" ) log mean of the viable cell concentration (cells mL" )  8 pi  wall of thickness (m) density of the liquid (kg m" ) net specific growth rate (h" ) viscosity of the liquid (kg m" s" ) pooled sample variance  a  x  y  am  L  1  z  1  1  3  p.net  pi <7  y  3  z  s  x  1  1  1  2 p  1  erf  variance of the sample  <j  standard deviation of the pooled sample  v,  degree of freedom of the sample  p  Dimensionless Number Pe Pr Re  Peclet number Prandtl number Reynolds number  0  Acknowledgements First of all, I would like to express my gratitude towards... life, destiny... whichever is the proper term. I consider myself privileged for having this wonderful opportunity to work with an outstanding team on a challenging project, to live in a beautiful environment and, at the same time, be able to learn the English language.  The success of my experience is principally due to an exceptional supervising team. I had the chance and pleasure to work with Dr. James M . Piret and Dr. Bruce D. Bowen and I would like to sincerely thank them. I would also like to strongly thank Dr. Volker M . Gorenfio who took care of me on my first day, taught me so much and guided me throughout this project. I would also like to thank the Piret lab group for providing an agreeable work atmosphere. I found more than just co-workers, I found friends. Many thanks to Joachim B. Ritter, Vincent Chow, Minh Luu, Sumitra Angepat, Chris Sherwood and Venkata Tayi for their help. I would like to thank Emilie Ruel and Marsha Cameron for being my English tutors.  I really appreciated all the support and the  confidence given to me by my friends, in particular my roommate Sylvain, and my parents: merci beaucoup. I would like to give a special thank you to my fiancee for her understanding and love.  Finally, I would like to acknowledge Le Fond Quebecois de la Recherche sur la Nature et les Technologies for their financial support.  1 Introduction 1.1  Overview  The population of the world is growing at a rate of 1.3 per cent per year, with an average of 78 million more poeple per year between 1995 and 2000 (UN, 1999). Meanwhile, this population has to contend with diseases that originate from around the world and an increasinly limited access to health services.  As a consequence, the production of  biopharmaceuticals needs to become more efficient in order to reduce the cost and increase the volume of production for an ever-increasing range of biopharmaceuticals.  1.2  Production Methods  The method of producing biopharmaceuticals is an important factor on the road to manufacturing efficiency. Different methods have been developed over the years to increase the productivity of these processes.  The most common, used by man for  hundreds of years, is the batch mode of operation.  The batch process involves  inoculating a fixed volume of medium with cells, and then culturing them for only a short period of time, usually about a week. The risk of contamination is low but the variability from batch to batch is high (Hu et al., 1997). In batch production, the maximum cell concentration is primarily limited by the accumulation of inhibitory factors, in other words, by toxic wastes (Hu et al., 1997).  The fed-batch process is similar to the batch process, except that, by the periodic addition of nutrients, the stationary phase of the culture can be increased. Thus, productivity is augmented and the operation can last longer, around two weeks.  The major 1  disadvantages of the fed-batch approach are that the productivity is limited by the fixed reactor volume and the buildup of toxic byproducts can affect the quality of the final product (Andersen et al., 1994).  Another alternative that improves significantly the volumetric productivity of a bioprocess is the perfusion mode of operation. Because this production method operates continuously, it can produce biopharmaceuticals over months of operation while reducing the downstream product purification requirements (Pui et a l , 1995). The constant culture environment, the short residence time of the product in the system and the high cell concentrations obtained are other marked advantages of perfusion cultures (Hu et al., 1997). The basic requirements of a perfusion system are to continuously feed nutrients and remove wastes, while retaining the cells in the bioreactor. The use of an appropriate cell retention device, therefore, is a key component to the effectiveness of this production method.  1.3  Types of Cell Retention Devices  Various types of cell retention devices are available on the market to continuously remove suspended cells from the harvested medium. Basically, a good cell retention device should provide a high separation efficiency (higher then 90% of the viable cells retained) at high perfusion rates for a long period of operation without having any negative effects on the cell culture (Woodside et al., 1998).  Furthermore, the cell  retention device has to be easy to operate, sterilize and clean in order to minimize the risk of contamination and to provide robust operation (Voisard et al., 2003).  2  Current cell retention devices separate cells from media based on differences between such physical properties as: size, density, compressibility, electrical charge and dielectric constant. From an industrial point of view, the size and the density-based techniques are interesting because of their scale-up possibilities. The most popular cell retention devices that fall in the latter category are: the centrifuge, the cross-flow membrane filter, the controlled shear filter, the gravity settler, the spin filter and the acoustic separator.  1.4  Acoustic Separators  This thesis is primarily concerned with the use of the acoustic separator. Acoustic separators have been employed in biotechnology applications for more than 10 years. Many unique features like the absence of moving parts or a physical barrier, the sanitary design and its operational flexibility, make this device particularly interesting for the biotechnology industry (see section 3.2.6 for more details). This type of system separates particles from fluids using resonant ultrasonic standing waves. The electrical energy input is converted into acoustic energy that creates the acoustic standing wave field. As a consequence of this field, acoustic forces result which are responsible for aggregating the cells and retaining them in the separator (see section 3.3 for more details).  3  2 Thesis Motivation In vivo, mammalian cells are subject to a highly controlled environment and do not tolerate significant deviations from their normal state.  Even small changes in  temperature, for example, can affect their viability, growth and productivity.  For  biopharmaceutical production in perfusion systems, the cell retention device must maintain a favorable environment for the cells in order to provide an efficient device that maximizes productivity.  In the acoustic separator, the acoustic energy is ultimately transformed into heat energy. As a consequence, the temperature of the medium passing through the separator increases. These generated temperature variation can induce negative effects on the cells and also can reduce the performance of the acoustic separator.  Previous studies of  acoustic separators have not thoroughly examined the temperature changes that take place as acoustic energy is converted to heat in these devices. Moreover, the effect on cells of cyclic variations of temperature during the typical duty cycle of an acoustic separator has not yet been investigated.  Thus, the goal of this thesis is to study the thermal behavior of the acoustic separator from both experimental and theoretical points of view. To this end, the effects on cells of variations of temperature are studied in order to determine an acceptable range of operational temperatures. Moreover, the characterization of the internal environment of the separator, the analysis of the system efficiency related to the temperature distribution and the modeling of the temperature distribution are also investigated.  4  y  3 3.1  Literature Review Effect of Temperature on Cell Cycle and Metabolism  In vivo, the environment surrounding each mammalian cell is rigorously controlled at the temperature of 37.0°C in order to provide the optimal condition for metabolic activity. To simulate this optimal condition, bioreactors are usually operated at the controlled temperature of 37°C. However, cells are able to adapt to variations of temperature by modifying their cycle and metabolism. The effects of temperature changes depend on the cell type and the target protein produced (Furukawa et al., 1998; Kaufmann et al., 1999; Yoon et al., 2003). The reasons for temperature-induced metabolism modifications are still poorly understood (Schatz et al., 2003) and the specific molecular mechanisms remain to be defined (Moore et al., 1997). The adaptation of cells to temperature changes below and above the normal set point has been extensively studied.  3.1.1  Effect of Low Temperatures in Batch Systems  Temperature is an easy parameter to adjust in order to obtain improved results from a culture process. In general, by reducing the temperature of the bioreactor in a Chinese hamster ovary (CHO) cell culture, the overall metabolic rate is reduced (Moore et al., 1997). Moreover, growth, viability and protein synthesis are also affected by the change of temperature.  In batch cultures of C H O cells (3u-lS) producing 799BglIIa-AE, six different temperatures (30, 32, 33.5, 35, 36 and 37°C) were tested (Furukawa et al., 1998). The results showed that the viability increased with the lowering of temperature while the cell  5  growth diminished and became completely arrested below 32°C. The maximal growth rate was observed at 36°C. The highest production rate and cellular productivity were obtained at culture temperatures of 35°C and 32°C, respectively. Glucose consumption also depended on temperature and was reduced by decreasing the temperature.  In this  case, culturing at lower temperatures reduced the consumption of most of the nutrients.  Two low temperatures, 33°C and 30°C, were compared with the usual temperature of 37°C in a batch cultivation of CHO cells producing human EPO (LGE10-9-27) (Yoon et al., 2003). Again, cell growth was suppressed but the cell viability stayed high. The highest specific productivity was obtained in the 30°C culture but the maximum EPO concentration was achieved in the 33°C culture. It was also shown that the negative effects on cell growth overcame the benefits of higher specific productivities at temperatures that are too low. Furthermore, the product quality obtained at 33°C was comparable to or even better than the one obtained in the 37°C culture.  Considering that lowering the temperature reduces cell growth, increases cell viability for a longer period, suppresses the release of proteins from the dead cells and improves productivity, many scientists have attempted to develop low temperature techniques to optimize cell culture processes. During the growth phase, the bioreactor temperature is kept at 37°C until the target cell concentration is reached and then the temperature is reduced (Rossler et al., 1996; Moore et al., 1997; Kaufmann et al., 1999; Schatz et al., 2003; Fox et al., 2004).  6  Schatz et al. cultivated C H O cells producing Fab antibody fragments and shifted the temperature from 37°C to 28°C. The consequences of the temperature shift were that the production of Fab became independent of growth rate and the specific productivity was boosted during production even though the 37°C culture productivity decreased. After a temperature shift from 37°C to 30°C, Kaufmann et al. showed a morphological transformation of their CHO-K1 cells (XM111-10).  Their results demonstrated a  prolongation of the G l phase and yielded a specific productivity that was eight times higher than the 37°C cultures for a 3.5-fold higher final product titer (on the fifth day). In addition, Fox et al. have carried out a modeling study to determine the optimal day for the temperature shift. The model correctly predicted the optimal day for the temperature shift from 37°C to 32°C for CHO cells producing interferon-y.  3.1.2  Effect of Low Temperatures in Perfusion Systems  Other fermentation systems, like perfusion systems, provide different culture conditions and the effect of lower temperatures on cell productivity could be different than with batch systems. CHO cells secreting therapeutic protein were studied in a perfusion run at a cell concentration of 20 million cells per mL (Chuppa et al., 1997). The experimental temperatures were set at 34, 35.5 and 37°C. The results showed a constant viability of 90% for all three temperatures. Also, the glucose metabolism was significantly reduced at 34°C, but the product titer and specific productivity were not significantly affected. The major advantages of reducing the temperature during perfusion runs are to economize on medium consumption and improve the molecular integrity of the product. On the other hand, the specific growth rate is diminished and can be an issue for growthlimited processes.  7  3.1.3  Effect of High Temperatures and Heat-Shock  CHO cells are very sensitive to temperatures above 37°C. For 3 p.-IS C H O cells, high temperatures cause an inhibition of cell growth, a decrease of viability, a reduction in productivity and an increase in glucose consumption (Furukawa et al., 1998). Continuous exposure to a culture temperature of 39°C of mutant CHO-K1 cells led to a fast decline in cell viability (Jenkins et al., 1993). Long exposures at high temperatures lead to negative consequences for the culture, but shorter exposures can actually produce some beneficial effects.  Non-lethal heat shock has been used in an optimized process to induce an increase in cell production. Temperature sensitive mutant CHO-K1 cells (HS-B2) were subjected to a heat shock at 0 and 24 hours of culture (Hovey et al., 1994). First, the temperature was increased to 42°C and then, after 2 hours, was decreased back to 34°C. It was found that the heat shock stimulated cell growth and also induced an increased production of recombinant protein. A similar study showed that, following exposures of 12 hours at 39°C and then 12 hours at 34°C, CHO-K1 cells producing metalloproteinase tissue inhibitor maintained a viability over 80% and a specific production rate of three- to fourfold higher than that of the control (Jenkins et al., 1993).  3.1.4  Range of Temperature for C H O Cells  Trying to summarize the information contained in the literature is in some ways misleading because temperature effects depend on the cell line. For different CHO cell lines, similar effects were found in several articles (Jenkins et al., 1993; Rossler et al., 1996; Furukawa et al., 1998; Yoon et al., 2003), so it is possible to extract an acceptable  8  range of operating temperatures. Cultures at 30°C and below are not effective as these temperatures have a significant negative effect on C H O cell growth and productivity. The major problems at low temperature are a reduction of membrane fluidity and impaired protein synthesis (Thieringer et al., 1998).  At the other end of the range,  temperatures over 37°C yielded no positive effects (Furukawa et al., 1998). At 39°C, cells begin to die and increasing the temperature above this point leads to a faster extinction. At 43°C, the cells all perish within 24 hours (Furukawa et al., 1998). The denaturation of proteins and membrane rupture are the major problems that occur at high temperature.  3.2  Types of Cell Retention Devices  As was mentioned in the introduction, many different commercial cell retention devices are available. The ultimate goal of each device is to operate for a long period of time at high separation efficiency without negatively affecting the cell culture (Voisard et al., 2003).  The following section describes the operation as well as the advantages and  disadvantages of several of the most popular cell retention devices.  3.2.1  Gravity Settlers  Gravity settlers, or inclined settlers, take advantage of the density difference between the cells and the medium to separate the cells. The cell suspension is pumped up into a chamber consisting of many parallel flat plates inclined at an angle of about 60° from the horizontal. Because the cells are denser than the liquid, they settle to the top surface of the plates and then slide by gravity to an outlet plenum where they are returned back to the reactor (Figure 3.1). In biotechnology applications, laboratory-scale inclined settlers  9  are usually made of a thin rectangular glass chamber with a water jacket to allow cooling of the liquid to be clarified. The volume of the settler is around 9% of the reactor volume and the temperature of the cell suspension is maintained around 4°C, to improve the settling by minimizing cell attachment to the surface (Searles et al, 1994).  Figure 3.1: Schematic drawing and photograph of an industrial inclined settler (Lamella Gravity Settler, Parkson Corporation)  As for their advantages, gravity settlers are simple, inexpensive, easy-to-maintain devices. They also provide a selective retention of cells, in other words, the nonviable cells and the cellular debris are selectively removed (Searles et al., 1994). This robust system is a good alternative for cells that are very sensitive to shear stress (Voisard et al., 2003).  Even if their design is very simple, gravity settlers have many disadvantages. The scalability is limited by the large size of the device (Berthold et al., 1994). Gravity settlers need a large area to be able to deliver a high perfusion rate. Also, the typical  10  mean residence time of 1.5 h means that the cells are maintained in an unoxygenated and unmixed environment for too long period (Searles et al., 1994; Woodside et al., 1998). 3.2.2  Centrifuges  Separation in the centrifuge is due to the difference in density between the particles and the liquid as amplified by the centrifugal force. This force is created by the high-speed rotation of the bowl. The centrifuge operation consists of pumping the cell suspension, to be separated, into the top part of the bowl (Figure 3.2). The suspension is clarified and separated in the disk set; the cells slide down in the compaction space and are continuously discharged.  The clarified liquid is pumped out of the bowl to the  downstream processing unit. Cell Suspension  Figure  3.2: Schematic drawing and photograph of a centrifuge; GEA Westfalia centrifuged separator  In comparison with all other cell retention devices, the centrifuge has the largest perfusion rate capability that can reach 3000 Lday"  1  (Voisard et al., 2003).  The  centrifuge provides high separation efficiency for a wide range of operations and remains free of clogging for relatively long periods of time (Takamatsu et al., 1996).  11  On the other hand, the cells are exposed to pressures in excess of 3 bars as well as high shear stresses induced by the high rotational speed. Moreover, the temperature of the outlet stream can be 10 to 20°C higher than that of the inlet (Berthold et al., 1994). Berthold et al. carried out an experiment with 30 L of hybridoma cells at 3.2 million cells per mL and found that, even though the separation efficiency was maintained at 100%, 20% of the cells died. During centrifuge operation, the long residence time inside the rotating bowl leads to the cells being starved of oxygen and nutrients. As a consequence, there is a diminution in production and a decrease in cell viability (Johnson et al., 1996; Woodside et al., 1998).  The mechanical complexity of the system, the presence of  moving parts and the potential mechanical problems that can occur during long periods of operation are other disadvantages (Tokashiki et al., 1990; Apelman S., 1992; Jager V., 1992; Bjorling T, 1995; Johnson et al., 1996; Ryll et al., 2000).  3.2.3  Spin Filters  A typical spin filter consists of a wire screen wrapped around a hollow shaft. This device can be either inside or outside the bioreactor. Although the pore size of the wire screen is sufficiently small to retain the cells, the filtration is, in fact, enhanced by the rotation of the screen. Thus, the separation principle is based on both size and density differences between the cells and the medium. The clarified liquid inside the hollow shaft is pumped continuously out of the system (Figure 3.3).  12  Figure 3.3: Schematic drawing and photograph of a spin filter (New Brunswick Scientific)  When located inside the reactor, the spin filter has the advantage of keeping the cells in a well-controlled culture environment. Also, filtration occurs at low hydrostatic pressures that provide less stress on sensitive cells (Voisard et al., 2003).  However, the duration of the perfusion operation is limited by the fouling of the device. Fouling appears to happen in two stages (Deo et al., 1996). First, the cells deposit on the screen by hydrodynamic interactions causing the initial fouling. Second, the deposited cells grow inside the wire screen eventually causing complete obstruction. Optimization of the operation can be achieved by increasing the pore size of the spin filter to reduce fouling or by changing the morphology of the cells to produce large clumps of cells to minimize entrapment (Avgerinos et al., 1990; Deo et al., 1996).  However, a better  mechanistic understanding of these processes is still needed (Deo et al., 1996).  13  3.2.4  Cross-Flow Membrane Filters  The size difference between the particle and the pore size of the membrane is the basic separation mechanism of the membrane filter. B y choosing a membrane with a smaller pore size than the particle, the particles are retained on one side of the membrane, thereby allowing recovery of the clarified liquid.  The driving force for this operation is the  pressure drop from one side of the membrane to the other. A particular feature of the cross-flow filter is the tangential flow over the filtration surface that prevents cells from being deposited on and clogging the membrane (Grabosch, 1986; Bowen, 1993; Berthold etal., 1994) (Figure 3.4).  Figure 3.4: Schematic drawing and photograph of a Millipore cross-flow filter  Cross-flow filtration allows higher perfusion rates for longer periods of time in comparison to dead-end filtration. The clarified liquid is essentially cell-free and that facilitates integration with the downstream purification step (Woodside et al., 1998). The major disadvantage with this technique is the eventual fouling of the membrane with cells, cellular debris and macromolecules (Voisard et al., 2003). Also, mechanical and hydraulic shear forces can easily damage the fragile cells. The wall shear rate is the  14  critical mechanism for cell damage in the laminar regime and it has a direct effect on the viability of the culture (Millward et al., 1994).  3.2.5  Controlled Shear Filters  The separation concept for the controlled shear filter is the same as for the cross-flow filter; i.e., it takes advantage of the size difference between the cells and the pores of the membrane. Here, a tangential flow is created by the rotation of a disk over the membrane and the angle of the disk surface (a) helps to control the shear rate on the membrane surface (Vogel et al., 1999; Vogel et al., 2002) (Figure 3.5). In fact, the wall shear rate is constant at all radial positions along the disk because the distance between the disk and the membrane increases proportionally with the increasing disk surface velocity from the centre to the edge of the disk.  Concentrated Cell Suspension (to reactor)  Cell Suspension (from reactor)  Clarified Liquid Figure 3.5: Schematic drawing of a laboratory-scale controlled shear filter (Vogel et al., 1999)  The controlled shear filter allows efficient, sterile separation of sensitive mammalian cells without affecting the viability of the culture (Vogel et al., 2002). Also, adding an affinity membrane, allows simultaneous isolation of the target protein.  15  Clogging problem at low flow rates indicates that there may be limitations for continuous operations (the device has so far only been used in the batch mode) (Vogel et al., 2002; Voisard et al., 2003). Also, no proof has been published for the scale-up possibilities of this device.  3.2.6  Acoustic Filters  The acoustic filter, or acoustic separator, or acoustic settler, allows separation based on differences in density and compressibility between the cells and the liquid. The acoustic forces generated by the transducer, enhance the aggregation of particles allowing larger aggregates to settle by gravity back into the reactor (Figure 3.6). The low operating frequency, around 2 M H z combined with low input power, around 5 W, are not high enough to produce cavitation and cell disruption (Pui et al., 1995).  The cavitation  induced by high-power, high frequency ultrasound creates intense local heating and pressure increases that are very damaging to cells (Chisti, 2003).  Acoustic filters are simple, robust, easily cleaned devices with no susceptibility to fouling or mechanical failure, since it was no moving parts and no physical barriers (Trampler et al., 1994; Pui et al., 1995; Woodside et al., 1998; Zhang et al., 1998; Ryll et a l , 2000; Gorenflo et al., 2002; Voisard et al., 2003). The use of acoustic standing waves has no apparent influence on cell growth, productivity or viability (Pui et al., 1995; Bierau et al., 1998; Zhang et al., 1998; Chisti, 2003).  Acoustic filters achieve high separation  efficiencies and are able to selectively remove non-viable cells thereby preventing the accumulation of cellular debris inside the bioreactor (Trampler et al., 1994; Woodside et  16  a l , 1998). Also, the cell hold-up time within the filter is reduced considerably relative to other sedimentation devices (Woodside et al., 1998). This type of cell retention device is especially suitable for very high-density perfusion cultures (Voisard et al., 2003).  Figure 3.6: Schematic drawing and photograph of acoustic filter (Applikon Biotechnology)  For example, Ryll et al. have shown that for a small-scale culture of Chinese hamster ovary (CHO) cells at 5 x 10 cells mL" and 5 Lday" perfusion rate, separation 7  1  1  efficiencies of 95% or more can be obtained. Before 2002, the acoustic filter was limited to small-scale perfusion cultures but with the appearance on the market of a larger device (BioSep 200L separator), larger scale perfusion operations are now possible (Gorenflo et al., 2002). This large-scale device has demonstrated high separation efficiencies, above 95%, for perfusion rates up to 200 L day" at 10 cells mL" (Gorenflo et al., 2002). These 1  7  1  results demonstrate the scale-up potential of acoustic filters. However, there still exists  17  no commercially available unit for perfusion rates higher than 1000 L day" (Voisard et 1  al., 2003).  