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Development of a venting valve for nursing bottles Amerehbozchalouee, Meitham 2017

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Development of a Venting Valve for Nursing Bottles by  Meitham Amerehbozchalouee  B.Sc., in Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Iran, 2015  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES  (Mechanical Engineering)   THE UNIVERSITY OF BRITISH COLUMBIA  (Okanagan) December 2017  © Meitham Amerehbozchalouee, 2017  ii  The following individuals certify that they have read, and recommend to the College of Graduate Studies for acceptance, a thesis/dissertation entitled:  Development of a Venting Valve for Nursing Bottles  submitted by Meitham Amerehbozchalouee     in partial fulfillment of the requirements of   the degree of  Master of Applied Science   Dr. Sunny Ri Li, School of Engineering, UBCO Dr. Keekyoung Kim, School of Engineering, UBCO Supervisors  Dr. Abbas Milani, School of Engineering, UBCO Supervisory Committee Member  Dr. Lukas Bichler, School of Engineering, UBCO Supervisory Committee Member  Dr. Bahman Naser University Examiner    iii  Abstract This project aims to develop an innovative venting technique for nursing bottles with natural flow. Conventional nursing bottles are completely sealed except for the small hole on the teat. Without appropriate venting, the partial vacuum (i.e., negative pressure) inside the bottle results in gastrointestinal disorders in infants such as colic and secretory otitis. In addition, intraoral negative pressure transmitted to middle ear causes secretory otitis with a risk for delayed speech development. This study presents the design, modeling and fabrication process of new venting system for the nursing bottle based on an innovative flexible valve. Liquid silicon rubber was used to fabricate the valve, which was able to respond to the pressure difference between the inside and outside of the bottle. It not only closes the air entrance when the bottle stands on its base but also opens the air path while the infant sucks the milk. The specific geometry of the valve adjusts the response based on the pressure difference. The static structural response of the valve to both positive and negative pressures was simulated with finite element analysis. Moreover, the fluid-structural interaction analysis was carried out to show the transient response of both fluid flow and flexible structure to the pressure difference. In order to optimize the design, valves with different thicknesses and curvatures were tested. An experimental set-up was built using a nursing bottle equipped with pressure sensors and a vacuum pump to test the actual infant’s sucking condition. Five valves with different geometries were fabricated for the experiments. The experimental results were validated by the simulation results. Criterion parameters of the system, such as intake volume of milk, minimum pressure, working pressure, and temporal characteristics of the valves were statistically analyzed. Finally, the optimization based on the statistical results provided the most reliable design that can deliver the more comfortable feeding condition. iv  Lay Summary In bottle-feeding, the pressure difference between inside and outside of the bottle affects the feeding performance. As an infant sucks the teat and takes out the milk, the decrease volume of the milk causes partial vacuum pressure inside the bottle. This difference pressure makes the suction difficult for the infant, which further leads to gastrointestinal disorders and otitis. This project presents a new technique to eliminate these harmful phenomena. A new venting valve is designed and tested to reduce vacuum pressure inside the bottle. This valve is bonded to the bottom of bottle without any leakage. When the infant takes out the milk and produces partial vacuum inside the bottle, the valve opens the air pass in response to the interior negative pressure. The air passes through the valve, enters inside the bottle, and removes the vacuum pressure. This venting in performed simultaneously during each cycle of infant’s suction.   v  Preface The presented project in this thesis is the original work of the author. This research was conducted under the supervision of Dr. Sunny Ri Li and Dr. Keekyoung Kim at Thermal Management and Multiphase Flows Laboratory and Integrated Bio-Micro/Nanotechnology Laboratory in the School of Engineering at UBC Okanagan Campus.  The presented studies in this thesis has been submitted in the following journal:   M. Amereh, S. Kheiri, K. Kim, R. Li, , A New Venting Valve for Anti-colic Nursing Bottles, Medical Engineering & Physics, (under review)  vi  Table of Contents  Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ......................................................................................................................... vi List of Tables ..................................................................................................................................x List of Figures ............................................................................................................................... xi List of Symbols .......................................................................................................................... xvii List of Abbreviations ................................................................................................................. xix Acknowledgements ......................................................................................................................xx Dedication ................................................................................................................................... xxi Chapter 1: Introduction ................................................................................................................1 1.1 Importance of bottle-feeding........................................................................................... 1 1.2 Conventional nursing bottles .......................................................................................... 2 1.2.1 Design of nursing bottles ............................................................................................ 2 1.2.2 Problem of conventional nursing bottles .................................................................... 4 1.3 Mechanism of infant feeding .......................................................................................... 9 1.3.1 Bottle-feeding process ................................................................................................ 9 1.3.2 Comparison between breast-feeding and bottle-feeding........................................... 11 1.3.3 Sucking pressure ....................................................................................................... 13 1.4 Research objectives ....................................................................................................... 15 1.5 Thesis outline ................................................................................................................ 16 vii  Chapter 2: Design and Simulation of New Venting Valve .......................................................17 2.1 Analysis of conventional venting method..................................................................... 17 2.1.1 Experimental set-up for current bottles analysis ....................................................... 17 2.1.2 Experimental results from various bottles ................................................................ 19 2.1.3 Bubble generation phenomena .................................................................................. 22 2.2 Analysis of current base venting method ...................................................................... 25 2.2.1 Experimental set-up for venting performance analysis ............................................ 26 2.3 Significance of venting ................................................................................................. 28 2.4 Design of new venting valve......................................................................................... 32 2.5 Computational simulation ............................................................................................. 34 2.6 Chapter summary .......................................................................................................... 38 Chapter 3: Material Characterization and Fabrication Process Design ................................39 3.1 Material selection .......................................................................................................... 39 3.2 Mechanical property characterization ........................................................................... 41 3.2.1 Tensile mechanical property ..................................................................................... 42 3.2.2 Dynamic mechanical analysis (DMA) ...................................................................... 47 3.2.3 Compression test ....................................................................................................... 49 3.3 Fabrication process of venting valve ............................................................................ 50 3.3.1 Mold design and fabrication ..................................................................................... 50 3.4 Integration of valve with nursing bottle ........................................................................ 54 3.5 Chapter summary .......................................................................................................... 56 Chapter 4: Experimental and Computational Investigation of Venting Valves ....................57 4.1 Working principle of venting valve .............................................................................. 57 viii  4.2 Computational simulation ............................................................................................. 60 4.3 Experimental investigation ........................................................................................... 63 4.3.1 Experimental design.................................................................................................. 64 4.3.2 Categorization of performance criterions ................................................................. 64 4.3.3 Experimental results and discussion ......................................................................... 66 4.4 Chapter summary .......................................................................................................... 69 Chapter 5: Transient Computational Simulation for Venting Valves ....................................70 5.1 Theoretical backgrounds ............................................................................................... 70 5.1.1 Fluid-solid interaction ............................................................................................... 70 5.1.2 Governing equations for fluid ................................................................................... 72 5.1.3 Governing equations for solid ................................................................................... 73 5.2 Modeling of structures .................................................................................................. 74 5.2.1 Solid structure modeling ........................................................................................... 74 5.2.2 Fluid flow structure modeling ................................................................................... 76 5.2.3 Fluid-solid structure coupling ................................................................................... 77 5.3 Computational simulation results ................................................................................. 78 5.3.1 Deformation of venting valve ................................................................................... 78 5.3.2 Pressure distribution around venting valve ............................................................... 80 5.3.3 Velocity distribution around venting valve............................................................... 83 5.4 Chapter summary .......................................................................................................... 86 Chapter 6: Conclusion and future work ....................................................................................87 6.1 Conclusion .................................................................................................................... 87 6.2 Limitations .................................................................................................................... 88 ix  6.3 Future works ................................................................................................................. 89 Bibliography .................................................................................................................................91 x  List of Tables Table 1.1. Parameters of NNS measured for nine infants (adopted from [58]). ........................... 15 Table 2.1. Summary of dripping, squeezing and suction response on bubble generation for different bottles............................................................................................................. 21 Table 3.1. Qualitative comparison between PDMS and LSR properties. ..................................... 41 Table 3.2. Dimensions of dumbbell dies for tensile test (adopted from ASTM standard [71]). .. 42 Table 4.1. Mechanical properties of LSR ..................................................................................... 61 Table 4.2. Geometry of four valves .............................................................................................. 61 Table 5.1. Geometry of valves. ..................................................................................................... 78   xi  List of Figures Figure 1.1. Percentage of mothers who breast-feed their infants (adopted from [16]). .................. 2 Figure 1.2. Construction and mechanics of action for non-vented, under-vented and fully vented (adopted from [1]). ....................................................................................................... 4 Figure 1.3. Correlation between bottle-feeding and middle ear pressure. (A) Setup used to measure the pressures at the level of teat and inside middle ear. (B) Eustachian tube connecting the oropharynx to the middle ear (adopted from [1]). ............................... 5 Figure 1.4. Graphs of pressures inside the bottles and middle ear. Induction of negative pressure in the (A) non-vented bottle, (B) under-vented bottle, and (C) fully-vented bottle. The pressure transfer from the oropharynx into the middle ear for (D) non-vented  and under-vented bottles and (E) fully-vented bottle (adopted from [1]). ................... 6 Figure 1.5. Negative pressure transferred to the middle ear causes otitis media (adopted from [42]). ............................................................................................................................. 