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Study of mass transfer and continuous chemical purification in two-dimentional electro-fluid-dynamic… Liu, Chang 2013

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STUDY OF MASS TRANSFER AND CONTINUOUS CHEMICAL PURIFICATION IN TWO-DIMENSIONAL ELECTRO-FLUID-DYNAMIC DEVICES by  Chang Liu B. Sc., Peking University, 2007 B. Ec., Peking University, 2007  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in  The Faculty of Graduate Studies (Chemistry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2013  Chang Liu, 2013  Abstract The development of separation science is one of the most important contributions in analytical chemistry, and current separation systems can analyze less than femtomoles of analyte. However, the need for such ultrasensitive technology is partly driven by the difficulties in obtaining appreciable quantities of pure substances. Therefore, a platform enabling the purification of chemicals in a preparative fashion from complex mixtures is required. In this thesis, a new continuous chemical purification platform is introduced, based on the interactions of analyte with multiple types of driving forces in a twodimensional electro-fluid-dynamic (2-D EFD) system, in which both electric field and hydrodynamic pressure are simultaneously utilized in 2-D microfluidic channel networks. Mass conservation is the guiding principle for analyte distribution in channel intersections. However, in EFD devices, the mass distribution is more complex. In order to understand the analytes’ transportation behaviour in multiple force fields, we studied the mass transfer in EFD devices, and discovered the effective volumetric flow rate conservation principle. It can be used to predict the analyte concentration in a channel, and provides a theoretical basis for investigating the mass distribution in EFD devices. Y-shaped microfluidic devices have been extensively used for mixing components. With the strategically applied electric potential and hydrodynamic pressure, such spontaneous mixing process can be reversed in the same device. A continuous solution stream containing a mixture of two analytes can be separated into two channels, each containing a pure compound. By increasing the geometry complexity, more ii  complex samples can be processed. A multiple-branched device is introduced for continuously purifying multiple analytes. Each component in the introduced mixture can be directed to enter its specific collection channel, without any contamination. In the study of sample injection methods, the hydrodynamic injection is superior to the electrokinetic injection in the purification process by providing faster sample processing and being more resistant to the fluctuating electroosmotic flow. In addition, the buffer depletion problem can be fully resolved. The stringent control and ease of operation of this technique could lead to a new generation of purification devices to serve the needs of academic research and commercial activities.  iii  Preface The majority of the research included in this dissertation was conducted by the author, Chang Liu. The contributions of other researchers are detailed below.  Contributions from other researchers:  Chapter 2:  The fabrication of microfluidic devices was partly contributed by Yong Luo. Ning Fang and David D. Y. Chen contributed in the manuscript editing.  Chapter 3:  The project was partly designed by E. Jane Maxwell and David D. Y. Chen. The fabrication of microfluidic devices was partly contributed by Yong Luo. E. Jane Maxwell, Ning Fang and David D. Y. Chen contributed in the manuscript editing.  Chapter 4:  The project was partly designed by E. Jane Maxwell and David D. Y. Chen. The fabrication of microfluidic devices was partly contributed by Yong Luo. E. Jane Maxwell, Ning Fang and David D. Y. Chen contributed in the manuscript editing.  Chapter 5:  Ning Fang and David D. Y. Chen contributed in the manuscript editing.  Publications arising from work presented in the dissertation:  Chang Liu, Yong Luo, Ning Fang and David D. Y. Chen. Analyte distribution at channel intersections of electro-fluid-dynamic devices. Analytical Chemistry (2011) 83, 11891192. Material from this article is included in Chapters 2. Reuse with permission. Copyright (2011) American Chemical Society.  iv  Chang Liu, Yong Luo, E. Jane Maxwell, Ning Fang and David D. Y. Chen. Reverse of mixing process with a two-dimensional electro-fluid-dynamic device. Analytical Chemistry (2010) 82, 2182-2185. Material from this article is included in Chapter 3. Reuse with permission. Copyright (2010) American Chemical Society  Chang Liu, Yong Luo, E. Jane Maxwell, Ning Fang and David D. Y. Chen. Potential of two-dimensional electro-fluid-dynamic devices for continuous purification of multiple components from complex samples. Analytical Chemistry (2011), 83, 8208-8214. Material from this article is included in Chapter 3 and Chapter 4. Reuse with permission. Copyright (2011) American Chemical Society.  Chang Liu, Ning Fang and David D. Y. Chen. Comparison of sample injection modes for continuous chemical purification in two-dimensional electro-fluid-dynamic devices. manuscript in preparation Material from this article is included in Chapter 5.  v  Table of Contents  Abstract ............................................................................................................................. ii Preface .............................................................................................................................. iv Table of Contents ............................................................................................................. vi List of Tables .................................................................................................................... ix List of Figures ................................................................................................................... x List of Symbols and Abbreviations ............................................................................ xviii Acknowledgements ........................................................................................................ xxi Dedication ..................................................................................................................... xxiii Chapter 1 : Introduction .................................................................................................. 1 1.1 Separation Science and Chemical Purification ......................................................... 2 1.2 Capillary Electrophoresis and Analyte Migration Driving Forces ........................... 3 1.3 Separation Resolution and Infinite Separation Resolution Theory .......................... 7 1.4 Some Techniques for Continuous Chemical Purifications ..................................... 10 1.4.1 Continuous Flow Counterbalanced Capillary Electrophoresis (cFCCE) ........ 11 1.4.2 Continuous Free Flow Electrophoresis (cFFE) ............................................... 15 1.5 Research Objectives................................................................................................ 17 Chapter 2 : Analyte Distribution at Channel Intersections of Electro-Fluid-Dynamic Devices ............................................................................................................................. 20 2.1 Introduction............................................................................................................. 21 2.2 Experimental Section .............................................................................................. 22 2.3 Theoretical Basis .................................................................................................... 25 2.4 Results and Discussion ........................................................................................... 28 2.4.1 Experimental Verifications .............................................................................. 28 2.4.2 Applications ..................................................................................................... 33 2.4.3 Applicable Conditions ..................................................................................... 35  vi  2.5 Conclusions ............................................................................................................ 37 Chapter 3 : Reverse of Mixing Process: Continuous Chemical Purification with a YShaped Two-Dimensional Electro-Fluid-Dynamic Device.......................................... 39 3.1 Introduction............................................................................................................. 40 3.2 Experimental Section .............................................................................................. 42 3.3 Theoretical Simulation............................................................................................ 45 3.3.1 Derivation of Some Equations ......................................................................... 45 3.3.2 Numerical Modeling ........................................................................................ 51 3.4 Theoretical Basis .................................................................................................... 57 3.5 Results and Discussions.......................................................................................... 61 3.5.1 Continuous Chemical Purification in EFD Device with 2:1 Cross-Sectional Area Ratio ................................................................................................................. 61 3.5.2 Symmetrical Y-Shaped EFD Devices with Different Cross-Sectional Area Ratios ........................................................................................................................ 65 3.5 Conclusions ............................................................................................................ 71 Chapter 4 : Multiple-Branched Two-Dimensional Electro-Fluid-Dynamic Devices for Continuous Purification of Multiple Components from Complex Samples ....... 72 4.1 Introduction............................................................................................................. 73 4.2 Experimental Section .............................................................................................. 75 4.3 Results and Discussions.......................................................................................... 77 4.4 Conclusions ............................................................................................................ 88 Chapter 5 : Comparison of Sample Injection Modes for Continuous Chemical Purification in Two-Dimensional Electro-Fluid-Dynamic Devices ............................ 89 5.1 Introduction............................................................................................................. 90 5.2 Experimental Section .............................................................................................. 92 5.3 Results and Discussions.......................................................................................... 93 5.3.1 The Electric Field and Hydrodynamic Fluid Field Distribution in the 2-D EFD Devices ..................................................................................................................... 94 5.3.2 Migration Behavior of an Analyte in 2-D EFD Devices ................................. 96  vii  5.3.3 The Effects of Changing Controlling Parameters on Critical Boundary Conditions ............................................................................................................... 102 5.3.4 The Continuous Chemical Purification in 2-D EFD Devices and the Sample Processing Speed .................................................................................................... 105 5.3.5 The Comparison of Hydrodynamic Injection and Electrokinetic Injection Modes in the Operation of Continuous Chemical Purification .............................. 108 5.4 Conclusions .......................................................................................................... 117 Chapter 6 : Concluding Remarks and Future Work ................................................ 118 6.1 Concluding Remarks ............................................................................................ 119 6.2 Future Work .......................................................................................................... 120 Bibliography .................................................................................................................. 126  viii  List of Tables  Table 2.1 Velocity of microbeads in individual channels ................................................ 32 Table 3.1 Electric field strengths and magnitudes of the pressure induced velocity in each channels at different migration conditions. The volumetric counter flow rates used in different conditions are 1.200, 0.800, 0.600, 0.200 µl/min, respectively………………………………………………………….………..63 Table 5.1 Electric field and fluid field distribution in different sample injection modes of symmetrical Y-shaped, and multiple-branched 2-D EFD devices ................... 96 Table 5.2 Comparison of different sample injection modes ........................................... 116  ix  List of Figures  Figure 1.1 Structure of electrical double layer and electric potential profile from the capillary surface to the bulk solution. .............................................................. 6 Figure 1.2 Separation resolution illustration at different conditions. (a) and (b): the separation resolution is finite; (c) and (d): the separation resolution is infinite. ......................................................................................................................... 8 Figure 1.3 The effect of EOF on resolution. The direction and magnitude of EOF can be adjusted to improve the resolution. ................................................................ 10 Figure 1.4 Schematic representation of cFCCE. (a) The inlets positioned in the sample vial while the outlet is positioned in a buffer vial. (b) Potential is applied to initiate the separation. Simultaneously, a counter-pressure is applied at the outlet end of the capillary that results in the slower migration component having a net velocity toward the inlet and the faster migrating component having a net velocity toward the outlet. (c) At the end of the run a portion of the faster migrating component has been isolated in the outlet vial. ............. 12 Figure 1.5 Purifying a non-fastest moving component in a mixture. In a group of analytes with electrophoretic mobilities of µep ,1 − µep ,4 , when a pressure is applied, both analytes 1 and 2 are allowed to migrate through the capillary. The net mobility of the analyte 2 is denoted as ∆µ1 in the first process. To obtain pure analyte 2, the polarity is reversed and pressure applied at the inlet vial. The net mobility of analyte 2 in this situation is illustrated by ∆µ 2 . It should be  x  noted that the slowest migrating component in a mixture can be obtained directly by using step 2 alone. ....................................................................... 14 Figure 1.6 Illustration of separation principles of CE and cFFE. (a) A separation in capillary electrophoresis. Analytes move through the capillary according to their electrophoretic mobility and electroosmotic flow. (b) A separation in free-flow electrophoresis. Analytes move down the chip by pressure driven buffer flow. Analytes are deflected in sample streams based on their electrophoretic mobility. ................................................................................ 16 Figure 2.1 The 2-D EFD devices used in this study. (a) Y-shaped device. The lengths of the main channel CF and lateral channels AC and BC are 3.6 cm and 3.0 cm respectively. The positive potential of 200 V and 150 V were applied at point A and B. Point E is grounded and the channel DE has the length of 1.5 cm. A volumetric flow rate of 0.020 µL/min was controlled at point F. (b) Crossshaped device. Channels AD, BD and CD have the same length of 0.6 cm, and a volumetric flow rate of 0.250 µL/min was controlled through the 4.4 cm long channel DE. The positive potentials of 500 V and 200 V were applied at point C and B, and point A was grounded. Intersection C in (a) and intersection D in (b) are monitored. (c) Flow directions of microbeads migrating through the intersection of the Y shaped channel structure. (d) Flow directions of microbeads migrating through the intersection of the cross-shaped channel structure. The flow directions were determined by the applied electric fields and pressure. ............................................................... 24  xi  Figure 2.2 Velocity measurement in the Y shaped device. (a) Flow directions of microbeads migrating through the intersection of the Y shaped channel structure. (b) An image of microbeads flowing in all three channels with a fixed exposure time. The longer image pattern is the result of the faster migration velocity. ......................................................................................... 30 Figure 2.3 The conservation of the effective volumetric flow rate for a non-uniform channel. .......................................................................................................... 36 Figure 3.1 Schematics of the setup: (a) channel geometry of the microflulidic EFD device and (b) a schematic of the device made from a 2.54 cm × 7.62 cm PDMS chip................................................................................................................. 42 Figure 3.2 Schematics of the optical imaging system with the dual-view filter............... 44 Figure 3.3 Demonstration of dye images under the duel-view microscope. (a) The device is filled with pure rhodamine 110. (b) The device is filled with pure ethidium bromide. (c) The device is filled with the mixture of rhodamine 110 and ethidium bromide. .......................................................................................... 45 Figure 3.4 Pressure-caused normal surface force in the x direction on an element of fluid. ....................................................................................................................... 48 Figure 3.5 Flow chart for the simulation process ............................................................. 53 Figure 3.6 Simulated results of the fork area (around point C) obtained from COMSOL Multiphysics. (a) Electric field distribution under the experimental conditions. (b) An example of fluid velocity field when a pressure is applied against the electric field in the direction from D to C. (c) An example of concentration  xii  distribution of the analyte. The concentration of the analyte from high to low is depicted by the colour scheme of red to blue. ............................................ 56 Figure 3.7 Behaviour of one analyte. (a) Simulated concentration distribution of R110 when (1) the pressure in the direction from D to C is high, preventing R110 from entering the device, (2) the counter pressure is adjusted so that R110 flows along ACB, (3) the pressure is adjusted so that R110 flows along both ACB and ACDE directions, and (4) the pressure is so small that all R110 flows along ACDE direction. The position of E is not shown in this figure. It is where the sample is collected in Condition 4, and its position is shown in Figure 3.1(a). The concentration of the analyte from high to low is depicted by the colour scheme of red to blue. (b) Experimental verification using R110. The fluorescence images of the fork of ACB were recorded using a CCD camera. (c) The boundary conditions for R110 to be localized in Vial A, moving along ACB, moving along both ACB and ACDE, and moving along ACDE only. ................................................................................................... 