Because acoustic energy is ultimately converted into heat, the use of a cooling device is necessary to remove the excess heat generated (Chisti, 2003). Without cooling, for a non-moving liquid inside the acoustic chamber, the temperature increases at a rate of 1.3°Cmin" (Pui et al., 1995). 1  For continuous flow-through operations, the local  temperature remains constant with time after steady state is reached. The direct cooling of the device reduces the temperature variations within the separator, thereby minimizing the negative effects on cells while, as the same time, helping to maintain a high separation efficiency (Trampler et al., 1994). The resonance frequency of a liquid is directly related to its temperature.  Consequently, minimizing the temperature gradient  within the separator helps to maintain the resonance frequency of the standing wave field, producing better stability and hence better performance (Trampler et al., 1994). Temperature control in an acoustic filter is a very important operational feature considering the heat sensitivity of cells and the device performance.  3.2.7  Summary  Each of the cell retention devices discussed above has its own specific advantages and disadvantages.  Filtration techniques have the major disadvantage that the filtration  barrier becomes fouled over time, thereby limiting the duration of the perfusion process. On the other hand, filtration provides a cell-free liquid and can deliver high perfusion rates. Sedimentation techniques do not deliver a cell-free harvest stream but have the advantage of being simple and having no physical barrier.  18  The choice of the appropriate cell retention device depends greatly on the scale of the process, the type of cells to be cultured and the bioreactor cell concentration desired. The reduction of the negative effects the cell retention device has on the culture is a key aspect to improving the productivity of perfusion processes and achieving high productivities.  3.3 3.3.1  Acoustic Filters Basic Principle  Ultrasound is widely used in industry, for example in medical imaging, sonochemical processing, ultrasonic cleaning of surfaces and as the basis for underwater sonar ranging (Chisti, 2003). In biotechnology, in particular in perfusion culture, ultrasonic waves are used to enhance the settling of cells in an efficient cell retention device called the acoustic separator (Kilburn et al., 1989; Doblhoff-Dier et al., 1994; Trampler et al., 1994; Pui etal., 1995).  The particles are separated from the fluid using resonant ultrasonic standing waves of about 2 M H z while the fluid is pumped through the system. A piezo-electric transducer on one side of the chamber generates acoustic waves that are reflected on the other side by a parallel glass reflector. The superposition of these waves creates a standing wave field that results in the formation of alternating parallel stationary planes referred to as node and antinode planes. The node planes correspond to the zero velocity or pressure amplitude and the antinode planes to maximum velocity or pressure amplitude. A n  19  important distinction is that the pressure nodes coincide with the velocity antinodes and vice versa (Woodside et al., 1997). This ultrasonic field generates forces that trap the cells in the separator. Three forces are responsible for this phenomenon: the primary radiation force, the secondary radiation force and the Bernoulli force (Hager, 1991; Doblhoff-Dier et al., 1994).  The primary radiation force drives the particles very quickly to the velocity antinode planes or pressure node planes (Doblhoff-Dier et al., 1994). The magnitude of the force depends on the differences of compressibility and density between the fluid and the particles exposed to the ultrasonic field (Pui et al., 1995; Hawkes et al., 1996). Generally, the primary radiation force has the greatest magnitude of the three forces.  The secondary radiation force occurs as a consequence of the generation of scattered fields radiated from each particle of the multi-particle system (Doblhoff-Dier et al., 1994; Pui et al., 1995).  The total scattered or secondary field results in secondary forces  between the particles that are attractive and act only at very short range and hence cause nearby particles to aggregate together.  Non-uniformities in the acoustic field caused by the two side walls of the chamber generate the Bernoulli force (Doblhoff-Dier et al., 1994; Pui et al., 1995). Within each velocity antinode, this dynamic force drives the particles toward the nearest local maximum of amplitude. The Bernoulli force results in the formation of striated columns  20  oriented perpendicular to the antinode planes. Figure 3.7 illustrates the action of the forces on particles inside the acoustic standing wave field.  The description of the acoustic separator and its operation is given in the section 4.3.2.  Velocity Node  Velocity Antinode  Velocity Node  D  C  Figure 3.7: Action of the forces on particles inside the acoustic standing wave field Acoustic standing wave field is generated by the superposition of the waves emitted by the transducer and reflected by the reflector (A). The ultrasonic field creates a primary radiation force (F ) that drives the particles to the velocity antinode plane (B). The Bernoulli force (F ) drives the particles to the local maximum of amplitude (C) and creates parrallel planes of aggregated particles (D). p  B  21  4  4.1  Materials and Methods  Cell Line and Medium  Chinese hamster ovary (CHO) cells expressing human tissue plasminogen activator (tPA) were provided by Cangene (CHO 540/24, Cangene, Winnipeg, M B ) . The cells were grown in a serum-free medium (CNJ S F M 2.1b, Cangene) containing 25 m M glucose, 4 m M glutamine and a proprietary set of additives. In perfusion culture, 100 mL of penicillin-streptomycin at 10 000 units mL" (GIBCO, Invitrogen Canada, Burlington, 1  ON) was added to the medium.  The inoculum train used for batch and perfusion cultures was prepared from a 1 mL frozen vial of between 10 and 1 0 C H O cells in cell freezing media (Catalogue #C6295 6  7  of Sigma Chemical, St. Louis, MO). The cells were resuspended in 20 mL of fresh medium in a 75 cm T-flask and grown for 24 h. The cells were then pipetted to further mix them, and then split 1:1 with fresh medium. After 3 days, cells were transferred to a larger 175 cm T-flask in a 1:3 split with fresh medium. Then, after 3-4 days, the cells were transferred to a 300 mL working volume spinner and grown until the 0.6 L bioreactor could be inoculated at 2-5 x 10 cells mL" , with at least 90% viability. For the 5  1  batch culture experiments, the spinners were inoculated at 1-2 x 10 viable cells mL" . 5  1  Cells were maintained in a humidified incubator at 37°C and 5 % C O 2 .  22  4.2  4.2.1  C e l l C u l t u r e Experiments  Batch Operation  Batch cultures were performed in three 100 mL working volume spinner flasks (Model 1967-00100, Bellco Glass, Vineland, NJ). The spinners were modified to allow aeration, sampling and pumping in/out. Figure 4.1 shows a photograph of the set up and the schematic is shown in Figure 4.2. The first spinner, used for conventional batch culture at 37°C, acted as the control. A 5 mL sample was taken every 24 hours from all spinners to analyze for pH, O2, glucose, glutamine, cell concentration and viability.  Culture  supernatants were centrifuged and kept at -20°C for later analysis. The initial volume in all spinners was 90 + 5 mL.  The pumped spinner control and the test spinner were connected to the tube side of a heat exchanger (Figure 4.3) in which a fraction of the culture was pumped in and out. The volume pumped inside the heat exchanger was 4 mL. A MasterFlex L S pump (model 7550-20, Cole-Parmer, Vernon Hills, IL) with two MasterFlex heads (model 7016-20, Cole-Parmer) was used to move this fraction of the culture in and out the heat exchanger. The pump was controlled by a computer using the WinLin software (Linkable Instrument Network, Cole-Parmer). The volume pumped to the tube side of the heat exchanger was constant.  23  Heat Exchanger Pumped Spinner Control Heat Exchanger Test Spinner Test Spinner Pumped Spinner Control  Control Spinner  Humidifier Figure 4.1: Photograph of the spinners and heat exchangers used for cell culture experiments  Pump (in & out)  [_ -  ••' "J A i r Filter  Pump (in & out)  Water out (to c i r c u l a t i n g bath) Heat E x c h a n g e r  Heat E x c h a n g e r  Water in (from c i r c u l a t i n g bath)  S a m p l e Port  Humidifier  C o n t r o l S p i n n e r (#1)  S a m p l e Port  P u m p e d S p i n n e r C o n t r o l (#2)  Sample Port  Teat S p i n n e r  Figure 4.2: Schematic drawing of the apparatus for cell culture experiments  24  ID : Inside Diameter Figure 4.3: Dimensions of heat exchanger used for cell culture experiment.  The internal liquid volume when the tube side was only partially filled to 20 cm, was 4 mL. The heat exchanger of the test spinner was connected to a circulating bath (Model 2095, Forma Scientific, Marietta, OH) to control.the temperature of the water flowing in the shell side (470 mL min" ). The water flow rate was adjusted with a flow meter (model 1  EW-32044-40, Cole-Parmer). The measurement of the temperature on the tube side of the heat exchanger and in the spinners was done during a non-aseptic run with water because it was not possible to aseptically introduce a thermocouple into the spinners. Model 5TC-TT-T-24-36-SMP-M (Omega Canada, Laval, QC) thermocouples were used for this experiment. During the cell culture experiment, the temperature of the shell side inlet was measured by a needle thermocouple HYP2-21-1-1/2-E-G-48-OST-M (Omega Canada) connected to a temperature meter HH506R (Omega Canada).  The data  measured were recorded on a computer using the software included with the HH506R temperature meter. 25  The spinners were housed in an incubator (Steri-Cult 200, Forma Scientific) maintained at 37 + 1°C. The incubated spinners were placed in an agitated water bath controlled at 36.7 ± 0.4°C to improve the heat transfer with the controlled environment and to keep a more constant temperature in the spinners. A magnetic stirrer (Multi-stir 4, Bellco Glass) operating at 88 ± 4 rpm provided the agitation of the bath and the spinners (Figure 4.1). The spinners were aerated with medical grade 5% carbon dioxide, 95% air (Praxair, Mississauga, ON) at a rate of 25 mL min" in each spinner. The inlet gas was sterile 1  filtered by an air filter (Aero 50 Vent Devices, Pall Gelman Laboratory, Ann Arbor, MI). The air flow rate was adjusted by a flow meter (model N112-02-C, Cole-Parmer). The inlet gas was bubbled through distilled water before entering the spinners.  4.3 4.3.1  Temperature Measurements in Perfusion Cultures Bioreactor Operation  A 3 L glass bioreactor (Applikon Inc, Foster City, CA) with a working volume of 0.6 L was inoculated with CHO cells at concentrations ranging between 2 - 5 x 10 cells mL" 5  1  from 150 - 200 mL of inoculum culture. With each inoculation, the reactor was run in batch mode for 2 - 3 days until the glucose concentration approached 5 m M . Perfusion was then initiated using 5 m M of glucose as a target set point for control. Temperature, pH and dissolved oxygen (DO) were monitored and controlled using a Bio Controller ADI 1030 digital controller (Applikon Inc.) and a computer data logger. A submerged silicone tube (length 3.8 m, inner diameter 2.2 mm, wall thickness 0.6 mm, Dow Corning, Midland, MI) allowed bubble-free aeration. The p H was maintained through  26  CO2 addition to the silicone tubing by on/off control o f a solenoid valve. The D O was maintained by adding pure oxygen via a solenoid valve into the silicone tubing. The headspace o f the bioreactor was aerated with a constant air purge o f approximately 160 m L min" to prevent excess CO2 and O2 levels and to maintain positive pressure. A n 1  air flow o f 10 m L min" was maintained through the silicone tubing to improve D O and 1  p H control. The off-gas was exhausted through a condenser maintained at approximately 10°C.  A marine impeller (Applikon Inc.) was used for agitation at a speed controlled  between 100 - 225 rpm. From the time o f inoculation until the cell concentration reached 10 cells m L " , the agitation was 100 rpm. 6  1  Figure 4.4 illustrates the perfusion system  used. The detailed description o f the perfusion system can be found in the Appendix 1. Computer  Biosep Controller  • 1  10 L / SO Ll  2.1 M H z  ® r  -  Air Backflush <  -  Q  Harvest • .  Air Cooling Inlet  Acoustic Separator  Air Cooling Outlet  Recirculation Bleed  Feed -  Q  Figure 4.4: Schematic of perfusion system  27  A separate bleed line was used to maintain the desired cell concentration and remove accumulated cellular debris. The bleed rate was based on the culture growth rate. The culture volume was kept at a constant level using a conductance-based sensor that triggered the harvest pump. During harvesting, cells were retained using a BioSep 10L acoustic separator (AppliSens, division of Applikon, Schiedam, Netherlands), while spent medium was pumped into a harvest bottle. The separator operation is explained in detail in section 4.3.2.  For all regular operations, except for separation efficiency and  temperature measurement experiments, the acoustic separator was run in the airbackflush mode (Gorenflo et al., 2003) with a backflush frequency of 10 h" , with a 1  power input of 3 W and with the harvest pump set to a perfusion rate of 2.87 L day" . 1  The stop time was set at 5 s and the run time at 45 s. Cole-Parmer Masterflex peristaltic pumps (models 7521-40 and 7550-20) equipped with L/S standard pump heads were used for the harvest, bleed, backflush and recirculation. The medium feed was added every hour using a P10T peristaltic pump (Dungey, Agincourt, ON). The medium feed, cell bleed, separator operation and backflush pump were controlled with programs written in Lab VIEW 6.1 (National Instruments, Austin, TX).  4.3.2  Acoustic Separator Operation  During the perfusion runs, the bioreactor was harvested to remove the spent medium and to maintain a constant volume. The cell suspension was pumped into the 10L acoustic separator (AppliSens) and the cells were retained in the chamber by the acoustic forces. The aggregated cells settled back to the bioreactor and the clarified liquid was pumped out of the system at a selected harvest flow rate (HF). The volume in the acoustic chamber was 7 mL and the operating frequency was 2.1 M H z . The power input was  28  adjusted between 1 - 7 W depending on the desired operating conditions. The heat generated within the transducer is controlled by blowing air across its outside surface at a constant air cooling flow rate (ACF). The operation of the separator was controlled with a BioSep SC 1010 10L/50L electronic controller (Sonosep Technology, Austria). The acoustic power and the harvest pump were turned off periodically to enhance the settling of cells to the bioreactor (stop time). The alternation between the stop time and the run time is called the duty cycle (DC). For example, a duty cycle value of 180/3s means 180 s of run time with 3 s of stop time. The net flow rate (NF) is the average harvest flow rate accounting for the stop time.  The acoustic separator was operated in two modes:  the recirculation mode and the  backflush mode. During the recirculation mode, the cell suspension was continuously pumped into the acoustic separator through a side inlet (Figure 4.5) at a constant recirculation flow rate (RF). This flow was split into two parts: one part returned to the reactor with the aggregated cells and the other passed through the acoustic chamber. In the backflush mode, the cell suspension was pumped into the acoustic separator via the return line (Figure 4.5) and there was no recirculation flow. After a period of pumping, the acoustic power and the harvest pump were turned off, and the separator was emptied by backflushing air from the bioreactor headspace. The separator was then refilled from the bioreactor by reversing the direction of the backflush air pump, followed by turning on the acoustic power and harvest pump. The backflush mode of operation is described in more detal by Gorenflo et al. (2003). The recirculation mode was used for all the  29  experiments described in this thesis and air backflush was only used between experiments.  Recirculation Mode  Backflush Mode  Figure 4.5: Flow diagrams for recirculation and backflush modes  4.3.3  Design of Temperature Measurement Equipment  The operating temperatures within a 10L acoustic filter have never before been reported for a perfusion run. The challenge in measuring these temperatures was to aseptically modify the acoustic filter by introducing appropriately placed thermocouples without perturbing its operation.  4.3.3.1 Thermocouple Positions The first step was to find the optimal positions for making temperature measurements. The thermocouples had to be positioned in such a way as to avoid disturbing the acoustic field inside the cuvette (Figure 4.6). Placing a thermocouple directly in the field not only would cause a local loss of resonance, but also, because of additional dissipation of acoustic energy into heat, would result in unrepresentatively high  temperatures.  Experiments were performed to assure that all thermocouple readings were representative of the true internal temperatures. One thermocouple was placed at the centre of the inlet manifold (Figure 4.7). Moving the thermocouple across the diameter of the assembly  30  yielded constant temperatures, indicating that the fluid was homogeneously mixed in this area.  The second thermocouple was placed at the centre of the upper cone-shaped  manifold just below the point where the harvest flow exited from the acoustic filter (Figure 4.7). The outlet position also gave a homogenous reading of the temperature when the thermocouple was moved in and out of the manifold.  In addition to these  validations, conductivity tests were also carried out to ensure that conduction between the thermocouple and the metal parts of the filter did not affect the reading. Autoclavable thermocouple needles made from stainless steel (model HYP2-21-1-1/2-E-G-48-OST-M, Omega Canada) were selected in consideration of the aseptic needs of the process.  Figure 4.6: Picture showing the cuvette of the acoustic separator  31  Figure 4.7: Picture showing the modified acoustic separator and the positions of the inlet and outlet thermocouples  4.3.3.2  Modified Acoustic Separator  The design of the modified separator needed to be robust and well sealed in order to allow continuous operation during long perfusion cultures (Figure 4.7). The seal was assured by the compression of a gasket between two stainless steel fittings (Figure 4.8). The thermocouple was pushed through the red silicone rubber gasket cut from the sealing ring of a spinner flask (#A541-119, Bellco Glass, Vineland, NJ).  A pressure test was performed on the connection to test the seal. The assembly was submerged in water and air was pumped inside by a Masterflex peristaltic pump (ColeParmer) in order to pressurize the connection. A pressure of 30 psig was reached and no air bubbles were detected in the water.  During normal operation, the pressure in the  acoustic chamber was low, less than 5 psig.  32  Figure 4.8: Photograph of the connection that allows aseptic sealing of each thermocouple in the modified acoustic separator  4.3.4  Convection Test  A key parameter for the convection experiments was the ambient temperature.  The  control of the ambient temperature was difficult because the tests were performed during the summer and the laboratory temperature fluctuated greatly each day.  A tent,  constructed from a plastic tarp, was erected and a mobile air conditioner (SP-816CD, Cypress, Glendora, C A ) was used to help control the ambient temperature within the tent. The ambient temperature was thereby varied from 19°C to 27°C during the experiments. To maintain the same convection pattern around the bioreactor, the fan was left on and the air conditioner turned off for the higher ambient temperatures targeted. The position of the air conditioner was selected to minimize direct blowing on the system. During the experiments, the temperatures of the outside walls (side wall and reflector) were periodically recorded with a surface probe (Model 88008, Omega).  33  4.3.5  Optical System  A n optical measurement system was developed to monitor cell concentration inside the acoustic filter (Gorenflo et al., in preparation). The system uses the basic photometry concept of light scattering that is linearly correlated with cell concentration inside the cuvette when it is well mixed. When the separator is operated (i.e., cells in pressure node planes) the scattered light gave results quanlitatively related to the cell concentrations.  The important components of the optical system were a Lumex Super Red L E D (SSLLX5093XRC/4, Lumex, Palatine, IL) rated to 20 degrees light spread and 2500 mcds, and an OPT301 photodiode (Texas Instrument, Dallas, T X ) placed at 90° to collect scattered light. A l l of the components were housed in separate Teflon compartments and mounted on a Teflon ring (Figure 4.9). This Teflon ring enabled the system to be mounted on the acoustic separator for online measurements.  Figure 4.9: Optical system set up. A) Teflon ring. B) Optical system mounted on the acoustic separator.  34  4.3.6  Design of Experiments  The bioreactor equipped with a modified acoustic separator was used to perform an experimental design aimed at characterizing the separation efficiency dependencies of the system.  The ambient, inlet and outlet temperatures were recorded simultaneously to  generate a second empirical model focused on the thermal behavior of the system.  A two-level factorial design augmented with centre points and axial points was employed in order to determine the surface response using a quadratic model with five factors. A 2 " factorial design (32 runs; half fraction & replicate) was selected in such a way that all 5  1  main effects and interactions could be evaluated. The axial points (20 runs) were used to obtain the quadratic curvature and the center points (12 runs) gave the estimation of the pure error. The experiments were divided into 8 blocks so it was possible to test one block per day (1 block = 8 points), each point approximately every half hour.  The data from the experimental design were analyzed using the program R (R 1.5.0, The R Development Core Team, open source software: http://cran.r-project.org/) and a trial version of Design Expert 6.0 (Statease Inc, Minneapolis, M N ) . Multiple regression methods were used to fit a quadratic model to all 5 factors investigated. Each term of the empirical equation was tested using analysis of variance (ANOVA).  The selection of an optimized model was done in a stepwise fashion such that the nonsignificant terms (p > 0.05) were removed. If a factor had a non-significant main effect but significant higher order terms, the main effect was kept in the model. The overall  35  quality of the model was analyzed by the goodness of fit test and residual plots. The last step was to test the refined model to see how well it could predict points that were not used for the initial estimation of the model parameters (other points than the 64 used in this analysis).  The sum of the squared error was then calculated and the plots of  predicted versus experimental results analyzed.  4.4  Modeling  A mathematical model based on the conservation energy equation has been developed to calculate the temperature distribution inside the acoustic chamber. This model estimates the temperature profile for any set of operational conditions, and also provides predictions of the outlet temperature.  The average outlet temperature was calculated  from the model predicted temperature distribution at the outlet of the cuvette.  The  differential equation that governs the temperature distribution was solved using a finite difference method known as the alternating direction implicit (ADI) method.  The ADI method is a standard solution method for three-dimensional parabolic equations. This method uses the concept of time splitting; it divides each time step (i.e., the finite increment in the parabolic direction) into two steps of size Af/2 (Press et al., 1986). The method is implicit since it requires simultaneous solutions of sets of algebraic equations and it alternates the direction of the calculation in the two non-parabolic directions, e.g., in the x direction for the first half-time step and in the y direction for the second. The advantage of the ADI method is that to update the solution at each new time step requires only the solution of simple tridiagonal matrices. Each tridiagonal matrix can be easily solved using the Thomas Algorithm.  36  The optimization needed to determine the unknown fitted variables in the model was performed using a previously coded genetic algorithm. The method is based on concepts of genetics, which involves crossover and mutations between individuals from generation to generation. It is a type of random search method. The genetic algorithm is robust in optimizing functions containing numerous local maxima or minima.  These different numerical methods were programmed and solved using the MatLab 6.1 (The Math Works Inc, Natick, M A ) computing language. The model precision required to match experimentally determined temperatures was 0.1 °C and, through trial-and-error, it was found that the grid size needed to obtain this accuracy for most cases of interest was 21 points in the two non-parabolic directions and 21 points in the parabolic direction. MatLab codes used for the calculation of the mathematical model are presented in the Appendix 3.  4.5 4.5.1  Analytical Methods Cell Concentration and Viability  A n automatic hemocytometer, the Cedex cell counter (Innovatis A G , Bielefeld, Germany), was used for direct cell counting and their viability was measured by the trypan blue exclusion method. The aggregated cells were dispersed by mixing 1 mL culture samples (1:1 by volume) with trypsin E D T A containing 0.25 % trypsin / 1 m M EDTA»4Na (GIBCO Invitrogen Canada, Burlington, ON). Phosphate-buffered saline (KC1 = 0.2 g L" , K H P 0 4 = 0.2 g L" , N a H P 0 4 = 1.51 g L" , NaCI = 8 g L" , pH adjusted 1  1  2  1  1  2  37  to 7.4 with NaOH) was also added and incubated at room temperature for 10 - 15 min. Viability was determined by analysis of non-trypsinized samples. Each sample was counted three times for the perfusion experiments and two times for the batch culture experiments.  