8 Figure 1.6. The negative pressure leads to otitis media and causes delay in speech  [42]. ............ 8 Figure 1.7. Mechanism of bottle-feeding. (A) Resting position. (B) Milk expression. (C) Negative pressure generation. (D) Breathing interruption and sallow. (E) Airway reopening and ending the cycle (adopted from [46]). ................................................ 10 Figure 1.8. Graph of sucking, swallowing and breathing coordination. (A) Swallow signals. (B) Superimposition of filtered swallows signals on the sucking (dashed line) and respiratory (solid line). (C) Polar illustration of the relative phase between sucking and breathing (adopted from [55]). ............................................................................ 11 xii  Figure 1.9. Comparison of oxygen saturation between breast-feeding and bottle-feeding for   both groups of infants who were fed with different bottles; (A) mean, (B) minimum (adopted from [55]). ................................................................................................... 13 Figure 1.10. 60 sec of the signals detected by the sensor during infant sucking. Peaks of expression and suction are magnified (adopted from [58]). ...................................... 14 Figure 2.1. Experimental set-up for testing performance of different types of nursing bottles.   (A) High-speed camera is set to visualize bubble generation. (B) Ameda Purely Yours Breast Pump. ................................................................................................... 18 Figure 2.2. Different types of bottles available in market. (A) Philips Avent bottle. (B) Bare bottle. (C) Born free bottle. (D) Comotomo bottle. (E) Dr. Brown's bottle. (F)  Playtex Nurser bottle. (G) Playtex VentAire bottle. (H) Prince Lionheart bottle. (I) ReliaBrand bottle. ...................................................................................................... 20 Figure 2.3. High-speed camera images of teat. (A) Time sequence of suction cycle without bubbles. (B) Time sequence of suction cycle with bubbles. ...................................... 23 Figure 2.4. High-speed camera images of teat. (A) Time sequence of squeezing cycle without bubbles. (B) Time sequence of squeezing cycle with bubbles. ................................. 24 Figure 2.5. Setup to test the bottle with venting valve. (A) Flexible rubber washer used in  current venting systems. (B) Schematic of the set-up comprises of sensors and vacuum pump. ............................................................................................................ 26 Figure 2.6. Real set-up. (A) Sensors, vacuum pump, container and interface to simulate actual sucking condition. (B) Sensors connections, sensor #I measures suction on the teat, sensor #II measures the vacuum inside the bottle. ..................................................... 27 Figure 2.7. ReliaBrand’s nursing bottles with petal venting valve. .............................................. 28 xiii  Figure 2.8. Pressure change inside the bottle with petal valve in three different conditions;     open valve, closed valve, and semi-open valve. ........................................................ 29 Figure 2.9. Teat deformation due to the inside vacuum. .............................................................. 30 Figure 2.10. Build up of negative pressure inside the bottle without venting. (A) Interior pressure. (B) Intake volume and flow rate. ................................................................ 31 Figure 2.11. Venting valve design. (A) Schematic illustration of the valve. (B) Schematic of bottle equipped with the venting valve under hydrostatic pressure. (C) Schematic     of the bottle equipped with the venting valve under inside vacuum pressure. .......... 33 Figure 2.12. Three drawing views of the venting valve design. ................................................... 34 Figure 2.13. FEA simulation of respons of the venting valve to the pressure difference. (A) Top view of volumetric mesh. Case I: vacuum pressure opens the crosscut: (B) deformation distribution, (C) equivalent (von-mises) strain distribution, (D) equivalent (von-mises) stress distribution. Case II: hydrostatic pressure closes the crosscut: (E) deformation distribution, (F) equivalent (von-mises) strain   distribution, (G) equivalent (von-mises) stress distribution....................................... 37 Figure 3.1. Bubbles generated after mixing components of PDMS and LSR. (A) At the time of mixing. (B) After 24 hours without vacuum. ............................................................. 40 Figure 3.2. The geometry of standard dumbbell dies for tensile test (adopted form ASTM standard [71]). ............................................................................................................ 42 Figure 3.3. 5960 Dual column tabletop testing system. ................................................................ 43 Figure 3.4. Mold used to cast LSR. (A) SolidWorks design. (B) LSR was poured into              3D-printd mold. (C) Casted dumbbell die and thin samples. ..................................... 45 Figure 3.5. Broken dumbbell die; Cavities in the surface close to the failure location ................ 46 xiv  Figure 3.6. Stress-strain curve of tensile test. ............................................................................... 46 Figure 3.7. DMA test. (A) Schematic representation of the RSA G2 controlled strain DMA.     (B) Sample is fixed in DMA machine. ...................................................................... 47 Figure 3.8. Dual cantilever clamp test. ......................................................................................... 48 Figure 3.9. Compressive test. (A) LSR disks under mechanical test machine. (B) Stress-Strain curves for cured LSR samples to calculate average Young’s modulus. .................... 50 Figure 3.10. Three drawing views of the designed molds. (A) Positive. (B) Negative. ............... 51 Figure 3.11. Fabricated molds and corresponding cured samples. (A) Printed with da Vinci     3D-printer. (B) Printed with poly jet 3D-printer. (C) Machined aluminum mold. .... 53 Figure 3.12. Fabricated venting valve. (A) Surgical blades used to make crosscut on top of the valve. (B) Leaflets on top of the valve. ...................................................................... 53 Figure 3.13. Thermal bonding. (A) Aluminum supports. (B) PP layer placed on the valve. (C) The support placed between the pp layer and machine’s plate. (D) The valve is sandwiched between PP layers and the bottle. ........................................................... 54 Figure 3.14. Final samples to be tested. (A) Inside and (B) outside view of the bonded valve.   (C) The bottom part of the bottle is screwed to the body. ......................................... 55 Figure 4.1. Bending analogy between leaflets and cantilever beam ............................................. 58 Figure 4.2. Maximum deflection of leaflets with different thicknesses. ...................................... 60 Figure 4.3. FEA simulation of the five different valves under two conditions. Case I:   hydrostatic pressure closes the crosscut, (A) deformation distribution, (B)   equivalent (von-mises) strain distribution, (C) equivalent (von-mises) stress distribution. Case II: vacuum pressure opens the crosscut, (D) deformation xv  distribution, (E) equivalent (von-mises) strain distribution, (F) equivalent (von-mises) stress distribution. ........................................................................................... 62 Figure 4.4. Fabricated valves with different curvatures. (A) 8.5 mm. (B) 7.5 mm. ..................... 63 Figure 4.5. The pressure change inside the bottle equipped with new venting valve................... 65 Figure 4.6. Pressure change inside tested bottles equipped with venting valve. .......................... 66 Figure 4.7. Results of experimental tests for five criterions of performance. (A) Intake volume after two minutes. (B) Minimum pressure. (C) Minimum working pressure. (D)  Time of minimum pressure. (E) Time of working pressure (n=5, *p < 0.05). .......... 68 Figure 5.1. The valve with hexahedral mesh. Fine mesh was applied to the regions close to the leaflets. ....................................................................................................................... 74 Figure 5.2. Fluid-solid interaction surfaces of the valve. ............................................................. 75 Figure 5.3. The fluid flow region. (A) The meshed geometry of fluid. (B) Illustration of the   inlet, outlet and the venting valve geometry. ............................................................. 76 Figure 5.4. Distribution of the mesh deformation in the valve structure. ..................................... 79 Figure 5.5. Deformation of the leaflets at three different time steps, (A) t=0 sec, (B), t=0.5 sec, and (C) t=1 sec. .......................................................................................................... 80 Figure 5.6. Contour of pressure at t=1 sec. ................................................................................... 81 Figure 5.7. Pressure drop across central axis at t=0.5 (blue line) sec and t=1 sec (red line). ....... 82 Figure 5.8. Pressure profile of the flow imidiately after passing the gap across the line close to the leaflets, at t=0. 5 sec (blue line) and t=1 sec (red line). ....................................... 82 Figure 5.9. Velocity contour at t=1 sec. ........................................................................................ 83 Figure 5.10. Velocity change across the central axis at t = 0.5 sec (blue line) and t = 1 sec (red line). ........................................................................................................................... 84 xvi  Figure 5.11. The velocity change imidiately after passing the gap across the line close to the leaflets, at t=0.5 sec (blue line) and t=1 sec (red line). .............................................. 85   xvii  List of Symbols m Mass ρ Density V Volume P Pressure V Velocity L Length of Crosscut R Radius of Curvature t Thickness u Velocity in x direction v Velocity in y direction w Velocity in z direction ɛ Strain 𝜎 Stress E Young’s Modulus ν Poisson’s Ratio 𝑙 Length of the sample 𝑤 Width S Stiffness  𝑡 Time δ Deflection I Second Moment of Inertia xviii  f Force M Bending Moment  xix  List of Abbreviations LSR Liquid Silicon Rubber PDMS Polydimethylsiloxane DMA Dynamic Mechanical Analysis FSI Fluid Structural Interaction GF Geometry Factor     xx  Acknowledgements Foremost, I would like to express my sincere thanks to my supervisors, Professor Sunny Ri Li and Professor Keekyoung Kim, for all supports and guidance they provided me in this project. Their motivation, enthusiasm, and knowledge helped me in all the time of research and writing of this thesis. It has been a period of intense learning for me, not only in the scientific area, but also in a personal level. Beside my advisors, I would like to thank the rest of my thesis committee; Professor Abbas Milani and Professor Lukas Bichler for their encouragement and insight comments. I thank my fellow labmates in Thermal Management and Multiphase Flows Laboratory and Bio-Micro/Nanotechnology Laboratory in the School of Engineering at UBC Okanagan Campus for assisting me to perform my experiments. Special thanks are owed to my parents, whose have spiritually supported me throughout my life and years of education.  xxi  Dedication    This work is dedicated to  my beloved family for all their support and encouragement1  Chapter 1: Introduction Bottle-feeding is the practice of feeding infants with an alternative formula instead of breast milk. Pediatricians mostly suggest exclusively breastfeeding during the first six months of life without supplementary formula for all full-term and healthy infants [8]. Although breast milk is the best nutritional formula for infants, it is not possible for all mothers to exclusively breast-feed their infants. Lifestyle, comfort level, and specific medical situations are among primary reasons why mothers switch to bottle-feeding. To maintain normal growth and standard health, the baby formula must include special nutrition such as carbohydrate, fat, protein, vitamins and minerals [9].  1.1 Importance of bottle-feeding Bottle-feeding is very important for the healthy growth and development of babies. As common as breast-feeding, a large number of infants throughout the world rely solely on the bottle-feeding [10]–[12]. Moreover, most breast-fed babies also need to switch to the bottle-feeding as they grow [13]–[15]. Figure 1.1 illustrates the statistics trend of the breast-feeding in different provinces of Canada between years 2003 and 2012 [16]. Although the graph shows the growth in the percentage of mothers who exclusively breast-feed their infants for six months or more, the percentage of mothers who do not exclusively breast-feed their infants is still dominant. For instance, in British Columbia, 41% of mothers exclusively breast-fed for six months or more in 2011-2012. This indicate that 59% of mothers might be still partially or even completely relying on the bottle-feeding, which means the importance of the bottle-feeding for infants. 2     1.2 Conventional nursing bottles 1.2.1 Design of nursing bottles Establishing a safe and efficient bottle-feeding is requisite for the healthy nourishment of newborn infants. Therefore, the design and fabrication of nursing bottles are essential for bottle-feeding. Conventionally, nursing bottles are entirely sealed except the small opening on the teat for delivering milk [17]. During feeding, infants suck the teat to withdraw the formula out of the bottle, and air enters through the teat to compensate the reduced volume of the formula. As a result, air bubbles are formed in the milk in proximity to the teat. When the infants keep sucking on the teat, these small air bubbles are often ingested by the infants. The ingestion of the air bubbles leads to colic and other gastrointestinal disorders. This unwanted ingestion of air is a long-recognized problem in the infant feeding [1]–[7].  As shown in Figure 1.2, three types of bottles have been studied to reduce the air ingestion of infants: non-vented, under-vented, and fully vented bottle [1]. The first type, which is called Figure 1.1. Percentage of mothers who breast-feed their infants (adopted from [16]). 