59 Figure 3.8 Behaviour of two analytes. (a) The relative boundary conditions that determine the flow directions of R110 and EB, and the relative conditions used in the experiment. (b) The fluorescence images at 530 nm for R110 and 600 nm for EB taken simultaneously to demonstrate (1) R110 flowing along ACB and EB flowing along both ACB and ACDE (the position of point E is shown in Figure 3.1(a)), (2) R110 flowing along ACB and EB flowing along ACDE only, demonstrating the reverse of a mixing process, and (3) R110 flowing along both ACB and ACDE but EB only flowing along ACDE...... 64  xiii  Figure 3.9 (a) Simulated concentration distributions in symmetrical Y-shaped EFD devices with three different cross-sectional area ratios during the decrease of applied hydrodynamic pressure. The concentrations from high to low are illustrated from red to blue. (b) The critical boundary conditions for four migration conditions. ..................................................................................... 70 Figure 4.1 Schematics of channel geometry for the multiple-branched EFD devices. A is the sample inlet, S1, S2 and S3 are branched separation channels and S1’, S2’ and S3’ are collection outlets with sequentially lowered voltages, G is the grounded waste outlet, and P is the presurized port connected to a syringe pump. ............................................................................................................. 75 Figure 4.2 Experimental setup of using the multiple-branched EFD devices for continuous chemical purification. .................................................................. 77 Figure 4.3 Directions of (a) pressure-induced velocity and (b) electric field in the intersecting channels. (c) Four possible steady-state velocity directions for the analyte in intersecting channels. .............................................................. 79 Figure 4.4 Migration behavior of the analyte: (a) Simulated concentration distribution. The concentrations from high to low are illustrated from red to blue. (b) Experimental verification using R110: the positive electrical potential of 2000 V and 1500 V were applied in point A and S1’, respectively, and the flow rate was controlled as (1) 5.0 mm/s, (2) 4.0 mm/s, (3) 3.0 mm/s or (4) 2.0 mm/s, respectively; (c) the critical boundary conditions for four migration conditions. ...................................................................................................... 81  xiv  Figure 4.5 Simulated migration behavior of two analytes in the intersecting area. The concentrations from high to low are illustrated from red to blue. (a) Relatively more negative, slower moving analyte; (b) relatively more positive, faster moving analyte. ..................................................................... 85 Figure 4.6 Proof-reading mechanism of the 2D-EFD devices. (a) The steady-state concentration distribution of an analyte. The arrows indicate the analyte migration velocity in each channel. (b) Analyte injection position. (d) and (f): The analyte distribution in the region indicated in (c) and (e), respectively. 86 Figure 4.7 Behaviour of two analytes in the EFD device. (a) and (b): Simulated analyte distribution for two analytes. The concentrations from high to low are illustrated from red to blue. (c) and (d): Experimental verification using R110 (green colour) and EB (yellow colour) at two intersection areas. The positive electrical potential of 2000 V and 1500 V were applied in point A and S1’, respectively and the flow rate was controlled as 3.8 mm/s. .......................... 87 Figure 5.1 The 2-D EFD devices used in this chapter: (a) symmetrical Y-shaped device; (b) multiple-branched device. ........................................................................ 92 Figure 5.2 Mass migration pathways of the analyte in 2-D EFD devices and critical boundary conditions on: (a) symmetrical Y-shaped device, and (b) multiplebranched device. .......................................................................................... 101 Figure 5.3 The effect of changing sample injection speed on the analyte sample migration velocity in different channels of the symmetrical Y-shaped device. During the change of the injection speed from 0.001 m/s to 0.003 m/s, the CBC X changes from X1 to X2, and the CBC Y does not change. The potential applied  xv  at point B is 5000 V, and the electrophoretic mobility of the analyte is 5x10-8 m2V-1s-1. ....................................................................................................... 103 Figure 5.4 The effect of changing electric field strength on the analyte sample migration velocity in different channels of symmetrical Y-shaped device. During the increase of the electric potential applied at point B from 5000 V to 10000 V, CBCs move from X1, Y1 to X2, Y2. The sample injection speed is 0.001 m/s, and the electrophoretic mobility of the analyte is 5x10-8 m2V-1s-1. ............. 104 Figure 5.5 Demonstrations of continuous chemical purification process in different 2-D EFD devices: (a) symmetrical Y-shaped device; (b) multiple-branched device. .......................................................................................................... 107 Figure 5.6 The effect of unstable EOF on the analyte sample migration velocity in different channels in the hydrodynamic sample injection mode. During the change of EOF, the migration velocities in different channels are not affected with the assumption of the constant fluid velocity in Channel CD. The sample injection speed is 0.001 m/s, the electric potential applied at point B is 5000 V, and the electrophoretic mobility of the analyte is 5x10-8 m2V-1s-1. ..................................................................................................................... 112 Figure 5.7 The effect of unstable EOF on the analyte sample migration velocity in different channels in the electrokinetic sample injection mode. During the change of electroosmotic mobility from 2x10-8 m2V-1s-1 to 6x10-8 m2V-1s-1, the migration velocities in Channel AC and BC are both affected if the fluid velocity in Channel CD is kept as a constant. The electric potential applied at  xvi  point A and B were 5000 V and 4250 V, respectively, and the electrophoretic mobility of the analyte is 3x10-8 m2V-1s-1. ................................................... 114 Figure 6.1 The combination of microsynthesis and micropurification .......................... 124  xvii  List of Symbols and Abbreviations  a  Acceleration  BGE  Background electrolyte  c  Concentration  CBC  Critical boundary condition  CBV  Critical boundary value  CE  Capillary electrophoresis  cFCCE  Continuous flow counterbalanced capillary electrophoresis  cFFE  Continuous free flow electrophoresis  D  Diffusion coefficient  dc  Channel diameter  E  Electric field  EOF  Electroosmotic flow  F  Force  Fe  Electrostatic force  Fd  Drag force  FWHM  Full width at half-maximum  g  Gravitational acceleration  IEF  Isoelectric focusing  J  Current density  Je  Externally generated current density  l  Channel length  m  Mass  n  Channel number  r n  Orthogonal unit vector  xviii  np  Particle number  p  Pressure  Q  Charge  Qj  Current source  R  Particle radius  Rs  Separation resolution  S  Channel cross-sectional area  SDS-PAGE  Sodium dodecyl sulphate polyacrylamide gel electrophoresis  t  Time  tr  Retention time  v  Velocity  V  Electric potential  Vtot  Sample volume  veo  Electroosmotic velocity  vep  Electrophoretic velocity  vf  Fluid velocity  vinj  Sample injection speed  vp  Pressure induced velocity  vparticle  Velocity of the particle  w  Peak width  2-D EFD  Two-dimensional electro-fluid-dynamic  α  Cross-sectional area ratio  ε  Dielectric constant  η  Viscosity coefficient  λab,max  Maximum absorbance wavelength  λem,max  Maximum emission wavelength  xix  µe  Electric field induced mobility  µeo  Electroosmotic mobility  µep  Electrophoretic mobility  ρ  Density  ρe  Free charge density  σ  Conductivity  ζ  Zeta potential  xx  Acknowledgements First and foremost, I want to thank my supervisor, Dr. David Chen, for being a wonderful mentor more than I could have wished for. I am deeply grateful for your thoughtful, wise, and patient guidance during every step in my PhD studies, and giving me every opportunity to develop and succeed in both research and beyond. You are the great example for me not only in science, but also as a wonderful person, and I wish I could be a person like you in the future. This thesis certainly would not have been possible without your help. I would also like to thank everyone who has provided mentorship through my study, and all the members of my guidance committee, especially Dr. Ning Fang from Ames Laboratory, U. S. Department of Energy, and Iowa State University, for allowing me to use the micro-fabrication and imaging facilities there. The time spent in Ames opens the door of optical imaging and microfluidics for me, and these experiences will be greatly helpful for my future career. This research is mainly supported by the Natural Sciences and Engineering Research Council of Canada (NSERC). The micro-fabrication and imaging facilities are supported by Ames Laboratory, U.S. Department of Energy. I would also like to acknowledge the financial support from Agnes and Gilbert Hooley Scholarship, PeiHuang Tung and Tan-Wen Tung Graduate Fellowship from the University of British Columbia, and American Chemical Society Division of Analytical Chemistry Graduate Fellowship sponsored by the Society for Analytical Chemists of Pittsburgh.  xxi  I have been so fortunate to work together with many exceptional people during my PhD study, and I would like to faithfully appreciate all of my colleagues for sharing their knowledge, and providing a friendly and supportive working community in the lab: Hong, Sharon, Jane, Koen, Xuefei, Roxana, Joe, Sherry, Laiel, Alexis, Akram, Cai, Cheng, Lingyu, Matthew, Jessica, and Caitlyn from Chen’s Group at UBC, as well as Gufeng, Yong, Lehui, Wei, Anthony, Yan, Kyle, Lin and Rui from Fang and Yeung’s Lab at Ames Laboratory. I am so grateful to have my lovely wife, Yang, with me in Vancouver through my study. It is you who made my every day enjoyable. Any place wherever we are together is our home. I would like to thank all my other friends as well, both in Vancouver and other places, for enriching my daily life. Finally, I want to say thank you to my parents for their endless encouragement and support. Although I am thousands miles away from home, I can strongly feel your unconditional love all the time. Your smile makes my every achievement more meaningful, and your voice makes me calm down when I am frustrated. It is you who made me who I am today, and I am proud of being a son of yours. The following pages are filled with my gratitude for having such wonderful parents, and I have been wishing you good health and with joy every day. I love you.  xxii  Dedication  To My Parents  xxiii  Chapter 1 : Introduction  1  1.1 Separation Science and Chemical Purification The development of separation science has been one of the most important contributing factors in modern chemistry and the life sciences. Without separation techniques, enzyme purification,1 DNA and protein sequencing,2-4 efficacy or metabolite studies in the pharmaceutical industry,5 and insights into many chemical and biological reactions6 would have been impossible. Separation systems that can analyze nanoliters of sample and less than femtomoles of analyte are remarkable. However, we should also notice that the need for such analytical technology is partly driven by the difficulties in obtaining appreciable quantities of pure substances, especially for those that only exist in complex matrices such as biological fluids. Although the development of highly sensitive technologies can potentially solve some problems on the analytical side, there are more challenges in the real world where an appreciable amount of biomolecules is needed for structural analysis and activity characterization. With the systems biology driven biopharmaceutical industry approaching maturity, the need for highly effective, large quantity purification technologies will significantly increase in the future. Since the first demonstration on plant pigments in the early twentieth century,7 several separation techniques based on different mechanisms have been well developed, such as liquid chromatography,8 gas chromatography,9 and capillary electrophoresis (CE).10 Because the separation in CE takes place in free solution with gentle separation conditions, the integrity of delicate or labile samples can be often preserved.11-14 Therefore, it has been used to separate species that cannot be resolved by other methods. The working principle of CE is introduced in the following section.  2  1.2 Capillary Electrophoresis and Analyte Migration Driving Forces The term electrophoresis was first introduced by Michaelis in 1909,15 and later, such electric field driven separation technique started to demonstrate its power in the separation of serum proteins.16 In the 1950s, gel electrophoresis17 and isoelectric focusing (IEF),18 were introduced, making electrophoresis a more useful tool for peptide and protein analysis. A couple of groups combined IEF with sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE) to achieve the two-dimensional separation.19,20 This approach was later fully developed by O’Farrell,21 making it a routine approach for protein separation, which is still widely used in research today. The most obvious disadvantage of conventional electrophoresis is the separation speed, which is limited by the poor dissipation of Joule heat generated by the current that flows through the conducting medium. In order to develop an electrophoresis system with a large surface to volume ratio for better heat dispersal, the capillary electrophoresis system was introduced.10,22 Performing the separation in a capillary also avoids the labour-intensive gel preparation processes and significantly lowers the sample amount needed for analysis. There are several kinds of driving forces for the analyte migration involved in a CE system. When a charged particle moves in an electric field, it feels the balanced forces of electrostatics (Fe) and drag (Fd):     F e  Q E  6 R v  F d  (1.1)  3  The electrophoretic mobility ( ep ) of a particle is defined as its equilibrium velocity per unit electric field strength:   v Q ep    E 6 R  (1.2)  where v is the velocity, E is the electric field, Q is the particle charge,  is the viscosity coefficient of the solution, and R represents the particle radius. From eq 1.2, it shows that the electrophoretic mobility is a characteristic of each individual ion, which is dependent on its charge to size ratio. Therefore, different analytes have distinctive electrophoretic velocities, which can be written as:   vep   ep E  (1.3)  and this discriminative velocity is the mechanism of separating analytes in CE. Another type of velocity is generated due to the surface charge on the capillary wall. For fused-silica capillaries, which are widely used in CE experiments now, the inner surface is covered with silanol groups (Si-OH). These surface silanol groups are deprotonated to negatively charged Si-O- groups at pH above 3. This negatively charged capillary wall attracts cationic species from the buffer solution, forming an electric double layer at the interface region (Figure 1.1). When an electric field is applied, the cations in the diffuse layer start to migrate toward the negative electrode, thereby causing the whole solution in the capillary to migrate with them. This phenomenon is called electroosmotic flow (EOF). The electroosmotic velocity (veo) is also proportional to the electric field strength:  4    veo  eo E  (1.4)  in which eo represents the electroosmotic mobility, determined by:  eo   Here,   4  (1.5)   is the dielectric constant of the fluid, and  is the zeta potential. In summary,  the net mobility of an analyte induced by the electric field is:   e   eo   ep  (1.6)  5  Figure 1.1 Structure of electrical double layer and electric potential profile from the capillary surface to the bulk solution.  6  In addition to the electric field, another driving force for the analyte migration is the hydrodynamic pressure. The pressure-induced velocity in a circular flowing channel can be predicted by the Poiseuille’s law:   2  pd vp  c 32l  (1.7)  Where p is the pressure difference between two ends of the channel, dc is the channel inner diameter, and l is the channel length.  1.3 Separation Resolution and Infinite Separation Resolution Theory The purpose of chromatography and capillary electrophoresis is to separate a sample mixture into a series of chromatographic peaks, each representing a single pure component. The separation ability is quantitatively described by the term of resolution (Rs). For two peaks, A and B, the separation resolution is defined as:  Rs   t r , B  tr , A 1  wB  wA  2    2tr wB  wA  (1.8)  where tr and w represent the retention time and peak width, respectively. A minimum resolution of 1.5 is required to completely separate the two components, and in this condition, the overlap is about 0.3%.23  7  Figure 1.2 Separration resollution illustrration at diffferent cond ditions. (a) aand (b): thee ( the sepaaration resoolution is in nfinite. separration resollution is finiite; (c) and (d):  A direct way w to increaase the amou unt of pure ssubstance reccovered from m a single separration processs is to increease the volu ume of the innjection mixtture plug. Hoowever, for a given n separation condition, th he retention time is not bbe affected bby the injectiion volume as lon ng as the staationary phasse has not beeen saturatedd. As a resultt, the increassed injectionn volum me broadenss the peak wiidth, reducin ng the separaation resoluttion, and the collected fractiion will havee a significan nt amount off impurities (Figure 1.2 (a) and (b)).. The resolu ution can bee improved by b lengthenin ng the separaation columnn. However,, the increeased separattion time is not n desirablee. If only on ne of two com mponents caan migrate thhrough a sepparation coluumn, while the other is comp pletely retain ned or even migrates m bacckward, the ttwo analytess can be 8  completely separated without overlap (Figure 1.2 (c)). This separation condition is referred to as infinite resolution. It has been demonstrated that infinite resolution for a pair of analytes can be achieved under certain conditions in chromatography, when one compound has very high affinity towards the stationary phase and the other has low affinity. The solution of the pure low affinity compound can be collected continuously at the outlet if the stationary phase is not saturated. In CE, the resolution can be improved by adding a hydrodynamic counter pressure from the outlet.24 The infinite resolution can be achieved relatively easily, at least in theory (Figure 1.3).25 For a charged particle moving in the free solution, the net velocity can be written as     v  v ep  v eo  v p  (1.9)   Here, electrophoretic velocity ( v ep ) is a discriminative velocity, which depends on the  electric field strength, and the size to charge ratio of the specific analyte. On the other    hand, electroosmotic velocity ( veo ) and pressure-induced velocity ( v p ) are nondiscriminative and have the same effect on all components. If these non-discriminative velocity parts can be carefully controlled, and precisely manipulated, the analytes with similar electrophoretic velocities can have reversed migration directions. In this condition, only the component that migrates faster can be collected at the outlet, and the slower analyte has the migration velocity towards the sample injection vial. The difference between their retention times is infinite, and the infinite separation resolution can be achieved.25 Therefore, the injection volume can be infinitely increased, even to  9  the co ontinuous saample injectiion, and the pure substannce can be ccontinuously collected from the outlet viial (Figure 1.2 1 (d)).  