For the batch experiments, the glucose, lactate and glutamine were measured with a YSI analyzer (Model 7100 M B S , YSI Incorporated, Yellow Springs, OH). A blood gas analyzer (Rapidlab, Bayer Diagnostic, Toronto, ON) read the concentration of dissolved oxygen/C02 and the pH. For the perfusion experiments, a Stat Profile 10 blood/gas analyzer (NOVA Biomedical, Waltham, M A , US) was used to determine glucose, lactate and blood urea nitrogen (BUN) concentrations.  4.5.2  t-PA Analysis  The enzymatic t-PA activity was determined through a modified colorimetric assay that uses a plasminogen activation system to measure plasmin activity through the use of a chromogenic peptide substrate.  Human t-PA (Calbiochem, L a Jolla, C A ) was serially  diluted with 0.1 M Tris-HCl buffer (adjusted to pH 8.0 with NaOH) and 0.1% v/v Tween 80 to make standards ranging from 0.25 to 10 U mL" . Supernatant culture samples were 1  also diluted with the Tris dilution buffer.  96-well microtiter plates (Nalge Nunc  International, Rochester, N Y ) were loaded with standards and samples, then a reaction mixture of plasminogen (Boehringer Mannheim Canada, Laval, QC), CNBr-fragmented fibrinogen (Calbiochem, L a Jolla, C A ) and the substrate D-Val-Leu-Lys p-nitroanilide (Sigma, St. Louis, MO) was added. The plates were sealed and incubated at 37°C for 3 h, during which the p-nitroanilide is cleaved from the substrate by plasmin.  The p-  38  nitroanilide was then detected at 405 nm using a microtiter plate reader (Molecular Devices, Sunnyvale, C A ) eventually yielding, through calibration curves, a measure of the t-PA activity. The concentrations were calculated by applying a conversion factor of 580, 000 U/mg (WHO standard specific activity).  4.6  4.6.1  Calculations  Cell Culture Experiment  Biological systems are challenging systems. Experiments with these systems are difficult because of the presence of unknown variability, noise and related phenomena. Measuring the growth kinetics of the biological system under different conditions provides the information required for future optimization of the system. Key nutrients such as glucose, oxygen and glutamine as well as environmental conditions like pH and temperature have to be measured continuously to understand and control the system. With this information, various characteristics of the culture can be calculated. In the following section, the different equations used to calculate the important results from the cell culture experiments are described.  The average temperature (T) of the fluid pumped into the tube side of the heat exchanger was determined during a non-aseptic experiment with water. T was found by integrating the temperature profile over the period of time in which the thermocouple was submerged in water, i.e.,  39  ]r(t)dt (4.1)  T =—  t  }dt <i  The integral in the numerator of Eq. (4.1) was determined by using the trapezoid rule:  f =^  (4.2)  t -t, n  1  where 7} is the temperature (°C) at the time U (hr).  The net specific growth rate was determined by integrating the equation 1 dX  where p.  (hr" ) is the net specific growth rate, X is the viable cell concentration 1  net  (cells mL" ) and t is the time (hr). Analytically integrating this equation from t=0 and 1  X=X  0  to t=t and X=X yields  \n(X) = ju t + HX ). nel  Thus  n t ne  (4.4)  0  can be found as the slope when  \w{X)  is plotted as a function of t for the  exponential phase only. The log mean of the viable cell concentration (XLM) between the two time points t\ and ^ was calculated from:  ln(^) X/  K  40  The glucose consumption rate during the exponential phase was determined from the following relationship:  where Q  is the glucose consumption rate (mM h" ), G is the glucose concentration 1  G  (mM) and t is the time (hr).  The specific glucose consumption rate (qc-) was then  calculated from  q  G  = ^ .  (4.7)  The specific t-PA production rate (q ) was calculated for the first 3 days of culture from P  P q=  (4.8)  P  where P is the t-PA concentration (mg L" ) and t=12 hr, approximately. 1  The different culture batches were not obtained with exactly the same set up and environmental conditions. In fact, experimental improvements were progressively added to gain better control and the number of cell passages was different from batch to batch. To minimize the effects of these variations, all the results were normalized by those obtained in the 37°C control spinner (#1), i.e., the results for the pumped spinner control and the test spinner were divided by those obtained with the control spinner.  4.6.2  Temperature Measurements in Perfusion Culture  The perfusion culture was performed with a modified acoustic separator.  The  modifications were made to allow the aseptic introduction of two thermocouples to  41  measure the inlet and outlet temperatures.  The measurements were recorded on a  computer and the average temperatures at steady state were taken as the results.  The separation efficiencies were calculated from the following equation: C  r  SE =  2 _  A  = 100  harvest  (4.9)  r bioreactor  V  J  where SE is the separation efficiency (%), C  harvest  harvest flow (cells mL" ) and C 1  bioreactor  is the viable cell concentration in the  is the viable cell concentration in the bioreactor  (cells mL" ). 1  4.6.3  Modeling  The mathematical model was used to describe the thermal behavior of the acoustic separator by predicting the internal temperature distribution as well as the average outlet temperature. The average predicted outlet temperature was calculated by averaging the outlet cross-section profile. The governing equations are explained in section 7.2.1. To validate one hypothesis, the following different dimensionless numbers were calculated.  The Reynolds number characterizes the flow regime and is defined as  Re =  (4.10) Mi  where Re is the Reynolds number, L is the characteristic dimension of the flow channel, in this case, the hydraulic diameter (m) of the acoustic chamber, v is the average velocity (m s"), pi is the density of the liquid (kg m") and jut is the viscosity of the liquid (kg m"  42  1  s" ). Re gives an indication of the relative importance of inertial and viscous forces in 1  the flowing fluid (Bird et al., 2002). To calculate Re in a square duct, L, the hydraulic diameter, can be determined from  (4.11)  L=  wp where A is the cross-sectional area of the duct (m ) and wp is the wetted perimeter (m). 2  The Prandtl number is the ratio of the momemtum diffusivity to the thermal diffusivity of the system, and can be calculated using the following equation:  Pr = ^  (4.12)  k, where Pr is the Prandtl number, C j is the heat capacity of the liquid (J kg" K" ) and ki is 1  1  p  the thermal conductivity of the liquid (W m" K" ). 1  1  Finally, the Peclet number is defined as the ratio of the convection of heat to the conduction of heat in the system, and is given by Pe = Re Pr  (4.13)  where Pe is the Peclet number. Pe >1 represents a system where the heat transfer by convection is dominant. Pe=l is the case where convection and conduction have equal importance.  A simple energy balance was performed to verify that the total energy inputted to the acoustic separator was sufficient to heat the liquid from its inlet to its outlet temperature.  43  Water was used as the test liquid. The energy needed to heat the liquid can be calculated from  q = mC AT pJ  (4.14)  where q is the heat transfer rate (W), m is the mass flow rate (kg s" ) and AT is the 1  difference between the inlet and the outlet temperatures (K) of the fluid passing through the chamber.  4.7 4.7.1  Error Analysis Cell Culture Experiment  The cell culture plot error bars in Chapter 5 correspond to ± 95% confidence intervals of the standard deviation calculated by multiplying the t value of the student distribution with the standard deviation. The error was calculated for the pumped spinner control (#2) that was repeated for every different temperature tested, i.e., from a total of 7 experiments.  4.7.2  Temperature Measurements in Perfusion Culture  The separation efficiency plot error bars in Chapter 6 correspond, unless otherwise stated, to ± 95% confidence intervals of the standard deviation calculated by multiplying the t value of the student distribution with the standard deviation. During these experiments, 3 cell counts were obtained for the harvest and bioreactor samples, allowing 9 different combinations of separation efficiency to be calculated. The standard deviation was then estimated using all 9 combinations.  44  4.7.3  Modeling  The unknown parameters of the mathematical model of the acoustic separator (section 7) were fitted using experimental measurements. Those measurements contained variation due to the experimental errors. To measure this variation, samples were obtained at the same settings and the variance of each sample was calculated. The calculation of the pooled sample variance was made assuming that the sample variances were similar. This pooled sample variance was estimated by  Zw  2  (4.15)  where cr is the pooled sample variance, v is the degree of freedom of the sample and 2  t  of is the variance of the sample. The standard deviation is <j . The limits were set to 2 p  times the standard deviation.  45  5 Cell Culture Experiments 5.1  Introduction  During perfusion, fractions of the cells pumped from the culture vessel are cyclically exposed to an acoustic field. The acoustic energy used to retain the cells in stationary parallel planes while harvesting the liquid, is gradually transformed into heat. Thus, the retained cells are subjected to changes in temperature.  The average residence time of  cells in the acoustic filter can be estimated considering the length of the duty cycle. During each cycle, perfusion proceeds for a certain length of time, and then the field is turned off and the harvest pump is stopped so that the retained cells can settle back to the bioreactor. For high cell densities and high perfusion rates, the run time lasts one minute while the stop time is set to five seconds. The volume pumped through the acoustic chamber during a cycle represents 1% of the 0.6 L working volume of the reactor. To maximize the productivity of perfusion operation, any negative effects on the cells during the period they are captured in the acoustic separator must be minimized.  The acoustic field on its own has been reported to have no apparent influence on cells (Pui et al., 1995; Bierau et al., 1998; Zhang et al., 1998; Chisti, 2003), but the cyclic variation of temperature has not been investigated.  The goal of the cell culture  experiments reported here was to simulate the thermal environment of the acoustic separator, in order to determine any effects that transient temperature changes may have on the CHO cells and their recombinant protein production. To increase the likelihood of detecting small effects, 4 to 6% of the spinner culture volume was pumped into the heat  46  exchanger. This corresponded to a volume of 4 mL being pumped in and out of the tube side of the heat exchanger.  5.2 Validation of Experimental System To determine the average exposure temperature of the cells, preliminary temperature measurements were performed with water on the tube side of the heat exchanger. The temperature as a function of time (Figure 5.1) was integrated over one cycle after a dynamic steady state was established to find the average temperature in the heat exchanger for the six cases shown in Table 5-1.  39 38.9 38.8 38.7  u 38.6 s S  38.5  u ii 38.4 a £ H  38.3 38.2 38.1  • Shell Side  Cycle (probe in liquid) ^1  ' Tube Side  38 10  12  Time ( min) Figure 5.1: Temperature profile during the cyclic pumping of water to the tube side of the heat exchanger and at the entrance of the shell side.  One cycle was integrated to determine the tube side average temperature.  47  Table 5-1: Average temperatures measured in the tube side of the exchanger for different shell-side inlet temperatures  Shell Side Inlet Temperature (± 0.1°C) 25 30 33 35 39 41  Average Tube Side Temperature (at 7 cm from the tube side inlet) 27.4 31.5 33.9 35.4 38.5 40.2  The spinner set-point temperature was verified by continuously measuring the temperature inside the spinners. Maintaining a constant temperature near 37°C in the spinners was important in order to isolate the bulk of the cells from the variations of temperature in the heat exchanger. For the most extreme case where the shell side inlet temperature was set at 25.0 ± 0.1°C, the spinner temperature was 36.2 ± 0.2°C compared to 37.1 ± 0.2°C in the absence of pumping. This result shows that the heat transfer in the water bath did not completely compensate for the cooling in the heat exchanger. However, a less than 1°C difference should not affect the cells greatly considering that the optimal cultivation temperature for C H O cells is in the range of 36°C to 37°C (Furukawa et al., 1998). For the higher heat exchanger temperatures investigated, the water bath maintained the temperature in the spinner within 0.5°C (Table 5-2).  48  Table 5-2: Temperatures inside spinners with and without pumping. Temperature inside spinners (± 0.2°C) with and without pumping either to a heat exchanger maintained at 37°C (control spinner) or to one with different inlet shell side temperatures (test spinner).The control spinner was only a comparison to monitor changes within the incubator during each experiment.  Temperature  5.3  Test spinner  Control Spinner  Shell Side  No Pumping  Pumping  No Pumping  Pumping  25 30 33 35 39 41  37.1 37.1 37.1 37.1 36.8 36.8  36.2  36.8 36.9 36.8 36.9 37.0 37.0  36.8 36.8 36.8 36.9 37.1 37.0  36.6 36.7 37.0 37.0 37.1  Cell Culture Results  In order to simulate the internal environment of an acoustic separator, the effects of a cyclic variation of temperature on the maximum specific growth rate, the specific glucose consumption rate, the t-PA concentration and the specific t-PA production of CHO cells were investigated.  The maximum specific growth rate decreased significantly (P<0.05)  compared with the control spinner at temperatures higher than 39°C and lower than 31°C. The most significant growth rate decrease of 48% was observed at the average heat exchanger temperature of 40.2°C. The cells exposed to 27.4°C had a 27% decreased growth rate (Figure 5.2). The final viable cell concentration results display similar trends (data not shown). These results demonstrate the sensitivity of CHO cells to high and low temperature transients.  49  27  29  31  33  35  37  39  41  A v e r a g e Temperature in Heat E x c h a n g e r (°C)  Figure 5.2: Effect on the specific growth rate and on the specific glucose consumption for CHO cells exposed to different average temperature. The error bars represent 9 5 % confidence intervals.  The glucose consumption increased by 43% at 40.2°C while the glucose metabolism of the cells was reduced at lower temperature, down by 16% at 27.4°C (Figure 5.2).  Finally, the production of t-PA was not significantly affected by the variation of temperature (P<0.05).  Figure 5.3 shows the results for t-PA concentration and  production. The specific t-PA production rate did not vary significantly with the cyclic variation of temperature.  The large variability can be explained by the addition of two  sources of error, due to the t-PA concentration assay and the cell concentration measurement,  to calculate the specific t-PA production.  At 40.2°C, the t-PA  concentration was significantly decreased by 45%, but the low growth rate and the low cell concentration were the cause of this result.  50  1.6  u 3  1.0 t-PA Concentration  1.4  O  £  TJ C O O  1.2  0.8 § o  p  < 5  5: 2  i 1  1 is = o  .__ __ Specific t-PA Production  1 0  '"^^^'•^  0.6  0  o §> 0.4 « CL  u *  CO*  a,  0.8  | «  0.2  0.6  I  27  !  29  31  "1  33  —  1  35  —  1  ——  37  39  —  0.0 41  Average Temperature in Heat Exchanger (°C) Figure 5.3: Effect on the cell specific t-PA production rate and on t-PA concentration for C H O cells exposed to different average temperature. The error bars represent 9 5 % confidence intervals.  The results at 37°C for the pumped spinner control isolated the effect of pumping a fraction of the cells out of the culture for one minute.  No significant effects were  observed for the specific glucose consumption rate and for the specific growth rate (Figure 5.2). On the other hand, the production of t-PA seems slightly lower, but, given the confidence limits, this result is not significant.  5.4  Discussion and Conclusions  For these experiments where 4 to 6% of the culture was cyclically exposed to one-minute intervals at different temperatures, no significant effects on C H O cells were detected between 31.5°C and 38.5°C. This should define an acceptable range of temperatures in an acoustic separator where only 1% of the cells are cycled to different temperatures. The specific growth rate and the final viable cell concentration were reduced at 27.4°C and also at 40.2°C. The specific glucose consumption rate decreased at 27.4°C while it  51  increased at 40.2°C. The t-PA production was not significantly affected by the variation of temperature.  During the stop time most of the cells in the separator are believed to settle back to the bioreactor, but some cells are likely to remain inside the separator for more than one cycle. However, the backflush mode used to maintain the bioreactor, completely emptied the acoustic separator every 6 minutes.  The diameter of the tube side of the heat  exchanger was purposely selected to be small in order to allow a rapid increase of the liquid temperature to better simulate acoustic heating. Nonetheless, the mechanism of heat generation in the acoustic chamber could have lead to "hot spots" that may have had a stronger, more local influence on the cells.  Additional experiments could be performed to test the effects on cells of longer residence times, over one minute, in an altered temperature environment. In this way, the effect of spending time in an environment with limited nutrients and oxygen could be investigated in detail. Also, replicates of the cell culture experiments could be performed to improve the statistical significance of the results. The ideal set up would have used nine parallel spinner cultures, but this was not practical. In addition, increased agitation of the water bath and a thinner spinner wall could have improved the control of the internal spinner temperature.  52  6 Temperature Measurement in Perfusion Culture 6.1  Introduction  During the operation of an acoustic separator, the acoustic energy is transformed into heat thereby increasing the temperature inside the separator.  Many parameters affect the  internal temperature distribution in the device such as power input, flow rate and ambient temperature.  This chapter describes how the effects of the important variables of the  system were investigated to determine their influence on the temperature distribution. The manufacturer-recommended operational settings were tested and recommendations made to improve the system operation. The cell separation efficiency of the acoustic filter was also affected by the system variables including the temperature variation in the cuvette. Thus, some separation efficiency results related to system temperature changes are included. Finally, empirical models that predicted the inlet and outlet temperatures of the filter were developed based on data from a factorial design.  6.2 6.2.1  Influence of System Variables Power Input  The electrical power input to the system is converted to the acoustic energy that creates the forces needed to retain the cells in the stationary pressure node planes. The strength of these forces is proportional to the magnitude of the power applied to the system. However, increased temperatures inside the acoustic separator are also directly related to the applied power. Figure 6.1 shows how the inlet and outlet temperatures changed as a function of the power input. At a low power of 1 W, the air cooling device (see section  53  6.2.2) removed more energy than was generated by the transducer.  Thus, the outlet  temperature was lower than that of the inlet. At 7 W, the outlet temperature reached 41.2°C, a value that is outside the acceptable limits for the cells (section 5). Even though increasing the power improves the strength of the retention forces, the high temperatures generated can reduce the efficiency of the system (see section 6.4 for more details). In Figure 6.1, it should be noted that the inlet temperature also increased with the input power even though all the other variables were kept constant.  This behavior can be  explained by the conduction of heat in the metal frame of the acoustic filter. At higher power inputs, the heat generated not only raised the temperature of the liquid but also that of the entire apparatus.  Because the inlet section is made of stainless steel, the  conduction of heat was substantial and, as a result, the inlet temperature increased. Some scattered acoustic energy can also be dissipated as heat in the inlet stream and increase its temperature.  54  A T  41  out  • Tin 39  o 2  £ s  •  37 35  H 33  1  31  •  *  • 1  I  0  1  2  3  •  •  4  i  i  1  5  6  7  8  Power ( W ) Figure 6.1: Effect of power input on inlet and outlet temperatures  Settings: ACF=10.7 L min , HF=8.1 L day , RF=16.3 L day" , DC=180/3s, [cell]=11.9xl0 cells mL , 1  1  1  6  1  I ambient  -25.0 ±0.3°C standard deviation for duration of experiment. 6.2.2  A i r Cooling  During the non-ideal conversion of electric energy into acoustic energy in the transducer, the lost energy is dissipated as heat. Blowing air on the outside surface of the transducer therefore helps avoid excessively high temperatures.  Without air cooling, the  temperature of the fluid flowing through the device increases more significantly (Figure 6.2). For example, in the absence of cooling, the difference of temperature between the inlet and the outlet reached 12.5°C at 7 W input power. The injection of 10.7 Lmin" of 1  air into the transducer heat exchanger reduced this temperature difference to 6.7°C. Figure 6.2 shows the effectiveness of the air cooling device in controlling the bulk fluid temperature in the acoustic separator.  55  13 11  A No A i r Cooling  9  • Air Cooling  H"  -  5 1  3  e  3 1 -1 0  1  2  3  4  5  6  7  8  Power ( W ) Figure 6.2: Effect of air cooling on the difference in temperature between the inlet and outlet.  Settings: ACF=10.7 L min" , HF=8.1 L day", RF=16.3 L day , DC=180/3s, [cell]=l 1.9x10 cells mL" , Tambient 25.0 ±0.3°C standard deviation for duration of experiment. 1  1  6  1  =  6.2.3  Flow Rate  The cell suspension was pumped into the side inlet of the acoustic separator (recirculation mode, Figure 4.5), and the flow split into two parts, the harvest flow and the return flow. The magnitude of these flows directly influenced the internal temperature of the acoustic separator.  The harvest flow rate, in particular, had a significant effect on the outlet  temperature. Increasing this flow rate reduced the residence time in the acoustic chamber so that the liquid received less energy.  Thus, the temperature of the outlet was  diminished at higher harvest flow rates (Figure 6.3).  The error bars represent the  standard deviation for replicates taken under similar operating conditions. The ambient temperature (section 6.2.4) was hard to maintain constant during these experiments and this effect accounts for some of the variability in the measurements.  Variations of the  56  acoustic properties in the system, like the resonance frequency, may also have affected the measurements by modifying the percentage of acoustic energy converted to heat.  43  •  41  ii  ™  3  o W  ii  o$  o g  a 5 S 2  h  39  33 31 29  35  • Tin B T ambient  m  33  A*  37 35  37  out  A T  31 •  •  • i  i  2  4  29  f  •  27 25  2  8  E  a  23  T'  6  3  C  •  1  r  10  12  Harvest Flow Rate ( L/day ) Figure 6.3: Effect of harvest flow rate on the inlet and outlet temperatures for a relatively constant ambient temperature.  Settings: P=5 W, ACF=10.7 L min" , RF=20 L day" , DC=300/3s, fcell] =7.4 xlO ± 1.3 cells mL" (std. dev.) 1  6  1  1  average  The recirculation flow rate primarily affected the inlet temperature.  Because of heat  transfer to the surrounding environment, the cell suspension was cooled during its transit through the recirculation tubing making the residence time of the fluid in the tubing important. The diameter and the length of the tubing, as well as the average velocity of the liquid determined the residence time.  For a perfusion system with a fixed tube  connection between the culture vessel and the acoustic filter, only the recirculation flow rate influenced the residence time.  A reduction of the residence time decreased the  amount of heat that was transferred and the cell suspension entered the acoustic separator at a higher temperature (Figure 6.4). The acoustic filter outlet temperature depended on  57  the inlet temperature but also on the heat dissipated in the separator.  Thus, the  recirculation flow influenced the outlet temperature less than the inlet temperature. However, observation of the measured temperature differences between the inlet and outlet shown in Figure 6.4 reveals an interesting phenomenon.  At the lowest  recirculation flow rate, this difference was positive, whereas for higher flow rates, the difference became negative with all other settings maintained constant. The explanation comes from two phenomena: the increase in the heat transfer between the environment and the separator and the conduction in the metal frame mentioned in section 6.2.1. A higher overall temperature of the acoustic separator increased the driving force of energy transfer with the environment at a lower ambient temperature.  In addition, the higher  recirculation flow rate improved the heat removal by conduction in the metal frame. With the resulting enhanced heat transfer rate, the outlet temperature became lower than the inlet temperature.  58  36  28 A T  out  35  • Tin • T ambient  27  O  c  3  <y  34  3  33  25 'JE  32  24  o  S o  H  •*»  •-  e  ® £  £  26  o  f  31 30 10  20  30  3  £ 2 a  <  C  E H  23 22  40  50  60  Recirculation Flow Rate ( L/day ) Figure 6.4: Effect of recirculation flow rate on inlet and outlet temperatures for a relatively constant ambient temperature.  Settings: P=3 W, ACF=10.7 L min' , HF=11.33 L day" , DC=45/6s, [cell] =9.7 ± 0.6 xlO cells mL" (std. dev.) 1  6  1  1  average  6.2.4  Ambient Temperature  The ambient temperature is a key parameter in determining the rate of heat transfer between the acoustic separator and the environment.  A variation in the ambient  temperature will have a direct effect on both the inlet and outlet temperatures.  Lower  ambient temperatures increase the rate of heat transfer to the environment and, hence, decrease both the inlet and outlet temperatures (Figure 6.5). The outlet temperature is more affected than the inlet because of the air cooling device. The air blown across the transducer in this device was taken from a different room within the building but, nonetheless, the air inlet temperature was within 0.4°C of the ambient value.  