3  none-vented bottle, is a simple solid walled design with a cape holding the teat. An under-vented bottle is the second type of designs with a modified cape [18]–[23]. This design has focused on adding a valve to the teat, which restricts the amount of air entering to the bottle through the teat. The flange of this design has slits or holes through which the air can enter the bottle. Once the milk volume decreases enough to form a vacuum inside the bottle, the air starts to flow through the flange. However, this design generates a partial vacuum inside the bottle, which makes a condition called under-vented. Infants have to suck harder to withdraw the milk, causing ambient air to enter the infant’s mouth and stomach and resulting in problems such as colic, spit-up, and burping [1]. In the fully-vented design, a direct air transfer is established across a tube between inside and outside the bottle [24]–[26]. This tube is connecting the threads of the cape and the cavity at the bottom of the bottle. Therefore, the airflow via the tube eliminates the vacuum inside the bottle. Although air is able to enter the bottle from the lateral part of the teat, the risk of mixing bubbles with the milk still remains. Additionally, some of the fully-vented designs consist of several parts which are in the risk of leakage and difficulty to be cleaned [27]. 4              1.2.2 Problem of conventional nursing bottles As shown in Figure 1.3, Brown and Magnuson developed a setup to test the three types of conventional bottles [1]. Two low-pressure sensors were used to measure the pressure from the teat, which equals the pressure of the middle part of infant throat (i.e., oropharynx), and the pressure from the infant’s middle ear. For all of the tested bottles, the pressure at the teat was initially positive and then dropped in non-vented and under-vented bottles by maintaining suction on the teat. This pressure drop formed negative pressures, which act as a resistance for fluid flow and make infants suck harder to gain the milk. This experiment shows that continuous suction can generate a partial vacuum inside the bottle for the non-vented and under-vented bottles. After the liquid was removed, high negative pressures, -10.25 kPa and -5.7 kPa, were formed in the non-vented and under-vented bottles, respectively. This causes ambient air entering to the bottles. Then,  Figure 1.2. Construction and mechanics of action for non-vented, under-vented and fully vented (adopted from [1]). 5  the infant swallowed the air mixed with the milk, which resulted in problems such as colic, spit-up, and burping. Additionally, this generates significant negative pressure in baby’s oral cavity, which may lead to secretory otitis [28]–[31]. As air bubbles keep entering into the milk, nutrient deterioration is another issue with the under-vented bottles [21], [32]. Figure 1.4 shows that the increment rate of vacuum in the non-vented bottle (A) is steeper than the under-vented bottle (B). The reason for this difference is that the under-vented bottle has some slits in the flange through which the air can enter the bottle. On the other hand, the positive pressure was observed in the fully-vented bottle as shown in Figure 1.4 (C). Figures 1.4 (D) and (E) show the direct correlation between the negative pressures generated at the teat due to the infant’s sucking and the pressures in the middle ear of infants.             A B Figure 1.3. Correlation between bottle-feeding and middle ear pressure. (A) Setup used to measure the pressures at the level of teat and inside middle ear. (B) Eustachian tube connecting the oropharynx to the middle ear (adopted from [1]). Oropharynx Eustachian tube 6   In the non-vented and under-vented bottles, once the negative pressure generated in the oropharynx is high enough, it transfers directly via Eustachian tube (Figure 1.3 (B)) to the middle ear. However, in the fully-vented bottle, the positive pressure in the middle ear is observed because there is no negative pressure inside the bottle transferring to the middle ear. The strong sucking on the teat due to the vacuum inside the bottle leads to the middle ear evacuation, which closes the Eustachian tube. The negative pressure in the middle ear is one recognized causes of serous otitis. This pressure causes an effusion of fluid that leads to hearing A B C D E Figure 1.4. Graphs of pressures inside the bottles and middle ear. Induction of negative pressure in the (A) non-vented bottle, (B) under-vented bottle, and (C) fully-vented bottle. The pressure transfer from the oropharynx into the middle ear for (D) non-vented and under-vented bottles and (E) fully-vented bottle (adopted from [1]). 7  impairment and a risk for delayed speech development, as shown in Figure 1.5. In otitis media, the eardrum is under pressure of the effused fluid. The transferred negative pressure is also related to some other middle ear diseases such as adhesive otitis and cholesteatoma [33]–[41]. In view of the above problems, increasing attentions have been paid to fully-vented bottles, which allow the direct air transfer from outside to inside the bottle. Because the venting system allows infants to take milk without fighting the negative effects of vacuum and teat collapse, infants are fed more comfortably. Currently, there are two major designs of fully-vented bottles on the market. One is a front-vented design for which airflow is allowed to enter from the front of the bottle. Another is a base-vented design for which the bottle has a vent located on its base. As the infants are fed, airflow goes through the valve directly into the bottom cavity. Although these designs have relatively solved the venting problem, there is still risk of leakage.  In summary, the negative pressure in the nursing bottle is a precursor to cause serious problems for infants. First, the release of fluid in the middle ear may lead to delayed speech and cognitive development for infants, as shown in Figure 1.6 [42]. This disease is due to the transmitted negative pressure induced by the inadequate venting from the bottle-feeding. Second, the vacuum can entrain the air into the bottle and generate bubbles in the milk to deteriorate the nutrient of the milk. The digestion of the milk mixed with air also results in problems such as colic, spit-up, and burping.  8                  Herein, more specialized investigation for infants feeding is necessary to resolve above concerns. Normal feeding dynamics is a complex process that includes series of fundamental information on feeding pattern. Comparison of variables involved in breast-feeding and bottle-feeding offers a deep sight to understand the nature of phenomena occurs during sucking. In the next section, therefore, the mechanism of feeding investigated in previous literature is discussed in detail.    Figure 1.5. Negative pressure transferred to the middle ear causes otitis media (adopted from [42]). NegativePressureOtitisDelayed in Speech DevelopmentFigure 1.6. The negative pressure leads to otitis media and causes delay in speech  [42].  9  1.3 Mechanism of infant feeding 1.3.1 Bottle-feeding process Different electrophysiological, radiographic and real-time ultrasound methods were conducted to investigate the intra-oral regime of the feeding process [43]–[45]. As shown in Figure 1.6, a general description of the feeding mechanism was illustrated by Bu'lock et al. [46]. The frequent movement of the tongue on the teat or teat from front-to-back (i.e., antero-posterior) delivers a bolus of milk to the pharynx (i.e., the part of throat behind mouth). Milk is trapped in the teat by the coordinated motion of the mandible and gums. Then, the compression of the teat in combination of the inter-oral negative pressure squeezes the trapped milk out. The precise contribution of the teat compression and the inter-oral negative pressure is required to produce both expression pressure and suction pressure. The term expression is corresponding to the tongue movement against the teat to withdraw the milk, and suction is due to the inter-oral negative pressure [47], [48]. The combined both pressures suck out the milk from the teat. Bu'lock et al. compiled a pictorial representation of the process of bottle-feeding as shown in Figure 1.7 [46]. The feeding starts with resting position. Tongue goes beneath the teat that is held in the mouth (A). After 0.25 sec, the expression of the milk is started by the elevation of the lower jaw and the jaw compresses the teat to squeeze the milk (B). The negative pressure formed by the movement of the tongue and lower jaw further squeezes the milk (C). Thereafter, the sallow starts by the wave of the tongue. At this step, the airway is closed and breathing is briefly interrupted (D). Finally, tongue goes into a position to start another cycle and airway reopens again (E). The entire process lasts approximately one second.   10                    A B C D E Figure 1.7. Mechanism of bottle-feeding. (A) Resting position. (B) Milk expression. (C) Negative pressure generation. (D) Breathing interruption and sallow. (E) Airway reopening and ending the cycle (adopted from [46]). 11  1.3.2 Comparison between breast-feeding and bottle-feeding Mechanism of infants feeding is a complex process that comprises of coordinated sucking, swallowing and breathing [49]–[51]. The overall coordination of these steps in breast-feeding and bottle-feeding are slightly different in terms of the elasticity of the breast nipple and the amount and stability of the milk flow. One of the important differences between breast-feeding and bottle-feeding is the level of oxygen saturation. Several studies have reported that breast-fed infants have higher oxygen saturation [52]–[54]. They implied that the coordination of sucking, swallowing and breathing firmly affected the level of oxygen in infants’ blood. Figure 1.8 depicts the graph of five second breast-feeding for an infant. Goldfield et al. [55] reported the uniform distribution of swallowing during breast-feeding. Figure 1.8 (A) shows four distinctive peaks during five-second detection. These sharp signals indicate that the infant could successfully produce four consecutive swallows.  Figure 1.8. Graph of sucking, swallowing and breathing coordination. (A) Swallow signals. (B) Superimposition of filtered swallows signals on the sucking (dashed line) and respiratory (solid line). (C) Polar illustration of the relative phase between sucking and breathing (adopted from [55]).  A B C 12  Figure 1.8 (B) shows filtered signals in which solid lines and dashed lines are respectively related to respiratory and sucking. Based on this figure, each swallow (peak) occurs at the peak of sucking at which the respiratory signal is flatted. These four swallows are also shown in polar coordinates, which specify their position in 360° distribution of sucking and respiratory as shown in Figure 1.8 (C). If the bottle-feeding can intimately simulate this physiologic pattern, it would deliver good oxygen saturation. The coordination of breast-feeding processes was also compared to the bottle-feeding among infants who used two different nursing bottles [55]. These researchers studied 36 healthy newborn infants who successfully finished the transition from breast- to bottle-feeding. One group of infants used bottle 1 (Playtex bottle that collapses during feeding) and the other group used bottle 2 (Avent newborn bottle). These two groups were tested within two weeks of bottle-feeding. Bottle 1 had a teat with elasticity and shape similar to the human nipple. In addition, the reservoir in this type of bottle was deformable which prevented incising from the hydrostatic pressure during feeding. As a result, only infants bottle-fed with bottle 1 could keep producing same coordinated sucking, swallowing and breathing as breast-feeding coordination. Figure 1.9 depicts the stability of coordination of feeding processes and oxygen saturation for both groups. The mean and minimum oxygen saturation for both groups during breast-feeding and bottle-feeding are shown in the figure. Based on this study, therefore, bottle-feeding extremely affect the coordination of feeding processes. Infants can promote same coordinated sucking, swallowing and breathing if they use a bottle that mimics characteristics of breast-feeding.     13                        1.3.3 Sucking pressure Among three elements of the coordinated feeding, described as sucking, swallowing and breathing, the sucking has been widely studied to understand the skills of infants while they transfer to bottle-feeding. The bottle-feeding performance of an infant is a consequence of both oral skills and external conditions such as the shape and flexibility of teats. Therefore, several studies were conducted on the development of sucking as a major component of skills in infants oral feeding [56]. Sucking may occur in two different patterns, nutritive (NS) and nonnutritive (NNS) pattern. NS pattern takes place in 1 cycle/s during which infant ingests the milk, however, NNS pattern occurs in 2 cycle/s and no ingestion is involved [56]. Both NS and NNS contain expression and suction. Mizuno and Ueda studied the difference between breast-feeding and bottle-feeding in terms of NS and NNS [57]. They reported that in breast-feeding, the sucking pressure in NNS is –Breast-feeding                    Bottle-feeding Breast-feeding                    Bottle-feeding A B Figure 1.9. Comparison of oxygen saturation between breast-feeding and bottle-feeding for both groups of infants who were fed with different bottles; (A) mean, (B) minimum (adopted from [55]). Bottle 1   Bottle 2 14  93.1±28.3 mmHg and in NS is –77.3±27.0 mmHg. In bottle-feeding, however, these pressures are respectively -27.5±11.2 mmHg and -87.5±28.5 mmHg. This means that the sucking pressure in bottle-feeding during NNS is lower than NS. In addition, the frequency is higher and the duration of sucking is shorter in NNS comparing to NS for both breast- and bottle-feeding. Grassi et al. developed a new sensor to measure the NNS [58]. The parameters, such as the number of sucks/sec (Hz), expression duration (sec), suction duration (sec), and time interval between peak suction and expression (tS-tE , sec) listed in Table 1.1, are derived from the figure for nine tested infants. Figure 1.10 shows 60 sec of the signals detected by the sensor during infant sucking. The 6.5 sec of this signal is filtered and magnified to investigate the bursts of sucking. The red lines represent the positive expression and the blue lines represent the negative suction, which are two components of sucking. Thus, the suction pressure is dominant and more important for simulating the bottle-feeding mechanism. In this research project, we developed an experimental set-up to measure suction pressures on the nursing bottles.        Figure 1.10. 60 sec of the signals detected by the sensor during infant sucking. Peaks of expression and suction are magnified (adopted from [58]). 15                   Table 1.1. Parameters of NNS measured for nine infants (adopted from [58]). Subject (tS-tE) (sec) Frequency of sucks s−1 (Hz) Expression  duration (s) Suction duration (s) 1 0.27 ± 0.04 2.7 0.3± 0.07 0.31 ± 0.07 2 0.27 ± 0.03 2.5 0.31 ± 0.07 0.32 ± 0.07 3 0.25 ± 0.02 2.6 0.32 ± 0.06 0.32 ± 0.06 4 0.35 ± 0.03 2.2 0.33 ± 0.08 0.34 ± 0.08 5 0.38 ± 0.05 1.9 0.35 ± 0.09 0.36 ± 0.09 6 0.31 ± 0.05 2.3 0.34 ± 0.09 0.36 ± 0.09 7 0.37 ± 0.03 2.2 0.35 ± 0.09 0.37 ± 0.09 8 0.36 ± 0.03 1.8 0.36 ± 0.09 0.38 ± 0.09 9 0.24 ± 0.02 3.3 0.35 ± 0.09 0.37 ± 0.09  1.4 Research objectives Bottle-feeding plays a substantial role for the healthy growth of infants. There is a huge demand to investigate babies normal feeding to establish standard criterions such as milk flow and suction pressure. For the safe and healthy bottle-feeding, theses criterions must be taken into account in the design of nursing bottles. Suction pressure and its dependency on the external parameters have been extensively studied. Exerting high suction pressure to gain the normal flow rate causes problems such as colic and otitis. The pressure inside the bottle controls the infant suction pressure. Therefore, it is important to compensate the pressure inside the bottle. This project aims to develop a new venting technique to enhance the performance of nursing-bottles.  