e of EO OF on resolu ution. The diirection and d magnitude of EOF Figure 1.3 The effect can be b adjusted to improvee the resoluttion. Reprinted from Bowser, B M. T.; T Bebault, G. M.; Pengg, X. J.; Chenn, D. D. Y. R Redefining ntial pathwaay to a unifieed separationn science, the seeparation facctor: A poten Electtrophoresis 1997, 1 18, 29 928. Copyrig ght (1997) wiith permissioon from Johhn Wiley andd Sons.  1.4 Some S Techniques for Continuou us Chemicaal Purificattions A num mber of reseearch groupss have develo oped methodds for perforrming fractioon collectionn in CE E.26,27 Thoug gh effective, it produces only small aamounts of ppurified sampple comp ponents due to limitation ns associated d with the sm mall dimensions of the caapillary colum mns. Therefo ore, a powerful and reliaable platform m that is capaable of purify fying 10  chemicals in a preparative fashion from complex mixtures is required. Arne Tiselius developed the technique of moving-boundary electrophoresis in 1937, and he was awarded the 1948 Nobel Prize in chemistry for separating colloids with this technique. Although this concept of continuous injection has been used in the chromatography separation process, also known as frontal analysis, it is not suitable for the chemical purification. In this section, I will introduce two other techniques enabling the fraction collection in a continuous manner, including continuous flow counterbalanced capillary electrophoresis (cFCCE), and continuous free flow electrophoresis (cFFE).  1.4.1 Continuous Flow Counterbalanced Capillary Electrophoresis (cFCCE) FCCE was first reported by Culbertson and Jorgenson for the analytical-scale separation of closely related species, including isotopomers of fluorescently derivatized amino acids.28,29 By applying a hydrodynamic counter-pressure in opposition to the direction of migration, the analytes could be kept on-column until the desired resolution was achieved. In order for this technique to be successful, very narrow internal diameter capillaries had to be used to prevent excessive peak broadening arising from the parabolic flow profile of the counter-pressure. Though originally intended for analytical purposes, Chankvetadze et al. demonstrated that this technique could also be used in a continuous fashion in normal-scale capillaries by recovering pure fractions from a binary mixture.30 The graphical representation of the separation process in cFCCE is shown in Figure 1.4. During the separation process, a hydrodynamic pressure is kept at the outlet buffer reservoir. The separation actually takes place in the injection inlet vial, and the  11  appliied pressure only allows the fastest component c too move into the separation column. Afterr a period off time, a porttion of the pu ure fastest coomponent caan be collectted from the outleet vial.  Figure 1.4 Schem matic repreesentation off cFCCE. (aa) The inletss positioned d in the ple vial whille the outlett is positioneed in a bufffer vial. (b) P Potential is applied to samp initia ate the separation. Simultaneously y, a counter--pressure iss applied at the outlet end of o the capilllary that ressults in the slower s migrration comp ponent having a net veloccity toward the inlet an nd the fasterr migrating componentt having a n net velocity towa ard the outleet. (c) At thee end of the run a portiion of the faaster migratting comp ponent has been b isolateed in the outtlet vial. Reprinted from McLaren, M D. G.; Chen, D. D D. Y. A quuantitative sstudy of conttinuous flow wcountterbalanced capillary eleectrophoresiss for samplee purificationn, Electrophooresis 2003,, 24, 2887. Copyriight (2003) with w permisssion from Johhn Wiley annd Sons.  12  Our group has reported several attempts to maximize the recovery of the collected pure components from cFCCE.31,32 By constructing an instrument with precise pressure control (±0.01 psi), closely migrating species could be purified. It has been determined that the judicious choice of a low conductivity background electrolyte and a large-bore capillary are of primary importance in optimizing both production rate and yield. In these studies, buffer depletion was found to be the major limitation in the amount of pure fractions recovered. Due to the application of the high voltage, the aqueous buffer solution is electrolyzed, and the reactions below occur:  Inlet(anodic vial) : 4OH   4e  2H 2 O  O2   pH   Outlet(cathodic vial) : 4H 2 O  4e  2H 2  4OH   pH   This electrolysis process results in a decreased pH value for the injection solution. For zwitterionic analytes such as amino acids, this decreasing pH leads to greater protonation of the amine functionalities, resulting in an increased electrophoretic mobility towards the cathode. Although several approaches, such as buffer replenishment and pressureramped cFCCE, have been developed to increase the yields, the recovery rate is still quite low.24,25 Another drawback of cFCCE is the low efficiency. As discussed above, only the fastest migration component can be collected from a single experiment. In order to collect the pure fraction of a non-fastest analyte, a two-step setup is necessary (Figure 1.5), significantly reducing the purification efficiency.  13  Figure 1.5 Purifying a non-fastest moving component in a mixture. In a group of analytes with electrophoretic mobilities of  ep ,1   ep ,4 , when a pressure is applied, both analytes 1 and 2 are allowed to migrate through the capillary. The net mobility of the analyte 2 is denoted as 1 in the first process. To obtain pure analyte 2, the polarity is reversed and pressure applied at the inlet vial. The net mobility of analyte 2 in this situation is illustrated by  2 . It should be noted that the slowest migrating component in a mixture can be obtained directly by using step 2 alone.  14  Reprinted from McLaren, D. G.; Chen, D. D. Y. Continuous electrophoretic purification of individual analytes from multicomponent mixture, Analytical Chemistry 2004, 76, 2298. Copyright (2004) with permission from American Chemical Soceity.  1.4.2 Continuous Free Flow Electrophoresis (cFFE)  Continuous free flow electrophoresis (cFFE) also allows the continuous acquisition of pure substances from a mixture, which has been developed and used for over fifty years.33,34 In cFFE, the sample is introduced as a constant stream into a chamber formed by two closely spaced plates. A continuous buffer flow moves in one direction through the chamber and this serves to sweep the sample from its introduction point toward a series of collection vials at the chamber exit. Sample components separate according to their electrophoretic velocities under an electric field that is applied perpendicularly to the buffer flow direction (Figure 1.5).35,36 Several instrumental designs have been reported for the practice of cFFE.37,38 As in CE, a variety of operating modes are available for cFFE, by simply changing the nature of the background electrolyte, such as free zone electrophoresis,39 chiral separations,40-43 and isoelectric focussing.18,19 Because the method development in cFFE is generally time-consuming and often costly, several attempts have been made to predict optimal conditions from analogous CE separations. Some of these attempts have proven to be successful,44-46 while other such efforts have demonstrated that CE runs fail to accurately predict the analyte behaviour in cFFE,37,47,48 suggesting that CE is only of limited use as a predictive tool in this regard. Another drawback of cFFE is that it is not well suited to the handling of complex mixtures. Because different sample bands are located at the exit boundary of the cFFE device, the separation resolution is not an infinite value. Therefore, purification of multi15  comp ponent samp ples is often complicated c by significaant overlap oof adjacent sample bandss, leadin ng to a decreeased purity in the colleccted fractionns.49,50  Figure 1.6 Illusttration of seeparation prrinciples of CE and cFF FE. (a) A seeparation in n capilllary electro ophoresis. Analytes A move through the capillarry according to their electrophoretic mobility m an nd electroosm motic flow. (b) A separration in freee-flow electrophoresis. Analytes move m down the t chip by p pressure drriven bufferr flow. Anallytes are defflected in sa ample stream ms based on n their electtrophoretic mobility. Reprinted from Turgeon, T R. T.; T Bowser, M. T. Microo free-flow eelectrophoresis: theory and applications a Analytical A and a Bioanalyytical Chemiistry 2009, 3394, 187. Copyright (2009 9) with perm mission from m Springer.  16  1.5 Research Objectives The purpose of our work is to develop a novel continuous chemical purification system with the capability of simultaneously purifying multiple components from a mixture with infinite resolution. The system was developed on a microfluidic platform, which has several important advantages. Moving the purification system into a chip format allows the use of wide, but shallow channels that give a large cross-sectional area but still have good heat dispersing properties. Moreover, the small dimensions of the chips shorten the analysis time significantly, and the lower applied voltage reduces the effect of buffer depletion. Because the separation resolution is infinite, the reduced separation column length does not harm the separation resolution. Variation of the micro-channel geometries provides the possibility of simultaneous collection of several pure substances, and the complete separation of collection vials for different analytes overcomes the bandbroadening problem. Such devices can be used for complete processing of samples and to obtain pure chemical species from complex mixtures. To achieve this goal, we developed a new generation of devices for the continuous chemical purification, based on the interactions of analyte with multiple types of driving forces. The two-dimensional electro-fluid-dynamic (2-D EFD) devices, in which both electric field and hydrodynamic pressure are simultaneously utilized in 2-D channel networks to drive mass transfer, provide better control on the analyte migration by simply adjusting the pressure magnitude. The analytes can either migrate with the medium driven by non-discriminative forces, such as pressure or electroosmosis, or migrate through the medium driven by discriminative forces from the applied electric field. These movements can exist simultaneously, giving a net migration determined by 17  the sum of velocity vectors of each movement. Mass conservation is the guiding principle for analyte distribution in intersections of connecting channels. However, in 2-D EFD devices, mass distribution is more complex. In order to understand the analytes’ transportation behaviour in multiple force fields, we studied the analyte distribution in EFD devices in Chapter 2, and discovered the effective volumetric flow rate conservation principle. This principle states that the analyte is distributed into different channels based on its effective volumetric flow rates in the channels downstream. It can be used to predict the analyte concentration in a channel, and provides a theoretical basis for investigating the mass transfer behaviour in EFD devices. In the following parts of the thesis (Chapter 3 and Chapter 4), we introduce two types of 2-D EFD devices for continuously obtaining pure substance from a twocomponent mixture and complex samples, respectively. The simultaneous application of multiple fields provides better manipulation on the objects’ migration and distribution in complex channel networks. Traditionally, Y-shaped microfluidic devices were used to introduce individual samples from interconnecting channels, and the mixing process has been studied extensively. With the strategically applied electric potential and hydrodynamic pressure, such mixing processes, which are spontaneous, can be reversed in the device with the same channel geometry. A continuous solution stream containing a mixture of two components can be separated into two channels, each containing a pure compound. By increasing the geometric complexity, more complex samples can be processed. Each component in the introduced mixture can be directed to enter its specific collection channel, without any contamination.  18  Chapter 5 compares different sample injection methods theoretically. The hydrodynamic injection approach is considered to be superior to the electrokinetic injection method in the continuous chemical purification process by providing faster sample processing, and is more resistant to the fluctuating EOF. In addition, the buffer depletion problem can be avoided. The predictable nature and ease of operation of this technique could lead to a new generation of purification devices to serve the needs of biomedical research and other commercial and academic activities.  19  Chapter 2 : Analyte Distribution at Channel Intersections of Electro-Fluid-Dynamic Devices  20  2.1 Introduction Microfluidic devices have demonstrated their usefulness for over two decades.51-54 The channel geometry utilized in various applications includes one-dimensional single channels, Y-shaped or cross-shaped intersecting channels, and highly complex channel networks.55,56 These platforms have been used in a wide variety of disciplines, including clinical diagnostics57,58 and organic synthesis.59 Electro-fluid-dynamic (EFD) devices, utilize both electric field and hydrodynamic pressure as the driving force, providing a better control on the analyte movement, and they have been used for particle separation,60 and continuous chemical purification.61,62 Many of these applications are based on different migration velocities of charged components in channels joining at an intersection. When molecules are present in a moving medium of an EFD device, they could either move with the medium driven by non-discriminative forces such as pressure or electroosmosis, or migrate through the medium driven by the discriminative force from the applied electric field. These two types of movement could also happen simultaneously, giving a net migration determined by the sum of the velocity vectors of each movement. While differential migration of analytes in a single channel for chemical separation is well understood, separation using two-dimensional channel geometries, and the driving forces for analytes’ distribution into different channels is not understood. Mass conservation is the guiding principle for the analyte distribution at channel intersections in microfluidic devices. It states that the amount of a component moving towards the intersection equals to the amount emerging from it, as long as no adsorption  21  or chemical reactions occur. This principle has been widely used in the devices where analyte migration is mainly driven by an applied electric field, as well as in the EFD devices, where multiple fields can be applied simultaneously on the same channel network. This chapter introduces another type of conservation, the conservation of the effective volumetric flow rate at channel intersections, when the conductivity of the solution in the intersecting channels is maintained constant. This principle provides an additional criterion to describe analyte migration in channels connecting to a common intersection, and to predict how analyte is distributed into individual channels in the channel network of EFD devices. The theoretical basis of this new principle is discussed and its potential use in conjunction with the mass conservation principle to predict the analyte concentration is demonstrated. EFD devices with different geometries are used to demonstrate the validity of these equations.  2.2 Experimental Section The EFD devices shown in Figure 2.1(a) and (b) were fabricated on soda lime glass (Nanofilm, Westlake Village, CA) using the standard photolithographic patterning and wet chemical etching method.63 The widths of the main and lateral channels for the Yshaped EFD device (Figure 2.1a) on the film mask were 80 m and 40 m, respectively. For the devices illustrated in Figure 2.1b, all channels have a width of 20 m. The positive potentials were provided by high-voltage power supplies (SL150, Spellman High Voltage Electrionics, Hauppage, NY), and the pressure-induced flow velocity was controlled through a syringe pump (Harvard Apparatus, Holliston, MA). During the  22  experiment, the sample solution was introduced through the reservoirs drilled on the chip. A Nikon Eclipse 80i microscope was used in this study, and the fluorescence signals were recorded by a Photometrics Evolve camera (Tucson, AZ). The optical band-pass filters were from Thorlabs (Newton, NJ), and their full width at half-maximum (FWHM) was 10 nm. Fluorescent particles have been reported to be used for the flow velocity measurement in microfluidic channels.64 The sample used in this study was a 2% (w/v), 2.0 m diameter carboxylate-modified fluorescent FluoSpheres beads solution (Invitrogen, Carlsbad, CA). The sample was diluted 1000 times and sonicated for 15 min before loading into the EFD device.  23  Figure 2.1 The 2-D EFD devices used in this study. (a) Y-shaped device. The lengths of the main channel CF and lateral channels AC and BC are 3.6 cm and 3.0 cm respectively. The positive potentials of 200 V and 150 V were applied at point A and B. Point E is grounded and the channel DE has the length of 1.5 cm. A volumetric flow rate of 0.020 L/min was controlled at point F. (b) Cross-shaped device. Channels AD, BD and CD have the same length of 0.6 cm, and a volumetric flow rate of 0.250 L/min was controlled through the 4.4 cm long channel DE. The  24  positive potentials of 500 V and 200 V were applied at point C and B, and point A was grounded. Intersection C in (a) and intersection D in (b) are monitored. (c) Flow directions of microbeads migrating through the intersection of the Y shaped channel structure. (d) Flow directions of microbeads migrating through the intersection of the cross-shaped channel structure. The flow directions were determined by the applied electric fields and pressure.  2.3 Theoretical Basis In microfluidic devices, two or more channels are often joined together by an intersection, forming complex channel networks. The conductivity of the solution in intersecting channels can be considered uniform (  i   ) if a relatively high concentration of buffer solution is used throughout the device, or the analyte is present at a quite low concentration. From Kirchhoff’s law, at the junction point of n channels ( n  2 ), the total current is zero, which can be written as: n  J S  i i  0  (2.1)  i 1  where Ji is the current density in each channel, and Si represents the cross sectional area for the specific channel. In this study, the fluid moving inside the microfluidic channel is the current carrying conductor. Therefore, the direction of current density, as well as the electric field vector discussed later, is along the channel length. For the derivation convenience, these vectors and velocity vectors are all expressed as scalars, and the  25  values are defined as positive when their directions are toward the intersection. If Ohm’s Law ( J   E ) is used in eq 2.1, it becomes: n  n  n  n  i 1  i 1  i 1  i 1   J i Si    i Ei Si    Ei Si    Ei Si 0  (2.2)  Since conductivity is a non-zero constant, eq 2.2 can be further rearranged to: n  E S i 1  i  i  0  (2.3)  The fluid in the EFD device is assumed to be incompressible, so the relationship of the fluid velocity can be written as: n  v i 1  f ,i  Si  0  (2.4)  where vf,i is the fluid velocity in each channel. The motion of a charged particle or molecule that is moving in the channel of an EFD device is driven by both the electric field and the pressure induced fluid migration. Normally, the fluid flow within the microchannel is laminar due to its small Reynolds number.65 The net velocity of an ion in a channel can be written as:  vi  veo ,i  vep ,i  v p ,i  Ei ep  v f ,i , where the discriminative electrophoretic velocity (vep) is proportional to the electrophoretic mobility (ep). The fluid velocity vf,i is the sum of two bulk flow parts, the pressure-induced velocity (vp ) and the electroosmotic velocity (veo). From eq 2.3 and 2.4, the electric field and the fluid velocity in a channel are  26  n  n  Ei      j 1, j i  EjS j  Si  and v f ,i      vf , jSj  j1, ji  , respectively. The net velocity of a charged  Si  component in any certain channel can be rewritten as:  vi  Ei ep  v f ,i n      j1, ji  Si  1  Si   E j ep S j  1 Si  n    j1, ji    n      j1, ji  v f , jS j  Si  S j E j ep  v f , j    (2.5)  n    v jS j  j1, ji  This equation can be rearranged to obtain the following: n  v S  i i  0  (2.6)  i 1  Equation 2.6 describes the general relationship of the migration velocity for charged components in a channel intersection of an EFD device, showing the effective volumetric flow rate conservation principle. There is no specific requirement for direction or magnitude of the applied pressure or electric voltages, nor the geometry or number of the channels. At the channel junction of an EFD device, where the hydrodynamic pressure and the electric field may be independently or simultaneously applied, the sum of term “viSi” is always zero. This term has the unit of m3/s, and can be considered as the “effective” volumetric flow rate, because it describes the volume traveled by the molecules per unit time, but not the bulk solution volumetric flow rate.  27  The mass conservation principle indicates that the amount of the analyte moving into an intersection should equal the amount emerging from it during a given time period: n  v c S t  0 i1  i i i  (2.7)  where ci is the analyte concentration, and t represents the time period. The term of viciSi is defined as the molecular flux, and it also conserves at the channel intersection: n  v c S i 1  i i  i  0  (2.8)  Here, the molecular flux has the unit of mol/s, and represents the amount of the analyte moving toward the intersection per unit time. It can be calculated by multiplying the effective volumetric flow rate with the analyte concentration. The conservations of both molecular flux and effective volumetric flow rate can be used together to predict the analyte concentration in a channel, which will be discussed in Section 2.4.2.  