The  efficiency of cooling was reduced at higher ambient temperatures and hence the outlet temperature reached higher values.  59  36 A  A T out  • Tin  A  •  30  H  18  1  1  1  1  1  1  i  1  19  20  21  22  23  24  25  26  Ambient Temperature (°C ) Figure 6.5: Effect of ambient temperature on the fluid inlet and outlet temperatures.  Settings: P=3 W, ACF=10.7 L min" , HF=5 L day" , RF=20 L day , DC=45/6s, 1  1  1  [cell] a e 6.7xl0 cells mL" . =  aver  6.2.5  6  1  g  Duty Cycle  The duty cycle is an important feature of the acoustic separator. During the stop time, the cells settle back into the reactor and, when the power is turned back on, the system automatically readjusts its resonant frequency. Also, natural convection creates a strong mixing action during the stop time, which causes fluctuations in the temperature measurements, particularly that of the inlet (Figure 6.6). The recirculation pump was kept on during the stop time such that energy continued to be removed, resulting in the low temperature minima. Shorter run times allowed the system to make frequency scans more often and helped to keep the system more stable.  At a duty cycle of 180/3s,  scanning only took place at 3 min intervals, and, compared to the 60/5s duty cycle, the system did not maintain a stable outlet temperature because it was unable to keep up with  60  the changing acoustic properties of the liquid.  The correlation between temperature,  efficiency of the system and frequency is explained in section 6.4.4.  10  15  20  25  Time ( min) Figure 6.6: Effect of duty cycle on the inlet and outlet temperatures.  Settings: P=5 W, ACF=10.7 L min" , HF=10.8 L day" , RF=21.7 L day" , [cell] =9.3 ± 1.4 xlO cells mL" (std. dev.) 1  1  6  1  1  average  For the different duty cycle settings of Figure 6.6, the data were averaged and standard deviations were calculated. The results are presented in the Table 6-1. Note that, at 180/3s, the standard deviation of the outlet temperature is 3 times higher than for the other two duty cycle settings. The average values of the inlet and the outlet temperatures for the 60/5 s and 120/10s duty cycles are almost the same. The difference between the inlet and outlet temperatures is the same for both cases.  These results show the  insignificant effect of the variation of duty cycle on the average temperatures. The fast recovery of the pseudo-steady state after the stop time is responsible for minimizing the effect of the duty cycle on the temperature of the system.  61  Table 6-1: Averaged values and standard deviations of the temperatures recorded in Figure 6.6  DC (s) 60/5 120/10 180/3  6.2.6  T  i  St. Dev.  n  r o  (T  34.1 34.3 34.4  i n  Tout  (°C) 36.7 36.9 36.7  )  0.2 0.2 0.1  St. Dev.  Tout " T i  CQ  (Tout)  0.1 0.1 0.3  2.6 2.6 2.3  n  Tambient  (°C) 24 24 24.8  Cell Concentration  The cell concentration in the bioreactor was adjusted during the perfusion run by controlling the medium feed rate and the bleed rate. At high concentration, the number of cells in the acoustic separator at any given time during the duty cycle is much higher than at low concentration (Figure 6.7).  A  B  Figure 6.7: Photograph of cell planes in the acoustic chamber.  A) low cell concentration, 2.2 million cells mL" and B) high cell concentration, 9.0 million cells mL"' (Settings: P=3 W, ACF=10.7 L min"', HF=11.4 L day"', RF=34 L day"', DC=45/6s). 1  The concentration of cells in the acoustic chamber does not have a important effect on the temperature (Figure 6.8). The slight increase in the outlet temperature with increasing  62  cell concentration might be explained by the possibility that the cells are locally intensifying the dissipation of the acoustic energy into heat. Because the cells are denser than the liquid, they may absorb more energy than the fluid.  38 A T  r  out  34  • Tin B T ambient  •  •  •  33  24 0  2  4  6  8  10  Cell Density ( million cells/mL ) Figure 6.8: Effect of cell concentration on the inlet and outlet temperatures.  Settings: P=5 W, ACF=10.7 L min" , HF=11.4 L day" , RF=34 L day" , DC=45/6s. 1  6.2.7  1  1  Discussion and Conclusions  The control of temperature in the acoustic separator is necessary to avoid negative effects on the cell culture and to reach maximal and consistent productivity during perfusion operation. Many system variables have a direct impact on the operating temperatures. The power input to the acoustic transducer provides the energy to retain the cells, but it also leads to the heating of the harvested fluid. Thus, the increase in temperature within the separator is directly related to the input power to the system and the operational power must be selected carefully to avoid excessive heating. A n air cooling device is essential to control the heat generation in the system and allow operation at a lower  63  temperatures.  The recirculation flow rate primarily affects the acoustic separator inlet  temperature but, because it enhances the overall heat transfer rate from the system, it also helps to reduce the outlet temperature.  The harvest flow rate is another important  variable that has a direct influence on the outlet temperature. Reducing the harvest flow rate increases the residence time of the liquid in the acoustic chamber and, as a result, the fluid absorbs more energy and reaches a higher outlet temperature.  The ambient  temperature influences heat losses from the system as well as the efficiency of the cooling device, and hence will affect both the inlet and outlet temperatures.  The duty  cycle and the cell concentration do not significantly affect the time-averaged temperatures of the system.  6.3 6.3.1  Investigation of Recommended Settings Introduction  Knowing the operating temperature range for which cells remain viable, it was important to investigate how well the separator performs, particularly from a temperature perspective, when it is operated at the settings recommended by the manufacturer. The user's manual for the AppliSens acoustic filter was developed based on the results obtained using perfused yeast cells. The mammalian cells used in perfusion processes are approximately 4 times larger than yeast cell and have somewhat different acoustic properties (Woodside et al., 1997). Thus, it is of interest to test a CHO cell system using the operating conditions recommended by the manufacturer to, possibly, refine the suggested settings for mammalian cells. From Table 6-2, six settings were selected and investigated. These settings represent the conditions that would be most likely to reach  64  extremes of temperature during the acoustic separator operation.  The analysis of the  results is presented in two sections: one dealing with temperatures and the second with separation efficiencies. Although reported separately, the results of both sections 6.3.2 and 6.3.3 were obtained from the same set of experiments.  Because the cell  concentrations were difficult to control, their actual values (Figure 6.10) are different from those in Table 6-2.  Table 6-2: Suggested power settings and duty cycle times at selected cell concentrations and perfusion rates.  (10L, BioSep APS 990, AppliSens, Division of Applikon, Schiedam, Netherlands). The circled values were investigated and RF is two times HF. Net Flow Rate  Cell Concentration  (L/day)  (million cells/mL) 2  3  5  1 0  A  15  20  30  2  10 min / 3s 10 min / 3s 10 min / 3s1 10min/3s \ 10 min / 3s 5 min / 3s 2W N 2W 2W 2W * 2W 2W  4  10 min / 3s 10 min / 3s 10 min / 3s ;5 min / 3s X 5 min / 3s 3W 3W 3W 3W  5 min / 3s 3W  6  10 min / 3s 10 min / 3s 10 min / 3s 5 min / 3s 3W 3W 3W 3W  3 min / 3s1 3min/3s X v. 3W  8  5 min / 3s 3W  5 min / 3s 3W  10  5 min / 3s 5W  5 min / 3s 3 min / 3s1 3 min / 3s \2 min / 3s •v. 5W 5W 5W  12  2 min / 3s 5W  2 min / 3s 5W  6.3.2  s  5 min / 3s/ 5W  5 mm / 3s 2W  ;----\B  —  D  5 min / 3s 3W  5 min / 3s  C  3 min / 3s \3 min / 3s 2 min / 3s 5W / 5W 5W  E  2 min / 3s 5W s  —  - J *  1 min / 3s\ 1 min /5s \ 5W  1 min / 3s 1 min / 3s 1 min / 3s 1 min / 5s 1 min / 5s 5W 5W 5W 7W 5W  Temperature Results  The recorded inlet and outlet temperatures were mostly in the acceptable range defined in section 5 (Figure 6.9). The 2 lower than 31.5°C temperatures obtained for settings A and  65  B were the result of very slow recirculation flow rates (set at twice the harvest flow rate as recommended by the user's manual). By increasing the recirculation flow from 2 to 15 L day" , the temperature was easily maintained in the acceptable range (Table 6-3). 1  40 39 . A T out 38 • T i n a = 37 • T ambient 53 w 36 s a 35 0 34 tm ** 33 1 a 32 31 30 29 • 28 s  36 35 34 33 32 31 S u 30 | 29 g 28 < 27 26 25 24 23  Z  * A  A  •  •  •  •  •  T  I  i  1  i  A  B  C  D  E  i F  Settings of Table 6-2 Figure 6 . 9 : Inlet, outlet and ambient temperatures for the investigated settings of Table 6 - 2 . RF is two times HF, ACF=10.7 L min" , the cell concentration is shown in the Figure 6.10 and the error bars are the standard deviations for the replicates. The dashed lines represent the acceptable operating range for CHO cells as determined in the section 5. 1  Table 6 - 3 : Inlet, outlet temperatures and their difference for two different recirculation flow rates for the setting " A " in Table 6 - 2 .  Settings: T =24.5°C, ACF= 10.7 L min" , [ceUl= 8.9 million cells mL" . Settings Recirculation Flow Rate T AT T out (Table 6-2) (Lday ) A 4 27.8 32.1 4.3 A 15 32.4 1.4 33.8 1  1  ambient  i n  1  CQ  CQ  CQ  For the 7 W F setting, the outlet temperature was 39.3°C with an ambient temperature of 24.4°C. A more typical room temperature of 22°C should improve the cooling of the acoustic chamber and hence reduce this F setting outlet temperature, maintaining it in the acceptable range.  66  6.3.3  Separation Efficiency Analysis  The acoustic separator is normally operated at a separation efficiency greater than 90%. The measured separation efficiency results for the 6 recommended settings investigated showed only one point (setting E) significantly below 90% (Figure 6.10). This low result can be explained by the excessive build-up of cells in the separator for this high harvest flow rate and long run time. The large error bars of setting D showed that, even though the system operated with an average separation efficiency close to 90%, SE varied significantly mainly because of variations in cell concentration. For example, at cell concentrations higher than 8 million cells mL"  1  (data not shown), the separation  efficiency was lower than 90% while at cell concentrations below 8 million cells mL" , 1  the separation efficiency was greater than 90%. In contrast, the operation for setting C was robust at -99% separation efficiency despite similar variations in cell concentration.  Settings in Table 6-2 Figure 6.10: Separation efficiency and cell concentration for the investigated settings of Table 6-2.  RF is two times HF, ACF=10.7 L min" and the error bars are the standard deviations for the replicates. The dashed line represents the minimum SE required for acceptable perfusion operation. 1  67  Improvements in the separation efficiency for settings D and E were obtained by modifying the duty cycle from 180/3s to 45/6s. For setting E the separation efficiency was found to increase from 65.9% to 89.0% when the duty cycle was changed in this fashion.  To further test this point, experiments were performed for 4 different duty  cycles for setting D at higher cell concentrations (Figure 6.11). The duty cycle 180/3s was tested at the beginning and replicated at the end. The standard deviations were small, - 1 % for the separation efficiency and 0.1 x l O cells mL" for the cell concentration 6  1  (error bars in Figure 6.11).  u  a  .22  c  S  u a CC  ^  70 60  • S.E. A Cell Concentration 180/3  120/6  45/4  45/6  Duty Cycle ( s ) Figure 6.11: Effect of variation of the duty cycle on separation efficiency.  The error bars represent 95% confidence intervals on the cell count readings and the condition at 180/3 was duplicated. Settings: P=5 W, ACF=10.7 L day" , HF=8 L day", RF=2*HF, ^^,=24.7 ± 1.4°C (std. dev.) 1  1  The shortest run time significantly improved the separation efficiency to 97%. The results were not significantly different between 4 or 6 s stop times at the 45 s run time (Figure 6.11).  68  6.3.4  Recommendations  Overall, the recommended settings (AppliSens) tested were generally appropriate for CHO cells in terms of separation efficiency and also temperature.  However, several  modifications are recommended to ensure successful operation of the device.  A  minimum recirculation flow rate (e.g. 15 L day" ) is suggested to avoid low inlet 1  temperatures, to prevent cell sedimentation in the recirculation line and to increase the heat transfer rate from the separator to the environment. The acoustic separation should be performed at a constant ambient temperature of about 22°C to improve the cooling and to reduce the outlet temperature. The run time of the duty cycle should be shorter, around 45 s, to provide a higher separation efficiency and to keep the system more stable.  6.4  6.4.1  System Efficiency  Natural Convection  The collection efficiency of the acoustic filter can be influenced by several phenomena associated with temperature gradients caused by the dissipation of acoustic energy to heat. One effect is that non-uniform heating within the acoustic chamber can lead to the formation of natural convection currents. Natural convection is normally induced near the transducer surface due to the difference in temperature between that wall and the bulk liquid inside the acoustic separator. For a low ambient temperature, around 19°C, and an air cooling flow rate of 10.7 L day" , the temperature at the transducer surface was lower 1  than that of the liquid. As a consequence, the slightly more dense fluid near the wall caused a downward movement of fluid and cells in the vicinity of the transducer (Figure 6.12). For a higher ambient temperature of 26°C, the temperature difference between the  69  transducer surface and bulk liquid was reversed and, consequently, the cells were observed to move upwards.  On Figure 6.12, the arrows show the directions of the  convective flow observed during these two experiments as documented by video.  A  B  Figure 6.12: Effect of natural convection during the operation of an acoustic separator with the ambient temperature at A) 19.0°C and B ) 26.0°C.  The arrows indicate the observed directions of cell (and hence fluid) movement. The transducer is on the right side of the cuvette.  Another experiment was performed using an air conditioner to control the ambient temperature. Cold air (air conditioner outlet at 15°C) was blown directly on the separator and, consequently, increased the rate of heat transfer  from the separator to its  surroundings. The separation efficiency was found to be lower with the air conditioner on than when it was off (Figure 6.13). This unusual phenomenon was induced by strong natural convection flows that perturbed the cell planes. The cold air blown directly on the separator increased the air cooling effect and favored natural convection inside the acoustic chamber by increasing the temperature difference between the bulk fluid and the acoustic separator walls. The experiment was done during a warm sunny day in August without effective room temperature control and, therefore, when the air conditioner was 70  off, there was a wide range of ambient temperatures (Figure 6.13). This experiment was not representative of the normal operation of the acoustic separator, where direct external blowing on the separator and the extreme ambient temperatures would be absent.  Air Conditioner  37  On  Off  36 i 53 3  o  w  o  •  35  A  100  •  a  a  34  ill  3  o g  •  33  a 32 £ S h 31 J*  A Tout  t90  |  f 80 70  2 O eg  o  a  • Tin  ^ w  60 eg  • S.E.  30  50 21  23  25  27  29  31  Ambient Temperature (°C ) Figure 6.13: Effect of variation of ambient temperature on the inlet and outlet temperatures and on the separation efficiency. Settings: P=3 W, ACF=10.7 L min , HF=11.3 L day' , RF=34 L day , DC=45/6s, [cell]=8xl0 cells mL". The error bars represent 95% confidence intervals. 1  6.4.2  1  1  6  1  Ambient Temperature  To investigate the effects of ambient temperature on the separation  efficiency,  experiments were performed in a temperature-controlled environment without direct external blowing on the separator, as described in section 4.3.4. The ambient temperature was controlled between 19 and 27°C (Figure 6.14). For normal operations, where the separation efficiency exceeded 90%, no significant effects on the separation efficiency were observed. At the lower separation efficiencies there appeared to be a small decrease at higher temperature, but these would not be common operating conditions.  71  100 •  95  u  c  r  i  90  .22 '5  E _  i  85 80  c £ .2 w  75  E eg a u  65  A  •  T  W  _  h  T  70  ^  T • P= 5 W, NFR= 4.5 L/day, [Cells]= 6.7 millions/niL AP= 5 W, NFR= 10 L/day, [Cells]= 10.1 millions/mL OP= 3 W, NFR= 10 L/day, rCellsl= 9 millions/mL  60 55 50 18  19  20  21  22  23  24  25  26  27  28  Ambient Temperature (°C ) Figure 6.14: Effect of variation of ambient temperature on the separation efficiency for different separation efficiency ranges.  The error bars represent 95% confidence intervals. Setting: DC=45/6s.  6.4.3  A i r Cooling  The recommended air cooling flow rate is between 6 and 10 L min" . Three experiments 1  were executed to determine i f the air cooling flow induced natural convection strong enough to affect the separation efficiency.  Again, different ranges of separation  efficiency (achieved by varying the power and the harvest flow rate) were selected to explore possible effects. The variation of the air cooling flow rate from 0 to 16 L min"  1  did not significantly affect the separation efficiency (Figure 6.15).  72  •torn  u 93  c.  »5  70 60 50  • P= 5 W, NF= 4.5 L/day, [Cells]= 6.7 millions/mL AP= 5 W, NF= 10 L/day, [Cells]= 10.1 millions/mL OP= 3 W, NF= 10 L/day. rCellsl= 9 millions/mL 4  6  8  10  Air Cooling Flow R a t e  12 (  14  i 16  18  L/min )  Figure 6.15: Effect of the air cooling flow rate on the separation efficiency for different separation efficiency ranges.  The error bars represent 95% confidence intervals. Settings: DC=45/6s, T i 26.1 ± 0.7°C std. dev. =  amb  6.4.4  em  Frequency  The resonance frequency also can be sensitive to variations in temperature.  For certain  operational settings, changes in the temperature appeared to shift the resonance frequency peak. This variation of frequency was recorded during a perfusion experiment (Figure 6.16) where the resonance frequency of 2.14 M H z was the normal level.  During the  period when the power is on, the conversion of the acoustic energy into heat takes place and the outlet temperature gradually increased (Figure 6.16). After the stop time of 3 s and when the outlet temperature reached approximately 38°C, the electronics adjusted the resonance frequency to 2.09 MHz. At this different frequency the temperature decreased, possibly because of a lower conversion of the electrical energy into acoustic energy. The liquid was now cooler and the frequency peak returned to 2.14 M H z . At that temperature the temperature increased, and so the pattern is repeated.  73  14  18  22  26  31  35  39  43  47  52  Time ( min ) Figure 6.16: Effect of frequency shift on the temperature of the acoustic separator.  Settings: P=5 W, ACF=10.7 L min , HF=7 L day", RF=20 L day", DC=300/3s, [cell]=8.3xl0 cells mL", 1  1  1  6  1  T mbient 24.0 C. =  a  The determination of the effect of the frequency shift on the separation efficiency measurements was carried out with the help of an optical system whose photodiode voltage was proportional to the cell concentration inside the acoustic chamber due to light scattering.  This photodiode was positioned higher than the middle of the acoustic  separator. During normal operation, the cells were principally retained in the bottom portion of the device. At a frequency of 2.09 M H z , the photodiode reading increased showing that the cells were less well retained in the chamber (Figure 6.17). On the contrary, when the frequency was 2.14 M H z , the photodiode reading was slightly lower and remained more constant. Therefore, a reduction of the separation efficiency appeared to occur at a lower frequency.  74  0:28  0:30  0:33 0:36  0:38 0:41  0:44  0:46 0:49 0:52  Time ( min) Figure 6.17: Effect of frequency shift on separation efficiency. Settings: P=5 W, ACF=10.7 L min" , HF=7 L day" , RF=14 L day" , DC=180/3s, [cell]=8.6xl0 cells mL" , 1  1  1  6  1  fambient 25.0 C. -  6.4.5  Discussion and Conclusions  The efficiency of the acoustic separator can be disturbed by internal natural convection. The variables that most significantly influenced natural convection were the ambient temperature and the rate of air cooling. The variation of the ambient temperature from 19 to 26°C did not negatively affect the separation efficiency. In the same way, the variation of the air cooling flow rate from 0 to 16 Lmin" did not influence the separation 1  efficiency. Blowing 15°C air on the device did decrease separation efficiency, but this practice is not representative of the normal operation of an acoustic separator.  Moreover, the changing temperature inside the separator appeared to modify the acoustic properties of the liquid and as a result shifted the resonance frequency to a higher value. In this case also the separation efficiency of the system was reduced according to the  75  photodiode readings.  Direct measurements of the separation efficiency changes for  different resonance frequencies are needed to assess the significance of these effects. 6.5 6.5.1  Design of E x p e r i m e n t Description  The initial goal of the factorial design was to characterize the separation efficiency of the acoustic separator during a perfusion culture of C H O cells.  The modified acoustic  separator allowed the measurement of the inlet and outlet temperatures during this experiment such that additional models could be generated for the inlet temperature (Tj ), n  the outlet temperature  (T t) ou  or the difference between the two (Delta T).  The  independent variables studied were the bioreactor cell concentration (BX), the power input (PI), the net harvest flow rate (PR), the ratio of the recirculation flow rate to the harvest flow rate (RR) and the stop time (ST). During these experiments, the run time was kept constant at 45 s and the air cooling flow rate was maintained at 10.7 L min" . It 1  was not possible to maintain a constant cell concentration in the bioreactor, so the model used to generate the surface response of the separation efficiency was a linear mixed effect, or split plot, that took into consideration this random effect. In addition to these 5 factors, the ambient temperature (TA) was recorded as an uncontrolled variable and was included in the analysis of the temperature factorial design.  The primary results calculated with the program R, showed that the cell concentration in the bioreactor did not have a significant effect on any of the three temperature responses (data not shown). As a consequence of this result, supported by previous experimental results (section 6.2.6), the bioreactor cell concentration was eliminated from the factorial  76  design analysis. Thus, the use of the split plot technique and the program R no longer became necessary, and a simpler program, Design Expert, could then be used to carry out the analysis. 6.5.2  Full Models Analysis  One objective of the factorial design analysis was to derive an empirical equation for predicting each selected response.  For this purpose, a quadratic model, which also  included the five terms and their interactions, was selected. For example, the model for the inlet temperature can be written as: T =P +/3 xPR 0  IN  + /J xPI  PR  xPR + p  pi  P  2  PPR.PI *PRXPI P ,«ST P  xPIxST  PST*TA  x PI + P  xSTxTA + P  RRXTA  +  P xTA TA  xST +/3 xRR +  + PPR^ST XPRXST PLXRR  m  2  st1  +P  + {] xRR  ST  2  pil  PRL  + P xST  xPIxRR  2  RR2  P  x TA + 2  ta2  + /3PRxRR XPRXRR  +P  PIXTA  + /3pRxTA  xPIxTA + P  xRRxTA  +  STXRR  xPRxTA +  xSTxRR  + (6.1)  where fi is the intercept and /?,. is the coefficient of the coded term or interaction i. The 0  full model for the inlet temperature had a significant lack of fit (p = 0.03) but was significant overall (p < 0.01) (Table 6-4). (The complete A N O V A and the coded terms for all the subsequent analyse are given in Appendix 2.)  77  Table 6-4: Factorial analysis of the full inlet temperature model. Source  Model Intercept PR PI ST RR TA PR2  PI ST RR TA PR* PI PR* ST PR* RR PR * TA PI * ST PI*RR PI*TA ST * RR ST * TA RR * TA Lack of Fit 2  2  2  2  Coefficient  P-value <0.01  33.936 1.710 0.269 0.166 0.938 0.276 -0.692 0.041 -0.147 -0.237 0.091 -0.073 -0.006 -0.306 0.258 -0.013 -0.011 0.047 -0.049 0.052 -0.006  <0.01 <0.01 0.02 <0.01 <0.01 <0.01 0.16 0.45 <0.01 0.14 0.07 0.92 <0.01 0.01 0.74 0.78 0.35 0.43 0.28 0.92 0.03  The lack of fit is the portion of the residual sum of squares that is due to the model not fitting the data. It is desirable to have an insignificant lack of fit (p>0.1). The outlet temperature and the delta T model both had an insignificant lack of fit and a significant overall model. Thus, only the inlet temperature model was not a representative model. The explanation for the lack of fit of the inlet temperature model is thought to be due to the poor control of the ambient temperature. A n air conditioner was used periodically to reduce the room temperature and maintain a relatively constant ambient temperature during the experiments.  The air conditioner was turned on when the laboratory  temperature exceeded 22°C, which, on sunny days, happened approximately after 11 am. The position, the frequency of operation and the intensity of the air conditioner were not  78  precisely recorded though the recirculation line was in the flow of cold air when the air conditioner was turned on.  The inlet temperature would also be more significantly  affected by the ambient temperature since it did not vary as much as the outlet temperature over the range of operating conditions of the experimental design (Figure 6.18). The outlet temperature was mainly affected by the air cooling device. For the factorial design experiments, the air blown into this device came from another room, so its temperature was generally higher than the ambient temperature caused by the air conditioner (Figure 6.19). Consequently, the heat removed was lower and compensated for the lower inlet temperature in obtaining an outlet temperature similar to the normal operation. Thus, the overall effect on the outlet temperature was in this way eased.  