Therefore, the objectives of this project can be listed as: 1. Design a simple venting valve that is able to eliminate the interior pressure inside nursing-bottles, and prevent bubble generation during feeding. 16  2. Propose fabrication process and bonding method to integrate the valve to the bottle. 3. Test the performance of the valve under actual feeding condition. 4. Optimize the design of the valve based on the various performance criterions. 5. Perform computational simulation to analyze the venting phenomena. To achieve the objectives, a simple venting valve was fabricated using liquid silicon rubber. The valve was bonded to the nursing-bottle and tested using an experimental set-up. The design of the valve was optimized by experimental and computation investigations.  1.5 Thesis outline This thesis describes development of a venting valve for nursing-bottles. As the first step, literature review was done in chapter 1 to understand the mechanism of infant feeding, particularly those parts related to the sucking process. Chapter 2 describes the performance of conventional nursing-bottles and the significance of venting. Then, the design of a new venting valve to eliminate the interior negative pressure inside bottle is proposed in detail. In chapter 3, the fabrication process of the venting valve using liquid silicon rubber is discussed. Chapter 4 includes the experimental and computational analyses to optimize the valve design. Different valves with different geometries were fabricated and experimental investigation was performed to compare their performances. Chapter 5 explains the transient computational simulation of the venting phenomena. Using fluid-structural interaction (FSI) in ANSYS, the transient phenomena of venting around the valve was visualize. Result of FSI simulation also demonstrated the effect of geometrical parameters, e.g., thickness and curvature radius of the valve, on the venting parameters such as pressure and velocity. Finally, chapter 6 gives a short conclusion and a future perspective of the development of the valve for nursing bottles. 17  Chapter 2: Design and Simulation of New Venting Valve  The objective of this chapter is to propose a new technique of venting to improve the performance of the nursing bottles. To aim this target, the first step was to find the problems with the conventional nursing bottles. An experimental set-up was developed to study different bottles. This set-up was also used to test the new venting valve. In addition, finite element method was used to evaluate the response of the valve to the operation condition. Results showed that the valve can successfully respond to the pressure difference inside the bottle.  2.1 Analysis of conventional venting method Venting, dripping and bubble generation are among important characteristics identifying the performance of nursing bottles. To have a thorough perspective of these essential parameters, available nursing bottles on the market were analyzed under both suction and squeezing conditions. The negative pressure in the suction condition plays a role in following two aspects: (1) to retain the teat and the breast in position within the mouth, and (2) to aid refilling the teat by milk. In the squeezing condition, the movement of the tongue and lower jaw on the teat withdraws the milk, which depends mostly on the shape and the size of the teat and the hole. However, expression of the milk by squeezing plays little role in obtaining the milk. The functionality of various current bottles to both suction and squeezing were experimentally tested.   2.1.1 Experimental set-up for current bottles analysis Once the lower jaw raises the teat, a pool of milk is captured within the teat. At this point, the bottle-feeding concurs with the breast-feeding. If the bottle teat is suitably compliant, the baby can constrict the neck of the teat and squeeze out the milk. If the material is relatively stiff, the teat 18  cannot be constricted and consequently the milk flows back into the bottle, which reduces the efficiency of feeding. Therefore, the suction pressure generated by the baby becomes more important and can be considered as the predominant mechanism for the bottle-feeding.  Figure 2.1 (A) illustrates an experimental set-up by which the behavior of each bottle can be tested. Each bottle is placed at 45º that is similar to actual feeding. The suction condition is applied on the teat using a vacuum pump (Figure 2.1 (B)). The plastic enclosure seals the connection between the vacuum pump and the teat. High-speed camera is used to visualize the fluid dynamics inside the teat.                       High-speed camera Formula Bottle Vacuum Pressure A B  Figure 2.1. Experimental set-up for testing performance of different types of nursing bottles. (A) High-speed camera is set to visualize bubble generation. (B) Ameda Purely Yours Breast Pump. 19  As described before, the infant feeding involves the sucking condition as well as squeezing condition. To simulate the sucking action of the baby, ‘Ameda Purely Yours Breast Pump’ was used as shown Figure 2.1 (B). The structure of the pump was modified to facilitate the testing of different bottles. The conical portion was cut and replaced by a syringe so that the testing could be done without affecting the venting in the front vented bottles. The pump has an option to vary the frequency of sucking as well as the suction strength. A high-speed camera system was used to visualize the air bubble generation  and teat deformation. The frequency of the breast pump was set to approximately 1 Hz. The bottle teat was placed inside the opening of the pump and the bottle was mounted at approximately 45 to the vertical.  The squeezing response was tested manually. For this, the teat on the bottle mounted on the stand was squeezed using pliers, while the high-speed camera was capturing video clips.   2.1.2 Experimental results from various bottles Various commercially available bottles with different venting design as depicted in Figure 2.2 were tested. The response of the bottles to the pressure in terms of bubble generation and dripping was summarized in Table 2.1. The occurrence of bubbles depends on the pressure difference between the inside of the bottle and the ambient resulting from the transfer of liquid from the bottle to outside. If the venting is adequate, air enters the bottle through the vents and no bubbles are generated from the teat. In case of poor venting, air enters the bottle in the form of bubbles through the teat.     20                             E F A B C  D G H I   Figure 2.2. Different types of bottles available in market. (A) Philips Avent bottle. (B) Bare bottle. (C) Born free bottle. (D) Comotomo bottle. (E) Dr. Brown's bottle. (F) Playtex Nurser bottle. (G) Playtex VentAire bottle. (H) Prince Lionheart bottle. (I) ReliaBrand bottle. 21    Table 2.1. Summary of dripping, squeezing and suction response on bubble generation for different bottles. Bottle Design Drip Squeezing response/ bubbles Bubbles in suction Comments Philips Avent Front-vented, vents on the curved portion Initial, stops after a while Yes/Yes Yes  Bare Plunger at the back, gets pulled inside due to vacuum No No No  Born Free Front vented, air enters through threads of the cap and ends up in the milk through a small cut in a rubber petal Little Yes/Yes Sometimes Bubbles seen only sometimes at low suction strengths ComoTomo Front Vented, vents on the curved portion No Yes/Yes No  Dr. Brown’s Front vented, air enters through threads of the cap and ends up at the bottom of the bottle through a pipe Continuous No None  Playtex Nurser Milk contained in a collapsible plastic bag Continuous No Yes  Playtex VentAire Back Vented, a petal in front of holes, air flows in due to pressure difference Initial, stops after a while Yes/Yes Yes  Prince LionHeart Liquid release in 2 stages. The air required enters through the section between the two zones No No No Bubbles passed through the teat when squeezed after the test, indicating vacuum inside the bottle Reliabrand Back Vented, a petal in front of holes, air flows in due to pressure difference No Yes/No No  22  2.1.3 Bubble generation phenomena In this section, various responses of the bottle to both suction and squeezing conditions are presented. For each condition, high-speed camera visualized the flow rate and bubble generation through the teat. Figure 2.3 (A) shows the flow phenomenon for one suction cycle without bubbles. As the magnitude of suction increased, the liquid initially flowed out as a series of droplets and developed into a continuous flow. The flow stopped in a symmetric manner with the fully developed flow. It was first converted into a series of droplets and then stopped altogether. The air required replacing the volume of liquid passed through the venting, and thus no bubbles were seen entering through the teat. Figure 2.3 (B) shows the flow phenomenon for one suction cycle with bubbles. The initial part was similar to the suction cycle without bubbles. However, during the last part of the cycle, the flow stopped altogether and air entered into the bottle through the teat in the form of bubbles. The venting was not able to provide sufficient air to compensate the negative pressure inside the bottle and hence air flowed through the teat.                 23                                     B A  Figure 2.3. High-speed camera images of teat. (A) Time sequence of suction cycle without bubbles. (B) Time sequence of suction cycle with bubbles. 24    A B  Figure 2.4. High-speed camera images of teat. (A) Time sequence of squeezing cycle without bubbles. (B) Time sequence of squeezing cycle with bubbles. 25  Figure 2.4 (A) shows the response of a bottle to squeezing without bubbles. The flow began with a series of small droplets transforming into a continuous flow and receding in a similar manner. Figure 2.4 (B) shows the response of a bottle to squeezing with bubbles. The initial part of the cycle is similar to the flow without bubbles. The venting did not provide sufficient air to compensate for the negative pressure inside the bottle. Hence, air entered through the teat and formed bubbles inside the bottle. Based on the results, it can be concluded that although the venting from the teat could partially remove the negative pressure inside the bottle, it still generated bubbles inside the milk. These bubbles are often ingested by infants. The ingestion of the air bubbles leads to colic and other gastrointestinal disorders. Therefore, the base venting is considered as the better method to be able to eliminate the above problems.   2.2 Analysis of current base venting method ReliaBrand Co. has manufactured bottles with the bottom venting method, which utilizes a simple washer connected to the bottom cap of the bottles. The venting part of the bottle has six petal holes as shown in Figure 2.5 (A). The flexible washer covering these holes is placed on the inner side of the bottom cap of the bottle. The outer part of the washer is thinner and therefore easier to be deformed. During suction, the negative pressure inside the bottle pulls this thinner part inward and opens the petal holes to let the airflow enter into the bottle. In addition, when the milk inside the bottle applies positive pressure on the washer, it covers the petal holes to prevent the bottle from leakage. As a result, this venting helps infants to gain the milk without fighting the inside vacuum.    26            2.2.1 Experimental set-up for venting performance analysis To examine the venting performance of current bottles, a set-up comprised of two pressure sensors, vacuum pump, container and interface device was developed as shown in Figure 2.5 (B) and Figure 2.6 (A). Correlation between the adjustment of the venting and the fluid flow can be investigated with the experimental set-up. As illustrated in Figure 2.6 (B), one sensor is connected to the suction enclosure close to the teat where the vacuum is exerted by the pump, and the other sensor is connected to the body of bottle measuring the inside pressure. The pump was set to apply a sinusoidal pressure with an amplitude of 18 kPa and 1 Hz frequency. The bottle was placed at 45 to the vertical and fixed with a clamp on the stand. The conical part sealed the place where the vacuum was being applied. This vacuum sucked the milk out of the teat and decreased the volume of liquid inside the bottle. As a result, the inside pressure dropped with the same frequency as the suction pressure, but different amplitude. The withdrawn liquid was collected into a container.   A Psuck PVacuum Pin t t Q B Figure 2.5. Setup to test the bottle with venting valve. (A) Flexible rubber washer used in current venting systems. (B) Schematic of the set-up comprises of sensors and vacuum pump. 27                          Vacuum pump Waste container Venting valve Pressure sensors Figure 2.6. Real set-up. (A) Sensors, vacuum pump, container and interface to simulate actual sucking condition. (B) Sensors connections, sensor #I measures suction on the teat, sensor #II measures the vacuum inside the bottle.  Sensor II Connection  Sensor I Connection  A B 28  2.3 Significance of venting  Commercially available ReliaBrand’s nursing bottles were tested to investigate the quality of venting as shown in Figure 2.7. Bottles were mounted on a fixed stand and the vacuum pump applied suction on the teat. The vacuum pulled out the water from the teat and caused insignificant deformation at the teat. Then, the pressure reached the minimum value at which the pump stopped sucking the teat (i.e., half a cycle). At this point, the slight deformation returned to the initial form. This physical change together with the slight negative pressure pulled the air and generated bubbles inside the teat.          Following three experimental cases were conducted. As shown in Figure 2.8, same suction pressure (red dashed line) as the previous test is applied.  Case I: The petal holes were covered with a tape to close the air pass. In this case, the valve was fully closed. Two sensors measured instant pressures at both teat and inside the bottle. Then, the suction pressure was applied and the liquid volume inside the bottle decreased. Following this decrement, the pressure (blue line) inside the bottle dropped as shown in Figure 2.8. No air entered the bottle and the negative pressure increased gradually. This condition continued until the vacuum Figure 2.7. ReliaBrand’s nursing bottles with petal venting valve. 