2.4 Results and Discussion 2.4.1 Experimental Verifications  In order to verify if this theoretical prediction is valid in real situations, we utilized two types of commonly used EFD devices to demonstrate the flow rate relationship in the three (Figure 2.1(a)) and four channel (Figure 2.1(b)) intersections. Y-shaped microfluidic devices have been used to introduce samples from interconnecting channels and to efficiently mix different solutions into a single channel.66  28  We have also demonstrated that a Y-shaped device can be used to reverse the mixing process when appropriate pressure and electric potential were applied, which will be discussed in Chapter 3. The channel cross section of glass chips fabricated by the wet etching method does not provide well defined shapes.67,68 Thus, the cross-sectional area ratio for the main and lateral channels of the Y-shaped device was estimated using the ratio of channel widths at the image plane. For main and lateral channels with widths of 120.1 m and 65.9 m, respectively, this ratio is 1.82. Based on eq 2.6,  v1S1  v2 S2  v3S3  v1 S1  v2 S2  v3 S3  0, and S2  S3 as shown in Figure 2.1c, the ratio of  v2  v3  : v1 should be 1.82 as well. The velocities of 100 fluorescent microbeads in three channels of the Y-shaped EFD device were measured, and the results are listed in Table 2.1. The net flow directions for the microbeads in each channel were marked in Figure 2.2 (a). Figure 2.2 (b) shows the image of the microbeads migration in the Y shaped EFD device. The microbeads had the greatest velocity in Channel 2, interpreted via the elongation of the image recorded due to the movement of the particle within the prescribed exposure time. The ratio of the average velocity of individual particles in Channel 2 plus that in Channel 3 vs. the average velocity of particles in Channel 1 agreed well with the predicted value, as shown in the last column of Table 2.1.  29  Figure 2.2 Velocity measurement in the Y shaped device. (a) Flow directions of microbeads migrating through the intersection of the Y shaped channel structure. (b) An image of microbeads flowing in all three channels with a fixed exposure time. The longer image pattern is the result of the faster migration velocity.  The cross-shaped microdevice, illustrated in Figure 2.1(b), was widely used for on-chip electrophoresis separation.69 Because the four channels have the same width on the film mask, their cross sectional areas are considered to be the same after the wet etching and wafer bonding fabrication processes. The net velocities of 100 fluorescent microbeads migrating in four channels were measured as well, when hydrodynamic pressure and electric fields were simultaneously applied. The net flow directions for the microbeads in each channel were marked in Figure 2.1(d). The determined result matched with the predicted ratio in this geometry as well (Table 2.1).  30  From the result listed in Table 2.1, we can conclude that the experimental velocity ratios agree well with those predicted by eq 2.6. Although the flow rate of the microbeads was different in each channel, the sum of the products of net velocity and cross sectional area was equal to zero at both three-channel and four-channel intersections in EFD devices.  31  Table 2.1 Velocity of microbeads in individual channels  Device  v1  v2  v3  v4  Y Intersection (m/s)  47.9  3.3  60.5  2.6  26.3  1.8  N/A  Cross Intersection (mm/s)  2.14  0.47 1.58  0.27 0.62  0.17 0.14  0.05 v1  v4  Ratio determined v2  v3 v1  v2  v3  Ratio predicted   1.81  0.13  v2  v3   1.04  0.28  v1  v4  v1  v2  v3   1.82   1.00  32  2.4.2 Applications n  The molecular flux conservation described in eq 2.8 (  vi ci Si  0 ) can only provide i 1  information about the cross sectional area Si and the conjugate variable vi ci , but not vi or ci individually. There may be unlimited possible combinations of flow rates and concentrations that can satisfy this equation. The effective volumetric flow rate balance equation (eq 2.6) provides the relationship of net velocities with the channel cross sectional areas, under the condition of the uniform conductivity in all channels joined at the intersection. If these two equations are used simultaneously, the analyte concentration in a channel can be obtained. Based on eq 2.6 and eq 2.8, we can have the relationship of n  v S    vjS j  i i j 1, j i   n v c S    v jc j S j  i i i j 1, j i  (2.9)  Thus, the concentration can be calculated:  vcS ci  i i i  vi Si  n      j 1, j  i n      n  v jc j S j  j 1, j  i   vjS j    j 1, j  i n    v jc j S j  j 1, j  i  (2.10)  vjS j  Eq 2.10 can be used to determine the analyte concentration in a channel where the concentration and net velocity of the analyte is difficult to measure directly, or the properties of other channels are known.  33  Because microbeads were used as the analyte in this work, the concentration is equivalent to the number of particles present in the channels. A video taken during the experiment showed that for 100 particles flowing into the intersection from Channel 1 of the Y-shaped device, 78 entered into Channel 2, and 22 entered into Channel 3, almost exactly as what is predicted by the theory, as shown below. For example, the concentration of particles in Channel 3 of the can be predicted:  c3   v3c3 S3 v3 S3    v1c1S1  v2 c2 S2 v1S1  v2 S 2    v1c1S1  v2 c2 S 2 v1S1  v2 S 2     n p ,1 / t  n p ,2 / t v1S1  v2 S 2  (2.11)  1 n p ,1  n p ,2 tS 2 1.82v1  v2    100   78  1 s/ m tS 2 1.82  47.9   60.5     0.825 s/ m tS 2  where np represents the particle number in a channel. The experimentally determined concentration in Channel 3 is:  c3   n p ,3 tv3 S3    1 n p ,3 1  22  0.836  s/ m= s/ m tS2 v3 tS2  26.3 tS2  (2.12)  which matches well with the predicted result in eq 2.11.  34  Similarly, in the case of the cross-shaped intersection, a video showed that of 100 particles entering into the intersection (94 from Channel 1 and 6 from Channel 4), 64 and 36 particles entered Channel 2 and Channel 3, respectively. The concentration in Channel 2 can be predicted:  c2   v2 c2 S 2 v2 S 2    v1c1S1  v3c3 S3  v4 c4 S4 v1S1  v3 S3  v4 S 4    v1c1S1  v3c3 S3  v4 c4 S4 v1S1  v2 S1  v3 S1    1 n p ,1 / t  n p ,3 / t  n p ,4 / t S1 v1  v3  v4    1 n p ,1  n p ,3  n p ,4 tS1 v1  v3  n4    94   36   4 1 s/mm tS1 2.14   0.62   0.14    37.4 s/mm tS 2  (2.13)  The experimental determined concentration in this channel is  c2   n p ,2 tv2 S2    1 n p ,2 1  64  40.5  s/mm= s/mm tS1 v2 tS2  1.58  tS2  (2.14)  2.4.3 Applicable Conditions  The new principle introduced in this chapter (eq 2.6) can be used to describe the analyte distribution in a non-uniform channel. At different positions of the channel with distinct cross sectional areas, the effective volumetric flow rate is conserved, which is a special  35  condition of eq 2.6, when n  2 (Figure 2.3). The intersection studied here can be either a conventional channel junction, or a more complex channel structure.  Figure 2.3 The conservation of the effective volumetric flow rate for a non-uniform channel.  Although the discussion in this chapter is focused on 2-D microchannel networks, the conservation of the effective volumetric flow rate is not limited to channels located on the same plane. The theoretical derivation is generally applicable for more complex 3D channel networks. The only requirement for this conservation principle is that the conductivity is uniform in all channels joined together. This assumption is applicable when a relatively high concentration of buffer is used (capillary electrophoresis on chip, or continuous chemical purification) or the concentration of analyte is very low (single particle or single molecule study). If the conductivity for the solutions in all channels cannot be assumed uniform, eq 2.6 must be modified. Equation 2.3 can be rewritten as  n   E S i 1  i  i i   0 and eq 2.5 changes  to:  36  vi  Ei  ep  v f ,i n    j 1, j  i      i Si 1 Si  n   j E j S j  ep     j 1, j  i  vf , jS j  Si  (2.15)   j   E j S j ep  v f , j S j  j 1, j  i   i  n    Thus, eq 2.6 can be modified:   j   E j S j ep  v f , j S j  j 1, j  i   i  n  j    Ei ep  v f ,i  Si    E j S j ep  v f , j S j  j 1, j  i   i  n       i Ei ep Si  v f ,i Si     j E j S j ep  v f , j S j   i  j 1, j i   i  n      i Ei Si ep  v f ,i Si  i 1   1  0 vi Si   n    (2.16)  where  1 is the conductivity in any specific channel. However, because in most cases the differing conductivities can’t be maintained when the channels are connected through the same intersection, it is difficult to make predictions unless the gradual changes in conductivities are taken into account.  2.5 Conclusions  The effective volumetric flow rate is conserved at channel intersections of EFD devices when the conductivity in channels is assumed uniform. This principle and the molecular flux conservation principle can be used together to determine the analyte concentration at 37  any channel, which is difficult to predict or measure directly in some cases. These relationships predict that the distribution of analyte at the channel intersections is determined by the migration behaviour of the species in each individual channel because the sum of the effective volumetric flow rates for all channels must be zero. With the proper arrangement of electric fields and pressure in each channel, analyte entering the channel intersection can be directed to enter into a predetermined channel, facilitating continuous processing of sample mixtures into pure components or simplified fractions. The application of this principle on the continuous chemical purification platform design will be shown in following chapters.  38  Chapter 3 : Reverse of Mixing Process: Continuous Chemical Purification with a Y-Shaped Two-Dimensional Electro-FluidDynamic Device  39  3.1 Introduction Column separation techniques such as chromatography and capillary electrophoresis (CE) can separate a mixture into zones of pure compounds according to their differential migration behaviour when interacting with a stationary phase in a flowing stream8 or in an electric field,10,70 or when both phenomena occur at the same time.71 Two-dimensional gel electrophoresis separates compounds into different locations along two orthogonal directions on a flat surface when the sample solution is loaded on a slab gel.72,73 However, most currently used mainstream separation techniques require the loading of a small sample amount to get satisfactory separation resolution. Continuous free flow electrophoresis (cFFE) is another two-dimensional separation method that is capable of continuously processing a mixture and separating different components into streams in a free flowing liquid continuum so that individual components can be collected in different locations downstream.74,75 However, because the separation mechanism is still based on one-dimensional differential migration in an electric field, resolution has been a major issue when it is used to separate similar molecules. Microfluidic devices have been used to introduce samples from interconnecting channels, and to efficiently mix different solutions into a single channel,66 which is a spontaneous process with a net increase of entropy. However, the reverse of the mixing process is usually not possible unless certain conditions are met. This chapter demonstrates that when a Y-shaped two-dimensional electro-fluid-dynamic (2-D EFD) device is used for separation, a mixture can be separated into two flow channels, and both components can be collected simultaneously in two isolated outlets. When electric fields and pressure are strategically applied in the interconnecting channels of an EFD 40  device, the conditions for reversing the mixing processes can be calculated by combining electric field and fluid dynamic calculations with the mass balance equation. If the pressure and electric potential at various inlets and outlets satisfy these predetermined conditions, the reverse of a mixing process is observed. Investigation of the mass transfer theory shows that critical boundary values (CBVs) are independent of the cross-sectional area ratio of the main channel and lateral channels. Devices designed according to these basic physicochemical principles can be used for complete processing of samples and to obtain pure chemical species from complex mixtures.  41  3.2 Experimen E tal Section n  Figure 3.1 Schem matics of th he setup: (a) channel geeometry of tthe microflu ulidic EFD devicce and (b) a schematic of the devicce made from m a 2.54 cm m × 7.62 cm m PDMS chip..  442  Rhodamine 110 (Exciton, Dayton OH, ab ,max  506 nm; em ,max  532 nm ), and ethidium bromide (Invitrogen, Eugene, OR, ab ,max  510 nm; em ,max  595 nm ) solutions at a concentration of 10 mg/mL for each were prepared in the background electrolyte (BGE, 160 mM borate, pH 9.0). The electrophoretic mobilities of these two dyes at the experimental conditions were determined on a PA800 plus capillary electrophoresis system (Beckman Coulter Inc., Brea CA), which are 1.72  10 8 m 2 /V  s and 0.30  10 8 m 2 /V  s , respectively. The EFD devices shown in Figure 3.1 were  fabricated with polydimethylsiloxane (PDMS) (Sylard184, Dow Coring, Midland MI) according to established protocols.76 The width of the lateral channels (AC, BC) and the main channel (CD) were 50 and 100 m, respectively. The depth of all PDMS channels was 200 m. The positive potentials at points A and B (1000 V and 900 V, respectively) were applied by high-voltage power supplies (SL150, Spellman High Voltage Electronics, Hauppage, NY), and the pressure-induced velocity was precisely controlled through a syringe pump (Harvard Apparatus, Holliston, MA) to achieve the required conditions. Point E is grounded through an electric cable. During the experiment, the analyte mixture was introduced through Vial A, while vials B and E were filled with BGE. A Nikon Eclipse 80i microscope was used in this study and the fluorescence signals were recorded by an Andor EM CCD camera (South Windsor, CT). The optical band pass filters used were from Thorlabs (Newton, NJ) and their full width at halfmaximum (FWHM) were 10 nm. When it was necessary to monitor the migration behaviours of two analytes simultaneously, the microscope was operated at two wavelengths using a MAG Biosystems dual-view filter (Optical in Sights, Tucson, AZ)  43  with a 565 nm diichroic filter. A 530 nm filter f was ussed for rhodaamine 110, aand a 600 nm m filter was used fo or ethidium bromide b (Fig gure 3.2, 3.3).  Figure 3.2 Schem matics of th he optical im maging systeem with the dual-view ffilter.  444  Figure 3.3 Demonstration of dye images under the duel-view microscope. (a) The device is filled with pure rhodamine 110. (b) The device is filled with pure ethidium bromide. (c) The device is filled with the mixture of rhodamine 110 and ethidium bromide.  3.3 Theoretical Simulation 3.3.1 Derivation of Some Equations  In order to simulate the analyte distribution in the EFD device, the electric field distribution in the conductive media needs to be calculated first. As long as the concentrations of analytes are much lower than that of the background electrolyte (BGE), the effect of analytes on the electric potential distribution could be omitted. Thus, the electric field does not vary with the analytes’ migration and counterbalance pressure. In a low frequency electrostatic system, the point form of Ohm's law states that:    J  E  Je  (3.1)  45    where J is the current density (current per unit area), is the conductivity of the media,   E is the electric field at the point and J e is an externally generated current density, e.g.  charge generated by the electrochemical reaction. Equation 3.1 can be rearranged to:     J   (V  J e )  (3.2)  The equation of continuity indicates that:      J   e  Qj t  (3.3)  where e is the free charge density and Qj is the current source. When the current source is zero, eq 3.3 can be derived to:    (V  J e )  0  (3.4)   If there is no externally generated current ( J e  0 ), this equation becomes the Laplace  equation:  2V  0  (3.5)  which will be used in the electric field numerical modeling. After solving the electric field distribution, the fluid velocity field was then calculated by the simplified Navier-Stokes equation.77 For a fluid particle moving in a velocity field in 3-D Cartesian coordinate system, at time t, it is at the position (x, y, z) and has a velocity corresponding to the velocity field at that point in space at time t:  46    v particle,t  v (x, y, z,t)  (3.6)  At time t+dt, the particle has moved to a new position, with coordinates (x+dx, y+dy, z+dz), and has a velocity given by:   v particle,tdt  v (x  dx, y  dy, z  dz,t  dt)  (3.7)   Thus, d v particle , the change in the velocity of the particle is:       v particle v particle v particle v particle d v particle  dx  dy  dz  dt x y z t  (3.8)  The total acceleration of the particle is given by:   d v particle   a particle dt      v particle dx  v particle dy  v particle dz  v particle     x dt y dt z dt t      v particle  v particle  v particle  v particle  vx  vy  vz  x y z t  (3.9)  Applying Newton's second law to an infinitesimal fluid particle of mass dm:         v particle v particle v particle v particle  dv particle  dm  vx  vy  vz  d F  dm     t  dt x y z   (3.10)    where dF is the net force applied to this fluid particle. To solve the velocity field at each    point, the suitable formulation for the force dF should be obtained. The forces acting on a fluid element can be classified as body forces, which is normally the gravity, and surface forces. Surface forces include both normal forces (with the direction  47  perpendicular to the surface), which are caused by pressure, and shear forces (with the direction parallel to the surface), which is caused by the fluid fiction.  Figure 3.4 Pressure-caused normal surface force in the x direction on an element of fluid.  