The analysis of the residual plots after the preliminary refinement of the model revealed one outlier (outside of the limit of 3 times the variance) for the delta T model corresponding to the run #54 (Figure 6.20). This point was removed from the design after which another point (run #53) became an outlier. These two points were replicates for the lowest net harvest flow rate and were due to the large effect that air conditioning had on the inlet temperature in this case. Both points were therefore removed from the design.  79  27  29  31  33  35  37  39  Replicate T,„  B 8-  R  2  f  0  = 0.97 *  **  ^  Af  *  R  2  y\  = 0.99  4  4 2,  *  \\  l'  27  29  31  33  Replicate T  C  35  37  39  2  4  6  1  — Replicate delta T  out  D  Figure 6.18: Distribution and variation of the replicate runs of the factorial design.  A) Ambient temperature with its correlation coefficient. B) Inlet temperature with its correlation coefficient. C) Outlet temperature with its correlation coefficient. D) Difference between outlet and inlet with its correlation coefficient. Dashed lines represent temperature derivation of ± 1°Cfromthe 45° line.  80  22.2 22  +22$  21.8  1.9  -•^21.8  21.6 #"2irtf21.4  * T air cooling B T ambient  21.2 21 20.8 20.7  20.6 20.4 20.2  20.7  20.6  20.3 10  20  15  Time ( m i n ) Figure 6.19: Example of differences in temperature between the air used in the cooling device and the ambient temperature provided by the air conditioner for a 22-minute time interval.  Q  1.44  •  -o  •a c <u  •  •  • a  •  m  o  -o  •  a  3  • •  • •  •  • •• • •  ID  •  • •  wa -1.44 -3.00 |  1  11 11ll11 111 11 111llIII ] 111 111 11111111 III 111111 111 [ II 11111 i ]  10  19  28  37  46  55 64  Run Number Figure 6.20: Residuals versus run number for the preliminary refinement of the delta T model.  81  The inlet temperature model with 62 runs had a higher p-value (p=0.05, Table 6-5) than the full model with 64 runs (p=0.02, Table 6-4) for the lack of fit. The factorial design without runs # 53 and 54 was therefore used to further refine the model.  Table 6-5: Factorial analysis of the full inlet temperature model without runs # 53 & 54. Source  Coefficient  Model Intercept. PR PI ST RR TA PR PI ST RR TA PR* PI PR* ST PR * RR PR * TA PI* ST PI*RR PI*TA ST * RR ST * TA RR * TA Lack of Fit  34.008 1.173 0.262 0.154 0.928 0.316 -0.522 0.045 -0.269 -0.239 0.079 -0.053 0.011 -0.326 -0.081 -0.001 -0.018 0.037 -0.020 0.052 -0.032  2  2  2  2  2  6.5.3  P-value <0.01  <0.01 < 0.01 <0.0T <0.01 <0.01 <0.01 0.03 0.06 <0.01 0.06 0.06 0.79 <0.01 0.36 0.98 0.50 0.29 0.64 0.12 0.44 0.05  Optimized Models Analysis  The selection of the optimized model was by backward elimination (section 4.3.6).  6.5.3.1 Optimized Inlet Temperature Model The optimized model had a low lack of fit, p-value of 0.05 (Table 6-6) such that its predictions must be interpreted with caution. The model was tested with data other than the ones used for the factorial design analysis (Figure 6.21). The results show that the  82  inlet temperature model predicts lowers values than were measured.  At higher inlet  temperatures, the recirculation flow rate was usually faster and the effect of the environment was reduced. Thus, the model had improved predictions for higher inlet temperatures.  The black points on Figure 6.2IB represent experiments performed  without the air conditioner. For the other points, no information was recorded to specify if the air conditioner was on or off. Considering only the black points, the four points below the 45° line were obtained at lower recirculation flow rates than the ones above (18 L day" compared to 34 L day" ). 1  1  Table 6-6: Factorial analysis of the optimized inlet temperature model. Source  Model Intercept PR PI ST RR TA  PR RR PR * RR ST * TA Lack of Fit 2  2  Coefficient  P-value <0.01  33.790 1.252 0.286 0.176 0.951 0.251 -0.319 -0.257 -0.332 0.080  <0.01 <0.01 <0.01 < 0.01 <0.01 <0.01 <0.01 < 0.01 0.01 0.04  83  T „ Experimental  T | l  Experimental  A  B  Figure 6.21: Predicted versus experimental inlet temperatures.  A) Points used in the factorial analysis. B) Additional test points (black diamonds are experiments with the air conditioner off). A l l 5 main effects were found to be significant. The stop time was significant in this analysis because the recirculation and harvest flow rate was depended on its value. For example, to maintain a constant net harvest flow rate for a longer stop time, both the harvest flow and recirculation rates had to be increased in compensation. Moreover, all coefficients were found to be positive (Table 6-6) therefore, the inlet temperature was directly proportional to all 5 first-order effects. For an increase of the net flow rate or the ratio of harvest to recirculation flow rate, the residence time in the recirculation line was shorter than the fluid entered the acoustic separator at higher value. 6.5.3.2 Optimized Outlet Temperature Model The outlet temperature was less influenced by the variations produced by the air conditioner. As a consequence, the overall model satisfied the lack of fit test (Table 6-7). When the model was tested with points not used in the fitting process, the predictions were better distributed along the 45° line than for the inlet model (Figure 6.22). Contrary  84  to the inlet model, the region of higher outlet temperatures was more affected by the experimental error. Higher temperatures at the outlet were usually obtained at lower harvest flow rates and hence longer residence times in the acoustic chamber and in the recirculation line. The black triangles below the 45° line all correspond to experiments at low recirculation flow rates compared to the ones close to or above this line.  Table 6-7: Factorial analysis of the optimized outlet temperature model. Source  Model Intercept PR PI ST RR TA  P R * PI PI * S T  Coefficient  <0.01 33.532 0.952 1.100 -0.030 0.679 0.348 -0.442 -0.115  Lack of Fit  32  33  34  35  36  Tout Experimental  A  37  P-value  38  <0.01 <0.01 0.02 <0.01 <0.01 <0.01 <0.01 0.72  32  33  34  T  35  o a t  36  37  38  Experimental  B  Figure 6.22: Predicted versus experimental outlet temperatures.  A) Points used in the factorial analysis. B) Additional test points (black triangles are experiments with the air conditioner off).  85  Again, the 5 main effects were significant. The ST coefficient had a negative value, meaning that, for an increase of ST, the outlet temperature decreased.  In fact, the  increase of ST required an increase of the harvest flow rate during the rest of the duty cycle. Thus, the fluid residence time in the acoustic chamber was reduced during this period, thereby leading to a reduction in the outlet temperature. On the other hand, the net flow rate had a positive coefficient. In this case, both the harvest and recirculation flow rates influenced the system behavior, but the effect of the recirculation rate was more dominant in increasing the overall temperature inside the separator.  6.5.3.3  O p t i m i z e d Delta T Temperature M o d e l  The temperature difference between the outlet and the inlet, delta T, was modeled to provide estimates of the increase in acoustic filter temperatures for bioreactors operating at temperature other than 37°C. The factorial design analysis concluded that the model was significant and had a non-significant lack of fit (Table 6-8). The distribution of the test data (Figure 6.23B) showed colder predictions for experimental differences of temperature greater than 1°C. This behavior is a consequence of the effect of the air conditioner on the inlet and outlet temperatures. The points on Figure 6.23B yielded a distribution similar to that of the Figure 6.23 A points for delta T values lower than 1°C.  86  Table 6-8: Factorial analysis of the optimized delta T model. Source  Coefficient  Model Intercept PR PI ST RR  RR PR* PI PR * RR PI* ST Lack of Fit 2  P-value <0.01  -0.050 -0.229 0.807 -0.162 -0.269 0.168 -0.405 0.203 -0.109  Delta T Experimental  <0.01 <0.01 <0.01 <0.01 <0.01 <0.0T <0.01 <0.01 0.93  Delta T Experimental  A  B  Figure 6.23: Predicted versus experimental delta T.  A) Points used in factorial analysis. B) Additional test points (black diamonds are experiments with the air conditioner off). The ambient temperature was found not to be significant in this case and, hence, was removed from the model. This result was expected because the ambient temperature affects both the inlet and outlet temperatures (section 6.2.4).  The PR, ST and R R  variables all had negative coefficients (Table 6-8). Here, the effect of the recirculation  87  flow rate cancelled out because it affected both the inlet and outlet temperatures. Thus, only the harvest flow rate had an influence on the value of delta T.  6.5.4  Process O p t i m i z a t i o n  Experimental design is a much more effective tool for optimizing processes than the trialand-error approach. The surface responses produced by the empirical model obtained from the experimental design data provide useful information about the effects on the operation of the various process variables. For the culturing of CHO cells, the acceptable temperature range has been found to lie between 31.5°C and 38.5°C (section 5). Thus, the settings of the acoustic separator should be adjusted so that the fluid temperature remains within this range. It was earlier recommended that the ambient temperature be controlled around 22°C (section 6.2.4) with a stop time of 6 s and a run time of 45 s (section 6.3.3). The bottom plane in Figure 6.24 projects Tj calculated as a function of n  net flow rate and power for RR=2.  Most combinations of conditions satisfied the  required 31.5 - 38.5°C range. The upper 38.5°C constraint was not active in this case, while the 31.5°C constraint required that, for the minimum PR, the input power had to exceed 5W. The response of the outlet temperature to these two independent variables is presented in Figure 6.25. The bottom plane shows the calculated T  out  contours and, as  can be seen from this figure, all values were in the acceptable range.  88  36.0 | 34.7 '  W  33.5  "~E  32.2  H  30.9  Figure 6.24: Response of inlet temperature to variations in power input (PI) and net harvest flow rate (PR).  Blue lines indicate the ranges of these two variables that provide inlet temperature between 31.5 and 38.5°C (Settings: RR=2, ST=6 s, TA=22°C).  Figure 6.25: Response of outlet temperature to variations in power input (PI) and net harvest flow rate (PR).  Red lines indicate the ranges of these two variables that provide outlet temperature between 31.5 and 38.5°C (Settings: RR=2, ST=6 s, TA=22°C).  For a higher value of RR=3, the surface plots, as a function of PI and PR, are transformed to Figure 6.26 for the inlet temperature and to Figure 6.27 for the outlet temperature. In particular, Figure 6.26 shows that the inlet temperature can be maintained in the  89  acceptable temperature range for the lowest values of PI and PR considered at RR=3. However, it is important to note that the inlet and outlet temperature models are not completely representative of reality as a consequence of the experimental variations described in section 6.5.2.  36.0 " 34.7 U e H  33.5 B  :  32.2 30.9  PI ( W )  Figure 6.26: Response of inlet temperature to variations in power input (PI) and net harvest flow rate (PR). Blue lines indicate the ranges of these two variables that provide inlet temperature between 31.5 and 38.5°C (Settings: RR=3, ST=6 s, TA=22°C).  90  18.0 15.2 7 2  PI ( W )  1  6.0  PR ( L/day)  Figure 6.27: Response of outlet temperature to variations in power input (PI) and net harvest flow rate (PR). Red lines indicate the ranges of these two variables that provide outlet temperature between 31.5 and 38.5°C (Settings: RR=3, ST=6 s, TA=22°C). 6.5.5  Discussion a n d Conclusions  The primary objective of the experimental design was to characterize the separation efficiency of an acoustic separator in a CHO cell perfusion culture. Thus, the variables selected for the design were not optimized to describe the thermal behavior of the system. For example, the effect of the stop time was hidden by the adjustment of the flow rates for the different settings.  The models for the inlet temperature, outlet temperature and delta T were compromised to some extent by the periodic operation of the air conditioner used in an attempt to maintain a relatively constant ambient temperature. The inlet temperature response was most affected by this experimental variation because of the cooling by the cold air of the recirculation tubing. The factorial design experiments should be repeated in a constant external environment without blowing cold air on the apparatus.  91  In general, the predictions of the three different models are more reliable for data at higher recirculation flow rates. The optimization of the factorial design showed that, for most of the conditions, the temperature was in the acceptable range.  In addition,  experimental design is a useful tool for rapidly and safely optimizing the process.  92  7 Modeling 7.1 Introduction The use of mathematical models is an important tool for scientists, in particular for engineers. In process optimization, the use of mathematical models can provide rapid prediction of results for many possible sets of input variables.  From such detailed  knowledge of the process behavior, the optimization of the process can be done rapidly, economically and safely.  The separation efficiency of the acoustic separator can be optimized by increasing the power input or by reducing the harvest flow rate, or both. However, the consequence of either change is to increase the temperature of the system, which can have a negative impact on the cells i f the temperature exceeds the acceptable operating range. Furthermore, knowledge of the temperature profile inside the acoustic chamber can provide information not only about the cell environment, but also about the effect of air cooling on the removal of heat from the device.  The acoustic chamber has been modeled in order to obtain detailed temperature distributions as well as average outlet temperatures for any set of operating conditions. The model inputs include the power input, the inlet temperature, the ambient temperature and the harvest flow rate. The mathematical model is described in the following section.  93  7.2 7.2.1  Mathematical Model Model Description  The control volume was defined to be the glass cuvette of the acoustic separator (Figure 4.6). Its geometry is that of a rectangular prism (Figure 7.1). The solution domain consists only of the wetted volume of the cuvette; heat loss and generation in the cuvette walls were incorporated into the solution as boundary conditions.  Flow  12.4 mm  12.4 mm  45.0 mm  Figure 7.1: Geometry used in developing a thermal model of the acoustic separator  The mathematical model was based on the resolution of the energy equation for the geometry shown in Figure 7.1. Several assumptions were made to allow the development of a simple but representative model. The cell suspension was assumed to be a pure Newtonian fluid with constant density and conductivity. The general form of the timedependent differential energy balance for a three-dimensional Cartesian control volume is (Bird et al., 2002):  94  PI PJ C  dT dT dT dT — +v — +v — +v — dt dx dy dz x  dT 2  dT 2  T +  z  dx  2  T+  dy  1  dT 2  T  (7.1)  dz  2  where T is the temperature (K), v , v and v (m s" ) are the fluid velocity components in 1  x  y  z  the x, y and z directions, respectively, and S is a uniform volumetric source term (W m" ) 3  a  that represents the dissipation of acoustic energy into heat within the liquid volume. S  a  was obtained by dividing the fraction of the input power converted into heat by the volume of the liquid inside the cuvette.  During the experiments, temperatures were measured only after the system had reached pseudo-steady state. Thus, the time derivative term in Equation 7.1 was taken to be zero. The flow was assumed to be essentially one-dimensional in the z direction and, hence, the velocity components v and v were zero. Also, the conduction term in the z direction x  y  could be neglected compared to the corresponding convection term. This hypothesis can be confirmed by calculating the Peclet number for the z direction. For a harvest flow rate between 2 L day" and 20 L day" , Pe was determined to be between 45 and 447. This 1  1  range shows that convection was the main mechanism of heat transport in the direction of flow. Thus, after simplification, the energy equation was reduced to: dT 2  T +  dx  2  dT 2  T  (7.2)  dy  2  At the four bounding walls of the acoustic chamber (i.e., in the x and y directions), the boundary condition equations were determined as follows. First, the differential energy balance for pure conduction in a wall of thickness S(m) was written (Figure 7.2).  95  Liquid  00  Air  Figure 7.2: Schematic of one cuvette wall used for deriving the boundary condition.  If it is assumed that the conduction process is steady, that conduction in the z direction can be neglected and that the corner regions where the walls join can be ignored, then the equation for conduction in the x direction becomes  0  (7.3)  where k is the solid conductivity, T - T (x) is the local solid temperature, and S is a s  s  s  x  uniform volumetric source term ( W m" ) that represents the transformation o f acoustic 3  energy into heat within that wall. This source term was obtained by dividing the fraction of the input power by the volume o f the wall (minus the corner section). Equation (7.3) is subject to two boundary conditions. The first is obtained by equating the energy flux in the wall at x=5to convection to the outside environment, i.e.,  (7.4)  where h is the heat transfer coefficient between the outside w a l l and the environment ( W m ^ K " ) , Ts is the wall temperature at x=S (K) and T«, is the ambient temperature ( K ) . 1  The second boundary condition equation is the energy flux in the wall with that in the liquid a t * = 0, i.e.,  , 8T _ dT_ S  dx  dx  (7.5)  96  When Equation (7.3) is solved subject to the boundary conditions (7.4) and (7.5), it is easily shown that \  f  -k,  h  K  v dx  J x = x  • + -  8 ^ 2k  sJ  1 —  h  8  (7.6)  + —  k.  where x is the position of the wall relative to the fluid co-ordinates shown in Figure 7.1. w  Equation (7.6) was used as the boundary condition for the fluid energy balance, Equation (7.1), with;; replacing x on two of the four walls. Thus, to solve the latter equation, three different wall source terms and three different outside convection heat transfer coefficients had to be specified, corresponding to the transducer, the reflector and the two side walls (assumed to have identical values although one side has a silicone gel layer). The major assumptions used in deriving Equation (7.6) were that the walls all had constant physical properties and the conduction in each wall was one-dimensional. The presence of the piezo-electric device, the transducer, on one of the glass walls was neglected and hence this wall was treated as i f it had the same physical properties as the other three walls. The 4 volumetric sources terms (in the liquid, in the transducer, in the reflector and in the side walls) and also the 3 external heat transfer coefficients (at the transducer, at the reflector and at the side walls) were obtained by fitting the model to experimentally measured temperature results (section 7.2.3).  7.2.2  Velocity Distribution  In the square cuvette, the flow rate was generally varied between 2 and 20 L day" . The 1  Reynolds numbers for this flow rate range lie between 3 and 28.  These numbers  correspond to the laminar regime (Re < 2100). In the absence of cells in the acoustic  97  chamber, it is expected that the z velocity component should have an almost fully developed laminar profile over the full length of the chamber. However, the presence of cells inside the chamber has the effect of creating numerous parallel-plate channels whose characteristic dimension is very small (-300 um).  These channels greatly  constrain the flow of the liquid and, as a consequence, modify the velocity distribution. In this case, the velocity profile is expected to have a flatter shape, more like a plug flow. Thus, in the results reported here, it was assumed, in calculating the different solutions of the mathematical model, that the z component velocity profile was perfectly uniform.  7.2.3  Model Refinement  The mathematical model contained seven variables that could only be determined by fitting the model to the experimentally measured temperature results. The variables were the four different volumetric source terms (in the liquid and within the walls) and the three heat transfer coefficients on the outside surface of each wall in the presence of air cooling. The strategy used to obtain these missing parameters was to first determine the volumetric source terms in the absence of air cooling by setting the three heat transfer coefficients to the same constant value representative of natural convection from a planar vertical surface (10 W m" K" ) estimated using a correlation from Perry et al. (1997). 2  1  Outlet and wall temperature (position #2 on Figure 7.3) measurements were then compared with the predictions of the mathematical model for different values of the source terms. A simple energy balance was made to ensure that the total energy input to the system was always greater than the energy needed to heat the liquid from the inlet to the outlet temperature (Eq. (4.14)).  In the second part of the analysis, the best-fit  volumetric source terms found previously were kept constant and the heat transfer  98  coefficients were varied until the model correctly predicted the measured temperature results obtained in the presence of air cooling.  The air cooling data represented the  normal operation of the acoustic separator that the model should be able to predict. Finally, the best-fit variables determined in this way were incorporated into the model to allow calculation of numerous predicted results that could be compared with other experimental data.  Two procedures were employed to determine the best-fit variables. The first was done manually and the second was performed automatically using the computer and the genetic algorithm to find the optimal parameter values. 7.2.3.1 Manual Refinement The major advantage of using the manual refinement method was that, at each step of the procedure, a critical interpretation of the results could be made in such a way as to reorient the next iteration.  Considering the large variability in the temperature  measurements, the manual refinement approach ensured that the model provided a good representation not only of the overall distribution of temperature, but also the trends observed during the experiments. Overall, the model parameters obtained in this way yielded predictions that were more representative of the acoustic separator thermal behavior.  In step 1, more than 60 different combinations of the volumetric source terms were tested to determine the distribution of temperature within the liquid and also within the bounding walls of the system.  Figure 7.3 is an example of one set of measured  99  temperature distribution results that was used in the analysis to find the missing parameters.  Predicting the exact temperature values of the wall was considered to be a  less important criterion than respecting the general trends in the measured temperature such as the observed 2°C difference between the side walls and the reflector wall. However, the parameters were adjusted to predict the exact liquid outlet temperature because this measurement was considered to be more accurate than the measurements of the wall temperature.  A l l of the models tested gave the same result regarding the heat  generation within the side walls, namely that it was zero (Table 7-1).  A "(3)  (3) 34.4 ° C  -(2)  (2) 34.3 °C  (2) 35.1 ° C  -to  (1) 33.2 °C  (1) 34.1 ° C  Side Wall  Legend :  (3) 35.3 ° C  — Cuvette X Position of Thermocouple Position Number  (1.2,3)  Reflector Wall  Figure 7.3: Experimentally measured data for the outside temperatures of the reflector and side wall of the acoustic separator.  Settings: P=3 W, HR=8.1 L day", RF=16.8 L day" , ACF=0 L min" , T =25.8°C, ^=33.2 °C, T =37.6°C, [cell]=8.3xl0 cells mL" . 1  1  1  amb  6  1  0Ut  The second step was to identify the values of the heat transfer coefficients in the presence of air cooling. Again, a critical analysis of the predictions helped to guide the subsequent iterations.  More than 30 different combinations of heat transfer coefficients were  attempted and the set of parameters that yielded the best comparison with the experimental results is shown in Table 7-1. Here, the source term is given in term of a percentage of the input power. A comparison of the delta T (i.e., difference between outlet and inlet temperatures) values predicted by the model using this set of parameters and those obtained from the experimental measurements is shown in Figure 7.4. Delta T was calculated by subtracting the measured inlet temperature from the predicted or  100  measured outlet temperature. The figure reveals that the results are well distributed along the 45° line. The model generally predicted delta T within 1°C.  Table 7-1: Best-fit parameters determined using the manual refinement method  Location Liquid Transducer Wall Reflector Wall Side Wall  Source Term (%) 56.0 6.5 2.0 0  Heat Transfer Coefficient (W m" -K"') 500 65 80 2  Delta T Measured (°C ) Figure 7.4: Comparison of delta T predicted by the model using parameters obtained by the manual refinement method and delta T measured.  7.2.3.2  Computer Optimization  A genetic algorithm was also used to find the best-fit parameters for the mathematical model. The lower and upper limits of each parameter were defined in the program in order to constrain the search. Because the experimental data contained a lot of variation, the sum of squared differences function had many local minima that resulted in many  101  different possible solutions. The algorithm was first used to identify the volumetric source terms by using temperature measurements made in the absence of air cooling and using a constant value of the outside heat transfer coefficients (10 W m" K" ) in the same 2  1  way as was done in the manual method. Two different sets of optimal parameters were found depending on the constraint ranges specified.  