29  at the teat could not overcome the inside vacuum and hence no liquid flowed out from the teat. At this point, further suction led to deform the teat to gain more liquid, as shown in Figure 2.9. After 120 sec of suction, 10 mL liquid was obtained. Case II: Petal holes were open for testing the performance of the valve. In this case, half of the holes were covered at the beginning of the experiment. The suction pressure was applied and two sensors measured the pressures. Results showed that the semi-open valve worked properly and no negative pressure (yellow line) was produced inside the bottle as shown in Figure 2.8. For the same period as Case I, the intake volume was 22 mL. Case III: Finally, all holes were completely open. Results showed no   difference comparing open valve-with the semi . As shown in Figure 2.8, the inside pressure (green line) proved that there was no vacuum produced inside the bottle. The intake volume was the same as the semi-open valve. These data reveal that the venting based on petal holes is not self-adjustable and the number of opening of petal holes does not affect the flow rate.                  Figure 2.8. Pressure change inside the bottle with petal valve in three different conditions; open valve, closed valve, and semi-open valve. 30             These results exhibit that the current ReliaBrand design is not effective to the number of petal holes to control flow. Although it works in venting, the leakage is not prevented due to the big size of holes. In addition, the rubber washer is not able to block the holes in an unbalanced condition such as bottle falling or harsh impact. Therefore, a new design to use a valve with better adjustability and more reliability is desired. The valve must possess two significant specifications: (1) it should perform venting and prevent leakage in any condition, and (2) it should be adjustable by infants with the different age ranges who would generate different suction pressures. To experimentally show how significance the venting is, a bottle without any opening was tested under actual feeding condition. The previous set-up was used to exert suction pressures and measure the resultant vacuum inside the bottle. Once the pump sucked the liquid, the inside pressure gradually decreased up to a constant value as shown in Figure 2.10 (A). This amount of negative pressure stopped the flow rate. After this point, the inside pressure remained constant, Figure 2.9. Teat deformation due to the inside vacuum. 31  and the exerted suction was not able to take out the liquid anymore. Figure 2.10 (B) shows both intake volume and flow rate. This figure experimentally demonstrated that without venting the inside negative pressure made suction harder and harder until the infant was no longer able to gain the milk.                     A  A B  B Figure 2.10. Build up of negative pressure inside the bottle without venting. (A) Interior pressure. (B) Intake volume and flow rate. 32  2.4 Design of new venting valve As describe previous chapter, several problems of the current base-vented bottles lead to come up with new design of the venting valve. Figure 2.11 (A) shows the proposed new valve design including the hemispherical part, flat part, and crosscuts. The proposed method utilizes a novel venting valve mechanism connected to the bottom of the bottle. Thickness (t), crosscut length (L) and the curvature radius (R) are three important geometrical parameters as shown in Figure 2.11 (B). The crosscut creates four separated leaflets on top of the valve. They enable the valve to respond two opposite reactions under pressure difference. The positive hydrostatic pressure inside the bottle pushes leaflets to the center of the curve. The force due to this pressure is calculated by integrating the pressure over the hemispherical surface. Integration of this pressure over the valve surface has a component in the surface of the cuts, which compress leaflets together to close the valve. The more pressure is applied to the leaflets, the more force acts to close the valve. This condition occurs when the bottle stands up and the liquid inside the bottle exerts the positive hydrostatic pressure on top of the valve. On the other hand, when the amount of liquid inside the bottle decreases because the liquid flows out through the teat as the infant sucks the milk, the decrement of the liquid generates the partial vacuum inside the bottle, as shown in Figure 2.11 (C). This vacuum exerts a negative pressure on top of the hemispherical surface and pulls the leaflets inward to open the crosscut. This negative vacuum pressure keeps the cut open and the outside air enters into the bottle to compensate the inside negative pressure until the end of sucking cycle. Figure 2.12 shows the drawing of the valve including the dimension of each part. The fabrication process is described in Chapter 4.    33                        Figure 2.11. Venting valve design. (A) Schematic illustration of the valve. (B) Schematic of bottle equipped with the venting valve under hydrostatic pressure. (C) Schematic of the bottle equipped with the venting valve under inside vacuum pressure. Vacuum  pressure C   Flat part  Flat part Hemispherical part   Hemispherical part  Crosscut  Cross-cut A  A Hydrostatic  pressure B  B 34                2.5 Computational simulation Finite Element Analysis (FEA) simulation was conducted to analyze the behavior of the venting valve to validate the proposed concept design of the valve. The valve geometry was designed in CAD design software (SolidWorks®, Waltham, MA, USA) and imported to the static structural toolbox in ANSYS workbench (Ansys Inc, Canonsburg, PA, USA). The structure was discretized to 8662 hexahedral elements with a minimum edge length of 1.5 × 10−3 mm, using Multizone mesh method. The average element quality and aspect ratio for the meshed geometry are respectively 0.68 and 2.4. The flat part of the valve was defined as a fixed support in all directions. The force was applied at each point normal to the hemispherical part of the valve to simulate the    Figure 2.12. Three drawing views of the venting valve design. 35  effect of the pressure difference. The property of LSR measured by the mechanical test was added to the ANSYS engineering data. For static structural analysis, displacements {𝑥} were solved based on matrix equation below [59]: [𝐾]{𝑥} = {𝐹};     {𝑥} = [𝐾]−1{𝐹}                                                (1) where [𝐾] is a linear elastic property of the material and {𝐹} is the static force applied to the structure. [𝐾] is constant and no time-dependent value is considered in {𝐹}. Displacement matrix {𝑥} includes displacement of each element in 𝑥, 𝑦 and 𝑧-direction as {𝑥} = {𝑢𝑣𝑤}. The stress and strain matrix can be calculated based on the displacement matrix. Firstly, normal and shear strains were calculated as: 𝜖𝑥𝑥 =𝜕𝑢𝜕𝑥 ,  𝜖𝑦𝑦 =𝜕𝑣𝜕𝑦,  𝜖𝑧𝑧 =𝜕𝑤𝜕𝑧    and     𝛾𝑥𝑦 =𝜕𝑢𝜕𝑦+𝜕𝑣𝜕𝑥 ,   𝛾𝑥𝑧 =𝜕𝑢𝜕𝑧+𝜕𝑤𝜕𝑥,   𝛾𝑦𝑧 =𝜕𝑣𝜕𝑧+𝜕𝑤𝜕𝑦     (2) Based on Hooke’s law, thereafter, normal and shear stress components were estimated as follow [59]: [     𝜎𝑥𝑥𝜎𝑦𝑦𝜎𝑧𝑧𝜏𝑥𝑦𝜏𝑦𝑧𝜏𝑧𝑥 ]     =[     ?̂?(1 − 𝜈) ?̂?𝜈 ?̂?𝜈?̂?𝜈 ?̂?(1 − 𝜈) ?̂?𝜈?̂?𝜈 ?̂?𝜈 ?̂?(1 − 𝜈) 0                0               00 0 00 0 0   0 0 00 0 00 0 0𝐺 0 00 𝐺 00 0 𝐺]     {    𝜖𝑥𝑥𝜖𝑦𝑦𝜖𝑧𝑧𝛾𝑥𝑦𝛾𝑦𝑧𝛾𝑧𝑥}                           (3) , where ?̂? =𝐸(1−2𝜈)(1+𝜈) is effective modulus function of Young’s modulus and Poisson’s ratio. The response of the valve was assessed in the form of the distribution of total deformation, equivalent strain, and equivalent stress. Equivalent (von-mises) stress (𝜎𝜈) and strain (𝜖𝜈) represent any arbitrary three-dimensional stress/strain as a single positive value to predict the material failure under multiaxial loading. For instance, equivalent stress can be calculated as [60]: 36  𝜎𝜈 = √12(𝜎𝑥𝑥 − 𝜎𝑦𝑦)2+ (𝜎𝑦𝑦 − 𝜎𝑧𝑧)2+ (𝜎𝑧𝑧 − 𝜎𝑥𝑥)2 + 6(𝜏𝑥𝑦2 + 𝜏𝑦𝑧2 + 𝜏𝑧𝑥2 )           (4) Results of total deformation, equivalent stress and equivalent strain were used to compare the effect of geometrical parameters on valve performance.  The function of the valve depends on the amount of pressure applied on the hemispherical part of the valve. We hypothesize that the more the negative pressure is applied to the leaflets, the wider the valve opens and the more the air flows into the bottle through the valve. For the FEA computational simulation to prove the hypothesis, the volumetric mesh was firstly applied for the structural analysis as shown in Figure 2.13 (A). Two different cases were investigated in this study. In the first case, we investigated the effect of the partial vacuum inside the bottle. Thus, a negative pressure, 2 kPa, was applied to the valve to intake the air into the bottle. As shown in Figure 2.13 (B), maximum deformations occurred at the edges around the center of cuts. Adjacent leaflets were touching each other and there was no structural connection between nearby elements. Therefore, as soon as the pressure overcame the friction between the walls, the free edges started moving outward to open the valve, letting the air flow through the opened valve. The distribution of equivalent (von-mises) strain and stress of the opened valve are shown in Figures 2.13 (C) and (D), respectively. Maximum values were observed at the end points of each cut of the valve. The end points are not free to move but receive a large amount of pressure, and hence they are under maximum equivalent stress and strain. In the second case, we assumed that the bottle was placed upward and hydrostatic pressure of a certain amount of milk was applied to the valve. By substituting the density of milk, 𝜌milk = 1.03 g/mL, gravitational acceleration, g = 9.81m/s2  and the height of milk, h = 15 cm, the hydrostatic pressure, P = ρgh, was obtained as 1.515 kPa. This constant pressure was applied to 37  the hemispherical surface of the valve. The center of the surface moved downward and the leaflets were compressed together to close the air path. Figures 2.13 (E) to (G) were correspondent to the deformation, equivalent strain, and stress over the valve due to hydrostatic pressure. Maximum values were observed at same locations as the first case.     Figure 2.13. FEA simulation of respons of the venting valve to the pressure difference. (A) Top view of volumetric mesh. Case I: vacuum pressure opens the crosscut: (B) deformation distribution, (C) equivalent (von-mises) strain distribution, (D) equivalent (von-mises) stress distribution. Case II: hydrostatic pressure closes the crosscut: (E) deformation distribution, (F) equivalent (von-mises) strain distribution, (G) equivalent (von-mises) stress distribution. 38  2.6 Chapter summary Experimental results of existing nursing bottle demonstrated that the bottles generated bubbles inside the milk, though the venting from the nipple could partially remove the negative pressure inside the bottle. These bubbles are often ingested by infants to cause colic and other gastrointestinal disorders. The base venting is consider to eliminate the above problems. In addition, an experimental set-up was develop to test the existing bottles with a base venting method. The leakage problem of the existing bottle with the base venting valve demonstrated that the new design of base venting valve was highly desirable. The concept of using a new flexible valve with the new geometry was elaborated to solve the both venting and leakage problems. The performance of the new valve was evaluated using FEA computational simulation. It was clearly observed that the response of the valve satisfied several conditions. For bottle in standing position, the valve closed the air pass when the interior liquid touched the valve and exerted positive pressure over leaflets (passive condition). On the contrary, valve unlocked the crosscut and let the air enter the bottle (active condition).  39  Chapter 3: Material Characterization and Fabrication Process Design This chapter describes the characterization of the selected material and the fabrication process of venting valve system. The material for fabricate the venting valve should have specific characteristics such as biocompatibility and elastic property letting air in and preventing leakage. Also, the fabrication process should be simple and applicable for mass production.  3.1 Material selection In this research, polydimethylsiloxane (PDMS) was first tested for the fabrication of the valve since PDMS is one of the well-known silicone based material which is commonly used for biomedical, commercial and industrial applications [61]–[63]. It is flexible, transparent and biocompatible. PDMS (Sylgard 184, Dow Corning Corporation, Midland, MI, USA) was used for testing. The PMDS fabrication process starts from adding the curing agent to the elastomer base and the mixture are mixed for a few minutes. Then, degassing takes about one hour to remove bubbles from the mixture. A simple vacuum pump is used to expedite the degassing process. The mixture was poured into the mold to form the desired shape and cured in the oven at 60 C for 4 hours.  Young’s modulus of PDMS is in range of 1 to 3 MPa [64], [65]., Mustafa et al. [64] has characterized average elastic modulus for 5:1, 10:1 and 20:1 ratios of PDMS (i.e., base to curing agent) equal to 3.03 MPa, 2.84 MPa, and 1.56 MPa, respectively. However, PDMS is too stiff and easily torn off when it is stretched, not being desirable for the venting valve of nursing bottles. In the meantime, we found that liquid silicon rubber (LSR) is widely used for the teat in baby bottles.  LSR (Shenzhen Lianuan silicone Rubber Co, China) is also biocompatible and more flexible than PDMS [66]–[70]. It also has two components that should be mixed together with 1:1 ratio. 40  The synthesis method is similar to PDMS. The two components were first mixed together in a petri dish. Unlike PDMS, the generated bubbles within the mixture were hard to remove due to the high viscosity of LSR, requiring high vacuum to degas the mixture. Otherwise, bubbles were trapped in the mixture and make many holes in the final cured sample. Therefore, the petri dish is placed inside a desiccator and vacuum pressure was applied to remove the bubbles. During this process, the desiccator was opened and closed the valve frequently to blow airs and burst the bubbles. This process lasts for 0.5~1 hour to remove all the bubbles. After degassing, the mixture was ready to pour into the molds and start casting.                               PDMS  PDMS LSR  LSR Figure 3.1. Bubbles generated after mixing components of PDMS and LSR. (A) At the time of mixing. (B) After 24 hours without vacuum. PDMS  PDMS LSR  LSR A  A B  A 41  As can be seen in Figure 3.1, bubbles in the PDMS mixture were removed after 24 hours without vacuum. For LSR, however, bubbles were trapped in the cured sample because no vacuum was used to degas the mixture. This was due to the viscosity difference between these two materials. Table 3.1 provides a summary of differences between PDMS and LRS.  