Considering the x component of the pressure-caused surface force acting on a rectangular fluid element (Figure 3.4), the forces on two opposite surfaces are pdydz p   and  p  dx  dydz , respectively, where p is the local pressure. Therefore, the x    pressure-induced net surface force is p  p  dFp , x  pdydz   p  dx  dydz   dxdydz x  x   (3.11)  48  In our solution system, the shear force should be considered as well. Here, we assume the fluid in the system is a Newtonian fluid, where the viscosity is a constant. The component of this force for a unit volume fluid in the x direction is 2 vx , where  is the viscosity coefficient. When the force of gravity is the only body force, the net force in the x direction is: dFx   gx dxdydz   p dxdydz  2 vx dxdydz x  (3.12)  where is the liquid density, and g represents the gravitational acceleration. Similarly, we can derive the expressions for the y and z components of the force:  dFy   g y dxdydz   p dxdydz   2 v y dxdydz y  p dFz   g z dxdydz  dxdydz   2 v z dxdydz z  (3.13)  Substituting these expressions for the force components into the Newton's second law motion equation for the fluid element and dividing both sides by dxdydz gives:  gx    v v v v  p   2 v x    v x x  v y x  v z x  x  y z t  x  x  gy    v v v v  p   2 v y    v x y  v y y  v z y  y  y z t  y  x  gz    v v v v  p   2 v x    v x z  v y z  v z z  z  y z t  z  x  (3.14)  These equations of motion are Navier-Stokes equations. Converting these equations to a vector expression:       v particle    v particle   v particle   g  p   2 v particle t      (3.15)  The Reynolds number of the fluid in a microfluidic channel is much smaller than 1. Therefore, the flow here can be considered the Stokes flow, in which the inertial force 49     v particle (   v particle   v particle ) is negligible. If we ignore the body force effect as well, t      the equation to solve the fluid flow field here is:  p  v particle  0    (3.16)    where v particle can be written as v f to represent the net fluid velocity, which will be used in the simulation process. The conservation of mass shows:      v f  0 t      (3.17)  In this case, the fluid is incompressible. Thus,  is a constant and eq 3.17 can be simplified to:  v f  0  (3.18)  This equation will be used together with the simplified Navier-Stokes equations (eq 3.16) to solve the fluid field. The last equation used in the simulation process is the mass balance equation:78,79  c    (  Dc )  v c  r t  (3.19)  where c is the concentration, D is the diffusion coefficient, r is the chemical reaction rate    for the studied species, and v is the sum of all direct displacement velocities of the analyte, including electrophoretic, electroosmotic, and pressure induced velocity:  50        v  v ep  v eo  v p  v ep  v f  (3.20)    Here, v f has been determined by the Navier-Stokes equation and vep is the  electrophoretic velocity:   v ep   ep E  (3.21)      where E has been determined in the earlier study using E  V . In this system, no reaction occurs ( r  0 ), therefore the mass transport equation becomes:   c    (  Dc )  v f   ep E  c  0 t      (3.22)  3.3.2 Numerical Modeling  The migration behaviour of analytes in a 2-D EFD device can be calculated based on the three equations derived in Section 3.3.1(eq 3.5, eq 3.17, eq 3.18, eq 3.22) using finiteelement-scheme simulation software, COMSOL Multiphysics 3.5a (COMSOL Inc., Los Angeles, CA). The modeling procedure with this program includes creating a virtual device, defining parameters, meshing, solving differential equations, and post-processing data presentation. In our case, the 3-D models with the exact EFD device dimensions were created. The motion of charged molecules in the EFD device is driven by the simulated electric field and hydrodynamic fluid field. Both the electric and fluid fields were calculated before solving the mass balance equation, through which the concentration distribution for analytes can be calculated either in steady state, or in a time-dependent manner. The main procedural flow chart of the simulation is illustrated in 51  Figure 3.5.  52  Figure 3.5 Flow chart for the simulation process  53  The electric field distributions in the conducing channels of EFD devices were calculated by solving the Laplace Equation (  2V  0 ) in the Conductive Media DC (emdc) module, and the boundary condition was set as either the applied electric potential    for open boundaries ( V  V0 ), or electrical insulation for channel walls ( n V  0 ),    where the unit vector n has the direction perpendicular to the boundary. When the concentrations of the analytes are much lower than that of the background electrolyte (BGE), the effect of analytes on the electric field distribution could be omitted. Thus the electric field distribution for a given device mainly depends on the applied potential and the channel geometry. With the finite-element-method simulation, the electrical potential (V) at any point along the EFD device can be calculated by solving the Laplace Equation,    and the electric field strength is determined by the equation E  V , as shown in Figure 3.6(a). These results would be used in the calculation process discussed below. The fluid velocity field of the solution in channels can be described by the  simplified Navier-Stokes equation p   2 v f  0 , where p is the pressure,  is the  viscosity coefficient, and v f represents the fluid velocity vector at any point in the fluid  field. The fluid is assumed to be incompressible and the principle of volume conservation  gives the relationship of   v f  0 , which is used in conjunction with the Navier-Stokes  Equation to solve for the pressure and the fluid velocity field. The boundary condition for fluid velocity at the channel wall is set as the electroosmotic flow (EOF) velocity   ( v f   eo E ), where the local electric field value has been determined from the previous    part. Other boundaries conditions are set either as a controlled velocity ( v f  v 0 ), or as  54  open boundaries to atmosphere ( p  p0 ). Through numerical modeling in the Stokes Flow (mmglf) module, the velocity vector and pressure at each point can be calculated. Figure 3.6(b) demonstrates a simulated fluid velocity field in the microdevice when a pressure is applied against the electric field. The migration behaviour of the analytes in the EFD devices is determined by numerically solving the mass balance equation in either steady state format   v  f    ep E c      Dc   0 , or the time dependent format     c   v f   ep E   c      Dc   0 , in the Electrokinetic Flow (chekf) module. Here, t        the values of v f and E are obtained from the previous calculation for the electric field and fluid velocity field. The boundary condition for the channel wall is set by    n   Dc  ep Ec  v f c  0 . At the sample inlet and outlet, the boundaries are set as        constant concentration ( c  c0 ) or convective flux ( n    D  c   0 ). With this final step of simulation, the analyte concentration and its variation with time at any location can be calculated to determine the analyte migration behavior, as shown in Figure 3.6(c).  55  Figure 3.6 Simulated results of the fork area (around point C) obtained from COMSOL Multiphysics. (a) Electric field distribution under the experimental conditions. (b) An example of fluid velocity field when a pressure is applied against the electric field in the direction from D to C. (c) An example of concentration distribution of the analyte. The concentration of the analyte from high to low is depicted by the colour scheme of red to blue.  56  3.4 Theoretical Basis As discussed in Chapter 2, the steady-state velocity of a charged particle that is moving         in the channel can be written as v  v ep  v eo  v p  ep E  eo E  v p , where  electrophoretic velocity ( v ep ) is discriminative and determined by its electrophoretic  mobility (  ep ), which is an intrinsic property for a particular analyte. On the other hand,    the electroosmotic velocity ( v eo ) and pressure-induced velocity ( v p ) are nondiscriminative and affect all components equally. With careful control of nondiscriminative velocities, analytes with similar ep can be made to migrate in opposite directions. The limiting factor in this case is the resolution of the pressure control system, which can be highly precise when a syringe pump is used. The syringe pump utilized in this work has a resolution of 0.001 L/min (1 nL/min). With a flow rate of 300 nL/min in the channels, the analytes pair with the electrophoretic mobility difference of  2 ~ 4 1010 m2 /V  s could be made to move in reverse directions. For the EFD device shown in Figure 3.1, lateral channels AC and BC are symmetrical about the main channel, and the width of the main channel (CD) is twice that of lateral channels. If the fluid in the device is uncompressible, the pressure-induced velocity in different channels has the relationship of:    v p ,CD SCD  v p , AC S AC  v p , BC S BC  (3.23)  57  With the cross-sectional area relationship of SCD  2S AC  2S BC , eq 3.23 can be rewritten as:    v p , AC  v p , BC  v p ,CD  (3.24)  Therefore the value of pressure-induced velocity is consistent in Channel AC, BC and  CD, which is expressed as v p in the discussion below.  The electric field strengths in the three channels have the relationship of    E CD SCD  E AC S AC  E BC S BC  (3.25)  With the cross-sectional area relationship of SCD  2 S AC  2 S BC , eq 3.25 can be converted to   1  E CD  E AC  E BC 2      (3.26)  The electric field strength in the main channel CD is the average of the values in the two lateral channels. In this experiment, the potential applied in Vial A is higher than that in Vial B, so that the electric field strength in AC is higher than CD, which is in turn higher than that in BC.  58  Figure 3.7 Behaviour of one analyte. (a) Simulated concentration distribution of R110 when (1) the pressure in the direction from D to C is high, preventing R110 from entering the device, (2) the counter pressure is adjusted so that R110 flows along ACB, (3) the pressure is adjusted so that R110 flows along both ACB and ACDE directions, and (4) the pressure is so small that all R110 flows along ACDE direction. The position of E is not shown in this figure. It is where the sample is collected in Condition 4, and its position is shown in Figure 3.1(a). The concentration of the analyte from high to low is depicted by the colour scheme of red to blue. (b) Experimental verification using R110. The fluorescence images of the fork of ACB were recorded using a CCD camera. (c) The boundary conditions for R110 to be localized in Vial A, moving along ACB, moving along both ACB and ACDE, and moving along ACDE only.  59  Figure 3.7(a) shows the simulated concentration distribution of a single analyte in the EFD device as the pressure-induced velocity is varied from high (1) to low (4). The direction of the steady-state analyte velocity in the channels is indicated as well. When the pressure against the electric field is high, the steady-state velocity of the analyte in  any channel of AC, BC and CD has the same direction as v p . In this case, the analyte  stays in the injection vial A and never migrates into AC or any other channel, as  illustrated in the first case (a1) in Figure 3.7. As the magnitude of v p decreases, the  steady-state velocity of the analyte reverses in channel AB first, forcing all of the analyte to migrate through point C to the collection vial B, as demonstrated in the second case  (a2) in Figure 3.7. In Case 3 indicated in Figure 3.7 (a), v p decreases to be small enough  to let the analyte reach point D, but at the same time not so small that it would stop the flow of the analyte in the C-B direction. When the pressure is very low, as in Figure 3.7 (a4), all of the analyte migrates along the direction of electric field, from injection vial A, through point C and D, towards the collection vial E, because the steady-state velocity of  the analyte in any channel of AC, BC and CD has the opposite direction compared to v p .   The values of v p for these four migration cases in the EFD device are indicated  in Figure 3.7(c). Here, the conditions of X, Y, and Z are defined as “critical boundary conditions (CBCs)”, at which the steady-state velocity of the analyte reverses at a channel. This concept will be used in the following discussion of this chapter, as well as in Chapter 4 and Chapter 5. The values of the pressure-induced velocity in the lateral channel at these CBCs are defined as “critical boundary values (CBVs)”.  60  Because these CBVs are analyte specific and are determined by the analyte electrophoretic mobility (  ep ), when a mixture of analytes is continuously injected from Vial A, the pressure can be adjusted so that specific analytes migrate to different vials according to the predetermined CBVs, achieving the reverse process of mixing. In order for such a process to be possible, the second CBV (Y in Figure 3.7c) for the slower component needs to be less than the third CBV (Z in Figure 3.7c) for the faster   component, as indicated in Figure 3.8(a): E CD  eo  ep , slow   E BC  eo  ep , fast  . Here,  the electric fields in different channels can be altered by changing the voltage applied at  vials A and B. Thus, we can control the pressure to get a proper v p value meeting the     relationship of E CD  eo  ep , slow   v p  E BC  eo  ep , fast  .Therefore, so long as there  is an electrophoretic mobility difference between two analytes, the appropriate values of the electric field and pressure can be chosen to demonstrate the reverse of the mixing process.  3.5 Results and Discussions 3.5.1 Continuous Chemical Purification in EFD Device with 2:1 Cross-Sectional Area Ratio  To verify the results from the theoretical predictions, we used the fluorescent dye rhodamine 110 to demonstrate the four different migration paths in the EFD devices for a single analyte, as the pressure-induced velocity was varied from high to low. The images in Figure 3.7(b) clearly show that the analyte migration in different branches of the EFD  61  device can be controlled by adjusting the counter-pressure value, once appropriate voltages are set at different inlet and outlet vials. To experimentally demonstrate the continuous purification process, the injection stream contained a mixture of two fluorescent dyes. Rhodamine 110 (upper part in Figure 3.8(a) and (b)) has a smaller  ep than ethidium bromide (lower part in Figure 3.8(a) and (b)) in the experimental conditions. In the first condition depicted in Figure 3.8, a relatively high pressure allows migration of some rhodamine 110 to collection vial B, while the rest, along with ethidium bromide are collected in Vial E. As the applied pressure goes down, Condition 2 is the state in which the mixture is separated into two channels each containing only one dye. Rhodamine 110 and ethidium bromide from the injection mixture in Vial A diverge into different channels at point C. In this case, Vial B collects pure rhodamine 110 and Vial E collects pure ethidium bromide. If the applied pressure is further reduced, rhodamine 110 may enter Vial E as well, co-migrating with ethidium bromide (Condition 3 in Figure 3.8). Electric field strengths, as well as the magnitudes of the pressure induced velocity in these four conditions are summarized in Table 3.1. Please note that the image contrast in Figure 3.8 has been adjusted, in order to indicate the migration pathway of different analytes within the image window with the limited size. These images are only for the proof-of-concept demonstration of the analyte flow directions, but not for the quantitative concentration determination.  62  Table 3.1 Electric field strengths and magnitudes of the pressure induced velocity in each channels at different migration conditions. The volumetric counter flow rates used in different conditions are 1.200, 0.800, 0.600, 0.200 l/min, respectively. A  A-C-B  A-C-B & A-C-D-E  A-C-D-E  Channel  AC  CD  BC  AC  CD  BC  AC  CD  BC  AC  CD  BC   E (V/m)  1.92  104  9.2  103  1.42  104  1.92  104  9.2  103  1.42  104  1.92  104  9.2  103  1.42  104  1.92  104  9.2  103  1.42  104   v p (m/s)  8.56  104  8.56  104  8.56  104  5.70  104  5.70  104  5.70  104  4.28  104  4.28  104  4.28  104  4.28  104  4.28  104  4.28  104  63  It should be pointed out that the simulation results (Figure 3.7(a2)) showed that it is possible for some analyte to go into the unintended channels initially because of the velocity field at different locations of the channel cross section (e.g., parabolic flow profile, angled areas) or because of diffusion. However, since the steady state flow defines the net migration behaviour away from the immediate vicinity of the channel intersections, the molecules are forced to go back to the proper channel if the channel is long enough. This phenomenon will be further discussed in Chapter 4.  Figure 3.8 Behaviour of two analytes. (a) The relative boundary conditions that determine the flow directions of R110 and EB, and the relative conditions used in the experiment. (b) The fluorescence images at 530 nm for R110 and 600 nm for EB taken simultaneously to demonstrate (1) R110 flowing along ACB and EB flowing  64  along both ACB and ACDE (the position of point E is shown in Figure 3.1(a)), (2) R110 flowing along ACB and EB flowing along ACDE only, demonstrating the reverse of a mixing process, and (3) R110 flowing along both ACB and ACDE but EB only flowing along ACDE.  3.5.2 Symmetrical Y-Shaped EFD Devices with Different Cross-Sectional Area Ratios  The symmetrical Y-shaped 2-D EFD device introduced above can be used for continuously obtaining pure substances from a two-analyte mixture. The cross sectional area of the main channel CD was exactly twice that of the lateral channels AC and BC, to  support two assumptions: the pressure-induced velocity v p has the same magnitude in all  channels of AC, BC and CD (eq 3.24), and the electric field strength in the main channel CD is the average of the values in two lateral channels (eq 3.26). The precise control of the channel cross-sectional area is feasible if PDMS is used as the material, as described in Section 3.2. However, the unstable surface properties and the elasticity of this material limit its practical usage. These problems can be solved by using glass as the chip material. Nevertheless, the cross section of the channel is irregular after the standard wet etching and high temperature wafer bonding processes. The channel width ratio on the photomask does not exactly reflect the real cross sectional area ratio of the channels. Therefore, it is difficult to fabricate the device, which can meet the requirement of the 2:1 channel cross-  65  sectional area ratio. In this section, the migration behaviour of analytes in Y-shaped EFD devices without a 2:1 channel cross sectional area ratio is discussed. In the symmetrical Y-shaped device shown in Figure 3.1, the conductivity of the solution is maintained uniform if a relatively high concentration of buffer solution is used:   AC   BC   CD where  (3.27)   is the conductivity of the solution inside each channel. From Kirchhoff's law,  the net current at the channel intersection is zero:     J AC S AC  J BC S BC  J CD SCD  (3.28)    where J is the current density vector in each channel and S represents the cross sectional      area of the respective channel. If Ohm's law J   E is used in eq 3.28, it becomes     E AC S AC  E BC S BC  E CD SCD  (3.29)  If channels AC and BC are symmetrical on the design mask, the resulting cross sectional areas after microfluidic device fabrication for these two lateral channels can be assumed to be the same, and defined as S AC  S BC  S0 . Thus, eq 3.29 can be rewritten as:   S  E CD  0 E AC  E BC SCD      (3.30)  The fluid in the EFD device is assumed incompressible, so the pressure driven flow at the intersection area has the relationship of:  66   vp  CD   SCD  v p  AC   S AC  v p  BC  (3.31)  S BC  Equation 3.31 can be rearranged into eq 3.32 by using the cross sectional area relationship.   vp  CD    2S0  vp SCD  (3.32)  0   where v p represents the magnitude of the pressure-induced velocity in the lateral 0  channel. As discussed in Section 3.4, if the width of the main channel is twice of that of the lateral channels, and the voltage applied at B is less than the potential at A, the analyte continuously injected into point A has four different possible migration states at the intersecting area, depending on the magnitude of the applied pressure in the channel CD (Figure 3.7). The CBCs between each migration cases are when the steady-state velocity in the specific channel reverses, and the corresponding CBVs as the pressure      1  decreases are v p  E AC eo  ep , v p  E AC  E BC 0 0 2          eo   ep  , and    v p  E BC  eo  ep  , respectively. 0  When the cross sectional area for the main channel is the exactly twice that of the lateral channels, the steady-state velocity direction of the analyte in either channel is still determined by the relative relationship of the magnitudes of the electrokinetic velocity    ( E  eo  ep  ) and pressure-induced velocity ( v p ).  