For a wide search range, the  algorithm found the following optimal combination of volumetric heat generation values: 39.5% of the input electric power occurred in the liquid, 24.7% in the transducer wall and 2.0% in the reflector wall. With a smaller search range set closer to the parameters found by manual refinement, the corresponding values were 55.0% in the liquid, 10.0% in the transducer wall and 0.5% in the reflector wall (Table 7-2). Both models were included in the second refinement step where the heat transfer coefficient values were determined using temperature measurements obtained with 10.7 L min" of air cooling. Even though 1  a wide search range was employed, the best-fit coefficients found were similar to those obtained by manual refinement. Because the data measured in the absence of air cooling contained more variability and because the genetic algorithm did not always converge to constant values, a fourth model was obtained by keeping the source terms found by manual refinement and only using the genetic algorithm to determine the heat transfer coefficients. The parameters obtained using all four procedures are presented in Table 7-2.  102  Table 7-2: Compilation of the best-fit volumetric source terms (SI) and heat transfer coefficients (hi) obtained for the liquid (Liq.), transducer (Trans.) reflector (Refl.) and side wall (side). 9  Model Name  Manual Refinement Manual & Computer Computer model 1 Computer model 2  Liq. 56.0 56.0 39.6 55.0  St  hi  (%)  (W m- -K-') Trans. Refl. Side 500 65 80 64 719 75 355 60 60 797 60 73  Trans. 6.5 6.5 24.7 10.0  2  Refl. 2.0 2.0 2.1 0.5  Side 0 0 0 0  Using all 137 experimental measurements and the four different sets of parameters given in Table 7-2, scatter plots comparing the predicted and the measured delta T values were prepared and are shown as the four panels of Figure 7.5.  Because the differences between the models were difficult to observe in Figure 7.5, the sum of squared errors (SS) was calculated in each case and the results are presented in Table 7-3.  103  •2 Delta T Measured ( ° C )  Delta T M e a s u r e d (*C )  C  D  Figure 7.5: Comparison of predicted and measured temperature differences using best-fit parameters obtained for four different optimized models. A) Manual Refinement. B) Manual & Computer. C) Computer model 1. D) Computer model 2. Dashed lines represent temperature derivation of ± 1°Cfromthe 45° line.  Table 7-3: Sum of squared errors between predicted and measured delta T for the four different models listed in Table 7-1. Model Name  SS  M a n u a l Refinement  33.1  M a n u a l & Computer Computer model 1  31.7 38.8  Computer model 2  32.4  104  Based on the results of Table 7-3, the model parameters obtained from a combination of manual refinement (for the source terms) and the genetic algorithm (for the heat transfer coefficients) offered the best predictions of the outlet temperature and hence were the only ones utilized for subsequent analyses. The residual plot for this model showed a relatively uniform distribution within ±1°C for most of the predictions (Figure 7.6). The limits were calculated as three times the variance on the experimental measurements and they demonstrate that the model predictions are reasonably accurate.  In fact, the  variation of the predictions was in most cases not significantly different than the measurement error.  2  T  1.5  Delta T Measured (°C ) Figure 7.6: Residual plot of the final mathematical model.  Dashed lines represent the standard deviation of the experimental measurements. To determine i f the assumption of setting all of the heat transfer coefficients to a constant value of 10 W m" -K" during the first step of parameter determination was representative 2  ]  of reality, a sensitivity analysis was performed using different constant heat transfer  105  coefficient values in the range of 5 to 20 W m'^K" . It was found that the model which 1  gave the best overall fit of the data obtained without air cooling was the one where h was 2  1  set to 10 W m" K" . Moreover, when all 6 parameters were determined using genetic algorithm and data measured only during air cooling, the results were found to be similar to those obtained for the best-fit (manual + computer) model. 7.2.4  Temperature Profiles  Once the values of the parameters have been determined, the mathematical model can then be used to determine the temperature distribution inside the acoustic separator for any set of operational conditions.  For example, it is of interest to compare the  temperature profiles obtained in the presence and absence of air cooling. The predictions shown in Figure 7.7 demonstrate how essential the air cooling device is to the operation of the acoustic separator.  Without air cooling, the temperatures inside the acoustic  chamber climb to values that are higher than the upper limit of the acceptable range. Also, the transducer (left side of Figure 7.7) produces hot spots along its wall that can affect either the cell kinetics or the efficiency of the system. With 10.7 L min" of air 1  cooling, the internal temperatures stayed within the required range within the entire volume of the cuvette and hence provided an optimal environment for the retained cells. Note also that the temperature along the transducer surface is now lower than the average value at the outlet cross-section.  106  Acoustic Separator ooling  No Air Cooling Air Cooling: T = 3 6 7°C out, exp  l  a  u  ,  /  v  -  N o A i r Cooling:  T 1  =401°C out, exp  ™ '  x  Figure 7.7: Predicted temperature distribution in the acoustic separator at the vertical midplane and at the outlet cross-section in absence (left) and presence (right) of air cooling. Settings: P=5 W, HF=10.6 L day" , RF=20 L day" , AC=10.7 L min" , Tin=33.9°C, Tamb=24.7°C. The transducer is on the left and the reflector on the right of each cross-section. 1  1  1  The selection between computer model 1 and manual & computer model (see Table 7-2) was based on the plots of the predicted versus the measured delta T (Figure 7.5) and the sum of squared errors (Table 7-3). Another point that gives further credence to the selection of the manual & computer model over computer model 01 is the comparison of the predicted temperature profiles shown in Figure 7.8. In the absence of air cooling, the computer model 01 parameters yield a very high predicted temperature of around 51°C for the transducer outside wall and only about 37°C for the reflector outside wall. B y comparison, using the manual & computer model parameters, these two temperatures are predicted to be 41°C and 38°C, respectively. Temperature measurements on an older acoustic separator displayed differences between the transducer and reflector outside walls of only about 4°C. Furthermore, the weak natural convection observed with and  107  without air cooling was assumed to be produced by a small temperature difference between the transducer inside surface and the bulk medium.  These results further  demonstrate that predictions based on the manual & computer model parameters provide a better representation of the observed thermal behavior of the acoustic separator than do those from computer model 01.  Air Cooling  No Air Cooling  Figure 7.8: Comparison of temperature profiles obtained using the manual + computer parameters versus the Computer Model 01 parameters.  Results are shown for the vertical middle plane and for the outlet cross-section. (Settings: P=5 W, HF=10.6 L day , RF=10 L day , ACF=10 L min" , Tin=33.9°C, Tamb=24.7°C). The transducer is on the left and the reflector on the right of each cross-section. 1  1  1  The model predicted temperature profiles are also useful for interpreting the behavior of the system under different conditions of operation.  As expected, the internal  temperatures increase when the power input to the separator is raised. Figure 7.9 shows how the profiles vary as the harvest flow rates are decreased. In general, the predicted  108  temperatures respect the behavior discussed in section 6.2.3. For a decrease in harvest flow rate, the residence time inside the chamber is lengthened and the outlet temperature increases.  Internal Temperature Profiles HF=10 L/da  HF=8 L/day  HF=6 L/day  HF=4 L/day  Figure 7 . 9 : Predicted temperature distribution at the vertical midplane and the outlet cross-section of the acoustic separator for different harvest flow rates. Settings: P=5 W, ACF=10 L min" , T =34°C, T =22 C. The transducer is on the left and the reflector on the right of each cross-section. 1  0  in  7.2.5  amb  Discussion and Conclusions  A model of the acoustic separator thermal behavior was developed in order to predict the average temperature of the harvest stream exiting from the device, and also to estimate the temperature distribution within the device. The mathematical model using the best set of empirically determined parameters yields outlet temperature predictions within 1°C of the measured values. The variability of the measured temperatures had a significant  109  influence on the estimated parameters and hence on the prediction accuracy of the model. The model was optimized by using measured temperature data to determine 7 unknown parameters:  4 volumetric source terms and 3 heat transfer coefficients.  The best-fit  volumetric source term for the side wall was found to be zero indicating that no dissipation of acoustic energy to heat occurs in this portion of the cuvette. Depending on the constraint ranges specified, the genetic algorithm yielded two sets of best-fit parameters for the volumetric heat generation rates in the liquid, transducer and reflector. One predicted that more than 10% of the power input was dissipated as heat in the transducer and less in the liquid, while the other suggested that less than 10% occurred in the transducer and more in the liquid. After considerable model testing, it was found that the best results were obtained i f 56.0% of the power input was dissipated in the liquid, 6.5% in the transducer wall and 2.0% in the reflector wall. The remaining 35.5% of the input power was lost from the system. These additional losses likely include the nonideal conversion of electricity into acoustic energy, the heating of the metal frame not included in the model, and other indirect losses by conduction or convection to the outside environment. Calculations show that the acoustic energy needed to retain the cells in the separator is very small, significantly less than 1% of the input electrical energy.  The outside heat transfer coefficients in the presence of air cooling were determined to be 719 W m" -K"' at the transducer wall, 64 W m" -K"' at the reflector wall and 75 W m" -K"' 2  for the two side walls.  2  2  These differences in heat transfer coefficient values were  expected because of the design of the separator. In the cooling device, ambient air is  110  blown directly on the outside transducer surface but a gap between the metal frame and the cuvette allows air to pass over and cool the side walls before reaching the reflector. Thus, the transducer was expected to have the highest heat transfer coefficient, while the side wall heat transfer coefficient was anticipated to be greater than that of the reflector.  The model predicted temperatures profiles provide important information about the thermal environment seen by the cells inside the chamber.  The large temperature  difference predicted between the transducer and the reflector walls in the absence of air cooling and using the M o d e l 1 parameters (Table 7-2) was not representative of the behavior observed during the operation of the system. In fact, tentative measurements of the transducer temperature compared to that of the reflector showed differences in the order of 4°C. Moreover, the weak natural convection observed inside the separator was assumed to be only possible for relatively small temperature differences between the wall and the liquid. Natural convection flows were also constrained by the presence of the planes of collected cells. Only extreme temperature differences, larger than 10°C, created natural convection flows that were strong enough to be observed. It should be added that the magnitude of the natural convection current was difficult to quantify accurately and that the model, as it stands, does not account for natural convection.  From another perspective, the temperature profiles generated by the mathematical model for different harvest flow rates (Figure 7.9) provided estimates about the environment that the cells were exposed to. For low harvest flow rates and high input powers, the temperature inside the separator exceeded the desired operating range. A n important fact  111  observed from the model predictions was the formation of a hot spot in the upper section of the cuvette. During operation, the cells are principally retained in the lower part of the cuvette. Thus, the cells are not directly exposed to these high temperature conditions and it might be possible to use a wider range of the settings without negatively affecting the cells.  7.3  Comparison of Models  In this section, the predictions of the mathematical model are compared with those of the empirical model developed as part of the factorial design study (section 6.5). Considering that the factorial design model needs a duty cycle having a 45 s run time, only the experimental points used to obtain that model will be included in the present analysis. On Figure 7.10, the outlet temperature predictions of these two models are plotted along with the measured data. The data were sorted from the smallest measured temperature to the highest but it is important to keep in mind that the measured data contain significant variations even though they appear to be rising monotonically. The mathematical model offers much better predictions than the factorial design model with the former having a sum of squared errors of 9.4 compared to 24.8 for the latter. As can be seen from Figure 7.10, the predicted outlet temperatures from the mathematical model follow the measured data more closely; in fact, they are within 1°C most of the time. Another important point to note is that the factorial design experiments were carried out under conditions where the ambient temperature was not well controlled. Thus, it is expected that its predictions of the outlet temperature will not be very reliable.  112  38 37 36 35  1  34 33 32 31 30  • Experimental • Factorial Design  •  •hr  A Mathematical  29 10  15  20  25  30  Data Number Figure 7.10: Comparison of measured outlet temperatures with those predicted from the mathematical model and the factorial design model.  113  8 Conclusions and Recommendations The goal of this thesis was to investigate the temperature distribution in an acoustic separator in order to define the effect on the cell culture and optimize separator operations.  Cell culture measurements were performed to study the effect of cyclic  variations of temperature in a simulated acoustic separator environment.  For the  temperature range of 31.5 to 38.5°C, no significant effects were observed on the growth rate, the glucose consumption or the t-PA production of CHO cells. Thus, 31.5 and 38.5°C were selected as the lower and upper limits of the acceptable range of operating temperatures. The experiment was designed to amplify any effect on the cell culture by periodically pumping 4-6% of the culture volume into the altered temperature environment compared to the perfusion bioreactor acoustic separator fraction of around 1%. In future experiments, a longer residence time of the cells in the heat exchanger could be tested.  The acoustic separator was modified to allow the measurement of the inlet and outlet harvest flow temperatures. Increasing the power input resulted in a direct increase of the system temperature, primarily at the outlet of the device. A i r cooling was necessary to remove a portion of the heat in order to maintain the temperature increases to within the acceptable range.  The outlet temperature was reduced by increasing the harvest flow  rate. The recirculation flow rate influenced principally the inlet temperature since heat transfer to the environment cooled the cell suspension during its transit from the bioreactor to the separator via the recirculation tube. This cooling of the recirculation flow also augmented the removal of some of the heat generated by the dissipation of 114  acoustic energy in the system. Warmer room temperatures decreased the heat transfer from the system resulting in higher inlet and outlet temperatures. The duty cycle and the cell concentration did not significantly affect the temperatures within the acoustic separator.  For different settings suggested by the acoustic separator user's manual, the temperatures were recorded and the separation efficiencies measured.  The main objective was to  verify i f the temperatures remained within the acceptable range for CHO cell cultures. In general, the settings provided high separation efficiencies and acceptable ranges of temperature. Nonetheless, three recommendations were made to improve the operation of the cell retention device. First, keeping the ambient temperature around 22°C so that the temperatures seen by the cells are kept below 38.5°C avoids the high fluid temperatures that can result at higher ambient temperatures.  Second, the recirculation  flow rate should be set to a minimum value of 15 L day" to ensure that the inlet 1  temperature is maintained above 31.5°C. This flow rate would also limit the settling of cells in the recirculation tubing and help remove some of the acoustically-generated thermal energy from the system. The last recommendation was to use shorter duty cycle times to reduce the build up of cells in the chamber and ensure the continuance of the optimal resonance frequency.  Both factors enhance the separation efficiency of the  device. The recommended settings provide efficient operation for yeast and CHO cell systems, demonstrating that the acoustic filter can be used with different types of cells. However, the acceptable temperature range might change as a function of the type of cell used.  115  For normal operations, the variation of the air cooling flow rate from 0 to 16 L min" did 1  not significantly affect the separation efficiency.  Similarly, ambient temperature  variations from 19 to 26°C had a negligible effect on the separation efficiency. efficiency of the separator can be affected by temperature phenomena.  The  Natural  convection inside the acoustic chamber can disturb the cell planes and reduce the separation efficiency. This negative effect was particularly observed during experiments where a cold stream from an air conditioner was blown directly on the system.  In order to predict the inlet and outlet temperatures, a central composite factorial design was performed for the 5 independent variables: bioreactor cell concentration, net harvest flow rate, power input, stop time and ratio of recirculation flow rate to harvest flow rate. The bioreactor cell concentration did not have a significant effect on the temperature model and hence was excluded from the analysis. However, the poorly uncontrolled ambient temperature was treated as an additional variable in the model. Three different response variables were examined; the inlet temperature, the outlet temperature and the difference between the outlet and inlet temperatures (delta T). The A N O V A results showed that the outlet temperature and the delta T models were significant and the lack of fit, was not significant. However, the inlet temperature model had a significant lack of fit probably due to the intermittent use of an air conditioner. Future factorial designs should be performed with more constant ambient temperatures.  116  A theoretical model was developed based on a differential energy balance in the acoustic chamber. This model predicted the outlet temperature and was also used to estimate the 3-dimensional temperature distribution inside the chamber.  This mathematical model  had 7 unknown parameters: 4 volumetric heat generation source terms (in the liquid, in the transducer wall, in the reflector wall and in the side walls of the acoustic chamber) and 3 heat transfer coefficients that determined the rate of convection from the outside walls of the cuvette when air cooling was being applied. These unknown parameters were estimated by both manual refinement and numerical optimization carried out on a computer. The percentage of the power input converted into heat was estimated to be 56% in the liquid, 6.5% in the transducer wall, 2% in the reflector wall and 0% in the side walls. The model predicted the outlet temperatures within ±1°C where as most of the predicted results fell between the limits represented by the variation of the temperaturemeasurements (±0.4°C std. dev.). The temperature profiles generated by the model again showed that the air cooling device was essential for keeping the internal temperature in the acceptable range. However, the warmer region in the acoustic chamber was in the upper portion while the cells were retained principally in the lower half. To validate the predicted temperature distribution inside the acoustic separator, a visualization system using a temperature sensitive dye could be used to experimentally determine the temperature profile. To improve the model, the pseudo-steady state assumed should be changed to a dynamic state in order to account for the periodic changes associated with the duty cycle. Three-dimensional conduction in the cuvette and the transducer should be also added in order to get a more accurate representation of the system. Plug flow applies only to the lower part of the acoustic chamber where the cells were mainly maintained.  117  Thus, the velocity distribution in the upper part should be more like a laminar flow profile.  A computational fluid dynamic analysis could be done to provide better  information about the velocity distribution. Furthermore, a characterization of the forced convection around the separator should be carried out to provide better estimates of the heat transfer coefficients when the air cooler is in operation. A n optimization of the cooling of the acoustic separator could be performed using the mathematical model that could eventually lead to a new design. A n improved model may show that a wider range of operational settings can be used while respecting the acceptable range of temperatures. 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High-density perfusion culture of insect cells with a biosep ultrasonic filter. Biotechnology and Bioengineering 59(3): 351-359.  122  Appendix 1: Perfusion System  Description of the Perfusion System Air Out Thermocouple Recirculation Blank Level Sensor Sample ** 0 probe 2  Inoculation & Harvest *  Legend  Separator  * : tube in liquid ** : tube with extention in medium (bottom reactor)  Figure Al.9.1: Bioreactor head plate description  Legend for P&ID tubing code: aa-b-cc aa : Tubing Length in cm b : Tubing Type: 1- Pharmed Tubing 2- C-Flex Tubing 3- Silicone Tubing cc : Tubing Diameter (code)  •a  Quick-disconnect female coupling for gas Luer lock female  124  Small Air Filter 5-3-15  Pipette 10 ml  10-3-16 Reactor  45-2-16  120-1-16  -fxe  -fXl  60-2-16 D  Figure A1.3: Feed line description  50-2-16  , Inoculation Bottle  Reactor 10-1-16 50-3-16  4  °- 2  1 6 D  Return Line  Figure A1.4: Inoculation and return line description  Large Air Filter  \ 30-1-16  Reactor  40-1-16  \ \  Air Female Fitting  Figure A1.5: head space air in line description  126  Small Air Filler  Luer Lock Female Pipette 10 ml  16-3-16 70-2-16  10-3-16 50-2-16  HXJ-  6  °- 2  Bleed Bottle  1 6 p  20-3-16 8-1-16  Air in  Head Space  80-3-16 Small Air Filter  45-1-16  45-1-16  Return Line  _ ^L  Q  f><  5-3-16  5-3-16  -txj-  100-1-16 I  40-2-16  Harvest Bottle  \7 t \  4U-1-1J  ^ Luer Lock  15-1-16  Female  25-3-16  -tXhC Separator  5-3-16  D—TXr-  Pipette 10 ml  15-3-16  -txj-Q 30-2-16  Small Air Filter  Figure A1.6: Sample, bleed and backflush line description  127  5-1-16 Large Air Filter  Reactor  60-1-16  -f^J] 5-1-15 10-1-15  Air Female Fitting  5-1-16  Air ~Cj \ Female  5-1-16  Air - M l Female Fitting  5-1-16  -m  5-1-15  Air  "VJJ Female Fitting  Figure A1.7: Gas in line description  Large Air Filter  10-1-15  Cooler 30-3-16  Glass Condenser 30-3-15  Reactor 10-3-16  10-1-15  Normally Closed Large Air Filter  Small Air Filter  Figure A1.8: Gas out line description  Reactor  :  —  A c o u s t i c  Separator Figure A1.9: Recirculation line description  128  E  l 5.5 mm  d=34.8 mm  6.7 mm  d=l 2.5 mm  5.2 mm  d=4.5mm  52 mm d=4.5mm  <  H <  28.5 mm 12.5 mm  1.9 mm  K->i K  23.5 mm  23.5 mm »  •  K-H  *\  12.5 mm  23.5 mm  •  < 45 mm  *\  12.5 mm 12.5 mm 8mm ->| 18 mm ^ 7 mm  -d,„,=4.5 mm  |<-  d=34.8 mm d=18.8mm  45°  d=4.5 mm 50 mm  195 mm  d,„,=4.5 mm  27.3 mm Legend |  = contact with the liquid flow  Figure ALIO: Dimensions of the 10L acoustic separator  129  Appendix 2: Raw Data  Cell Culture Experiments Figure A2.1 shows an example of the graphical calculation of the growth rate and the glucose consumption rate for the cell culture experiment at average tube side temperature of31.5°C.  B Figure A2.1: A) Growth rate and B) glucose consumption rate for the control spinner (Average tube side temperature=31.5°C)  1 0 G  100  -1 -2  y = 0.0402x-2.2346 R = 0.9994  -3  150  1  20  3  10  I  3  _yjEi^0.169_8xi22.331  _R1^.0.95655  o  50  100  time (h)  time (h)  A  B  150  Figure A2.2: A) Growth rate and B) glucose consumption rate for the pumped spinner control (Average tube side temperature=31.5°C)  131  y = -0.1499x + 22.14 R = 0.9792  ISO  100  y = 0.0382x- 2.321 R = 0.9987 50  100  time (h)  time (h)  A  B  150  Figure A2.3: A) Growth rate and B) glucose consumption rate for the tested spinner (Average tube side temperature=31.5°C)  Table A2.1: Results summary of the viable cell concentration, growth rate and the log mean of the viable cell concentration related to cell culture experiments Average Tube Side Temperature  4th sample  fi(hr-l)  (°C) 27.4  control  pumped test  control  pumped  test  control  pumped  test  2.224  2.246 1.822  0.051  0.047  0.037  0.523  0.562  0.510  31.5  1.251  1.246  1.161  0.039  0.040  0.038  0.333  0.325  0.282  33.9  1.521  1.665 1.338  0.036  0.038  0.039  0.718  0.761  0.608  35.4  1.635  1.619 1.493  0.040  0.045  0.040  0.537  0.521  0.523  38.5  1.503  1.685 1.297  0.040  0.041  0.035  0.507  0.445  0.445  40.2  1.023  0.829 0.459  0.037  0.033  0.019  0.292  0.289  0.210  Table A2.2: Results summary of the glucose consumption rate, the specific glucose consumption rate, the t-PA concentration and the specific t-PA concentration related to cell culture experiments Average Tube Side Temperature  Glucose (mM/h)  specific glucose (mM/h/cell)  t-PA concentration (ug/mL)  specific t-PA (ug/mL/cell)  (°C) 27.4  control  pumped  test  control  pumped  test  control  pumped  test  control  pumped  test  0.203  0.208  0.167  3.89E-07  3.70E-07  3.27E-07  36.2  33.1  33.6  6.92E-05  5.89E-05  6.60E-05  31.5  0.174  0.170  0.150  5.22E-07  5.23E-07  5.31E-07  28.2  27.4  27.7  8.47E-05  8.44E-05  9.82E-05  33.9  0.261  0.267  0.249  3.64E-07  3.51E-07  4.09E-07  31.1  28.6  29.0  4.33E-05  3.76E-05  4.78E-05  35.4  0.212  0.209  0.210  3.95E-07  4.01E-07  4.00E-07  28.2  24.8  28.0  5.25E-05  4.76E-05  5.35E-05  38.5  0.187  0.199  0.195  3.68E-07  4.48E-07  4.38E-07  35.7  35.2  30.4  7.04E-05  7.93E-05  6.85E-05  40.2  0.155  0.151  0.159  5.29E-07  5.22E-07  7.57E-07  28.0  24.5  15.5  9.59E-05  8.48E-05  7.35E-05  132  Temperature Measurement in Perfusion Culture Table A2.3: Summary of the data presented in the different plots in the temperature measurement in perfusion culture section. PI  HF  RF  DC  [cell]  Tin  Tout  Tamb  ACF  SE  (W)  (L/day)  (L/day)  (s)  (10 cells/mL)  CQ  CC)  (°C)  (L/min)  (%)  1  5  7  20  300/3  3.2  33.6  38.1  23.7  10.7  2  5  7  20  300/3  8.3  34.1  37.7  24  10.7  3  5  10.83  21.66  60/5  0.8  33.7  36.5  24.1  10.7  4  5  10.83  21.66  60/5  10.7  33.9  36.5  23.6  10.7  -  5  5  11.33  34  45/6  4.69  34.93  36.88  25.5  10.7  -  6  5  11.33  34  45/6  2.66  34.93  36.61  26  10.7  -  7  5  11.33  34  45/6  8.31  34.97  36.97  25  10.7  -  8  5  8.15  16.3  180/3  14.88  32.9  36.3  23.8  10.7  88.1  9  5  8.15  16.3  180/3  14.77  33.8  37.6  25.6  10.7  87.8  10  5  8.4  16.8  120/6  14.14  33.4  36.9  24.6  10.7  89.5  11  5  8.7  17.4  45/4  14.45  33.7  37.5  25.3  10.7  97.2  12  5  9.1  18.1  45/6  14.51  33.9  36.6  24.7  10.7  97.6  13  2  1  15  600/3  8.32  32.3  34  24.6  10.7  99.8  14  2  2  4  600/3  8.87  27.8  32.1 .  