Table 3.1. Qualitative comparison between PDMS and LSR properties. Material/Properties PDMS LSR Biocompatibility Yes Yes Flexibility Yes Yes Transparency Yes Transparent in low curing temperature Mixing ratio 1:5 1:10 1:20 1:1 Stiffness (Young’s modulus MPa) [64] 1.56 2.84 3.03 3.7 Solution viscosity low high Solution degassing No vacuum is needed Strong vacuum is needed   3.2 Mechanical property characterization The mechanical property of the cured LSR was characterized by various techniques. This characterization was necessary to define the material properties for the FEM simulation. Among various mechanical properties, Young's modulus, a measure of the stiffness of the solid material, was the important property that is calculated from the stress-strain curve. In this section, three different methods were used to characterize the mechanical properties of LSR.   42  3.2.1 Tensile mechanical property For the tensile mechanical test, ASTM standard mechanical test for rubbers was  employed. In this method, dumbbell die geometry was used to cast the  LSR specimen [71]. The die should be sharp free of necks. The geometry and dimensions of dumbbell samples are depicted in Figure 3.2 and Table 3.2, respectively.              Figure 3.2. The geometry of standard dumbbell dies for tensile test (adopted form ASTM standard [71]). Table 3.2. Dimensions of dumbbell dies for tensile test (adopted from ASTM standard [71]). 43  Figure 3.3 shows 5960 Dual Column Tabletop Testing System (Instron®, Norwood, MA, USA). Two jaws were used to fix the dumbbell die and moved in opposite direction for applying tensile strain to the sample. The positions and forces were recorded during the experiment until the sample was fractured. These data were converted to stress and strain to calculate the Young’s modulus. Figure 3.4 (A) and (B) show the SolidWorks design and 3D-printed mold used to cast two different LSR samples. Beside the dumbbell shape in the middle, two rectangular samples were also casted for the other mechanical test. The degassed mixture of LSR was poured into the mold and then cured at room temperature overnight as shown in Figure 3.4 (B). Then, both samples were peeled off and cut out for testing as shown in Figure 3.4 (C).               Figure 3.3. 5960 Dual column tabletop testing system. 44  Figure 3.5 shows that the dumbbell die sample had failure on the location where some cavities are on the surface. These cavities were mostly accumulated around the two ends and lead the sample to be broken from the neck during the tensile test. Because the die was relatively thick, it was difficult to remove all the bubbles from the solution. Although a strong pump was used to degas samples, some bubbles remained due to the high viscosity of LSR. The other samples cured beside the die, which was used for other test, had no cavities because they were thin comparing the dumbbell die as shown Figure 3.4 (C). The tensile test was conducted for three dumbbell die samples. The elongation and force from the test were recorded and converted to the strain and stress curves. As shown in Figure 3.6, the slope within 5% strain defines the average Young’s modulus of the sample of 0.97 ± 0.05 MPa. As described before, one of the problems in casting dumbbell die was the process of degassing. Because the high viscosity and the large thickness of the geometry provided by ASTM standard, it was difficult to remove all the bubbles from the sample forming cavities inside the cured sample. In the normal tensile test, the stress is concentrated on the narrow center part to avoid the fracture at both ends of the specimen. However, the cavities around one side of the end of the sample caused the failure near the clamp, as shown in Figure 3.5. Thus, the dynamic mechanical analysis (DMA) method was also employed in which the specimens can be smaller and thinner as shown in Figure 3.4 (C). These samples were prepared on the same mold as the dumbbell die sample and all the bubbles were easily removed.      45                         Figure 3.4. Mold used to cast LSR. (A) SolidWorks design. (B) LSR was poured into 3D-printd mold. (C) Casted dumbbell die and thin samples. A  A B  A C  A 46              Figure 3.6. Stress-strain curve of tensile test. Figure 3.5. Broken dumbbell die; Cavities in the surface close to the failure location 47  3.2.2 Dynamic mechanical analysis (DMA) The DMA test is useful especially for viscoelastic behavior of polymers. A sinusoidal vibration in form of stress is applied on a thin specimen, and the resultant strain is measured. This test provides complex modulus, which is a combination of loss modulus and storage modulus. Figure 4.7 shows the both ends of sample are held by Q800 DMA (TA Instruments, New Castle, DE). Dual cantilever clamp method was conducted as shown in Figure 3.7. The applied point load bends the specimen at the center. The position and force, which are converted to the stress and strain, are recorded simultaneously to calculate Young’s modulus.     Figure 3.7. DMA test. (A) Schematic representation of the RSA G2 controlled strain DMA. (B) Sample is fixed in DMA machine. 48         The modulus is calculated as [72]: 𝑚𝑜𝑑𝑢𝑙𝑢𝑠(𝐸) = 𝑆𝑡𝑖𝑓𝑓𝑛𝑒𝑠𝑠(𝑆) ∗ 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑦 𝐹𝑎𝑐𝑡𝑜𝑟(𝐺𝐹) (5) and 𝐺𝐹 =12𝑙3[1 +125(1 + 𝜈) (𝑡𝑙)2]24𝑤𝑡3    (6) where 𝑙, 𝑤, 𝑡 and ν are the length, width, thickness and Poisson’s ratio of the sample, respectively. If the ratio of length /thickness > 10, the Poisson’s ratio can be ignored [72]. Thus: 𝐺𝐹 =𝑙32𝑤𝑡3 (7) By substitution of 𝑙, 𝑤, 𝑡 of the casted sample, the geometry factor was equal to 𝐺𝐹 =5.21 × 105. The average stiffness measured by the device was 2.316 ± 0.19 𝑁/𝑚. The Modulus can be calculated as:  𝐸 = 𝑆 × 𝐺𝐹 (8) Therefore, the average Young modulus measured by DMA test was 1.21 ± 0.098 𝑀𝑃𝑎 .The Young’s modulus measured by DMA was slightly higher than the one measured by tensile test, which may be due to no bubbles trapped inside the samples.  Figure 3.8. Dual cantilever clamp test. L w t 49  3.2.3 Compression test  The mechanical property of the cured LSR was also characterized by a compression test (Mach-1, Biomomentum Inc., Laval, QC, Canada). The compression test was relatively simpler than previous tensile and DMA methods in terms of specimen preparation and testing procedure. The samples for previous tests were prepared at relatively low temperature because the 3D printed mold was not applicable for a high temperature process. However, the mechanical property of LSR is intrinsically temperature dependent and the suggested processing temperature is around 180 C.  For compression test, LSR prepared at 180 C for 10 min. Figure 3.9 (A) shows the specimens with 2 mm thick and 8 mm in diameter were cut out from a cured sample. For each test, stress-strain curves were obtained based on the recorded force and displacement data as shown in Figure 3.9 (B). For small elastic deformations, there is no difference between Young’s modulus obtained from compression and tensile tests. Young’s modulus was calculated using the results of stress-strain curve within the first 5% strain of each graph, because in this range both tensile and compressive tests have same results [64]. The average Young’s modulus E = 3.7 ± 0.32 MPa was obtained. In addition to Young’s modulus, Poisson’s ratio ν = 0.49 and density ρ = 1.2 g/cm3 were also used to define LSR properties in ANSYS for FEM simulation [69], [73], [74].             50      3.3 Fabrication process of venting valve 3.3.1 Mold design and fabrication In order to fabricate the designed venting valve, the positive and negative molds were first designed as shown in Figure 3.10. These two molds were paired together, in which the mixture of LSR was poured. Thereafter, the mixture was cured under the specific condition to form the designed valve. Two important properties affect the shape and quality of the cured samples. First, each mold should have a smooth surface, which depends on the 3D printer or machining resolution. Second, the mold can endure high curing temperature, which affects the mechanical properties of the LSR.      0400800120016000 4 8 12 16 20Stress (kPa)Strain(%)A  A B  B Figure 3.9. Compressive test. (A) LSR disks under mechanical test machine. (B) Stress-Strain curves for cured LSR samples to calculate average Young’s modulus. 51           A normal 3D-printer (da Vinci 2.0, XYZprinting Inc, San Diego, CA, USA) was first used to fabricate the molds To align the male and female molds, four pins were designed at the corners of each mold. Because of the low surface quality of 3D printed molds, the casted valve samples  has an observable surface pattern which was transferred from the mold and result in low quality of the fabricated valves as shown Figure 3.11 (A). A high precision poly jet 3D-printer (Object500 Connex, Stratasys Ltd., Eden Prairie, USA) with 20 microns resolution was then used to print the molds. Figure 3.11 (B) shows the printed molds and the fabricated valve with better surface quality. However, the 3D printed molds were not applicable for curing the LSR materials with high temperature over 60C. The fabricated samples through the 3D printed molds were softer than expected because of low curing temperature.  Also, the fabricated samples were sticky which is the result from the undercuring of LSR at room temperature. To fabricate valve samples under high temperature and fully cured conditions, aluminum-based molds were machined as shown in Figure 3.11 (C). Then, the LRS casted in molds was placed into the oven and cured at 180 C for about 15 min. Thereafter, the mold was cooled A  A B  B Figure 3.10. Three drawing views of the designed molds. (A) Positive. (B) Negative.  52  down to the room temperature and the sample was peeled off. The fabrication process using the aluminum molds was much faster than the process with 3D printed molds and capable of fabricating one valve per hour. The fabricated valves were not sticky anymore and mechanically stiffer as described in the previous section.  After fabricating the valves, a surgical blade with a very sharp tip was used to make crosscut on top of the hemispherical part, as shown in Figure 3.12 (A). To make each line of the crosscut, the center of the hemispherical part was first marked by a pen. Then, the tip of the blade was placed on the marked center point and pushed down to cut the fabricated LSR in vertical direction. The more the downward movement, the longer the line was cut. For the second line of the crosscut, the blade was placed normal direction to the first cut and cut down the LSR in the same way. No material was removed by the sharp blade; hence, there was no gap between the cut lines. This crosscut divided the top part of the valve into four leaflets. These leaflets can automatically close and open the air pass in response to pressure difference during infant feeding, as shown in Figure 3.12 (B).  53                 Figure 3.11. Fabricated molds and corresponding cured samples. (A) Printed with da Vinci 3D-printer. (B) Printed with poly jet 3D-printer. (C) Machined aluminum mold. A  A B  A C  A A  A B  A Figure 3.12. Fabricated venting valve. (A) Surgical blades used to make crosscut on top of the valve. (B) Leaflets on top of the valve. 54  3.4 Integration of valve with nursing bottle The valve was integrated with the bottle using glue bonding method and thermal press method. For the glue bonding method, the flat part of the valve placed on the bottom part of the bottle, making the leaflets oriented toward inside the bottle. Then, the contact region was glued to the bottle using a Sil-poxy (Smooth-On Inc, Macungie, Pennsylvania, USA). One of the problems for the bonding method was the weak water resistance of the glue when it was in contact with water. The bonding region was gradually detached when the valve was in direct contact with water for long-term operation. The bottom part of the bottle was made of polypropylene (PP), while the valve was made of LSR. Polymers usually have very low surface energy and thus it is difficult to bond two polymers together.                 A  A C  C A  A B  B C  C D  D Figure 3.13. Thermal bonding. (A) Aluminum supports. (B) PP layer placed on the valve. (C) The support placed between the pp layer and machine’s plate. (D) The valve is sandwiched between PP layers and the bottle.   55  Figure 3.13 (D) shows the valve sandwiched between two layers of PP. The venting valve assembly was then screwed to the body of bottle for testing. The bonding was perfect and no leakage was observed. To overcome this problem, the thermal bonding method has been adopted whereby the valve was thermally sandwiched between two PP layers. In this method, the valve was placed on bottom part of the bottle that is made of PP. This part of the bottle was then placed on an aluminum supports, as shown Figure 3.14 (A), which transfers the heat from the bottom plate of the thermal press machine to the bottom part of the bottle. Then, another PP layer cut out from a PP sheet was placed on the valve (Figure 3.14 (B)).                A  A B  A C  A Figure 3.14. Final samples to be tested. (A) Inside and (B) outside view of the bonded valve. (C) The bottom part of the bottle is screwed to the body. 56  Around aluminum, support was also put on top of the assembly to transfer the heat to the system (Figure 3.14 (C)). Then, thermal press machine hold the assembly under pressure to bond them together for one minute at 180 .  3.5 Chapter summary In summary, PDMS and LRS were used to fabricate the valve. However, LSR was selected because it has several advantages such as the simple fabrication process and mechanical properties. The mechanical properties of the LSR were characterized with three different techniques: tensile test, DMA, and compression test. Young’s modulus from the compression test was calculated as 3.7 ± 0.32 MPa. Different molds were employed to cure the valve with LSR. Finally, the aluminum mold was used to cure the valve at high temperature. Crosscut for venting was made on top of the valve using surgical blades. Two different techniques, such as epoxy glue bonding and thermal press methods, were proposed to bond the valve to the bottom part of the bottle. Finally, the bonded valve was screwed to the body of the bottle to assemble the entire system for experiments.   57  Chapter 4: Experimental and Computational Investigation of Venting Valves The interaction between the hemispherical part of the flexible valve, particularly leaflets, and the fluid pressure is the key idea of the new venting valve. This chapter discusses the experimental result of various tests on the bottle integrated with the fabricated venting valve. Different valves were installed on the bottom cavity of the bottle, which was then loaded to the set-up for experimental test. The first objective of this chapter is to establish criterions whereby the performance of the valve can be evaluated by computational analysis. Moreover, several valves were fabricated with different designs in terms of geometrical parameters such as thickness, curvature, and length of the crosscut. These valves were then tested and compared to find the best design.  