67        v  v ep  v eo  v p  E  ep  eo   v p  (3.33)  Based on the experimental setup shown in Figure 3.1, the electric field has the reverse direction as compared to the hydrodynamic pressure. Thus, when the magnitude of the  pressure-induced velocity is larger than the electrokinetic velocity ( E  eo  ep  ), the  analyte's steady-state velocity has the same direction as the applied pressure. The CBC occurs when the magnitudes of the pressure-induced velocity and the electrokinetic velocity are equal. After passing this point, the analyte will have a steady-state velocity in the direction of the electric field. For the symmetrical Y-shaped EFD devices, the first CBC, where the steady-state velocity direction of the analyte reverses in channel AC, is    at the condition that v p  E AC eo  ep . Similarly, the third CBC, where the steady-    0    state velocity direction of the analyte reverses in channel BC, is reached when    v p  E BC  eo  ep  . The second CBC, where the velocity direction reverses in the 0    main channel CD, should occur when v CD  0 , which is    v p  E CD  eo  ep  0  (3.34)  By rearranging eq 3.34 with eq 3.30 and 3.32, the second CBV can be expressed as   1  vp  E AC  E BC 0 2      eo   ep  . Therefore, the second CBV (at the CBC Y) is the  average of the first (at the CBC X) and the third (at the CBC Z) CBVs, which is consistent with the situation when the cross sectional area ratio is 2:1.  68  Thus, we can conclude that CBVs are independent of the cross sectional area ratios for the main channel and lateral channels in the symmetrical Y-shaped EFD      1  devices. These CBVs are v p  E AC eo  ep , v p  E AC  E BC 0 0 2          eo   ep  , and    v p  E BC  eo  ep  , respectively. By varying the magnitude of pressure-induced 0  velocity, the analyte continuously injected from point A will have the same four migration behaviors as the 2:1 ratio Y-shaped EFD devices sequentially (illustrated in Figure 3.7). The simulated analyte migration conditions during the change of hydrodynamic pressure in EFD devices with different cross sectional area ratios are shown in Figure 3.9.  69  Figure 3.9 (a) Simulated concentration distributions in symmetrical Y-shaped EFD devices with three different cross-sectional area ratios during the decrease of applied hydrodynamic pressure. The concentrations from high to low are illustrated from red to blue. (b) The critical boundary conditions for four migration conditions.  70  Since CBVs are analyte specific and dependent on the electrophoretic mobility of the analyte, when a mixture of two analytes is continuously injected at A, the pressure can be adjusted so that specific analytes can migrate to different vials according to the predetermined critical boundary values, achieving the continuous chemical purification in the Y-shaped devices with any cross sectional area ratio of the main channel and lateral channels.  3.5 Conclusions The geometry of flow channels can be used to enhance the separation of chemical or biological materials, in addition to the commonly used driving forces such as chemical equilibrium and electric or magnetic field. The continuous separation achieved with the simple EFD devices allows complete processing of samples to obtain pure compounds from complex matrices. The results demonstrated in Figure 3.7 show that analytes can either be forced to stay in Vial A, or forced to go into Channel CB or CD depending on their intrinsic electrophoretic mobilities, suggesting that any component from a complex mixture can be collected in Vial B if proper voltages and pressure are set for a system. In addition, the CBVs are independent of the cross sectional area ratio. Therefore, any symmetrical Y-shaped 2-D EFD devices can be used for the continuous purification of analytes from a two-analyte mixture. The predictable nature and ease of operation could lead to a new generation of purification devices to serve the needs of biomedical research and other commercial and academic activities.  71  Chapter 4 : Multiple-Branched Two-Dimensional ElectroFluid-Dynamic Devices for Continuous Purification of Multiple Components from Complex Samples  72  4.1 Introduction In Chapter 3, we introduced a novel Y-shaped 2-D EFD device for continuous chemical purification. This device expands the geometry of separation from the one-dimensional single column to two-dimensional complex channel networks, providing an alternative means to overcome the drawbacks of cFCCE, and still achieving infinite separation resolution. The small dimensions of the microfluidic channels significantly reduce the necessary electrical potential and the separation time, and the complex channel networks make it possible to simultaneously collect more components from a mixture. A solution stream containing a mixture of two compounds can be separated into two channels, each containing a single compound, when the electric potentials and pressure are strategically applied in the interconnecting channels of the EFD device. The only requirement for separation is that the analytes have different electrophoretic mobilities, which indicates that any pair of analytes with different charge to size ratios can be potentially purified. This continuous nature provides the possibility of complete processing a mixture. More importantly, any component from a complex mixture can be collected if proper voltages and pressure are set for a system. These properties could lead to the development of purification devices to serve the needs of continuous micro-purification of biomolecules, and sorting of organelles and cells in biomedical research and other commercial and academic activities. In the work described in Chapter 3, only two analytes from the mixture can be purified at a time by using the symmetrical Y-shaped devices, which limits the potential applications. In this chapter, we will discuss the theory of mass transfer in more complex geometries. With this multiple-branched 2-D EFD device, multiple pure substances can 73  be collected from a complex mixture simultaneously. The migration behavior of analytes is based on the manipulation of steady-state velocity in different channels. The infinite resolution condition, in which two analytes migrate in opposite directions, can be achieved, providing a "proof-reading" mechanism for the purification process to improve the purity of the collected fractions.  74  4.2 Experimental Section  Figure 4.1 Schematics of channel geometry for the multiple-branched EFD devices. A is the sample inlet, S1, S2 and S3 are branched separation channels and S1’, S2’ and S3’ are collection outlets with sequentially lowered voltages, G is the grounded waste outlet, and P is the presurized port connected to a syringe pump.  75  The chemicals, high voltage power suppliers, and the syringe pump used in this study were the same as described in Section 3.2. The EFD device shown in Figure 4.1 with two separation side channels was fabricated with soda lime glass (Nanofilm, Westlake Village, CA) using standard photolithographic patterning and wet chemical etching methods.63 A 3-D illustration of the device was shown in Figure 4.2. The size of the fabricated device is 2.54 x 7.62 cm and the distance between S1 and S2 is 1.5 cm. The widths of the main channel and lateral channels was 80 m and 40 m, respectively, in the photomask. The depth of all channels were 50 m. Before introducing the analytes into the EFD device, the channels were filled with BGE. The analyte mixture, prepared by diluting the stock solution (1 mg/mL) by 100 times, was then introduced into the device for separation. A Nikon Eclipse 80i microscope was used in this study, and the fluorescence signals were recorded by a Photometrics Evolve camera (Tucson, AZ), and a Photometrics CoolSnap ES CCD camera. A MAG Biosystems dual-view objective (Optical in Sights, Tucson, AZ) with a 565 nm dichroic filter was used when it was necessary to monitor the migration behaviors of two analytes simultaneously. A 540 nm filter was used for rhodamine 110, and a 600 nm filter was used for ethidium bromide detection. The optical band-pass filters were from Thorlabs (Newton, NJ), and their full width at half-maximum (FWHM) were 10 nm. The migration behaviour of analytes in the 2-D EFD device was calculated using finite-element-scheme simulation software, COMSOL Multiphysics (COMSOL Inc., Los Angeles, CA).  76  Figure 4.2 Experimental setup of using the multiple-branched EFD devices for continuous chemical purification.  4.3 Results and Discussions The symmetrical Y-shaped EFD devices discussed in Chapter 3 have the capacity of continuously processing two components. However, in order to utilize the EFD device as a more efficient tool for separation, a new geometry design capable of simultaneously processing more components is required. The new multiple-branched EFD device is illustrated in Figure 4.1. The sample mixture is continuously introduced into the device from the injection point A, where a positive electric potential is applied. The separation section may contain as many lateral channels as needed, and an additional potential is applied at the end of each lateral channel (Si’) to achieve the required electric field. During the purification process, each lateral channel can continuously collect a purified analyte and may be considered as an independent separation unit. The vial at the far end of the main channel is grounded (G), which also provides an outlet for the waste.  77  The directions of the pressure-induced velocity and electric field for the channels at an intersecting point (Si) are indicated in Figure 4.3(a) and 4.3(b). In any of the  channels, the electrokinetic velocity ( E  eo  ep  ) and the pressure-induced velocity  ( v p ) have opposite directions. According to the equation        v  v ep  v eo  v p  E  ep  eo   v p  (4.1)  the steady-state velocity is determined by their relative magnitudes and has the direction with whichever is larger. When the pressure applied at point P is high, the steady-state   velocity of the analyte in any channel has the same direction as v p . In this case the analyte is forced to stay in the previous separation unit Si-1. Here, the magnitude of the pressure should meet the requirement:   v p , Si1Si  E Si1Si  ep  eo   (4.2)  78  Figure 4.3 Direcctions of (a) pressure-in nduced veloocity and (b)) electric fieeld in the our possiblee steady-staate velocity d directions fo for the interrsecting channels. (c) Fo analy yte in interssecting chan nnels.   If the presssure is redu uced so that v p falls beloow the valuee indicated inn eq 4.2   ( v p ,Si1Si  E Si1Si  ep  eo  ), ) the directio on of the anaalyte’s steaddy-state velocity reversess  in secction Si-1Si, so s that it mo oves forward d through thee main channnel and enterrs the studiedd separration unit. There T are fou ur possible situations forr the steady-state velocitty direction comb binations in Channel C SiSi’ and Chann nel SiSi+1, deemonstrated in Figure 4.3(c). In Chap pter 2, we inttroduced thee conservatio on of effectivve volumetriic flow rate aat channel  779  intersections of EFD devices, when the conductivity of the solution in the intersecting channels is constant:80 n  v S  i i  0  (4.3)  i 1  The relationship described by eq 4.3 indicates that the sum of products for the net velocity and cross sectional area is zero at the intersecting point. For condition (3) in Figure 4.3 (c), the component has the net velocity towards the intersecting point in all of three channels, making the sum of “vS” positive, which contradicts eq 4.3. Thus, condition (3) cannot actually exist. The remaining three conditions and the situation described by eq 4.2 are summarized in Figure 4.4. The simulated concentration distributions and the CBCs between the cases are shown as well. When the pressure is very high, the analyte is forced to stay in the previous purification section (Si-1) and never moves down to the section studied. As the magnitude of the pressure is reduced, the analyte will migrate into the collection channel SiSi’ at the intersection point Si. If the pressure is further reduced, the analyte at point Si may migrate into collection channel SiSi’ as well as further along the main channel to the next purification section Si+1. When the pressure is very low, all of the analyte migrates along the direction of electric field, through the main channel SiSi+1 to the next purification section (Si+1) for further separation. Similar to Figure 3.8, the image contrast in Figure 4.4(b) has been adjusted to demonstrate the flow direction of the analyte, but not to be used to determine its concentration.  80  Figure 4.4 Migration behavior of the analyte: (a) Simulated concentration distribution. The concentrations from high to low are illustrated from red to blue. (b) Experimental verification using R110: the positive electrical potential of 2000 V and 1500 V were applied in point A and S1’, respectively, and the flow speed was controlled as (1) 5.0 mm/s, (2) 4.0 mm/s, (3) 3.0 mm/s or (4) 2.0 mm/s, respectively; (c) the critical boundary conditions for four migration conditions.  81  To have all of these four conditions indicated in Figure 4.4 during the decrease of the pressure, the CBCs, at which the steady-state velocity in each channel reverses, need to occur sequentially as illustrated in the Figure 4.4c (the sequence of X’ Y’ and Z’ during the decrease of the pressure). As discussed earlier, from Kirchhoff's law and Ohm's law, the electric field strength in the intersecting channels has the relationship:     E Si Si1 S Si S I 1  E Si1Si S Si1SI  E Si Si' S S S ' i i  (4.4)  If the fluid in the EFD device is considered to be incompressible, at the point C, the following holds:     v p , Si Si1 S Si Si1  v p , Si1Si S Si1Si  v p ,Si Si' S S S ' i i  (4.5)  For the device illustrated in Figure 4.4, Channels Si-1Si and SiSi+1 are both located in the main channel, and if the uniform cross sectional area is assumed for this main channel, we can define the factor  as  SSi1 Si   SSi Si1  SS S ' . Thus, we can rewrite eq 4.4 and eq i i  4.5:      E Si1Si  E Si Si1   E Si Si'       v p,Si1Si  v p,Si Si1   v p,Si Si'   (4.6)    At the first CBC illustrated in Figure 4.4 (X’), v p , Si1Si  E Si1Si  eo  ep  . Equation 4.6  can be rearranged:  82    v p , Si1Si  E Si1Si  eo  ep   0       v p , Si Si1  E Si Si1  eo  ep      v p , Si Si'  E Si Si'  eo  ep        (4.7)  It is indicated from eq 4.7 that when the first critical boundary condition illustrated in Figure 4.4(c) is satisfied, the steady-state velocities of the analyte in channels SiSi+1 and SiSi’ are both with or against the electric field.     When v p , Si1Si  E Si1Si  eo  ep  , and v p , Si Si'  E Si Si'  eo  ep  , the   relationship v p , Si Si1  E Si Si1  eo  ep  is satisfied, which means that if the pressure  applied is smaller than the first CBV (at X’), the second CBC (Y`) will be satisfied before the third CBC (Z`), during the pressure reducing process. Thus, as long as either the second (Y`) or the third (Z`) CBC is satisfied at a smaller pressure value than the first CBC (X`), it will be possible to achieve the boundary condition sequence illustrated in Figure 4.4 (X’ Y’ and Z’) during the decrease of the applied hydrodynamic pressure. This can be easily achieved by making a low flow resistance or a low electric field in the side channels. Consequently, any analyte continuously injected from the top of the device can have four different migration paths, as shown in Figure 4.4, at each intersecting area through changing the pressure magnitude. As illustrated in Figure 4.4(c), the counter-pressure values at CBCs are proportional to the electrophoretic mobility of the analyte. Thus, pressure can be synergistically arranged for any analyte with a known electrophoretic mobility to achieve different migration pathways. During the process of reducing pressure, the analyte with a higher electrophoretic mobility changes its migration condition first compared to an  83  analyte with a smaller electrophoretic mobility. If a mixture of analytes is introduced into the EFD device, the slower analyte may have the steady-state migration path Si-1-Si-Si’, leading to the separation channel SiSi’, while the analyte with a greater electrophoretic mobility continues to move through the main channel Si-1-Si-Si+1. This phenomenon is demonstrated in Figure 4.5. It should be noted that the analytes indicated in Figure 4.5 have the opposite steady-state migration directions in channels SiSi’ and SiSi+1, which are at the infinite resolution condition. As long as the channel SiSi+1 is long enough, any molecules of the electrophoretically slower analyte (Figure 4.5(a)) entering channel SiSi+1 will be pushed back by the fact that their steady-state velocity in that channel is towards the intersection, returning them to their intended track along SiSi’. Channel SiSi+1 is the assigned track for the analyte indicated in Figure 4.5(b). This mechanism also allows the sample injection from other locations. If the analyte has the steady-state velocity in each channel indicated in Figure 4.6(a), the only possible destination collection channel is the lower one. Even if the analyte is injected from the place shown in Figure 4.6(b), it does not migrate to the upper collection vial, but back to the main channel, and then trends towards the correct channel. The simulated analyte migration behaviour is indicated in Figure 4.6(c)-(f). This “proof-reading” mechanism can help ensure the purity of the analyte collected. This “proof-reading” mechanism is capable of directing the component with greater migration velocity from the unintended channel SiSi’ back to the correct way of SiSi+1. To ensure that this mechanism works for the slower moving analyte as well, the section of SiSi+1 should be long enough. As indicated in Figure 4.5(a), some slower moving analyte may enter Channel SiSi+1, due to diffusion or the inertia of the fluid.  84  Because the direction of its steady-state velocity is from Si+1 to Si, the fraction entering to this wrong way would be eventually pushed back to Channel SiSi’, if the section of SiSi+1 is long enough. Otherwise, this analyte may enter the collection channel Si+1Si+1’, and contaminate other fractions collected. The minimum required length of the section of SiSi’ depends on the electrophoretic mobility of the analyte, counter-pressure value, fluid viscosity, channel geometry, etc. In our setup, the distance between S1 and S2 was 1.5 cm, and R110 (the green dye) was not observed at the S2 area (Figure 4.7 (d)).  Figure 4.5 Simulated migration behavior of two analytes in the intersecting area. The concentrations from high to low are illustrated from red to blue. (a) Relatively more negative, slower moving analyte; (b) relatively more positive, faster moving analyte.  85  Figure 4.6 Proof-reading mechanism of the 2D-EFD devices. (a) The steady-state concentration distribution of an analyte. The arrows indicate the analyte migration velocity in each channel. (b) Analyte injection position. (d) and (f): The analyte distribution in the region indicated in (c) and (e), respectively.  86  As illustrated in Figure 4.1, the EFD device can contain as many purification side channels as necessary. The analytes passing by the separation modules in the earlier part of the main channel can be considered as the injection stream for the subsequent separation section. Each analyte can be continuously collected at its specific side channel. Electrophoretically slower analyte can be purified in the upper channel and faster analytes will continue to go down for further analysis. The purification process is shown in Figure 4.7, by both simulated result and experimental demonstration.  Figure 4.7 Behaviour of two analytes in the EFD device. (a) and (b): Simulated analyte distribution for two analytes. The concentrations from high to low are illustrated from red to blue. (c) and (d): Experimental verification using R110 (green colour) and EB (yellow colour) at two intersection areas. The positive electrical potential of 2000 V and 1500 V were applied in point A and S1’, respectively and the flow speed was controlled as 3.8 mm/s.  87  4.4 Conclusions Although the Y-shaped device introduced in Chapter 3 was limited to a maximum of two analytes, a new 2-D EFD device design with multiple side channels is demonstrated that has the capability of processing multiple analytes simultaneously. These 2-D EFD devices are developed based on the theory of infinite resolution conditions and the fact that analytes have the opposite steady-state velocity directions in the main channel during the separation process. Therefore, an analyte entering the unintended channel will be forced back to its right track. This “proof-reading” mechanism improves the purity of the collected analyte at each branch of the device. The only requirement of separation is the different electrophoretic mobilities of the analytes, thus the EFD devices introduced here can be potentially used to sorting cells or particles with difference size or surface properties. These EFD devices offer the potential for continuous purification of individual analytes from complex sample mixtures.  