24.6  10.7  99.1  15  2  2  15  600/3  8.87  32.4  33.8  24.5  10.7  99.2  16  3  4.04  8.05  300/3  7.9  30.7  34.4  24.4  10.7  99.1  17  5  6.1  12.3  180/3  7.9  32.9  38  24.3  10.7  98.3  18  5  8.15  16.3  180/3  8.89  33.4  36.8  24.2  10.7  82.8  19  7  10.8  21.7  60/5  8.89  35  39.1  23.9  10.7  89.9  20  5  6.1  12.3  180/3  6.02  32.9  38  25.2  10.7  99.5  10.7  97.1  # Reference  6  •  -  21  5  8.15  16.3  180/3  6.3  33.3  37.7  24.2  22  5  9.1  18.1  45/6  6.72  33.9  36.7  24.7  10.7  96.9  23  5  9.1  0  -  5.51  34.9  37.3  24.9  10.7  90.6  24  7  10.8  21.7  60/5  5.89  34.3  39  23.5  10.7  94.8  25  7  10.8  21.7  60/5  5.86  35.1  39.8  25.5  10.7  97.5  26  7  13.9  0  -  6.05  36.1  38.8  24.4  10.7  92.2  27  5  6.1  12.3  180/3  9  33  38.6  25  10.7  99.4  28  5  8.15  16.3  180/3  9.78  33.7  37.9  25.2  10.7  90.5  29  5  9.1  18.1  45/6  9.29  33.6  37  25  10.7  96.8  30  5  9.1  0  -  9.3  34.9  36.9  24.6  10.7  92.6  31  5  10.8  21.7  180/3  9.18  34.2  36.6  24.8  10.7  65.9  32  5  11.3  22.7  45/6  8.4  34.5  37.1  25.3  10.7  89  33  7  10.8  21.7  60/5  8.57  34.3  39.2  24.1  10.7  93.3  34  7  10.8  21.7  60/5  9.79  34.8  39.4  25  10.7  94.7  35  7  13.9  0  -  9.97  36.1  38.8  24.5  10.7  82.9  36  3  10.22  30.67  45/1  9  33.1  33.3  22.9  10.7  37  3  11.33  34  45/6  9  33.3  33.6  22.6  10.7  -  38  3  13.16  34  45/6  7.7  33.6  34.3  22  10.7  -  39  3  13.16  54.4  45/6  7.7  34.2  33.7  22  10.7  -  40  1  11.33  34  45/6  9.69  33  31.6  22  10.7  -  133  Table A2.3: Summary of the data presented in the different plots in the temperature measurement in perfusion culture section, (continued) # Reference  PI  HF  RF  DC  [cell]  (W)  (L/day)  (L/day)  (s)  (10 cells/mL)  TO  3  10.22  30.67  45/1  9.89  33.7  42  3  11.33  34  45/6  9.59  33.9  43  3  11.33  34  45/6  10.2  33.9  44  3  11.33  34  45/6  9.47  45  3  11.33  54.4  45/6  46  3  12.44  37.33  47  3  2.27  48  3  49  3  50  Tamb  ACF  SE  (°C)  CQ  (L/min)  (%)  33.8  22.8  10.7  33.5  22.3  10.7"  -  33.6  22.4  10.7  -  34.1  33.8  23.4  10.7  -  9.74  35  34.6  22.4  10.7  -  45/11  9.01  34.2  33.6  22.3  10.7  -  6.8  45/6  9.48  27.6  33  21.8  10.7  -  11.33  13.6  45/6  9.2  31.5  32.6  22.3  10.7  -  2.27  6.8  45/6  9.17  27.8  32.8  21.8  10.7  -  3  11.33  34  45/6  9.79  33.7  33.4  21.4  10.7  -  51  3  11.33  34  45/6  9.36  33.7  33.2  21.5  10.7  -  52  3  20.4  61.2  45/6  8.99  34.8  34.9  21.8  10.7  -  53  3  20.47  61.2  45/6  9.63  34.9  34.9  21.7  10.7  -  54  7  11.33  34  45/6  9.3  34.9  37.8  21.1  10.7  -  55  7  11.33  34  45/6  9.23  35.1  38.4  21.8  10.7  -  56  2  6.47  13.58  45/3.5  12.5  30.3  30.2  21.1  10.7  -  57  2  7.13  27.82  45/8.5  12.6  32.9  31.7  21.7  10.7  -  58  2  15.09  58.85  45/3.5  12.4  34.6  34.3  21.9  10.7  -  59  2  16.64  34.95  45/8.5  13  33.8  33.4  22  10.7  -  60  5  6.47  25.22  45/3.5  12.8  33.7  36.7  21.7  10.7  -  61  5  15.09  31.69  45/3.5  13.7  34.3  35.6  22.1  10.7  -  62  5  16.64  64.91  45/8.5  12.7  35.3  35.9  21.8  10.7  -  63  3  18.4  22.08  45/1  2  32.4  32.3  20.6  10.7  -  64  3  22.4  94.08  45/11  2  35.1  35  20.9  10.7  -  65  2  6.47  13.58  45/3.5  13.5  30.1  29.7  21.6  10.7  -  66  2  7.13  27.82  45/8.5  14  32.6  31.1  21.3  10.7  -  67  2  15.09  58.85  45/3.5  12.8  34.5  34.3  21.4  10.7  -  68  2  16.64  34.95  45/8.5  11.9  33.4  33.1  21.4  10.7  -  69  5  6.47  25.22  45/3.5  12.7  33.4  36.2  21.4  10.7  -  70  5  7.13  14.98  45/8.5  14.2  31.5  34.3  21.6  10.7  -  71  5  15.09  31.69  45/3.5  12.6  33.8  35.3  21.4  10.7  -  72  5  16.64  64.91  45/8.5  12.3  35.1  35.7  21.4  10.7  -  73  3  11.33  34  45/6  17.9  33.4  33.7  20.9  10.7  -  74  3  11.33  34  45/6  16.8  33.5  33.8  21.3  10.7  -  75  3  11.33  34  45/6  8.64  33.6  33  21.3  10.7  -  76  3  11.33  34  45/6  9  33.6  32.9  21.3  10.7  -  77  3  11.33  34  45/6  9.83  33.6  33.1  21.6  10.7  -  78  3  11.33  34  45/6  8.78  33.6  33  21.6  10.7  -  79  3  11.33  34  45/6  8.21  33.6  33.2  21.7  10.7  -  80  2  6.47  25.22  45/3.5  4.76  32.2  31.2  21.1  10.7  -  81  2  7.13  14.98  45/8.5  4.63  29.8  29.4  21.6  10.7  -  82  2  15.09  31.69  45/3.5  5.02  33  32.2  20.9  10.7  -  83  2  16.64  64.91  45/8.5  4.62  34.6  33.8  20.9  10.7  -  84  5  6.47  13.58  45/3.5  4.9  30.7  34.8  21  10.7  -  41  6  Tin  Tout  134  Table A2.3: Summary of the data presented in the different plots in the temperature measurement in perfusion culture section, (continued) DC  (cell)  Tin  Tout  Tamb  ACF  SE  (L/day)  (s)  (10 cells/mL)  (°C)  (°C)  (°C)  (L/min)  (%)  7.13  27.82  45/8.5  5.28  33.4  35.4  20.8  10.7  5  15.09  58.85  45/3.5  4.76  35  35.7  20.7  10.7  -  5  16.64  34.95  45/8.5  4.69  34  34.4  21.1  10.7  -  88  2  6.47  25.22  45/3.5  5.2  32.5  31.5  20.7  10.7  -  # Reference  PI  HF  RF  (W)  (L/day)  85  5  86 87  6  89  2  7.13  14.98  45/8.5  5.09  29.9  29.5  21  10.7  -  90  2  15.09  31.69  45/3.5  5.49  33  32.2  20.7  10.7  -  91  2  16.64  64.91  45/8.5  5.55  34.6  33.9  20.9  10.7  -  92  5  6.47  13.58  45/3.5  5.32  30.4  34.2  20.8  10.7  -  93  5  7.13  27.82  45/8.5  5.11  33.2  35.2  20.6  10.7  -  94  5  15.09  58.85  45/3.5  5.44  35  35.6  20.7  10.7  -  95  5  15.09  58.85  45/3.5  4.76  35.1  35.8  20.9  10.7  -  96  5  16.64  34.95  45/8.5  5.03  33.8  34.2  20.8  10.7  -  97  3  11.33  34  45/6  0.979  33.1  33.1  20.7  10.7  98  3  11.33  34  45/6  1.05  33.3  33.2  21  10.7  -  99  2  6.47  25.22  45/3.5  5.38  34  34  22.6  10.7  -  100  2  17.24  36.21  45/3.5  5.28  34.1  33.5  22.1  10.7  -  101  2  19.02  74.19  45/8.5  4.94  35.6  34.8  22.7  10.7  -  102  5  7.13  27.82  45/8.5  5.18  34  37.1  21.8  10.7  -  103  5  17.24  67.25  45/3.5  5.26  35.8  36.8  22.7  •••10.7  104  5  19.02  39.95  45/8.5  5.16  35  35.8  22.7  10.7  -  105  2  6.47  25.22  45/3.5  5.72  33.7  33.2  22.7  10.7  -  106  2  7.13  14.98  45/8.5  5.52  31  30.6  20.7  10.7  -  107  2  17.24  36.21  45/3.5  5.24  34.5  33.9  22.8  10.7  -  108  2  19.02  74.19  45/8.5  5  35.5  34.8  22.8  10.7  -  109  5  6.47  13.58  45/3.5  5.6  32.8  37.5  22.7  10.7  -  110  5  7.13  27.82  45/8.5  5.33  34.5  36.9  22.7  10.7  -  111  5  17.24  67.25  45/3.5  5.48  35.8  36.9  22.7  10.7  -  112  5  19.02  39.95  45/8.5  4.93  35  35.7  21  10.7  -  113  3  2.32  0  45/5  9  31.2  33.5  21  10.7  -  21  10.7  -  114  3  5.12  0  45/5  9  33.9  35.4  115  5  20.35  0  45/5  9  35.5  36  21  10.7  -  116  5  30.14  0  45/5  9  36.7  36.1  21  10.7  -  117  5  7  0  45/5  8.3  35.1  37.2  23.6  10.7  -  118  1  11.33  34  45/6  9.41  33.8  32.4  23.5  10.7  -  119  3  11.33  13.6  45/6  10.3  30.8  31.5  22.5  10.7  120  3  11.33  34  45/6  9.41  34.5  34.3  23.2  10.7  -  121  3  11.33  34  45/6  9.41  34.7  34.8  23.8  10.7  -  122  3  11.33  54.4  45/6  10.3  35.1  34.8  22.9  10.7  -  123  3  12.44  37.3  45/11  8.53  34.9  34.7  23.9  10.7  -  124  3  2  20  300/3  8.4  32.6  36.5  23.8  10.7  -  125  3  5  20  300/3  8.4  33.5  35.9  24.4  10.7  -  126  3  10.6  20  300/3  8.4  33.2  34.4  24.4  10.7  -  33.6  34.5  24.7  10.7  -  34.1  42.2  24.4  10.7  -  127  3  10.6  20  300/3  8.4  128  5  2  20  300/3  8.4  135  Table A2.3: Summary of the data presented in the different plots in the temperature measurement in perfusion culture section, (continued) # Reference  PI  HF  RF  DC  [cell]  Tin  Tout  Tamb  ACF  SE  (W)  (L/day)  (L/day)  (s)  (10 cells/mL)  (°C)  (°C)  (°C)  (L/min)  (%)  129  5  5  20  300/3  8.4  34  38.8  24.4  10.7  -  130  5  10.6  20  300/3  8.4  33.9  36.6  24.5  10.7  -  131  5  10.6  20  300/3  8.4  33.9  36.7  24.6  10.7  -  132  5  15  30  300/3  8.4  34.8  37.2  24.5  10.7  -  133  1  8.13  16.3  180/3  11.9  32.3  31.9  25.5  10.7  -  134  2  8.13  16.3  180/3  11.9  32.7  32.7  24.7  10.7  -  135  3  8.13  16.3  180/3  11.9  32.7  33.9  24.8  10.7  -  136  5  8.13  16.3  180/3  11.9  33.5  37.5  24.9  10.7  -  137  7  8.13  16.3  180/3  11.9  34.5  41.2  25  10.7  -  138  1  8.13  16.3  180/3  11.9  32.8  34.0  25.5  0  -  139  2  8.13  16.3  180/3  11.9  32.8  34.9  24.7  0  -  140  3  8.13  16.3  180/3  11.9  33.0  37.3  24.8  0  -  141  5  8.13  16.3  180/3  11.9  34.1  42.6  24.9  0  -  142  7  8.13  16.3  180/3  11.9  34.9  47.4  25.0  0  -  6  Table A2.4: Summary of the data presented in Figure 6.13. PI  HF  RF  DC  [cell]  Tin  Tout  Tamb  ACF  SE  Air conditioner  (W)  (L/day)  (L/day)  (s)  (106 cells/mL)  CC)  CC)  CC)  (L/min)  (%)  (on/off)  3  11.3  34  45/6  8  33.8  33  22.1  10.7  73.4  On  3  11.3  34  45/6  8  34.1  33.4  22.9  10.7  73.9  On  3  11.3  34  45/6  8  34.4  34  23.5  10.7  71.2  On  3  11.3  34  45/6  8  34.5  34.6  24.8  10.7  71.5  On  3  11.3  34  45/6  8  35.6  36.3  27.6  10.7  73.7  Off  3  11.3  34  45/6  8  35.5  36.2  28.4  10.7  77.6  Off  3  11.3  34  45/6  8  35.7  36.5  29.7  10.7  80.7  Off  3  11.3  34  45/6  8  35.9  36.7  30.5  10.7  82.5  Off  3  11.3  34  45/6  8  35.2  35.6  26.7  10.7  70.5  Off  3  11,3  34  45/6  8  34.2  33.8  22.7  10.7  66.8  On  3  11.3  34  45/6  8  33.1  32.7  21.8  10.7  69.5  On  136  Table A2.5: Data used in the calculation of separation efficiency presented in Figure 6.13. Viable Cell Concentration (trypsonize sample) Sample Name  Estimation  3 Cedex Readings  (10 cells/mL) (10 cells/mL) (10 cells/mL) (10 cells/mL) 6  6  Reactor 1 Reactor 2  6  Reactor 6  Reactor 8  (%)  -  -  -  -  8.318  7.422  -  -  -  -  -  -  8.087  7.783  -  -  -  -  -  -  7.36  8.399  7.504  -  -  -  -  -  -  8  7.855  8.303  -  -  -  -  -  -  7.591 7.8  7.9  Reactor 9 Reactor 10  (%)  8 7.9  Reactor 7  95% CI  8.062  7.9  Reactor 5  SE  8.091  Reactor 3 Reactor 4  6  7.9  7.634  Harvest 1  1.935  2.219  2.171  73.4  4.2  Harvest 2  2.132  2.041  2.026  73.9  3.1  Harvest 3  2.344  2.277  2.19  71.2  3.9  Harvest 4  2.628  2.012  2.079  71.5  18.5  Harvest 5  2.19  1.978  1.988  73.7  3.5  Harvest 6  1.74  1.80525  1.6785  77.6  3.5  Harvest 7  1.362  1.714  1.408  80.7  5.7  Harvest 8  1.372  1.401  1.377  82.5  0.8  Harvest 9  2.315  2.257  2.551  70.5  4.2  Harvest 10  2.608  2.644  2.66  66.8  1.4  Table A2.6: Summary of the data presented in Figure 6.14. PI  HF  RF  DC  [cell]  Tin  Tout  Tamb  ACF  SE  (W)  (L/day)  (L/day)  (s)  (xl06 cells/mL)  CC)  CO  CC)  (L/min)  (%)  3  11.33  34  45/6  9  32.9  32.2  20.1  10.7  76.5  3  11.33  34  45/6  9  33.1  32.2  20.4  10.7  73.9  3  11.33  34  45/6  9  34.7  34.6  24.9  10.7  72.5  3  11.33  34  45/6  9  34.7  34.9  25.4  10.7  69.4  5  5  20  45/6  6.7  30.4  30.5  18.7  10.7  96.5  5  5  20  45/6  6.7  30.7  31  19.2  10.7  95.2  5  5  20  45/6  6.7  31.8  31.5  22.1  10.7  95.2  5  5  20  45/6  6.7  33.2  34.7  24.8  10.7  97.0  5  5  20  45/6  6.7  33.9  35.6  25.8  10.7  97.2  5  11.33  34  45/6  10.1  33.7  34.2  19.8  10.7  87.3  5  11.33  34  45/6  10.1  33.9  34.8  20.7  10.7  86.2  5  11.33  34  45/6  10.1  35.4  37.3  26.3  10.7  78.3  5  11.33  34  45/6  10.1  35.4  37.8  26.9  10.7  81.4  .  137  Table A2.7:  Summary of the data presented in Figure 6.15.  PI  HF  RF  DC  [cell]  (W)  (L/day)  (L/day)  (s)  (10 cells/mL)  3  11.33  34  45/6  9  3  11.33  34  45/6  9  3  11.33  34  45/6  5  5  20  45/6  5  5  20  45/6  5  5  20  5  11.33  34  5  11.33  5  11.33  Table A2.8:  T out  T airib  ACF  ro  CC)  CC)  (L/min)  (%)  34.7  34.9  25.4  10.7  69.4  34.7  36.9  25.2  0  71.2  9  34.5  34.1  25.4  16  66.2  6.7  35.6  33.9  25.8  10.7  97.2  6.7  34.3  39.6  26.4  0  98.7  45/6  6.7  34.1  34.9  26.7  16  96.9  45/6  10.1  35.4  37.3  26.3  10.7  78.3  34  45/6  10.1  36  40.5  27  0  78.0  34  45/6  10.1  35.6  36.9  27.1  16  83.0  6  .  Data used in the calculation of separation efficiency presented in Figure 6.14 & 6.15.  Viable Cell Concentration (trypsonize sample) Sample Name  Estimation  3 Cedex Readings  (10 cells/mL) (10 cells/mL) (10 cells/mL) (10 cells/mL) 6  6  6  6  T amb  ACF  SE  9 5 % CI  (°C)  (L/min)  (%)  (%)  Reactor 1  -  8.693  9.694  9.583  20.1  10.7  Reactor 2  9.3  -  -  -  20.4  10.7  -  -  Reactor 3  -  9.266  9.04  9.006  24.9  10.7  -  -  Reactor 4  9.1  -  -  -  25.4  10.7  -  -  Reactor 5  8.3  -  -  -  25.2  0  -  -  Reactor 6  -  7.788  7.817  6.989  25.4  16  -  -  Reactor 7  -  6.31  6.383  5.92  18.7  10.7  -  -  Reactor 8  6.3  -  -  -  19.2  10.7  -  -  Reactor 9  -  6.686  6.017  6.575  24.8  10.7  -  -  Reactor 10  6.3  -  -  -  25.8  10.7  -  -  Reactor 11  -  6.835  5.949  5.954  26.4  0  -  -  16  Reactor 12  5.9365  -  -  -  26.7  -  -  Reactor 13  -  5.925  5.372  5.584  22.1  10.7  -  -  Reactor 14  -  7.239  8.428  19.8  10.7  -  -  Reactor 15  7.239  -  -  -  20.7  10.7  -  -  Reactor 16  -  7.543  7.34  6.83  26.3  10.7  -  -  10.7  Reactor 17  7.543  -  -  -  26.9  -  -  Reactor 18  -  9.771  8.756  8.963  27  0  -  -  Reactor 19  9.771  -  -  -  27.1  16  -  -  138  SE  Table A2.8:  Data used in the calculation of separation efficiency presented in Figure 6.14 & 6.15. (continued)  Viable Cell Concentration (trypsonize sample) Sample Name  Estimation  3 Cedex Readings  (10 cells/mL)(10 cells/mL)(10 cells/mL)(10 cells/mL) Harvest 1 Harvest 2  T amb  ACF  SE  95% CI (%)  (°C)  (L/min)  (%)  -  2.253  2.156  2.142  20.1  10.7  76.5  3.1  2.041  2.556  20.4  10.7  73.9  15.8  6  6  6  6  -  2.686  Harvest 3  -  2.671  2.484  2.363  24.9  10.7  72.5  3.5  Harvest 4  -  2.878  2.777  2.7  25.4  10.7  69.4  4.2  Harvest 5  -  2.325  2.599  2.238  25.2  0  71.2  9.8  Harvest 6  -  2.835  2.368  2.402  25.4  16  66.2  8.2  Harvest 7  -  0.212  0.217  0.231  18.7  10.7  96.5  0.4  Harvest 8  -  0.313  0.274  0.313  19.2  10.7  95.2  1.5  0.188  0.154  0.231  24.8  10.7  97.0  1.3  Harvest 9 Harvest 10  -  0.144  0.193  0.202  25.8  10.7  97.2  2.1  Harvest 11  -  0.159  0.048  0.043  26.4  0  98.7  2.1  Harvest 12  -  0.183  0.183  0.183  26.7  16  96.9  0.0  Harvest 13  -  0.308  0.308  0.193  22.1  10.7  95.2  2.4  Harvest 14  -  0.996  0.948  1.03  19.8  10.7  87.3  3.0  Harvest 15  -  0.967  1.073  0.963  20.7  10.7  86.2  3.7  Harvest 16  -  1.637  1.487  1.574  26.3  10.7  78.3  3.1  Harvest 17  -  1.444  1.367  1.406  26.9  10.7  81.4  2.2  Harvest 18  -  1.882  1.945  2.205  27  0  78.0  4.5  1.661  1.603  1.723  27.1  16  83.0  2.6  Harvest 19  139  Factorial Design  Table A2.7: ANOVA for the full inlet model without run #53 & 54 Source  Sum of Squares  DF  Mean Square  F Value  Block  14.3312  7  2.0473  Prob > F  Model  110.0040  20  PR  4.9299  1  5.5002  107.8189  < 0.0001  4.9299  96.6396  PI  3.1890  1  3.1890  < 0.0001  62.5131  < 0.0001  ST  0.6471  1  0.6471  12.6845  0.0011  RR  17.7980  1  17.7980  348.8902  < 0.0001  TA  0.9939  1  0.9939  19.4832  < 0.0001  PR2  0.7351  1  0.7351  14.4091  0.0006  PI  2  0.2558  1  0.2558  5.0141  0.0318  ST  0.2013  1  0.2013  3.9451  0.0551  RR  2  1.5193  1  1.5193  29.7821  < 0.0001  TA  2  0.1886  1  0.1886  3.6968  0.0629  3.9301  0.0556  2  PR* PI  0.2005  1  0.2005  PR* ST  0.0038  1  0.0038  0.0752  0.7856  PR * RR  3.2809  1  3.2809  64.3151  < 0.0001  PR * TA  0.0448  1  0.0448  0.8775  0.3555  PI * ST  0.0000  1  0.0000  0.0005  0.9822  PI*RR  0.0237  1  0.0237  0.4636  0.5006  PI*TA  0.0594  1  0.0594  1.1646  0.2881  ST * RR  0.0117  1  0.0117  0.2294  0.6351  ST * TA  0.1284  1  0.1284  2.5175  0.1218  0.6078  0.4410  21.6182  0.0451  k * TA  0.0310  1  0.0310  Residual  1.7345  34  0.0510  Lack of Fit  1.7295  32  0.0540 0.0025  Pure Error  0.0050  2  Cor Total  126.0697  61  :  Table A2.8: ANOVA for the full outlet model without run #53 & 54  Source  Sum of Squares  DF  Mean Square  F Value  Prob > F  Block  11.2791  7  1.6113  Model  185.7195  20  9.2860  113.1180  < 0.0001  PR  2.0340  1  2.0340  24.7776  < 0.0001  PI  33.7722  1  33.7722  411.3999  < 0.0001  ST  0.4225  1  0.4225  5.1472  0.0297  RR  7.8772  1  7.8772  95.9563  < 0.0001  TA  0.9609  1  0.9609  11.7053  0.0016  PR2  0.4473  1  0.4473  5.4489  0.0256  PI  0.2714  1  0.2714  3.3064  0.0778  ST  2  0.2317  1  0.2317  2.8224  0.1021  RR  2  0.1305  1  0.1305  1.5903  0.2159  TA  2  2  0.5855  1  0.5855  7.1327  0.0115  PR* PI  13.7126  1  13.7126  167.0419  < 0.0001  PR* ST  0.2373  1  0.2373  2.8910  0.0982  PR * RR  0.3374  1  0.3374  4.1100  0.0505  PR * TA  0.1456  1  0.1456  1.7742  0.1917  PI * ST  0.9464  1  0.9464  11.5285  0.0018  PI*RR  0.1684  1  0.1684  2.0512  0.1612  PI*TA  0.0310  1  0.0310  0.3779  0.5428  ST * RR  0.0660  1  0.0660  0.8043  0.3761  ST * TA  0.1257  1  0.1257  1.5312  0.2244  RR * T A  0.0466  1  0.0466  0.5679  0.4563  Residual  2.7911  34  0.0821  Lack of Fit  2.4661  32  0.0771  0.4742  0.8620  Pure Error  0.3250  2  0.1625  Cor Total  199.7897  61  Table A2.9: ANOVA for the full delta T model without run #53 & 54 Source  Sum of Squares  DF  Mean Square  F Value  Prob > F  78.8279  .< 0.0001  Block  6.4877  7  0.9268  Model  99.8183  20  4.9909  PR  0.6307  1  0.6307  9.9610  0.0033  PI  16.2055  1  16.2055  255.9550  < 0.0001  ST  2.1154  1  2.1154  33.4113  < 0.0001  RR  1.9942  1  1.9942  31.4963  < 0.0001  TA  0.0003  1  0.0003  0.0044  0.9475  PR2  0.0355  1  0.0355  0.5615  0.4588  PI  0.0002  1  0.0002  0.0037  0.9521  0.0011  1  0.0011  0.0169  0.8973  0.7591  1  0.7591  11.9899  0.0015  2  ST  2  RR TA  2  0.1095  1  0.1095  1.7298  0.1972  PR* PI  10.5970  1  10.5970  167.3717  < 0.0001  PR* ST  0.1808  1  0.1808  2.8558  0.1002  PR * RR  1.5141  1  1.5141  23.9136  < 0.0001  PR * TA  0.3519  1  0.3519  5.5581  0.0243  PI * ST  0.9365  1  0.9365  14.7917  0.0005  PI * RR  0.0658  1  0.0658  1.0396  0.3151  PI*TA  0.0046  1  0.0046  0.0722  0.7898  ST * RR  0.0221  1  0.0221  0.3497  0.5582  2  ST * TA  0.0000  1  0.0000  0.0002  0.9879  RR * TA  0.0016  1  0.0016  0.0251  0.8752  Residual  . 2.1527  34  0.0633  Lack of Fit  1.7427  32  0.0545  0.2657  0.9660  Pure Error  0.4100  2  0.2050  Cor Total  108.4587  61  33  •  "  •  u  •  5  •  - 1 . 5 0 —^  •  •riff  -e-  i  %  H  E  •  i 1 1 1 1 1 1 1 1 1 1 1 11 1 1 111 iT if 11" i I'I 11 i I I i 1 1 i 11 1 1 ll I 1 1 11 ] I 1 1 1 1 1111JI 41 21 51 61 31  Run Number Figure A2.4: Residuals versus run number for the full inlet model without run #53 & 54.  B  B  B  B  B  B  3 B m  a  •  111111111 I I 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ] 1 1 1 1 1 21 31  11111 41  I I 1 1 1 1 1 1 1 1 1 1 1 1 I I 111 51 61  Run Number Figure A2.5: Residuals versus run number for the full outlet model without run #53 & 54.  3.00-  1.50-  •  • •  v Pi  • 0.00-  -a  •  ID  °-  N •  • •  W  -1.50-  -3.00-  11 III I I III |I 11 11 II 11 | 11M11 II I 11 11 11 11 I 11I I III 11 11 11 I I III I I 11 I 1  11  21  31  41  51  61  Run Number Figure A2.6: Residuals versus run number for the full delta T model without run #53 & 54.  Table A2.10: ANOVA for the optimized inlet model without run #53 & 54  Sum of Squares  DF  Block  14.3312  7  2.0473  Model  109.1884  9  PR  50.3468  Source  Mean Square  F Value  Prob > F  12.1320  214.0855  < 0.0001  1  50.3468  888.4334  < 0.0001  PI  8.2118  1  8.2118  144.9083  < 0.0001  ST  1.2120  1  1.2120  21.3881  < 0.0001  RR  43.3001  1  43.3001  764.0855  < 0.0001  TA  0.9523  1  0.9523  16.8051  0.0002  PR  1.6282  1  1.6282  28.7323  < 0.0001  2  RR  1.8566  1  1.8566  32.7616  < 0.0001  PR* RR  3.5136  1  3.5136  62.0019  < 0.0001  ST * TA  0.3949  1  0.3949  6.9681  0.0114  Residual  2.5501  45  0.0567  Lack of Fit  2.5451  43  0.0592  23.6755  0.0413  0.0025  2  Pure Error  0.0050  2  Cor Total  126.0697  61  Table A 2 . l l : ANOVA for the optimized outlet model without run #53 & 54  Source  Sum of Squares  DF  Mean Square  F Value  Block  11.2791  7  1.6113  Prob > F  Model  182.5961  7  PR  8.2908  1  26.0852  207.2891  < 0.0001  8.2908  65.8841  PI  123.0961  1  < 0.0001  123.0961  978.1993  < 0.0001  ST  0.7828  1  0.7828  6.2208  0.0162  RR  22.1462  1  22.1462  175.9879  < 0.0001  TA  2.2031  1  2.2031  17.5070  0.0001  PR* PI  14.1634  1  14.1634  112.5512  < 0.0001  PI * ST  0.9740  1  0.9740  7.7402  0.0077  Residual  5.9145  47  0.1258  Lack of Fit  5.5895  45  0.1242  0.7644  0.7196  Pure Error  0.3250  2  0.1625  Cor Total  199.7897  61  Table A2.12: A N O V A for the optimized delta T model without run #53 & 54  Source  Sum of Squares  DF  Mean Square  Block  6.4877  7  0.9268  Model  98.3024  8  PR  12.8778  1  PI  71.7479  ST  F Value  Prob > F  12.2878  154.0778  < 0.0001  12.8778  161.4759  < 0.0001  1  71.7479  899.6531  < 0.0001  2.7324  1  2.7324  34.2619  < 0.0001  RR  3.4669  1  3.4669  43.4714  < 0.0001  RR  0.7976  1  0.7976  10.0007  0.0028  2  PR* PI  12.0250  1  12.0250  150.7830  < 0.0001  PR * RR  1.3203  1  1.3203  16.5555  0.0002  PI * ST  0.8860  1  0.8860  11.1090  0.0017  Residual  3.6685  46  0.0798  Lack of Fit  3.2585  44  0.0741  0.3613  0.9263  0.2050  Pure Error  0.4100  2  Cor Total  108.4587  61  • •  •  D  •  O EI  „ •  •  J3_  • •  •  • •  | I I 11 I f I I 11 I 11 I iTl'l'l I I I I I I I I I I I I I I t I I I I I I I I 11 I I I I I I I I ll  21  31  41  51  61  Rim Niunber Figure A2.7: Residuals versus run number for the optimized inlet model without run #53 & 54.  • •  •  CP  e-  Eh  •  •  El  11 I 1M I 11 l| I II 11 11 11 I 11 11 11 11 I |l 11 11 11 I IJ 11 11 I 11 11 11 11 11 I 11 11 I 1  11  21  31  41  51  Run Number Figure A2.8: Residuals versus run number for the optimized outlet model without run #53 & 54.  61  3.00  111 ii 11111111111111111111 M 111111111111111111 II 111111111111111 1  11  21  31  41  51  Run Number Figure A2.9: Residuals versus run number for the optimized delta T model without run #53 & 54.  61  Table A2.13: Data used to test the models but not used in the factorial design fitting process DC  [cell]  Tin  Tout  Tamb  ACF  Air conditioner  (L/day)  (s)  (106 cells/mL)  (oC)  (oC)  (oC)  (L/min)  (on/off)  22.08  45/1  2  32.4  32.3  20.6  10.7  7  PI  HF  RF  (W)  (L/day)  3  18.4  3  22.4  94.08  45/11  2  35.1  35  20.9  10.7  ?  2  6.47  25.22  45/3.5  5.38  34  34  22.6  10.7  ?  5  7.13  27.82  45/8.5  5.18  34  37.1  21.8  10.7  ?  2  17.24  36.21  45/3.5  5.28  34.1  33.5  22.1  10.7  ?  2  19.02  74.19  45/8.5  4.94  35.6  34.8  22.7  10.7  ?  5  17.24  67.25  45/3.5  5.26  35.8  36.8  22.7  10.7  ?  5  19.02  39.95  45/8.5  5.16  35  35.8  22.7  10.7  ?  2  6.47  25.22  45/3.5  5.72  33.7  33.2  22.7  10.7  ?  2  7.13  14.98  45/8.5  5.52  31  30.6  20.7  10.7  ?  5  6.47  13.58  45/3.5  5.6  32.8  37.5  22.7  10.7  ?  5  7.13  27.82  45/8.5  5.33  34.5  36.9  22.7  10.7  ?  2  17.24  36.21  45/3.5  5.24  34.5  33.9  22.8  10.7  ?  2  19.02  74.19  45/8.5  5  35.5  34.8  22.8  10.7  9  5  15.09  58.85  45/3.5  5.44  35  35.6  20.7  10.7  ?  5  17.24  67.25  45/3.5  5.48  35.8  36.9  22.7  10.7  ?  5  19.02  39.95  45/8.5  4.93  35  35.7  21.0  10.7  ?  3  11.33  34  45/6  9  33.6  32.9  21.3  10.7  ?  3  13.16  34  45/6  7.7  33.6  34.3  22.0  10.7  ?  3  13.16  54.4  45/6  7.7  34.2  33.7  22.0  10.7  ?  5  8.7  17.4  45/4  14.45  33.7  37.5  25.3  10.7  Off  5  9.1  18.1  45/6  14.51  33.9  36.6  24.7  10.7  Off  5  9.1  18.1  45/6  6.72  33.9  36.7  24.7  10.7  Off  5  9.1  18.1  45/6  9.29  33.6  37  25.0  10.7  Off  5  11.3  22.7  45/6  8.4  34.5  37.1  25.3  10.7  Off  5  11.33  34  45/6  8.31  34.97  36.97  25.0  10.7  Off  5  11.33  34  45/6  4.69  34.93  36.88  25.5  10.7  Off  5  11.33  34  45/6  2.66  34.93  36.61  26.0  10.7  Off  148  Table A2.14: Description of the #Run  Block  64 runs used in the factorial design analysis  PR  PI  (10 cells/mL)  (10 cells/mL)  (L/day)  (W)  (s)  BXtarget  ST  RR  TA  T  in  Tout  delta T  (°C)  ro  (°C)  1  2  13  12.5  6  2  3.5  2.1  21.1  30.3  30.2  -0.1  2  2  13  12.6  6  2  8.5  3.9  21.7  32.9  31.7  -1.2  3  2  13  12.8  6  5  3.5  3.9  21.7  33.7  36.7  3  4  2  13  12.9  6  5  8.5  2.1  21.6  31.2  34.1  2.9  5  2  13  12.4  14  2  3.5  3.9  21.9  34.6  34.3  -0.3  6  2  13  13  14  2  8.5  2.1  22  33.8  33.4  -0.4  7  2  13  13.7  14  5  3.5  2.1  22.1  34.3  35.6  1.3  8  2  13  12.7  14  5  8.5  3.9  21.8  35.3  35.9  0.6 0.7  6  6  (°C)  9  6  9  10.3  10  3  6  1.2  22.5  30.8  31.5  10  6  9  9.2  10  3  6  1.2  22.3  31.5  32.6  1.1  11  6  9  10.3  10  3  6  4.8  22.9  35.1  34.8  -0.3  12  6  9  9.74  10  3  6  4.8  22.4  35  34.6  -0.4  13  6  9  9.36  10  3  6  3  21.5  33.7  33.2  -0.5  14  6  9  9.59  10  3  6  3  22.3  33.9  33.5  -0.4  15  6  9  9.41  10  3  6  3  23.2  34.5  34.3  -0.2  16  6  9  9.79  10  3  6  3  21.4  33.7  33.4  -0.3  17  3  5  4.76  6  2  3.5  3.9  21.1  32.2  31.2  -1  18  3  5  4.63  6  2  8.5  2.1  21.6  29.8  29.4  -0.4  19  3  5  4.9  6  5  3.5  2.1  21  30.7  34.8  4.1  20  3  5  5.28  6  5  8.5  3.9  20.8  33.4  35.4  2  21  3  5  5.02  14  2  3.5  2.1  20.9  33  32.2  -0.8  22  3  5  4.62  14  2  8.5  3.9  20.9  34.6  33.8  -0.8  23  3  5  4.76  14  5  3.5  3.9  20.7  35  35.7  0.7  24  3  5  4.69  14  5  8.5  2.1  21.1  34  34.4  0.4  25  1  5  5.2  6  2  3.5  3.9  20.7  32.5  31.5  -1  26  1  5  5.09  6  2  8.5  2.1  21  29.9  29.5  -0.4  27  1  5  5.32  6  5  3.5  2.1  20.8  30.4  34.2  3.8  28  1  5  5.11  6  5  8.5  3.9  20.6  33.2  35.2  2  29  1  5  5.49  14  2  3.5  2.1  20.7  33  32.2  -0.8  30  1  5  5.55  14  2  8.5  3.9  20.9  34.6  33.9  -0.7  35.1  35.8  0.7  4.76  14  5  3.5  3.9  20.9  5  5.03  14  5  8.5  2.1  20.8  33.8  34.2  0.4  9  9.41  10  1  6  3  23.5  33.8  32.4  -1.4  5  9  9.69  10  1  6  3 •  22  33  31.6  -1.4  5  9  9.3  10  7  6  3  21.1  34.9  37.8  2.9  36  5  9  9.23  10  7  6  3  21.8  35.1  38.4  3.3  37  5  9  9.41  10  3  6  3  23.8  34.7  34.8  0.1  38  5  9  10.2  10  3  6  3  22.4  33.9  33.6  -0.3  31  1  5  32  1  33  5  34 35  39  5  9  9.16  10  3  6  3  22.6  33.3  33.6  0.3  40  5  9  9.47  10  3  6  3  23.4  34.1  33.8  -0.3  41  4  13  13.5  6  2  3.5  2.1  21.6  30.1  29.7  -0.4  42  4  13  14  6  2  8.5.  