4.1 Working principle of venting valve The crosscut divides the hemispherical part of the valve into four symmetric leaflets. As shown in Figure 4.1, each leaflet represented by black color can be considered as a 3D triangular beam under uniform distributed load. Each of these beams is fixed at one side to the continuous part of the hemisphere. The beam is free at two other sides, where the crosscut is made, and the only force acting on these sides is friction forces between interfaces of leaflets. Therefore, the movement of each leaflet resembles the bending of a cantilever beam. This theoretical perspective helps to understand the effect of some parameters on the valve response. For example, assume a simple triangular beam with length L, Young’s modulus E, shear modulus G, second moment of inertia I, thickness h, and base side b, under load 𝑤, as shown in Figure 4.1. The shear force F and bending moment 𝑀 = 𝐹𝑥 were applied to the vertical plane at distance x from the tip of the beam.  58                   Using Castigliano’s method, the deflection 𝛿 at the tip of the beam can be calculated as [75]: 𝛿 = ∫𝑀(𝜕𝑀/𝜕𝐹)𝐸𝐼𝑑𝑥𝐿0+∫6𝑉(𝜕𝑉/𝜕𝐹)5𝐺𝐴𝑑𝑥𝐿0 (9) where 𝐼 =𝑏′ℎ312=𝑏𝑥ℎ312𝐿 and 𝐴 = 𝑏′ℎ =𝑏𝑥ℎ𝐿  By substitution of I and A into Equation (9), the deflection is obtained as: F L b h x b´ Figure 4.1. Bending analogy between leaflets and cantilever beam 59  𝛿 = ∫𝐹𝑥(𝑥)𝐸𝑏𝑥ℎ312𝐿𝑑𝑥𝐿0+∫6𝐹(1)5𝐺ℎ𝑏𝑥𝐿𝑑𝑥𝐿0= 12𝐿∫𝐹𝑥𝐸𝑏ℎ3𝑑𝑥𝐿0+ 𝐿∫6𝐹5𝐺ℎ𝑏𝑥𝑑𝑥𝐿0 = 6𝐹𝐿3𝐸𝑏ℎ3+6𝐹𝐿5𝐺ℎ𝑏 [ln(𝐿) − ln (0)] (10) By neglecting the contribution of the transverse shear, the approximate deflection can be written as: 𝛿 =6𝐹𝐿3𝐸𝑏ℎ3  (11) Based on this equation, the deformation is inversely proportional to the thickness of the beam. Each leaflet can be considered as a cantilever triangular beam and the above explanation can be extended for the valve. The negative pressure inside the bottle is around 2 kPa. This pressure exerts a distributed load on each leaflet. This force can be obtained by multiplying the pressure by the area of each leaflet. By assuming that this force is being applied as a localized force on the tip of the leaflet, then the approximate deflection of each leaflet can be obtained by Equation (11). Considering the Young’s modulus of the valve and geometrical parameters of leaflets, the deflections of leaflets is plotted versus the thickness of the valve, in range of 0.5 mm to 2.5 mm, as shown in Figure 4.2. Increasing the thickness of the valve will decrease the deflection of the leaflets. This analogy provides the relation between the valve thickness and the leaflets deflection. Reducing the thickness of the valve will make it more sensitive to the pressure difference. The more deflection, the more opening is obtained. Therefore, thinner valve will react to the pressure change in shorter time.  60           4.2 Computational simulation The simplified triangular cantilever beam model is good to preliminarily understand the deflection of the leaflet. However, the complex boundary condition and loading conditions are not exactly reflected to optimize the parameters of the venting valves. Therefore, the computational simulation with various geometrical parameters has been conducted to investigate the optimized design for the venting valves. There are three geometric parameters of the venting valve such as the length of cuts, thickness and curvature of the valve as shown in Figure 2.11 (B). Table 4.1 contains the mechanical properties of LSR used for the computational simulation. Considering the fabrication capability, four different valve designs in combination of two different thicknesses and curvatures have been chosen as summarized on Table 4.2. In addition, the length of the crosscut was chosen to be constant as 3 mm.    Figure 4.2. Maximum deflection of leaflets with different thicknesses. 61                                           Table 4.1. Mechanical properties of LSR Material/Property Density (g/cm3) Young’s modulus (MPa) Poisson's ratio LSR 1.2 3.7 0.49                               Table 4.2. Geometry of four valves Valve/Geometry Thickness (mm) Curvature radius (mm) Valve #1 1.5 7.5 Valve #2 2 7.5 Valve #3 2 8.5 Valve #4 1.5 8.5   Figure 4.3 shows the results of simulation for five different valves. The maximum deformation, strain, and stress of each valve were investigated under two different cases described as follows. Figures 4.3 (A) to (C) correspond to the case that an infant sucking the milk out of the teat. The decrement of the liquid volume inside the bottle produces a partial vacuum pressure. The more the deformation and strain exerted, the more the air entered the bottle to compensate the negative pressure. Figures 4.3 (D) to (F) correspond to the case that the bottle is placed upward.        62                        A  A B  A C  A D  A E  A F  A Figure 4.3. FEA simulation of the five different valves under two conditions. Case I: hydrostatic pressure closes the crosscut, (A) deformation distribution, (B) equivalent (von-mises) strain distribution, (C) equivalent (von-mises) stress distribution. Case II: vacuum pressure opens the crosscut, (D) deformation distribution, (E) equivalent (von-mises) strain distribution, (F) equivalent (von-mises) stress distribution. 63  Comparison between valve #1 and valve #2 indicates that the thickness has a reverse effect on venting performance. In addition, the comparison between valve #2 and #3 shows that the radius of curvature has a positive effect on venting. In addition, the maximum deformation and strain from the valve #4 were higher than other valves. This indicates that the valves with thinner thickness and smaller curvature perform better. However, our preliminary experiment showed that the decrement of thickness and increment of the curvature of the valve had higher chances of leakage, causing problems for nursing bottles. Valve #5 has the same geometry as valve #4 but it has only one opening cut. The simulation result shows that the valve deformed very less than the valves with the crosscut opening as it was expected. Therefore, the results of computational analysis demonstrated that the best venting could be achieved with valve #4 among five different samples.   4.3 Experimental investigation  In order to experimentally optimize the design, many samples with different thicknesses and curvatures should be fabricated. This fabrication requires many different molds, which is not realistic. Therefore, the five valves with different geometrical parameters chosen for computational simulation were fabricated for experiments.  Figure 4.4. Fabricated valves with different curvatures. (A) 8.5 mm. (B) 7.5 mm. 64  4.3.1 Experimental design A set-up comprises of two pressure sensors, vacuum pump, container and interface system was prepared to test the valve performance as described in chapter 2. One sensor was used to measure the suction pressure in the teat enclosure. The second sensor was connected to the body of the bottle, measuring the inside pressure. A computer interface program continuously displayed pressures measured by the sensors. Periodic suction was exerted to the bottle as an input (i.e., pressure at the teat). The amplitude of this pressure was 20 kPa with 0.5 Hz frequency, which was approximately equal to the infants’ suction pressure. The periodic suction pressure was applied for two minutes, and the volume of extracted liquid was measured for the entire time-period.   4.3.2 Categorization of performance criterions Minimum pressure (𝑃𝑚𝑖𝑛), time to reach minimum pressure (𝑡𝑚𝑖𝑛), working pressure (𝑃𝑤𝑜𝑟𝑘), time to reach working pressure (𝑡𝑤𝑜𝑟𝑘) and intake volume (𝑉𝑖𝑛) are among important criterions that show the valve performance as shown in Figure 4.5. Here, these parameters are described in detail. The minimum pressure (𝑃𝑚𝑖𝑛) is the minimum value of the interior negative pressure and 𝑡𝑚𝑖𝑛 is the duration to reach the minimum pressure. Once the suction reduces the pressure inside the bottle lower than the ambient atmospheric pressure (~1 atm), the leaflets start to be deformed by this vacuum pressure. However, at the initial a few tens of sec of this suction, the vacuum pressure is not sufficient to open the valve. The vacuum pressure keeps increasing due to the depletion of the inside air which makes the suction harder over time. At a specific time, 𝑡𝑚𝑖𝑛, the interior vacuum pressure reaches the minimum value (𝑃𝑚𝑖𝑛), and finally overcomes the stiffness of the valve leaflets to be opened. Then, the air enters immediately into the bottle to compensate the vacuum pressure.  65     Working pressure (𝑃𝑤𝑜𝑟𝑘) is the pressure for the valve to reach stable, constant pressure and 𝑡𝑤𝑜𝑟𝑘 is the time to reach working pressure. After vacuum pressure is compensated, the inside pressure increases to reach a constant value (𝑃𝑤𝑜𝑟𝑘) and starts oscillating with the same frequency as the suction pressure. At each cycle, the valves open and close. Therefore, the working pressure region has no change in the sinusoidal pressure inside the bottle. The pressure is stable and no additional vacuum is generated inside the bottle.  The effects of the geometrical parameters on the performance criterions were studied to optimize the venting valve geometry. The optimized venting valve is capable of delivering the maximum intake volume, minimum 𝑡𝑚𝑖𝑛 and 𝑡𝑤𝑜𝑟𝑘 and maximum 𝑝𝑚𝑖𝑛 and 𝑝𝑤𝑜𝑟𝑘, without any leakage.    Figure 4.5. The pressure change inside the bottle equipped with new venting valve. 8688909294960 20 40 60 80 100 120Pressure (kpa)Time (sec)Working pressure region𝑝𝑤𝑜𝑟𝑘  𝑝𝑤𝑜𝑟𝑘 𝑝𝑚𝑖𝑛   𝑡𝑚𝑖𝑛  𝑡𝑚𝑖𝑛 𝑡𝑤𝑜𝑟𝑘   𝑡𝑤𝑜𝑟𝑘  Ambient pressure (~1 atm) 66  4.3.3 Experimental results and discussion Each valve was assembled to the bottom of the bottle, and then the bottle was placed on the suction system. Each valve was tested five times. The vacuum pump applied a harmonic pressure of 20 kPa to gain the milk. The pressure inside the bottle decreases gradually up to 𝑃𝑚𝑖𝑛  for the duration of 𝑡𝑚𝑖𝑛 as shown in Figure 4.6. Until 𝑡𝑚𝑖𝑛, the valve was closed and the inside negative pressure increased gradually. As soon as the pressure reached 𝑃𝑚𝑖𝑛, the crosscut of the valve was opened and the air entered the bottle. The pressure raises up to 𝑃𝑤𝑜𝑟𝑘 for the duration of 𝑡𝑤𝑜𝑟𝑘. At this point, the inside pressure oscillated around constant value and no pressure increment was observed. This condition was stable up to the end of the experiment. This means that the crosscut of the valve quickly was opened and air intake removed the negative pressure at the same frequency as the suction pressure cycles.             Figure 4.6. Pressure change inside tested bottles equipped with venting valve. Closed Open 67  The vacuum pump kept running for two minutes and the volume of intake milk was measured at the end. Figure 4.7 shows the results for five valves. To verify all our experimental result in this research study, the one-way Analysis of Variance (ANOVA) in Excel (Microsoft, Redmond, WA, United States) was used. Each pair of data sets were individually subjected to one-way ANOVA analysis (single factor). Each bar in the figure shows the average value. Figure 4.7 (A) shows that the valves #3 and #4 have the highest value of intake milk. In addition, the valves #1 and #4 have the highest value of Pmin and the valves #1, #3, and #4 have the highest value of Pwork (Figures 4.7 (B) and (C)), respectively, which mean that the vacuum pressure and working pressure are less than other valves. As shown in Figure 4.7 (D), tmin for the valves #1 and #4 are less than other valves, which mean that they have a faster response to the vacuum pressure. However, twork for all valves were not statistically significant (p > 0.05) as shown in Figure 4.7 (E), which mean that the valves reach the working pressure in ~80 sec regardless of geometrical parameters. In summary, valve #4 fabricated with thinner thickness and smaller curvature (larger R) than other valves shows the best performance for all criterions.  This experimental analysis is well matched with FEA computational analysis. Valve #4 with 1.5 mm thickness, 8.5 mm radius of curvature and 3 mm crosscut had the highest Vin and fastest response to suction. This venting valve removes the inside vacuum faster and becomes stable in shorter time. In addition, it keeps the inner pressure lower than other valves, which is actually more comfortable for infants to be fed. In term of the opening cut, the valve #5 has same geometry as valve #4 besides one opening cut, which did not show as good performance as valve #4. For the same length of cut, the crosscut always gets more liquid volume than one cut. Crosscut has four leaflets that are touching each other and free to move. However, one cut has two leaflets. In each cycle of opening, the vacuum pressure pulls two leaflets on the hemispherical part of the valve 68  outward. The more the leaflets are exit, the larger the deformation occurs. Hence, the center of the hemispherical part produces wider gaps with the crosscut opening comparing to the one line cut opening. Therefore, more air enters into the bottle through the crosscut to remove the vacuum pressure.                         * * * * * * * * * * * * * * * * * * * * * * Figure 4.7. Results of experimental tests for five criterions of performance. (A) Intake volume after two minutes. (B) Minimum pressure. (C) Minimum working pressure. (D) Time of minimum pressure. (E) Time of working pressure (n=5, *p < 0.05). A  A B  A C  A D  A E  A 69   4.4 Chapter summary The air enters the bottle through the venting valve and eliminates the interior partial vacuum. Any increment in liquid volume causes partial vacuum inside the bottle. The leaflets on hemispherical part of the valve respond to this pressure change and perform ventilation by opening the air pass. FEA simulation was performed to assess effects of different parameters such as thickness and curvature on the valve performance. Then, results were experimentally validated by the actual feeding conditions. Each valve was bonded to the bottom of bottle and suction pressure was applied to the teat. Experimental analysis showed that this new design has a fast response to the airflow. Based on computational and experimental investigation, the valve with 1.5 mm thickness, 8.5 mm radius of curvature and 3 mm crosscut has the best venting performance.      70  Chapter 5: Transient Computational Simulation for Venting Valves The operation of the venting valve involves complicated fluid and structure dynamics. The information related to the pressure and velocity of the air and the valve deformation is important for the further optimization of the valve. This information is difficult to obtain experimentally. Therefore, a transient fluid-structural method was developed, which could be used as a tool for further optimization of the venting valve. Fluid-structural interaction (FSI) method requires the coupled analysis between computational fluid dynamics and structural mechanics. The FSI corresponds to the problems in which there is a strong interdependence between the solid structure and fluid flow. The FSI problem is applicable for various areas of engineering such as fluid mechanics, biomedical and aerospace engineering. For instance, airfoil flutter, membrane valves, and pumps require FSI solution to precisely predict the behavior of the system. Continuum mechanics provides the solution for FSI problems with which then the problem can be solved by numerical methods. However, complex geometries of fluid and solid interaction and complicated physics of fluids always challenge to solve such problems with numerical methods, requiring computational analysis.  