88  Chapter 5 : Comparison of Sample Injection Modes for Continuous Chemical Purification in Two-Dimensional Electro-Fluid-Dynamic Devices  89  5.1 Introduction In Chapter 3 and Chapter 4, we have introduced a new generation of devices for continuous chemical purification, based on the interactions of analyte with multiple types of driving forces. Two-dimensional electro-fluid-dynamic (2-D EFD) devices, in which both electric field and hydrodynamic pressure are simultaneously utilized in 2-D channel networks to drive the mass transfer, provide better manipulation on the analyte migration by simply adjusting the magnitude of the pressure. In Chapter 3, we introduced the use of symmetrical Y-shaped 2-D EFD devices to continuously obtain pure substance from a two-analyte mixture. With the strategically applied electric potential and hydrodynamic pressure, a continuous solution stream containing a mixture of two components can be separated into two channels, each containing a single compound.62 In Chapter 4, we demonstrated the use of a multiplebranched 2-D EFD device, for continuously purifying multiple components.61 Each component in the introduced mixture can be directed to enter its specific collection channel. The predictable nature and ease of operation of this technique could lead to a new generation of purification devices to serve the needs of biomedical research and other commercial and academic activities. In previous studies, there was a positive potential applied at the sample vial. The electric field driven flow overcame the counter-pressure and delivered the sample into the injection channel. Therefore it is considered as an electrokinetic injection method. The quantity of the sample introduced into the device is dependent on a number of parameters, including the electrophoretic mobilities of the analytes and the  90  electroosmotic flow velocity. This method may be advantageous if the analyte of interest has a large electrophoretic mobility.81 In the electrokinetic injection mode, the buffer-depletion problem induced by the high voltage applied in the sample vial has not been resolved. In addition to this sample introduction method, there is an alternative approach widely used in CE experiments, which is the hydrodynamic sample injection method. In this chapter, the electric field and fluid field distributions are systematically studied in different 2-D EFD devices, when the sample is continuously introduced into the channel networks by the hydrodynamic pressure. The results of the steady-state mass transfer study indicate that hydrodynamic injection mode could be used for the continuous chemical purification in 2-D EFD devices. The theoretical comparison of two sample injection modes shows that the hydrodynamic injection method is superior to the electrokinetic injection method by providing a faster sample processing speed and being more resistant to the fluctuating electroosmotic flow (EOF). In addition, because no external electric potential is applied to the sample vial, the buffer depletion problem for the sample solution can be fully resolved.  91  5.2 Experimental Section  Figure 5.1 The 2-D EFD devices used in this chapter: (a) symmetrical Y-shaped device; (b) multiple-branched device.  The chemicals and imaging system used in this chapter are the same as described in Section 4.2. The 2-D EFD device shown in Figure 5.1(b) was the same as used in Chapter 4, and the Y-shaped device indicated in Figure 5.1(a) was also fabricated with soda lime glass (Nanofilm, Westlake Village, CA). The width of the main channel and lateral channels of both devices was 80 and 40 m, respectively, on the photomask. The depth of all channels was 50 m. During the experiment, two syringe pumps were used to control the injection speed in Channel AC, and the counter pressure at F, respectively. The positive electric potential at B was controlled by a high-voltage power supply. The  92  current in Channel AC was monitored during the experiment, which was kept as zero to ensure the electric field strength in this channel was zero.  5.3 Results and Discussions In Chapter 3 and Chapter 4, we have introduced the utilization of symmetrical Y-shaped and multiple-branched shaped 2-D EFD devices for continuously purifying two or multiple analytes from a mixture, respectively.61,62 In those investigations, the electric field applied on the sample introduction channel overcame the effect of back pressure, and delivered analytes into the device in the electrokinetic injection mode. In this study, no electrical potential is applied in the injection channel, and a hydrodynamic pressure applied at the sample inlet delivers the sample into the device. In the discussion below, the directions of vectors are all along the channel length. Thus, these vectors are expressed as scalars, and the values are defined as positive when the vector direction is toward the intersection point C (see Figure 5.1). The cross-sectional area ratio of lateral channels and the main channel is defined as for both 2-D EFD devices shown in Figure 5.1 ( S AC  S BC   SCD for the symmetrical Y-shaped device, and  S BC   S AC   SCD for the multiple-branched device).  93  5.3.1 The Electric Field and Hydrodynamic Fluid Field Distribution in 2-D EFD Devices  The conductivity of the solution in the device can be considered uniform if a relatively high concentration of buffer is used.   AC   BC   CD  (5.1)  where  is the conductivity of the solution inside each channel. From Kirchhoff’s law, the net current at the intersection is zero:  J AC SAC  J AC SBC  J AC SCD  0  (5.2)  in which J is the current density in each channel and S represents the cross-sectional area of the respective channel. If Ohm’s law J   E is used in eq 5.2, it becomes  EAC SAC  E AC SBC  E AC SCD  0  (5.3)  For different 2-D EFD devices, eq 5.3 can be reformatted according to the relationship of their channel cross-sectional area, which is  E AC   EBC  ECD  0 and  E AC   EBC  ECD  0 for symmetrical Y-shaped and multiple-branched devices, respectively. In the hydrodynamic injection mode, no external electric potential is applied at Vial A. Therefore, point A has the same electric potential as C, and the electric field strength in Channel AC is zero. The electric field distribution changes to   EBC  ECD  0   E AC  0  (5.4)  for both kinds of 2-D EFD devices. 94  The fluid in the EFD device is assumed to be incompressible, so the fluid velocity in intersecting channels has the relationship of  v f ,AC SAC  v f ,BC SBC  v f ,CD SCD  0  (5.5)  Equation 5.5 can be reformatted according to the cross-sectional area relationships of the channels, resulting to  v f ,AC   v f ,BC  v f ,CD  0 and v f ,AC   v f ,BC  v f ,CD  0 for symmetrical Y-shaped and multiple-branched devices, respectively. In the hydrodynamic injection mode, the syringe pump delivers analytes toward the intersection point at a fixed velocity vinj in the injection channel AC. Therefore, the hydrodynamic fluid field distribution relationships can be written as  vinj   v f ,BC  v f ,CD  0 and vinj   v f , BC  v f ,CD  0 for different types of 2-D EFD devices, respectively. The results  discussed in this section have been summarized in Table 5.1.  95  Table 5.1 Electric field and fluid field distribution in different sample injection modes of symmetrical Y-shaped, and multiplebranched 2-D EFD devices  Device Injection Method Electric Field Fluid Field  Symmetrical Y-Shaped Devices Electrokinetic Injection Hydrodynamic Injection   E AC   EBC  ECD  0  v f ,AC   v f ,BC  v f ,CD  0   EBC  ECD  0   E AC  0  vinj   v f ,BC  v f ,CD  0  Multiple-Branched Devices Electrokinetic Injection Hydrodynamic Injection  EAC   EBC  ECD  0 v f ,AC   v f ,BC  v f ,CD  0   EBC  ECD  0   E AC  0 vinj   v f , BC  v f ,CD  0  96  5.3.2 Migration Behavior of an Analyte in 2-D EFD Devices  The steady-state velocity of a charged particle that is moving in the channel can be written as  v  vep  veo  v p  ep E  eo E  v p  ep E  v f  (5.6)  where electrophoretic velocity ( vep ) is discriminative and determined by its electrophoretic mobility ( ep ), which is an intrinsic property for a particular analyte. On the other hand, the electroosmotic velocity ( veo ) and pressure-induced velocity ( v p ) are nondiscriminative and affect all components equally. It is illustrated in Figure 5.1 that the electric field and hydrodynamic pressure have reversed directions in Channel BC and Channel CD. Therefore, the steady-state migration direction reverses at the critical boundary condition (CBC) where the magnitudes of the reverse components are equal. In Chapter 3 and Chapter 4, we have reported that the analyte has four possible mass transfer pathways in 2-D EFD devices according to the various combinations of electric field and pressure, when the sample is introduced into the device in the electrokinetic injection mode.61,62 When the pressure is high, the steady-state velocity of the analyte in either channel has the same direction as the pressure, and the analyte is forced to stay at Vial A and does not migrate into Channel AC or any other channels. As the magnitude of applied pressure reduces, the steady-state velocity of the analyte reverses in Channel AC first, making the analyte migrate through point C to the collection vial B. If the pressure is further reduced, the analyte at point C may migrate into both Channel CB and Channel CD. When the pressure is very low, all the analytes  97  migrate along the direction of the electric field, from injection Vial A, through the intersecting point C and enter Channel CD. In the hydrodynamic injection mode, the applied pressure delivers the analyte mixture into the device with the velocity vinj , and each analyte can have only three possible mass transfer pathways in the device. In Channel BC and Channel CD, the net velocity of analyte is determined by eq 5.6. In the symmetrical Y-shaped device, the migration velocity in BC is  vBC  EBC ep  v f ,BC  (5.7)  Based on eq 5.4 to eq 5.6, the velocity in Channel CD is vCD  ECD ep  v f ,CD   EBC ep   vinj   v f , BC    vBC  vinj   (5.8)  in which vinj is positive. There are three possible migration pathways for the analyte. When vBC is negative and vCD is positive, the analyte has the migration path of A-C-B, and in this condition, the relationship below should be satisfied: v f , BC  EBC  ep  vinj  (5.9)  When both vBC and vCD are negative, the analyte can migrate through the pathway of either A-C-D and A-C-B, and in this condition, the following holds EBC ep  v f , BC  EBC ep  vinj  (5.10)  98  When vBC is positive and vCD is negative, the analyte migration through the path of A-CD, and the relationship below should be satisfied: v f , BC  EBC  ep  (5.11)  Similarly, in the multiple-branched EFD device, the net velocity in channel BC is:  vBC  EBC ep  v f ,BC  (5.12)  and the velocity in channel CD is vCD  ECD  ep  v f ,CD   EBC ep   vinj  v f , BC   vBC  vinj  (5.13)  in which vinj is positive. There are three possible migration pathways for the analyte in the multiplebranched device as well. When vBC is negative and vCD is positive, the analyte has the migration path of A-C-B, and in this condition, the relationship below should be satisfied:  v f , BC  E BC  ep   1    (5.14)  vinj  When both vBC and vCD are negative, the analyte can migrate through the pathway of either A-C-D and A-C-B, and in this condition, the following holds E BC  ep   v f , BC  E BC  ep   1    vinj  (5.15)  When vBC is positive and vCD is negative, the analyte migration through the pathway of A-C-D, and the relationship below should be satisfied:  99  v f , BC  EBC  ep  (5.16)  The migration behaviour of analytes in different EFD devices in the hydrodynamic injection mode were demonstrated by the fluorescence dyes, as illustrated in Figure 5.2, and critical boundary conditions (CBCs) were shown as well. With the comparison of the electrokinetic injection mode discussed in Chapter 3 and Chapter 4,61,62 the differences between  v f , BC values at CBCs are independent of the electric field strength, and are only determined by the sample injection speed. This property provides a more convenient approach to control the migration behaviour of the analyte in the EFD device, which will be discussed in more details in the following part.  100  Figure 5.2 Mass migration pathways of the analyte in 2-D EFD devices and critical boundary conditions on: (a) symmetrical Y-shaped device, and (b) multiplebranched device.  101  5.3.3 The Effects of Changing Controlling Parameters on Critical Boundary Conditions  In this chapter, the critical boundary value (CBV) is defined as the value of  v f , BC at the critical boundary condition (CBC). As discussed in the previous part, the fluid velocity in Channel BC at CBCs is crucial to the migration behaviour manipulation of the analyte in the 2-D EFD device. By changing the controlling parameters of the device, e.g. syringe pump controlling fluid velocity or applied electric potential, CBVs can be manipulated into the appropriate value, making the components follow the proper migration pathways. In the electrokinetic injection mode described in Chapter 3 and Chapter 4, CBVs are dependent on the electric field strength at the specific channel.61,62 As described by eq 5.3, it is impossible to change the electric field strength in only one channel by simply adjusting only one electric potential, while leaving other critical boundary conditions unchanged. This complex relationship makes it difficult to control the analyte migration behaviours. In the hydrodynamic injection mode, the sample mixture is introduced into the EFD device by the hydrodynamic pressure, and the electric field is only dependent on the electric potential applied at point B. From the critical boundary conditions illustrated in Figure 5.2, the change of the sample injection speed does not affect the second CBV (Y), at which the steady-state velocity of the analyte reverses at the lateral channel BC. In contrast, the first CBV (X), where the analyte changes the migration direction in Channel CD, is moved with a magnitude of vinj for the symmetrical Y-shaped EFD device (Figure 5.3), and  1    vinj for the multiple-branched EFD device. Therefore, changing the  102  samp ple injection speed provid des a conven nient approaach to adjust the differennce between two CBVs, C whilee the second CBV remain ns the same (Figure 5.3)).  Figure 5.3 The effect e of cha anging samp ple injection n speed on tthe analyte ssample migrration velociity in differeent channells of the sym mmetrical Y Y-shaped devvice. Duringg the change c of th he injection speed from 0.001 m/s tto 0.003 m/ss, the CBC X changes from m X1 to X2, an nd the CBC C Y does nott change. Th he potentiall applied at point B is 5000 V, and the electrophorretic mobiliity of the an nalyte is 5x110-8 m2V-1s-1.  Adjusting g the electricc potential att point B is aanother way to control thhe CBV valuees in the hyd drodynamic injection i mo ode. Becausee the differennce between the two  1003  CBV Vs is only dep pendent on the t sample in njection speeed, the changge of the eleectric field strength moves th he two criticcal boundary y values withh the same m magnitude off EBC ep foor both symmetricall Y-shaped and a multiplee-branched 22-D EFD devvices (Figuree 5.4).  e of cha anging electric field streength on th he analyte saample Figure 5.4 The effect migrration velociity in differeent channells of symmeetrical Y-shaaped devicee. During the increease of the electric e poteential applieed at point B from 50000 V to 100000 V, CBCs movee from X1, Y1 to X2, Y2. The samplee injection sspeed is 0.0001 m/s, and the electrophoretic mobility m of the analyte is 5x10-8 m 2V-1s-1.  1004  The combined utilization of these two approaches provides a convenient and powerful approach to regulate the position of the two CBCs. The position of the second CBC (Y), at which the steady-state migration velocity of the analyte reverses at Channel BC, can be manipulated by adjusting the electric potential at the point B. The position of the first CBC (X) can then be set by controlling the difference between the two CBCs, in the way of changing the sample injection speed.  5.3.4 The Continuous Chemical Purification in 2-D EFD Devices and the Sample Processing Speed  Based on the discussion above, the CBVs are dependent on the electrophoretic mobility of the analyte. Therefore, different components may have distinctive migration pathways at certain electric field and hydrodynamic pressure conditions, and they can be directed into their specific collection locations. In order to achieve this continuous chemical purification, the applied electric potential and counter-pressure make the slower migration component follow the pathway of A-C-B, while all of the faster migration components go through the main channel CD at the intersecting point C and have a migration pathway of A-C-D. Therefore, for the symmetrical Y-shaped device, the magnitude of the net fluid velocity in Channel BC needs to be within the range of: EBC  ep , slow  vinj  v f . BC  EBC  ep , fast  (5.17)  Consequently, as long as the sample injection speed is kept in the range of:    vinj  EBC ep, fast  ep,slow    (5.18)  105  the magnitude of the fluid velocity in Channel BC can be arranged into the range indicated in eq. 5.17 to achieve the continuous chemical purification. Because of the existence of the maximum injection speed, the minimum processing time for the sample mixture can be calculated:  t  Vtot Vtot  vinj SAC EBC ep, fast  ep,slow SAC      (5.19)  in which t is the time required to process the sample mixture with the volume of Vtot. Similarly, for the multiple-branched EFD device, the magnitude of the fluid velocity at Channel BC when the continuous chemical purification occurs is: E BC  ep , slow   1    vinj   v f . BC  E BC  ep , fast  (5.20)  The requirement of the sample injection speed is:    vinj   EBC ep, fast  ep,slow    (5.21)  and the minimum sample processing time is  t  Vtot Vtot  vinj S AC  EBC  ep , fast  ep , slow  S AC  (5.22)  The continuous chemical purification processes in different EFD devices were demonstrated in Figure 5.5. It should be pointed out that the image contrast in Figure 5.5 has been adjusted to indicate the migration pathway of different analytes within the detection window. These images are only for the proof-of-concept demonstration for the analyte flow directions, but not for the quantitative concentration determination. It is 106  indicated in Figure 5.5 that some analyte may enter the unintended channels initially, as discussed for the electrokinetic injection mode in Chapter 4 and Chapter 5. However, since the steady state flow defines the net migration behaviour away from the immediate vicinity of the channel intersections, the molecules are forced to go back to the proper channel if the channel is long enough. The “proof-reading” mechanism introduced in Section 4.3 is still valid in the hydrodynamic injection mode.  Figure 5.5 Demonstrations of continuous chemical purification process in different 2-D EFD devices: (a) symmetrical Y-shaped device; (b) multiple-branched device.  