3.9  21.3  32.6  31.1  -1.5  43  4  13  12.7  6  5  3.5  3.9  21.4  33.4  36.2  2.8  44  4  13  14.2  6  5  8.5  2.1  21.6  31.5  34.3  2.8  .  •  149  Table A2.14: Description of the 64 runs used in the factorial design analysis, (continued) #Run  Block  BXtargel  BXactual  PR  PI  ST  RR  TA  T,„  Tout  delta T  (10 cells/mL)  (10 cells/mL)  (L/day)  (W)  (s)  (°C)  (°C)  (°C)  (°C)  4  13  12.8  14  2  3.5  3.9  21.4  34.5  34.3  -0.2  46  4  13  11.9  14  2  8.5  2.1  21.4  33.4  33.1  -0.3  47  4  13  12.6  14  5  3.5  2.1  21.4  33.8  35.3  1.5  48  4  13  12.3  14  5  8.5  3.9  21.4  35.1  35.7  .0.6  49  7  9  9.02  10  3  1  3  22.9  33.1  33.3  0.2  50  7  9  9.89  10  3  1  3  22.8  33.7  33.8  0.1  51  7  9  8.53  10  3  11  3  23.9  34.9  34.7  -0.2  52  7  9  9.01  10  3  11  3  22.3  34.2  33.6  -0.6  53  7  9  9.17  2  3  6  3  21.8  27.8  32.8  5  54  7  9  9.48  2  3  6  3  21.8  27.6  33  5.4  55  7  9  8.99  18  3  6  3  21.8  34.8  34.9  0.1  56  7  9  9.63  18  3  6  3  21.7  34.9  34.9  0  57  8  17  17.9  10  3  6  3  20.9  33.4  33.7  0.3  58  8  17  16.8  10  3  6  3  21.3  33.5  33.8  0.3  59  8  9  9.83  10  3  6  3  21.6  33.6  33.1  -0.5  60  8  9  8.21  10  3  6  3  21.7  33.6  33.2  -0.4  61  8  9  8.78  10  3  6  3  21.6  33.6  33  -0.6  62  8  9  8.64  10  3  6  3  21.3  33.6  33  -0.6  63  8  1  0.979  10  3  6  3  20.7  33.1  33.1  0  64  8  1  1.05  10  3  6  3  21  33.3  33.2  -0.1  6  45  6  Modeling Table A2.15: Data used in fitting the volumetric source term. Temperatures recorded in absence of air cooling. PI  HF  RF  DC  [cell]  Tin  Tout  Tamb  ACF  Tside  Trefl  (W)  (L/day)  (L/day)  (s)  (10 cells/mL)  (°C)  CC)  (°C)  (L/min)  (°C)  CQ  6  1  8.13  16.3  180/3  11.9  32.8  34  25.5  0  -  2  8.13  16.3  180/3  11.9  32.8  34.9  24.7  0  -  -  3  8.13  16.3  120/6  8.3  33.4  37.8  25.95  0  -  -  3  10.6  20  300/3  9  33.6  37.3  24.7  0  -  -  5  8.13  16.3  180/3  11.9  34.1  42.6  24.9  0  -  -  5  10.6  20  300/3  9  33.9  40.1  24.5  0  -  7  8.13  16.3  180/3  11.9  34.9  47.4  25  0  -  -  36  36.1  3  11.33  34  45/1  8.7  35.0  38  24.8  0  3  11.33  34  45/6  9  34.7  36.9  24.8  0  34.5  33.8  5  11.33  34  45/6  10  35.7  40.4  27  0  37  38.5  3  5  20  45/6  10  34.2  39.7  26.4  0  35  36.5  3  8.13  16.3  120/6  8.3  33.2  37.6  25.8  0  34.3  35.1  150  Table A2.16: Data used in fitting the heat transfer coefficients. Temperatures recorded in presence of air cooling. PI  HF  RF  DC  [cell]  Tin  Tout  Tamb  ACF  Tside  T refl  (W)  (L/day)  (L/day)  (s)  (10* cells/mL)  (°C)  (°C)  (°C)  (L/min)  (°C)  ("C)  3  11.33  34  45/1  8.7  34.7  34.8  24  10.7  31.5  32.5  3  11.33  34  45/1  8.7  34.7  35.5  24.8  10.7  32  33.6  3  11.33  34  45/6  9  34.5  34.6  24.7  10.7  31.8  32.5  5  11.33  34  45/6  10  35.3  37.2  26.1  10.7  34.4  34.5  5  11.33  34  45/6  10  34.5  37.7  26.5  10.7  34.2  34.3  3  5  20  45/6  10  34.1  35.8  26  10.7  32.3  32.5  5  8.13  16  120/15  11  34.1  37.6  25.5  10.7  32.6  33.3  Note: The data used to test the selected model are in the Table A 2 . 3 , reference number 1 to 137.  151  Appendix 3: Matlab Code  Mathematical Model Based on the Energy Balance of the Acoustic Separator function AcousSepModel % % % % %  profile.m is a function m-file Solves a simple three-dimensional parabolic PDE using the Alternating-Direction Implicit (ADI) method Model of the energy generation in an acoustic separator Heat generation in liquid and walls, Air cooling adjustable for the four walls  % Dimension of the chamber xmax=0.0124; zmax=0.045;  thick=0.006;  % Water, wall and air proprieties ro=992.965; Cp=4.1775e3; k=0.628; mu=0.657e-3; ks=1.4; %heat transfer coefficient (ho: side walls, hoi: transducer wall, ho2: reflector wall) ho=75; ho 1=719; ho2=64; % Number of point in x, y and z direction m=input('\n Number of x or y points = '); n=input('\n Number of z points = '); mm=m-l; nm=n-l; p=m; pm=p-l; dx=xmax/mm; dz=zmax/nm; minc=mm/10; ninc=nm/5; x=0:dx:xmax; Y=x; nz=0:dz:zmax; % Enter the value of the system settings Power=input('\n Enter the value of the power input = '); Tin=input('\n Enter the value of temperature at the inlet flow ='); Tamb=input('\n Enter the value of ambiant temperature ='); % Energie from acoustic waves Watts per cubic meter Se=0.56*Power/(zmax*xmax 2); A  % Energy generate in the walls Note: qy is the energy in ONE side wall, so time 2 for the system... qxl=0.065*Power/(zmax*thick*xmax); qxm=0.02*Power/(zmax*thick*xmax); qy=0*Power/(zmax*thick*xmax); % Initial temperatures T=ones(m,p)*Tin; Tstar=T; Trans=ones(m,n); Trans(:,l)=Tin; Reflec=Trans; Side=Trans; MiddleX=Trans; MiddleY=Trans; % Calculation of the velocity with plug flow velocity distribution Flow2=input('\n Enter the value of the flow rate (L/day) ='); Flow=Flow2/1000/24/60/60; Vm=Flow/(xmax 2); Vz=ones(m,p)*Vm; Vav=Vm; A  % Initialization of constants ct5=-k*(l/ho+thick/ks); ct5A=-k*(l/hol+thick/ks); ct5B=-k*(l/ho2+thick/ks); ctl=l/dx 2; ct2=2*ctl; ct3=2/ct5/dx; ct3A=2/ct5A/dx; ct3B=2/ct5B/dx; ct4=2*ro*Cp/k/dz; inc=0; ct6=thick*( l/ho+thick/2/ks); ct6A=thick*( 1/ho 1 +thick/2/ks); ct6B=thick*( 1 /ho2+thick/2/ks); A  % Initialization of constants Wall Temperature ct8=thick 2/2/ks; ct9=ho*thick*Tamb/ks; ct9A=ho 1 *thick*Tamb/ks; ct9B=ho2*thick*Tamb/ks; ctl0=l+ho*thick/ks; ctl0A=l+hol*thick/ks; ctlOB=l+ho2*thick/ks; A  CX1 =-ct3 A*(-qx 1 *ct6A-Tamb); CXM=-ct3B*(-qxm*ct6B-Tamb); C Y=-ct3 *(-qy *ct6-Tamb); % Initialization of important values for thefirsthalf time al=zeros(l,m); bl=al; cl=al; dl=al;  al(l)=0; cl(l)=ct2; al(2:mm)=ctl; al(m)=ct2; cl(m)=0;  cl(2:mm)=ctl;  % Initialization of important values for the second half time a2=zeros(l,p); b2=a2; c2=a2; d2=a2; a2(l)=0; c2(l)=ct2; a2(2:pm)=ctl; c2(2:pm)=ctl; a2(p)=ct2; c2(p)=0; % ADI method with Thomas algorithm to solve the unknown for iz=2:n izm=iz-1; z=izm*dz; % First half-time step for z=0 ifiz==2 forj=l:p jp=j+l;jm=j-l; if j—1 b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (l)=-Se/k-ct3 A*(-qx 1 *ct6A-Tamb)+(ct2-ct4*Vz( 1 j))*T( 1 j)-ct2*T(l jp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k+(ct2-ct4*Vz(io))*T(ij)-ct2*T(ijp); end bl(m)=-ct2-ct4*Vz(mj)+ct3B; dl(m)=-Se/k-ct3B*(-qxm*ct6B-Tamb)+(ct2-ct4*Vz(mj))*T(mj)-ct2*T(mjp); elseifj==p b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 -ct2*T( 1 jm)+(ct2-ct4* Vz( 1 j))*T( 1 j); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); d 1 (i)=-Se/k-ct2*T(i jm)+(ct2-ct4*Vz(i j))*T(i j); end b 1 (m)=-ct2-ct4*Vz(m j)+ct3B; d 1 (m)=-Se/k+CXM-ct2*T(m jm)+(ct2-ct4*Vz(m j))*T(m j); else b 1 (1 )=-ct2-ct4* Vz(l j)+ct3A; d 1 (1 )=-Se/k+CX 1 -ct 1 *T( 1 jm)+(ct2-ct4* Vz( 1 j))*T( 1 j)-ct 1 *T( 1 jp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k-ctl*T(ijm)+(ct2-ct4*Vz(ij))*T(ij)-ctl*T(ijp); end b 1 (m)=-ct2-ct4* Vz(m j)+ct3B; dl(m)=-Se/k+CXM-ctl*T(mjm)+(ct2-ct4*Vz(mj))*T(mJ)-ctl*T(mjp); end Tstar(: j)=tdma(a 1 ,b 1 ,c 1 ,d 1)'; end else % First half-time step for z>0 forj=l:p jp=j+l;jm=j-l; ifj=l b 1 (1 )=-ct2-ct4*Vz( 1 j)+ct3A; d 1 (1 )=-Se/k+CX 1 +CY+(ct2-ct4* Vz( 1 j)-ct3 A)*T(1 j)-ct2*T( 1 jp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k-ct3*(-qy*ct6-Tamb)+(ct2-ct4*Vz(ij)-ct3)*T(ij)-ct2*T(ijp); end bl(m)=-ct2-ct4*Vz(mj)+ct3B; d 1 (m)=-Se/k+CXM+CY+(ct2-ct4*Vz(mj)-ct3B)*T(mj)-ct2*T(m jp); elseif j==p b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 +CY-ct2*T( 1 jm)+(ct2-ct4*Vz(l j)-ct3 A)*T( 1 j); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k-ct3*(-qy*ct6-Tamb)-ct2*T(ijm)+(ct2-ct4*Vz(ij)-ct3)*T(ij); end b 1 (m)=-ct2-ct4*Vz(m j)+ct3B; dl(m)=-Se/k+CXM+CY-ct2*T(mjm)+(ct2-ct4*Vz(mj)-ct3B)*T(mj); else  b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 -ct 1 *T( 1 jm)+(ct2-ct4* Vz( 1 j))*T( 1 j)-ct 1 *T( 1 jp);  for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl (i)=-Se/k-ctl *T(i jm)+(ct2-ct4*Vz(i j))*T(i j)-ctl *T(i jp); end b 1 (m)=-ct2-ct4*Vz(m j)+ct3B; d 1 (m)=-Se/k+CXM-ct 1 *T(m jm)+(ct2-ct4* Vz(m j))*T(m j)-ct 1 *T(m jp); end Tstar(:j)=tdma(al,bl cl dl)'; end end )  )  % Second half-time step for i=l :m ip=i+l; im=i-l; ifi=l b2( 1 )=-ct2-ct4* Vz(i, 1 )+ct3 A; d2( 1 )=-Se/k+CX 1 +CY+(ct2-ct4* Vz(i, 1 )-ct3 A)*Tstar(i, 1 )-ct2*Tstar(ip, 1);  for j=2:pm b2(j)=-ct2-ct4*Vz(ij); d2(j)=-Se/k+CXl+(ct2-ct4*Vz(ij)-ct3A)*Tstar(ij)-ct2*Tstar(ipj); end b2(p)=-ct2-ct4*Vz(i,p)+ct3A; d2(p)=-Se/k+CXl+CY+(ct2-ct4*Vz(i,p)-ct3A)*Tstar(i,p)-ct2*Tstar(ip,p); elseif i = m b2( 1 )=-ct2-ct4* Vz(i, 1 )+ct3B; d2( 1 )=-Se/k+CXM+C Y-ct2*Tstar(im, 1 )+(ct2-ct4* Vz(i, 1 )-ct3B)*Tstar(i, 1); forj=2;pm b2(j)=-ct2-ct4*Vz(ij); d2G)=-Se/k+CXM-ct2*Tstar(imj)+(ct2-ct4*Vz(ij)-ct3B)*Tstar(ij); end b2(p)=-ct2-ct4*Vz(i,p)+ct3B; d2(p)=-Se/k+CXM+CY-ct2*Tstar(im,p)+(ct2-ct4*Vz(i,p)-ct3B)*Tstar(i,p); else b2(l)=-ct2-ct4*Vz(i,l)+ct3; d2( 1 )=-Se/k-ct3 *(-qy*ct6-Tamb)-ct 1 *Tstar(im, 1 )+(ct2-ct4*Vz(i, 1 ))*Tstar(i, 1 )-ct 1 *Tstar(ip, 1);  for j=2:pm b2(j)=-ct2-ct4*Vz(ij); d2(j)=-Se/k-ctl*Tstar(imj)+(ct2-ct4*Vz(ij))*Tstar(ij)-ctl*Tstar(ipj); end b2(p)=-ct2-ct4*Vz(i,p)+ct3; d2(p)=-Se/k-ct3*(-qy*ct6-Tamb)-ctl*Tstar(im,p)+(ct2-ct4*Vz(i,p))*Tstar(i,p)-ctl*Tstar(ip,p); end T(i,:)=tdma(a2,b2,c2,d2); end % Select some temperature profile (x-y) along z if z=5*dz | rem(izm,ninc)=0 inc=inc+l; TT(;,:,inc)=T; zposition(inc)=z; end % Record inside wall temperature profile Trans(:,iz)=T(l,:)'; Reflec(:,iz)=T(m,:)'; Side(:,iz)=T(:,l); MiddleX(:,iz)=T(:,mm/2); MiddleY(:,iz)=T(mm/2,:)'; end % Calculation of the average .outlet temperature vT=Vz.*TT(;,:,inc); Tout=(sum(sum(vT(2:mm,2:mm)))+0.5*(sum(vT(l,2:mm))+sum(vT(m,2:mm))+sum(vT(2:nim l))+sum(vT(2:mmm)))+0.25*(sum(v T( 1,1 ))+sum(vT( 1 ,m))+sum(vT(m, 1 ))+sum(vT(m,m))))*dx 2/xmax 2/Vav; fprintf('\n The outlet temperature is : %3.1f ,Tout) >  A  )  A  % Print the temperature distribution at the upper cross-section fprintf('\n\n Temperature distribution at z = zmax \n') fprintfC %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f \n\TT(m:-mm/10:l,p:-pm/10:l,inc)')  155  %Calculation of temperature at the outside walls WTrans=(qxl*ct8+ct9A+Trans)/ctlOA; WReflec=(qxm*ct8+ct9B+Reflec)/ctlOB; WSide=(qy*ct8+ct9+Side)/ctlO; % Print of the outside wall temperature distributions fprintf('\n\n Temperature distribution on outside Wall Transducer \n') fprintfC %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f \n',WTrans(m:-mm/10:l,n:-nm/10:l)) fprintf('\n\n Temperature distribution on outside Wall Reflector \n') fprintfC %5-lf %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f V,WReflec(m:-mm/10:l,n:-nm/10:l)) fprintf('\n\n Temperature distribution on outside Wall Side \n') fprintfC %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f \n',WSide(m:-mm/10:l,n:-nm/10:l)) incl=inc-l;  inc2=inc-2;  % Creation of the graphical temperature profile lateral cross-section inside the cuvette figure('Name','Temperature profile of the section of an acoustic seperator (z = height)','Menubar','none') subplot(3,3,l); pcolor(x,Y,TT(:,:,inc)) caxis([30 45]) shading interp title(['Outlet z = ' num2str(zposition(inc),4)],'FontSize',14) axis off subplot(3,3,2); pcolor(x,Y,TT(:,:,incl)) caxis([30 45]) shading interp title(['z =' num2str(zposition(incl),4)],'FontSize',14) axis off subplot(3,3,3);pcolor(x,Y,TT(:,:,inc2)) caxis([30 45]) shading interp title(['z =' num2str(zposition(inc2),4)],'FontSize',14) axis off subplot(3,3,4); pcolor(x,Y,TT(:,:,3)) caxis([30 45]) shading interp title(['z =' num2str(zposition(3),4)],'FontSize',14) axis off subplot(3,3,5); pcolor(x,Y,TT(:,:,2)) caxis([30 45]) shading interp title(['z =' num2str(zposition(2),4)],'FontSize',14) axis off subplot(3,3,6); pcolor(x,Y,TT(:,:,l)) caxis([30 45]) shading interp xlabel('Transducer side') title(['z =' num2str(zposition(l),4)],'FontSize',14) % Creation of the graphical temperature profile verticale cross-section figure('Name','Temperature profile of the inside walls of an acoustic seperator (z = height)','Menubar','none') subplot(2,2,1); pcolor(x,nz,Trans') caxis([30 45]) shading interp title([' Transducer Wall '],'FontSize',14) axis off subplot(2,2,3); pcolor(x,nz,Reflec') caxis([30 45]) shading interp title([' Reflector Wall '],'FontSize',14) axis off subpIot(2,2,2); pcolor(x,nz,MiddleY') caxis([30 45]) shading interp title([' Middle Y 'yFontSize',14) axis off subplot(2,2,4); pcolor(x,nz,MiddleX') caxis([30 45]) shading interp  156  title([' Middle X '],'FontSize',14) axis off  Thomas Algorithm to Solve Tridiagonal Matrices function x=tdma(a,b,c,d) % 'tdma.m' is a function m-file that uses the Thomas algorithm to solve % tridiagonal sets of linear algebraic equations of the form: % a(i)*x(i-l) + b(i)*x(i) + c(i)*x(i+l) = d(i) % Input arguments: % a, b, c, d = row vectors of tridiagonal equation coefficients %  % Output arguments: % x = row vector of solution values n=length(a); % Forward substitution step: P(l)=-c(l)/b(l); Q(l)=d(l)/b(l); for i=2:n im=i-l; denom=a(i)*P(im)+b(i); P(i)=-c(i)/denom; Q(i)=(d(i)-a(i)*Q(im))/denom; end % Back substitution step: x(n)=Q(n); for i=n-1:-1:1 x(i)=P(i)*x(i+l)+Q(i); end  Genetic Algorithm to Optimize Unknown Parameters function main2 clear all; m=3; options = [30,-1,0.12,5,10,2000,1 e-4,1,0]; options( 1) = 20; % Population size options(5) = 200; % Maximum number of generations vb = [0.4 0.05 0; 0.7 0.2 0.05]; % Bound values of parameters [x,bf,ind] = sga('optfun',vb,options); fprintf('\n Optimum values:\n'); for i=l:m fprintf('\n Parameter %3i = % 10.3e',i,x(i)); end fun= l/bf-1.0e-13; fprintf('\n\n Objective function = %6.3e\n',fun); [sum2error,Tout,TSide,TReflec,TsideEXP,TreflecEXP,ToutEXP]=funcProfiIe(x); fprintf('\n\n Results \n') fprintf('\n\n Tout ToutEXP TSide TsideEXP TReflec TreflecEXPVi') fprintfC %5.1f %5.1f %5.1f %5.1f %5.1f %5.1f \n',[Tout;ToutEXP;TSide;TsideEXP;TReflec;TreflecEXP]);  function [beta,bestfun,stopcode] = sga(funstr,parspace,options,pl,p2,p3,p4,p5,p6,p7,p8,p9) %  % OUTPUTS: % beta = (1 x K) parameter vector maximizing funstr % bestfun = Best value of objective function  157  % % % % % % % % % %  stopcode = code for terminating condition == 1 if terminated normally = 2 if maximum number of iterations exceeded INPUTS: funstr = name of function to be maximized (string). parspace = (2 x K) matrix is [min; max] of parameter space dimensions or, if (3 x K), then bottom row is a good starting value options = vector of option settings pl,p2,...,p9 are optional parameters to be passed to funstr  % % where: % options(l) = m (size of generation, must be even integer) % options(2) = eta (crossover rate in (0,1) or use Booker's VCO if < 0) % options(3) = gamma (mutation rate in (0,1)) % options(4) = printcnt (print status once every printcnt iterations) % Set printcnt to zero to suppress printout. % options(5) = maxiter (maximum number of iterations) % options(6) = stopiter (minimum number of gains < epsln before stop) % options(7) = epsln (smallest gain worth recognizing) % options(8) = rplcbest (every rplcbest iterations, insert best-so-far) % options(9) = 1 if function is vectorized (i.e., if the function % can simultaneously evaluate many parameter vectors). % Default option settings: [20,-l,0.12,10,20000,2000,le-4,50,0] % % Notes: % 1. The function is maximized with respect to itsfirstparameter, % which is expressed as a row vector. , % Example: % Say we want to maximize function f with respect to vector p, % and need also to pass to f data matrices x,y,z. Then, % write the function f so it is called as f(p,x,y,z). GA will % assume that p is a row vector. % 2. Intermediate results are saved to "gabest.mat". This allows % you to pick up where you left off after an interruption. gaver='1.13'; defopt=[24,-1,0.12,10,20000,2000,1 e-4,50,0]; months = ['Jan';'Feb';'Mar';'Apr';'May';'Jun';... 'Jur;'Aug';'Sep';'Oct';'Nov';'Dec']; if nargin>2 if isempty(options) options=defopt; end else options=defopt; end m=options(l); eta=options(2); gam=options(3); printcnt=options(4); maxiter=options(5); stopiter=options(6); epsln=options(7); rplcbest=options(8); vecfun=options(9); % Use Booker's V C O if eta=-l vco=(eta<0); eta=abs(eta); % Cancel rplcbest if <=0 if rplcbest<=0, rplcbest=maxiter+l; end K.=size(parspace,2); % Draw initial Generation G=rand(m,K).*(parspace(2*ones(m,l),:)-parspace(ones(m,l),:))... +parspace(ones(m,l),:); bOrows=size(parspace, 1 )-2;  ifbOrows>0 G( 1 :b0rows,:)=parspace(3 :b0rows+2,:); parspace=parspace([l 2],:); end % Initial 'best' holders inarow=0; bestfun=-Inf; beta=zeros(l,K); % Score for each of m vectors f=zeros(m, 1); % Setup function string for evaluations paramstr=',pl,p2,p3,p4,p5,p6,p7,p8,p9'; evalstr = [funstr,'(G']; if-vecfun evalstr=[evalstr, end if nargin>3, evalstr=[evalstr,paramstr(l:3*(nargin-3))]; end evalstr = [evalstr,')']; % Print header if printcnt=100 disp(['GA (Genetic Algorithm), Version ',gaver,' by Michael Gordy']) disp(['Maximization of function ',funstr]) disp('i = Current generation') disp('best_i = Best function value in generation i') disp('best = Best function value so far') disp('miss = Number of generations since last hit') disp('psi = Proportion of unique genomes in generation') end if printcnt>0 disp(sprintf(['\n',blanks(20),'i best_i best miss psi'])) end iter=0; stopcode=0; oldpsi= 1; % for VCO option while stopcode==0 iter=iter+l; % Call function for each vector in G if vecfun f=eval(evalstr); else for i=l:m f(i)=eval(evalstr); end end fO=f; [bfO,bx]=max(f); bf=max([bfO bestfun]); fgain=(bf-bestfun); if fgain>epsln inarow=0; else inarow=inarow+1; end if fgain>0 bestfun=bf; beta=G(bx(l),:); end if printcnt>0 & rem(iter-l,printcnt)=0 % psi is number of unique rows in G divided by m. psi=( 1 +sum(diff(sort(G*rand(K, 1 )))^0))/m; ck=clock; ckhr=int2str(ck(4)+100); ckday=int2str(ck(3)+100); ckmin=int2str(ck(5)+100); cksec=int2str(ck(6)+100); timestamp=[ckday(2:3),months(ck(2),:),' ckhr(2;3),':',ckmin(2:3),':',cksec(2:3),'']; disp([timestamp,sprintf('%6.0f %8.5e %8.5e %5.0f %5.3f,... [iter-1 bfO bestfun inarow psi])])  save gabest beta timestamp iter funstr end % Reproduction f=(f-min(f)). ( 1 +log(iter)/l 00); pcum=cumsum(f)/sum(f); r=rand( 1 ,m); r=sum(r(ones(m, 1 ),:)>pcum(:,ones( 1 ,m)))+1; G=G(r,:); % Crossover if veo % psi is number of unique rows in G divided by m. psi=( 1 +sum(diff(sort(G*rand(K, 1 )))~=0))/m; eta=max([0.2 min([l ,eta-psi+oldpsi])]); oldpsi=psi; end y=sum(rand(m/2,l)<eta); ify>0 % choose crossover point x=floor(rand(y, 1 )*(K-1 ))+l; for i=l:y tmp=G(i,x(i)+l:K); G(i,x(i)+1 :K)=G(i+m/2,x(i)+l :K); G(i+m/2,x(i)+l:K)=tmp; end end % Mutation M=rand(m,K).*(parspace(2*ones(m,l),:)-parspace(ones(m,l),:))... +parspace(ones(m,l),:); domuta=find(rand(m,K)<gam); G(domuta)=M(domuta); % Once every rplcbest iterations, re-insert best beta if rem(iter,rplcbest)==0 G(m,:)=beta; end stopcode=(inarow>stopiter)+2*(iter>maxiter); end A  if printcnt>0 if stopcode=l disp(sprintf('GA: No improvement in %5.0f generations.\n',stopiter)) else disp(sprintf('GA: Maximum number of iterations exceeded.W)) end end %% end of sga.m function fitness = optfun(x) [sum2error,Tout,TSide,TReflec,TsideEXP,TreflecEXP,ToutEXP]=funcProfile(x); fitness = l/(1.0e-13+sum2error);  function [sum2error,Tout,TSide,TReflec,TsideEXP,TreflecEXP,ToutEXP]=funcProfile(x) %Select data in absence or in presence of air cooling %Data convection with NO air Power=[l 2 3 3 Tin=[32.8 32.8 33.35 33.6 Tamb=[25.5 24.7 25.95 25.8]; 8.13 Flow=[8.13 8.13 8.13];  5 34.1 24.7  5 33.9 24.9  7 34.9 24.5  3 35 25  3 34.7 24.8 ••  5 35.7 24.8  3 34.2 27  3]; 33.2]; 26.4  10.6  8.13  10.6  8.13  11.33  11.33  11.33  5  ToutEXP=[34 37.6];  34.9  37.8  37.3  42.6  40.1  47.4  38  36.9  40.4  39.7  TsideEXP=[0 34.3]; TreflecEXP=[0 35.1];  0  0  0  0  0  0  36  34.5  37  35  0  0  0  0  0  0  36.1  33.8  38.5  36.5  160  %Data convection with Air Cooling %Power=[3 3 3 %Tin=[34.7 34.7 34.5 %Tamb=[24 24.8 24.7 %Flow=[ 11.33 11.33 11.33 %ToutEXP=[34.8 35.5 34.6 31.8 %TsideEXP=[31.5 32 %TreflecEXP=[32.5 33.6 32.5  5 35.3 26.1 11.33 37.2 34.4 34.5  5 34.5 26.5 11.33 37.7 34.2 34.3  3 34.1 26 5 35.8 32.3 32.5  5]; 34.1]; 25.5]; 8.13]; 37.6]; 32.6]; 33.3];  n=size(Power,2); Tout=ones(l,n); TSide=ones(l,n); TReflec=ones( 1 ,n); sum2error=0; for i=l:n a=Power(i); b=Tin(i); c=Tamb(i); d=Flow(i); [Tout(i),TSide(i),TReflec(i)]=funcModel(a,b,c,d,x); Rout=Tout(i)-ToutEXP(i); Rside=0; Rreflec=0; ifTsideEXP(i)~=0 Rside=TSide(i)-TsideEXP(i); Rreflec=TReflec(i)-TreflecEXP(i); end sum2error=sum2error+5 *Rout 2+12*Rside 2+12*Rreflec 2; end A  A  A  function [Tout,TSide,TReflec]=funcModel(pow,in,amb,flo,heat) % profile.m is a function m-file % Solves a simple three-dimensional parabolic PDE using % the Alternating-Direction Implicit (ADI) method % Model of the energy generation in an acoustic separator % Heat generation in liquid and walls, Air cooling adjustable for the four walls % Dimension of the chamber xmax=0.0124; zmax=0.045; thick=0.006; % Water, wall and air proprieties (ho: side walls, hoi: transducer wall, ho2: reflector wall) ro=992.965; Cp=4.1775e3; k=0.628; mu=0.657e-3; ks=1.4; ho=10; hol=10; ho2=10; %ho=10; hol=10; ho2=10; % Number of point in x, y and z direction m=21; n=21; mm=m-l; nm=n-l; p=m; pm=p-l; dx=xmax/mm; dz=zmax/nm; minc=mm/10; ninc=nm/5; x=0:dx:xmax; Y=x; nz=0:dz:zmax; % Enter the value of the system settings Power=pow; Tin=in; Tamb=amb; % Energie from acoustic waves Watts per cubic meter Se=heat( 1 )*Power/(zmax*xmax 2); A  % Energy generate in the walls Note: qy is the energy in ONE side wall, so time 2 for the system... qxl=heat(2)*Power/(zmax*thick*xmax); qxm=heat(3)*Power/(zmax*thick*xmax); qy=0*Power/(zmax*thick*xmax);  161  % Initial temperatures T=ones(m,p)*Tin; Tstar=T; Trans=ones(m,n); Trans(:,l)=Tin; Reflec=Trans; Side=Trans; MiddleX=Trans; MiddleY=Trans; % Calculation of the velocity with plug flow velocity distribution Flow2=flo; Flow=Flow2/l 000/24/60/60; Vm=Flow/(xmax 2); Vz=ones(m,p)*Vm; Vav=Vm; A  % Initialization of constants ct5=-k*( 1 /ho+thick/ks); ct5A=-k*( 1 /ho 1+thick/ks); ct5B=-k*( 1 /ho2+thick/ks); ctl=l/dx 2; ct2=2*ctl; ct3=2/ct5/dx; ct3A=2/ct5A/dx; ct3B=2/ct5B/dx; ct4=2*ro*Cp/k/dz; inc=0; ct6=thick*(l/ho+thick/2/ks); ct6A=thick*(l/hol+thick/2/ks); ct6B=thick*(l/ho2+thick/2/ks); A  % Initialization of constants Wall Temperature ct8=thick 2/2/ks; ct9=ho*thick*Tamb/ks; ct9A=hol *thick*Tamb/ks; ct9B=ho2*thick*Tamb/ks; ctl0=l+ho*thick/ks; ctlOA=l+hol*thick/ks; ctlOB=l+ho2*thick/ks; A  CX 1 =-ct3 A*(-qx 1 *ct6A-Tamb); CXM=-ct3B*(-qxm*ct6B-Tamb); CY=-ct3 *(-qy *ct6-Tamb); % Initialization of important values for thefirsthalf time al=zeros(l,m); bl=al; cl=al; dl=al; al(l)=0; cl(l)=ct2; al(2:mm)=ctl; cl(2:mm)=ctl; al(m)=ct2; cl(m)=0; % Initialization of important values for the second half time a2=zeros(l,p); b2=a2; c2=a2; d2=a2; a2(l)=0; c2(l)=ct2; a2(2:pm)=ctl; c2(2:pm)=ctl; a2(p)=ct2; c2(p)=0; % ADI method with Thomas algorithm to solve the unknown for iz=2:n izm=iz-l; z=izm*dz; % First half-time step for z=0 if iz=2 forj=l:p jp=j+l;jm=j-l; ifj=l b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k-ct3 A*(-qx 1 *ct6A-Tamb)+(ct2-ct4* Vz( 1J))*T( 1 j)-ct2*T( 1 jp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k+(ct2-ct4*Vz(ij))*T(ij)-ct2*T(ijp); end bl(m)=-ct2-ct4*Vz(mj)+ct3B; dl(m)=-Se/k-ct3B*(-qxm*ct6B-Tamb)+(ct2-ct4*Vz(mj))*T(mj)-ct2*T(mjp); elseif j==p b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 -ct2*T( 1 jm)+(ct2-ct4* Vz( 1 j))*T( 1 j); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k-ct2*T(ijm)+(ct2-ct4*Vz(ij))*T(ij); end bl(m)=-ct2-ct4*Vz(mj)+ct3B; dl(m)=-Se/k+CXM-ct2*T(mjm)+(ct2-ct4*Vz(mj))*T(mj); else b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 -ct 1 *T( 1 jm)+(ct2-ct4* Vz( 1 j))*T( 1 j)-ct 1 *T( 1 jp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); d 1 (i)=-Se/k-ct 1 *T(i jm)+(ct2-ct4* Vz(i j))*T(i j)-ct 1 *T(i jp); end  b 1 (m)=-ct2-ct4* Vz(m j)+ct3B; d 1 (m)=-Se/k+CXM-ct 1 *T(m jm)+(ct2-ct4* Vz(m j))*T(m j)-ct 1 *T(m jp); end Tstar(: j)=tdma(a 1 ,b 1 ,c 1 ,d 1)'; end else % First half-time step for z>0 forj=l:p jp=j+l;jm=j-l;  ifj=l  b 1 (1 )=-ct2-ct4* Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 +CY+(ct2-ct4* Vz( 1 j)-ct3 A)*T( 1 j)-ct2*T( 1 jp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k-ct3*(-qy*ct6-Tamb)+(ct2-ct4*Vz(ij)-ct3)*T(ij)-ct2*T(ijp); end bl(m)=-ct2-ct4*Vz(mj)+ct3B; dl(m)=-Se/k+CXM+CY+(ct2-ct4*Vz(mj)-ct3B)*T(mj)-ct2*T(mjp); elseif j==p b 1 (1 )=-ct2-ct4*Vz( 1 j)+ct3 A; d 1 (1 )=-Se/k+CX 1 +CY-ct2*T( 1 jm)+(ct2-ct4* Vz( 1 j)-ct3 A)*T( 1 j); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl(i)=-Se/k-ct3*(-qy*ct6-Tamb)-ct2*T(ijm)+(ct2-ct4*Vz(ij)-ct3)*T(ij); end b 1 (m)=-ct2-ct4*Vz(mj)+ct3B; d 1 (m)=-Se/k+CXM+CY-ct2*T(m jm)+(ct2-ct4*Vz(m j)-ct3B)*T(m j); else b 1 (1 )=-ct2-ct4* Vz(l j)+ct3A; dl(l)=-Se/k+CXl-ctl*T(ljm)+(ct2-ct4*Vz(lj))*T(lj)-ctl*T(ljp); for i=2:mm bl(i)=-ct2-ct4*Vz(ij); dl (i)=-Se/k-ctl *T(i jm)+(ct2-ct4*Vz(i j))*T(i j)-ctl *T(i jp); end bl (m)=-ct2-ct4*Vz(mj)+ct3B; dl(m)=-Se/k+CXM-ctl*T(mjm)+(ct2-ct4*Vz(mj))*T(mj)-ctl*T(mjp); end Tstar(: j)=tdma(a 1 ,b 1 ,c 1 ,d 1)'; end end % Second half-time step for i=l:m ip=i+l; im=i-l; ifi==l b2( 1 )=-ct2-ct4* Vz(i, 1 )+ct3 A; d2( 1 )=-Se/k+CX 1+C Y+(ct2-ct4*Vz(i, 1 )-ct3 A)*Tstar(i, 1 )-ct2*Tstar(ip, 1); for j=2:pm b2(j)=-ct2-ct4*Vz(ij); d2(j)=-Se/k+CXl+(ct2-ct4*Vz(ij)-ct3A)*Tstar(ij)-ct2*Tstar(ipj); end b2(p)=-ct2-ct4*Vz(i,p)+ct3A; d2(p)=-Se/k+CXl+CY+(ct2-ct4*Vz(i,p)-c6A)*Tstar(i,p)-ct2*Tstar(ip,p); elseif i=m b2(l )=-ct2-ct4*Vz(i, l)+ct3B; d2(l)=-Se/k+CXM+CY-ct2*Tstar(im,l)+(ct2-ct4*Vz(i,l)-ct3B)*Tstar(i,l); for j=2:pm b2(j)=-ct2-ct4*Vz(ij); d2(j)=-Se/k+CXM-ct2*Tstar(imj)+(ct2-ct4*Vz(ij)-ct3B)*Tstar(ij); end b2(p)=-ct2-ct4*Vz(i,p)+ct3B; d2(p)=-Se/k+CXM+CY-ct2*Tstar(im,p)+(ct2-ct4*Vz(i,p)-ct3B)*Tstar(i,p); else b2(l)=-ct2-ct4*Vz(i,l)+ct3; d2( 1 )=-Se/k-ct3 *(-qy *ct6-Tamb)-ct 1 *Tstar(im, 1 )+(ct2-ct4* Vz(i, 1 ))*Tstar(i, 1 )-ct 1 *Tstar(ip, 1); for j=2:pm b2(j)=-ct2-ct4*Vz(ij); d2G)=-Se/k-ctl*Tstar(imj)+(ct2-ct4*Vz(ij))*Tstar(ij)-ctl*Tstar(ipj); end  b2(p)=-ct2-ct4* Vz(i,p)+ct3; d2(p)=-Se/k-ct3*(-qy*ct6-Tamb)-ctl*Tstar(im,p)+(ct2-ct4*Vz(i,p))*Tstar(i,p)-ctl*Tstar(ip,p); end T(i,:)=tdma(a2,b2,c2,d2); end % Select some temperature profile (x-y) along z if z=5*dz | rem(izm,ninc)==0 inc=inc+l; TT(:,:,inc)=T; zposition(inc)=z; end % Record inside wall temperature profile Trans(:,iz)=T(l,:)'; Reflec(:,iz)=T(m,:)'; Side(:,iz)=T(:,l); MiddleX(:,iz)=T(:,mm/2); MiddleY(:,iz)=T(mm/2,:)'; end % Calculation of the outlet temperature and the mean value vT=Vz.*TT(:,:,inc); Tout=(sum(sum(vT(2 :mm,2 :mm)))+0.5 *(sum(vT( 1,2 :mm))+sum(vT(m,2 :mm))+sum(vT(2:mm, 1 ))+sum(vT(2:mm,m)))+0.25*(sum(v T( 1,1 ))+sum(vT( 1 ,m))+sum(vT(m, 1 ))+sum(vT(m,m))))*dx 2/xmax 2/Vav; Toutmean=mean(mean(TT(2:mm,2:mm,inc))); A  A  %Calculation of temperature at the wall (outside) WTrans=(qxl*ct8+ct9A+Trans)/ctlOA; WReflec=(qxm*ct8+ct9B+Reflec)/ct 1 OB; WSide=(qy*ct8+ct9+Side)/ctl 0; TSide=WSide(mm/2+1 ,mm/2+1); TReflec=WReflec(mm/2+1 ,mm/2+1);  164  

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