107  5.3.5 The Comparison of Hydrodynamic Injection and Electrokinetic Injection Modes in the Operation of Continuous Chemical Purification  In Section 5.3.3, we have demonstrated that the hydrodynamic injection mode provides a more convenient approach to control the position of critical boundary conditions. Here, we theoretically compare the sample processing speed and the resistance to the fluctuating electroosmotic flow (EOF), and studied which sample injection mode provides better operability in the continuous chemical purification process. In the following discussion, we took the symmetrical Y-shaped EFD device as an example to make the comparison. Because of the continuous nature of the chemical purification, the amount of the sample mixture injected to the device during a time period equals the amount of the analytes processed and collected during that time. Therefore, the sample processing speed can be described by the injection speed. In the hydrodynamic injection mode, the sample injection speed for every analyte is the same, which is vinj . As discussed in Section 5.3.4, the maximum sample injection speed to achieve the continuous chemical      purification is vinj  EBC ep, fast  ep,slow (eq 5.18). In the electrokinetic injection mode, the speed of delivering components into the EFD device is analyte dependent, which is      vinj  E AC eo  ep  v p,AC  (5.23)  If the counter-pressure is relatively high, the analyte is forced at the injection point A, and the injection speed is negative. When the back pressure is reducing and the analyte  108  has the migration path of A-C-B, the magnitude of the pressure-induced velocity in the injection channel AC is in the range of 1  EAC  EBC  eo  ep  v p,AC  v p,AC  EAC eo  ep , and the range of the injection 2          speed of in this migration situation is:  0  vinj   1  EAC  EBC  eo  ep 2      (5.24)  Similarly, if the analyte has the migration pathway of both A-C-B and A-C-D, the injection speed range is: 1  EAC  EBC   eo  ep  vinj   EAC  EBC   eo  ep 2          (5.25)  If the analyte migrates along the way of A-C-D, the injection speed range is    vinj   E AC  EBC  eo  ep    (5.26)  For the continuous separation of analytes, the pressure-induced velocity in the injection channel AC should be controlled in the range of making the faster migration components have the migration path of A-C-D, while the slower components have the migration path of A-C-B, which is 1  EAC  EBC  eo  ep,slow  v p,AC  v p,AC  EBC eo  ep, fast 2          (5.27)  The sample processing speed for the mixture is limited by the injection speed of the slower component, which is  109          E AC eo  ep,slow  EBC eo  ep, fast  vinj,slow   1  EAC  EBC  eo  ep,slow 2      (5.28)  Assuming that the electric fields in the lateral channel have the same strength in both hydrodynamic and electrokinetic injection modes, the difference in the maximum injection speed between these two modes is   12  E    EBC ep, fast  ep,slow   AC     EBC  eo  ep,slow    1 1 1 1  EBC ep, fast  EBC ep,slow  EBC eo  E AC eo  E AC ep,slow 2 2 2 2 1  EBC eo  ep, fast   E AC  EBC  eo  ep,slow 2        (5.29)    From the discussion about eq 5.27, the value of eq 5.29 is positive during the continuous chemical purification process. Thus, the hydrodynamic sample injection mode could provide a faster sample processing speed. The discussion above is based on the assumption that the electric field strength in Channel BC is the same in the two different injection modes. If the electrical voltage at point B, not EBC , is kept the same in both sample injection methods, an additional electrical potential applied at A in the electrokinetic injection approach decreases the value of EBC , resulting in an even slower sample processing. Therefore, the hydrodynamic sample injection mode can provide a faster sample processing speed compared with the electrokinetic sample injection method. Another comparison is the effect of a fluctuating EOF in different sample injection modes. During the continuous chemical purification process, the surface property of the microfluidic channel wall may change over time. The application of the positive electric potential could induce electrolysis of the buffer solution, which may  110  change the buffer pH and EOF as well. Therefore, a sample injection approach, which is more resistant to the fluctuating EOF, is preferred. The effect of the unstable EOF on the sample processing speed, and the analyte migration velocity, are studied here. In the hydrodynamic injection mode, the electric field strength in the injection channel is zero. The sample injection speed is only controlled by the syringe pump at point A. The range of the injection speed during the continuous chemical purification is      0  vinj  EBC ep, fast  ep,slow , which is EOF independent. Because the counter-pressure is controlled in the way of volumetric flow rate by the syringe pump, we assume that the net fluid velocity in the main channel CD remains the same in different EOF conditions. In Channel CD, the net velocity of the component is  vCD  ECD ep  v f ,CD  (5.30)  which is not affected by the EOF value. Because the migration velocity in Channel AC is a fixed value of vinj , due to the effective volumetric flow rate conservation principle (described in Chapter 2),80 the migration velocity in Channel BC is not affected by the unstable EOF either (Figure 5.6).  111  Figure 5.6 The effect e of unsstable EOF on the anallyte sample migration vvelocity in different channeels in the hy ydrodynamiic sample in njection mod de. During tthe change OF, the mig gration veloccities in diffferent chann nels are nott affected wiith the of EO assum mption of th he constant fluid velociity in Chann nel CD. Thee sample injjection speed is 0.0 001 m/s, the electric pottential applied at pointt B is 5000 V V, and the electrophoretic mobility m of the analyte is 5x10-8 m 2V-1s-1.  112  In the electrokinetic injection mode, the sample injection speed was described by      eq 5. 23 ( vinj  E AC eo  ep  v p,AC ). Because v p , AC    1 v p ,CD and 2  v p ,CD  v f ,CD  ECD  eo , eq 5.23 can be rearranged to  1  v f ,CD  ECD eo  2 1 1    E AC ep  v f ,CD   E AC  ECD  eo 2 2    vinj  E AC  eo  ep    (5.31)  Due to the electric field strength relationship described in Section 5.3.1 (  E AC   EBC  ECD  0 ), and E AC  EBC during the purification process in the symmetrical Y-shaped device, E AC   1 ECD doesn’t equal to zero. Therefore, the 2  unstable EOF can cause the fluctuation of the sample injection speed. As described in eq 5.27, in the electrokinetic injection mode, the magnitude of the pressure-induced velocity in lateral channels is kept in the range of 1  EAC  EBC  eo  ep,slow  v p,AC  vp,AC  EBC eo  ep, fast . During the continuous 2          chemical purification process, the injection speed for the faster moving component ( vinj , fast  E AC  eo  ep , fast   v p , AC ) is in the range of: 1 2   EAC  EBC   eo  ep, fast   vinj, fast  EAC  eo  ep, fast    EAC  EBC   eo  ep,slow  (5.32) and for the slower migration component, the injection speed range      ( vinj,slow  E AC eo  ep,slow  v p,AC ) is:  113          E AC eo  ep,slow  EBCC eo  ep, fasst  vinj,slow   1  EAC  EBBC  eo  epp,slow 2      (5.33))  ossible rangee of the samp ple injectionn speed is EO OF dependennt for both Thereefore, the po fasterr and slowerr migration analytes. a  Figure 5.7 The effect e of unsstable EOF on the anallyte sample migration vvelocity in he change oof different channeels in the eleectrokineticc sample inj ection modee. During th m from 2x10-8 m2V-1s-1 to 6x 10-8 m2V-1s--1, the migraation electroosmotic mobility veloccities in Cha annel AC an nd BC are both b affected d if the fluid d velocity in n Channel CD was w kept as a constant. The electric potential aapplied at p point A and d B are 50000 V an nd 4250 V, respectively,, and the eleectrophoret ic mobility of the analyyte is 3x10-8 - -1 m2V-1 s .  114  It is indicated that the sample injection speed, as well as the range of possible injection speed flow rates, are all affected by the fluctuating EOF value in the electrokinetic injection mode. As indicated in Figure 5.7, although the analyte net migration velocity in Channel CD is unchanged, the fluctuating injection speed in Channel AC can induce the changing velocity in Channel BC based on the effective volumetric flow rate conservation principle introduced in Chapter 2. Another advantage for the hydrodynamic injection approach is that it can avoid the buffer depletion problem during the prolonged sample injection. In the electrokinetic injection mode, an electrode is directly placed into the injection sample vial, and the long-period processing time is accompanied by significant buffer electrolysis, affecting the solution pH. However, in the hydrodynamic injection mode, it is the pressure that delivers the sample into the device, and the injection solution is not affected by the external electrode. Therefore, the buffer depletion problem can be completely avoided. The comparisons of two sample injection methods are summarized in Table 5.2.  115  Table 5.2 Comparison of different sample injection modes Unstable EOF Maximum Sample Processing Speed  Hydrodynamic Injection Electrokinetic Injection Comparison  v  Buffer Depletion  Sample Processing Speed  vAC  vBC  vCD  v  EBC  ep , fast  ep , slow   Not Affected  Not Affected  Not Affected  Not Affected  No  1  E AC  EBC   eo   ep , slow  2  Affected  Affected  Affected  Not Affected  Yes  EBC  ep , fast   ep , slow    EBC  eo   ep , fast    1  E AC  EBC   eo  ep ,slow  2  1  E AC  EBC   eo  ep ,slow   0 2  Hydrodynamic Injection Method is Preferred.  116  Therefore, the hydrodynamic injection approach is considered to be superior to the electrokinetic injection method in the continuous chemical purification process, which can provide faster sample processing, and be more resistant to the fluctuating EOF. In addition, there is no buffer depletion problem in this setup.  5.4 Conclusions Mass transport in different 2-D EFD devices was studied in this chapter when the sample was injected into the device by the hydrodynamic pressure. The continuous chemical purification processes were successfully demonstrated in both symmetrical Y-shaped device and multiple-branched device. The comparison of two sample injection methods was carried out theoretically. The hydrodynamic injection approach was determined to be superior to the electrokinetic sample introduction method because it can provide faster sample processing and be more resistant to the unstable EOF. In addition, it can avoid the buffer depletion problem in the sample vial.  117  Chapter 6 : Concluding Remarks and Future Work  118  6.1 Concluding Remarks In this thesis, multiple-field driven mass transfer is studied in two-dimensional channel networks. We developed a new generation of platforms for continuous chemical purification, based on the interactions of analyte with electric field and hydrodynamic pressure in a 2-D EFD device. The simultaneous application of both fields provides better control of the analyte molecule, which can either migrate with the medium driven by non-discriminative forces, such as pressure or electroosmosis, or migrate through the medium driven by the discriminative force from the applied electric field. These movements can exist simultaneously, giving a net migration determined by the sum of the velocity vectors. Mass conservation is the guiding principle for analyte distribution in intersections of inter-connecting channels. However, in 2-D EFD devices, the situation of mass distribution is more complex. In order to understand the analyte transportation behaviour in multiple force fields, we studied the analyte distribution in EFD devices, and discovered the conservation of effective volumetric flow rate in addition to the mass conservation in channel intersections. This principle states that analyte is distributed into different channels based on the effective volumetric flow rates of these analytes in the channels downstream. It can be used to predict the analyte concentration in a channel, and provides a theoretical basis for investigating the mass transfer behaviour in EFD devices. The simultaneous application of multiple fields provides better manipulation of the object migration and distribution in complex channel networks. Y-shaped  119  microfluidic devices have been used to introduce individual samples from interconnecting channels and the mixing process has been studied extensively. With the strategically applied electric potential and hydrodynamic pressure, the mixing process, which is spontaneous, can be reversed in the device with the same channel geometry. A continuous solution stream containing a mixture of two components can be separated into two channels, each containing a single compound. By increasing the geometry complexity, more complex samples can be potentially processed. We demonstrated the use of a multiple-branched 2-D EFD device, for continuously purifying multiple components. Each component in the introduced mixture can be directed to enter its specific collection channel. The sample injection methods were theoretically compared as well. The hydrodynamic injection approach is considered to be superior to the electrokinetic injection method in the continuous chemical purification process, which can provide faster sample processing, and be more resistant to the fluctuating electroosmotic flow (EOF). In addition, the buffer depletion problem can be completely avoided. The predictable nature and ease of operation of this technique could lead to a new generation of purification devices to serve the needs of biomedical research and other commercial and academic activities.  6.2 Future Work Although the resolution could be infinite in theory, it could be limited by various factors in practice, such as the pressure induced parabolic flow profile, the heat generated by the  120  current resulting in convection, the non-uniform electric field strength distribution at the intersection point, and the precision of the syringe pump and high voltage power supply used in the experiment. In order to use the EFD device with more confidence in obtaining pure chemicals from a complex mixture, quantitative description of the limit in resolution needs to be established. In addition, the purity determination for collected samples is another important work to do in the future. With the 2-D EFD device as a continuous chemical purification tool, complex mixtures can be processed to obtain pure substances. One of the unique advantages of this technique is that the sample can be introduced into the device over a long time period, and also, the “proof reading” mechanism allows the sample to be injected from different locations of the device. Because of these characteristics, 2-D EFD devices could be applied as a micropurification tool for the microreactor synthesis process in the future. Since the successful synthesis of urea, organic chemists have been running reactions in round bottom flasks for several hundred years. In such traditional equipment, many types of organic molecules can be synthesized. The modern pharmaceutical synthesis in the glasswares leads to the development of many therapeutic drugs, saving and improving quality of life for billions of people. Although the synthesis in conventional batch reactors has proven to be incredibly successful, we should also notice that it is inherently wasteful and inefficient. It is estimated that about 25-100 kg of waste is generated from the synthesis process for every 1 kg of active pharmaceutical product,82 creating significant disposal cost and an environmental problem. In addition, almost all raw materials for organic synthesis arise from petroleum feedstock, which was thought to be a practically limit resource.83 The increasing costs of starting materials will limit the  121  productivity unless a new technique is developed to make traditional synthesis more efficient. Recently, continuous flow microreactor technology has begun to emerge as an enabling tool for organic synthesis and has received much attention. Microreactors facilitate reactions by continuously passing reagents and starting materials through welldefined reaction channels in the dimensions of 10-1000 m. The small dimensions of the channel provide millisecond mixing times, and prevent hot spots which are typically generated in batch reactors.59 Microreactors enable the synthesis optimization to be done rapidly on a small scale, reducing the waste generated. Laminar flow dominates in the reaction channels and the mixing occurs by diffusion, which leads to excellent control over reaction times. The high surface to volume ratio allows the rapid change of reaction temperature through the application or removal of heat. More importantly, avoiding large reactors can reduce safety risk during the synthesis process.84 These advantages make continuous flow microreactors highly attractive for many synthetic applications. Various types of reactions have been successfully performed on such inexpensive, simple to build and easy to modify devices by both academic and industrial researchers.85 However, there are always significant amounts of impurities present in the collected synthesis products and the typical post-reaction purification processes are labor intensive. To fully exploit the advantages of the microreactor technique, continuous-flow microsynthesis should be followed by the continuous-flow micropurification to remove the unwanted by-products. However, such a combination has not been developed yet.86 The need for a highly effective, reliable and continuous flow micropurification technique for the synthesized molecules will significantly increase in the future. An existing 122  method, continuous free-flow electrophoresis, is one type of continuous purification technique. However, a limited resolving power for species with similar charge to size ratios restricts its practical applicability.36 The micropurification technique described in this thesis is suitable for purifying microsynthesis products. Because the theoretical separation resolution is infinite, the resolving power problem of the continuous free-flow electrophoresis can be solved, even for the separation of chiral isomers that usually exist together in the product mixture. Although the electrophoretic mobility difference between isomers is small, chiral selectors, such as cyclodextrins or crown-ethers could be added in the buffer solution to achieve the continuous purification of the isomers. Some other methods such as proportionally increasing the electric field and counter-pressure, utilizing controlling instruments with high precision, controlling device temperature during the purification process, would also help to increase the isomer purification ability in the 2-D EFD device.  123  Figure 6.1 The combination of microsynthesis and micropurification  As shown in Figure 6.1, the reaction process and the following micropurification can be integrated in the same microfluidic device. The product channel for the synthesis module could be considered as the sample injection channel for the purification portion, and the reaction product can be purified immediately after synthesis. The desired product can be continuously collected for further analysis, the by-products can be directed to the waste reservoir, and the unreacted reagents can be brought back to the initial reagent bottles. Such design would significantly increase the synthesis efficiency and reduce the amount of waste. The continuous nature allows the complete processing of the product mixtures that constantly migrate out, and the complex 2-D channel networks make it possible to simultaneously collect more than one component from a mixture. According to the discussion on the maximum sample processing speed in Chapter 5 (eq 5.24), a sample injection speed of 4.35 mm/s can be used to continuous purify the 124  analytes with the electrophoretic mobility difference of 5x10-8 m2V-1s-1 (a 5000 V electric potential is used). In this case, one milliliter sample can be purified within 15 min, if both width and depth of the channel are 500 m. This speed is much faster than other chromatography systems. Because the fabrication cost of the EFD devices are quite low, several parallel purification devices can be used simultaneously to increase the purification output. Typically, organic synthesis processes involve a series of many reaction steps, and micropurification devices can be added into any position as a module to purify the intermediate products. In addition, by integrating detection functional parts onto the device, such as a UV-Vis or laser-induced fluorescence detector, real-time product characterization can be conducted in situ. Thus, microsynthesis, micropurification and product characterization can be integrated on a single multifunctional microdevice. 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