5.1 Theoretical backgrounds 5.1.1 Fluid-solid interaction Methods to solve FSI problems are categorized as monolithic and partitioned methods [76]–[80]. In the partitioned method, the solid and fluid domains are solved with the sequential order of distinct solvers. A non-conformal mesh can be applied in this method, which indeed means the positions of nodes are not necessarily matched. There are two types of the monolithic method: (1) one-way coupling and (2) two-way coupling. In the one way coupling, quantities are only 71  transferred from one domain to another one in one direction. For instance, if there is a solid boundary on which the pressure due to the fluid flow is being applied, a good approximation for this system is one-way coupling in case that the deformations in this system are not large. Therefore, the one-way coupling method transfers the fluid pressure to the solid domain solver. However, the solid deformation is not sent back to the fluid solver. In two way coupling, data is transferred between solid and fluid solver at the fluid-structure interface. For the previous case in which the solid boundary is under the fluid pressure, if the solid structure is flexible enough and boundaries move with relatively large deformation due to the fluid pressure, the two-way coupling method can solve these coupled problems. In this method, the data of deformations in solid structure and the pressure in fluid domain are transferred simultaneously between both domains. In this research, the monolithic two-way coupling method has been chosen.     The interface is the region that separates the fluid and solid domain. At this interface, the governing equations of solid and fluid are connected and data are transferred between the coupled regions. Series of coupling conditions determine which data must be transferred. This transformation requires a mapping algorithm to pass quantities from one mesh to another. In FSI problems, the boundary conditions at the interface are kinematic and traction coupling condition. Two types of the solid-fluid coupling model are used: (1) kinematic model and (2) dynamic model which correspond to the motion and force balance, respectively [81]–[84]. Kinematic coupling represents the equality of velocity and motion in solid and fluid at the interface, which is called no-slip condition. Also, both regions should be locally in equilibrium in traction condition [84], [85]. The kinematic condition is satisfied once the fluid velocity equal to the velocity of solid elements at the interface as shown in Equation (12). In solid structure, the velocity is the time derivative of the displacements [82], 72  𝑢𝑖 =𝑑𝑎𝑖𝑑𝑡 (12) where 𝑢𝑖 and 𝑎𝑖 represent the fluid velocity and displacement of solid elements, respectively. For traction condition, the force (stress) between solid and fluid should be balanced. Stresses can be expressed by traction vector, as shown for solid and fluid in Equations (13) and (14), respectively.  𝑡𝑖𝑠 = 𝜎𝑖𝑗𝑛𝑗𝑠 (13) 𝑡𝑖𝑓 = −𝑝𝑛𝑖𝑓 + 𝜏𝑖𝑗𝑛𝑗𝑓 (14) Equation (15) shows the traction balance [82], 𝑡𝑖𝑠 + 𝑡𝑖𝑓 = 0 (19)  5.1.2 Governing equations for fluid Governing equation for the fluid flow domain is based on mass and momentum conservations, which are also known as continuity equation and Navier-Stokes equation. The continuity equation can be written as:  𝑑𝜌𝑑𝑡+ 𝜌𝜕𝑢𝑖𝜕𝑥𝑖= 0 (20) Fluid with Mach number less than 0.3 is considered as an incompressible flow. The continuity equation can be reduced to: 𝜕𝑢𝑖𝜕𝑥𝑖= 0 (21) The momentum equation is:  𝜌𝑑𝑢𝑖𝑑𝑡=𝜕𝜎𝑖𝑗𝜕𝑥𝑗+ 𝜌𝑓𝑖 (22) 73  where 𝑓𝑖  is body force per unit mass and 𝜎𝑖𝑗 is stress tensor. By neglecting 𝑓𝑖, the Navier-Stokes equation can be written as: 𝜌𝑑𝑢𝑖𝑑𝑡= −𝜕𝑝𝜕𝑥𝑖+𝜕𝜏𝑖𝑗𝜕𝑥𝑗= −𝜕𝑝𝜕𝑥𝑖+ μ𝜕2𝑢𝑖𝜕𝑥𝑖𝑥𝑗 (23) The Navier-Stokes equation is then solved for the fluid flow boundary. It is noted that model variables are decomposed to mean and fluctuation values for turbulent. Time averaging simplifies the Navier-Stokes equation to the Reynolds Averaged Navier-Stokes (RANS) equation. As a result, a new term −𝜌𝑢𝑖′𝑢𝑗′̅̅ ̅̅ ̅̅ ̅ called Reynolds stresses appears.  5.1.3 Governing equations for solid The governing equations for the solid structure are derived based on conservation of mass, momentum, and energy. For instance, the relationship between stress and strain gives the momentum equation. Hook’s law is the simplest model, which expresses the linear relation, as: 𝜎𝑖𝑗 = 𝐶𝑖𝑗𝑘𝑙𝜖𝑘𝑙 (24) The momentum equation for static equilibrium is written as: −𝜕𝜎𝑖𝑗𝜕𝑥𝑗= 𝜌𝑓𝑖 (25) By integrating over the entire elements, the problem can be then solved using FEM method. The internal forces are used to solve the displacements and predict the deformations for the nonlinear solver.  74  5.2 Modeling of structures Transient structural, fluid analysis and system coupling were used for analyzing two-way transient fluid-structure interaction problem. The model was set up in ANSYS workbench (Ansys Inc, Canonsburg, PA, USA). Settings specific to the coupled analysis was then established in mechanical and fluent parts. The analysis uses a flexible venting valve with a crosscut assembled with a closed bottle containing the fluid.  5.2.1 Solid structure modeling To model the valve, a mechanical transient structure system was set up. This system receives force data from fluid analysis. The valve geometry was designed in CAD design software (SolidWorks®, Waltham, MA, USA), as depicted in chapter 2, and imported to the transient structural analysis. The round edges were defined as fixed boundaries. These surfaces were bonded to the bottle in a real application. Figure 5.1 shows the meshed valve. The hex dominant method was used to generate hexahedral elements. In addition, the edge-sizing method was utilized to control the size of the mesh to produce fine mesh particularly for the elements nearby the crosscut. The average aspect ratio and element quality of generated mesh were 0.66 and 3.6, respectively.        Figure 5.1. The valve with hexahedral mesh. Fine mesh was applied to the regions close to the leaflets. 75  Fluid geometry was designed as a cylinder that encloses the valve. The system was allowed to share the geometry with the fluid analysis. The enclosure geometry containing the fluid was suppressed for the transient structural analysis. The solid geometry (i.e., venting valve) was similarly suppressed for the fluid analysis. Thus, each system had its own active geometry. Sixteen surfaces including surfaces inside the crosscut gap plus both inside and outside of the hemispherical part of the valve were selected as the fluid-solid interfaces. These surfaces were later defined as a system-coupling zone for the dynamic mesh setting. Figure 5.2 shows fluid-solid interfaces displayed by red color.           The time duration, which was one second, was actually controlled by the system coupling. The structural system needs a step-end time to be a duration equal to the time duration in the system coupling. An auto time stepping function was set to be off for the system coupling analysis, and subsets of the analysis for each time point occurred in each coupling iteration.   Figure 5.2. Fluid-solid interaction surfaces of the valve. 76  5.2.2 Fluid flow structure modeling To model the fluid in and outside the reservoir that was around the venting valve, the fluid analysis was used. Fluid geometry was designed with a transient structural toolbox as a cylinder that enclosed the valve as shown in Figure 5.3 (A). This geometry was shared with structural analysis and received displacement data from the transient structural analysis. Figure 5.3 (B) shows the inlet, outlet, and the suppressed valve design. The gravity is not considered and the domain size has been chosen to be much larger than the orifice.              Incompressible air entered the fluid region from the inlet. The inlet pressure was defined to increase linearly from 0 to 2 kPa for 1 sec and the outlet pressure was set to be zero. Based on this pressure difference between inlet and outlet, the airflow entered into the fluid region, reached the A  A B  A Figure 5.3. The fluid flow region. (A) The meshed geometry of fluid. (B) Illustration of the inlet, outlet and the venting valve geometry. Inlet Outlet Venting valve 77  valve, and pushed the leaflets to pass through the crosscut. Pressure-velocity coupling was considered to solve the system. Since the airflow and the mesh of fluid region were not aligned perfectly, resulting in the flow obliquely passed through the mesh, second-order discretization method was used to solve the coupled analysis. Hundred time steps with five iterations per a step were set for 1 sec computation, which is the period of one cycle suction in infants actual feeding. A dynamic mesh enables the fluid mesh to move in response to the displacement of the flexible valve. For the fluid walls that were in coincident with the valve, the dynamic mesh was utilized for the system coupling. The fluid analysis received force data on the fluid walls. The dynamic mesh setting defined the surfaces where displacement data was received from the system coupling. It also allowed the mesh around the fluid walls to deform.  5.2.3 Fluid-solid structure coupling  The coupled-simulation of the solid structural and fluid analysis is controlled by a system coupling. The system coupling connects the two systems by transferring data between each analysis. It can control the solution processes. In this research, the analysis type for the system coupling is transient analysis. The end time is 1 sec, which should be equal to the time duration set in transient structural analysis and overwrites the number of time steps in fluid analysis. The step size is a time interval at which data transfers are resolved. It defines the step size in structural analysis and overwrites the time step size set in fluent. The coupling iterations occur within each step and allow both transient structural and fluid analysis to reach convergence within each coupling step. The solid-fluid interface was applied to the solid surfaces, which was in contact with the surrounding air in the reservoir. It defines the surfaces in transient structural analysis where force data is received from the system coupling and displacement data is transferred to the system 78  coupling. The next step is to create two data transfers for the surfaces that transfer data between the coupled systems. One data transfer sends displacement data from structural to fluid simulation, and another data transfer sends force data from fluid to structural simulation.  5.3 Computational simulation results The geometry was shared between both analyses and the solutions were connect to the system coupling setup. The airflow goes into the fluid domain due to the pressure difference, which applies pressure on the inner surface of the valve. The force generated on the valve moves the leaflets and opens the gap between crosscuts. Three geometries with different thickness and curvature, as shown in Table 5.1, are respectively analyzed. Valve #2 in this table has the same geometry as valve #3 in chapter 4. Incompressible air flow with density ρ = 1.225 kg/m3 and dynamic viscosity µ = 1.7894×10-5 kg/m·s was considered for the fluid flow. Also, same properties, as shown in Table 4.1, were used for the solid structure.                               Table 5.1. Geometry of valves. Valve/Geometry Thickness (mm) Curvature radius (mm) Valve #1 1 8.5 Valve #2 2 8.5 Valve #3 1 7.5  5.3.1 Deformation of venting valve Dynamic mesh allows the fluid mesh to move and deform in response to the solid structure movement. The fluid pressure generates the force normal to the surface of the valve and the leaflets 79  move in response to this force. This movement leads the surrounding mesh to move along with the leaflets. Figure 5.4 shows the distribution of the mesh deformation in the valve #1 at the end of the one-second simulation. The leaflets were deformed more than other parts of the hemisphere and the maximum deformation occurred where the meshes were closer to the center of the crosscut.             Figures 5.5 (A-C) show the deformation of the leaflets at three different time steps, t=0 sec, t=0.5 sec, and t=1 sec. As the pressure increased by the time, the force acting on the valve increased and deformed the leaflets further. The corresponding maximum total deformations for each time step were 1.6 × 10−6 m , 1.5 × 10−5 m, and 3.14 × 10−5 m, respectively.  Figure 5.4. Distribution of the mesh deformation in the valve structure. 80   5.3.2 Pressure distribution around venting valve Based on the result of the pressure change inside the bottle, the inlet pressure set to the linear increment from 0 to 2 kPa. This boundary condition is identical to the real case in which the inside pressure linearly drops from ambient pressure to 93 kPa. The pressure change inside the fluid region was analyzed in 1 sec. Figure 5.6 shows the pressure contour at the end of the analysis of the valve #1. As can be seen, the pressure was well distributed throughout the fluid region except for the area close to the valve. The maximum pressure change occurred where the air passed through the gap between the leaflets. Once the air reached the leaflets, because of the small area across the crosscut, the pressure dropped while the velocity increased. On the other hand, when the air exited the gap, the velocity decreased due to the area increment.         Figure 5.5. Deformation of the leaflets at three different time steps, (A) t=0 sec, (B), t=0.5 sec, and (C) t=1 sec. A  A B  A C  A 81           The pressure change along central axis of the fluid geometry for t=0.5 sec and t=0.1 sec is shown in Figure 5.7. The central axis  was connected to center points of the inlet and outlet across the center of the crosscut of the valve #1. This graph illustrates that the pressure in the center of the cavity near the inlet is close to 2 kPa and drops while the flow reaches the leaflets. The gap between the leaflets behaved similar to oriffice. The fluid was forced to converge through the gap between the leaflets, letting the pressure reduced and the velocity increased. After passing the gap, the pressure was equalized to the outlet pressure. The x-axis of the figure is the number of meshes. The length of the axial line where it passed the gap between the leaflets was very short (~2 mm).  But, because the mesh in that region was finer comparing to the regions nearby the inlet/outlet, the graph shows the wider part of the gap. Another post-processing could be the observation of the pressure profile across the line close to the reservoir. A new line normal to the central axis at a distance of 3 mm from the leaflets was defined to show the pressure profile of the flow immediately after passing the gap. Figure 5.8 shows the pressure profile on the valve #1 at t=0.5 sec and t=1 sec. Figure 5.6. Contour of pressure at t=1 sec. 82              Figure 5.7. Pressure drop across central axis at t=0.5 (blue line) sec and t=1 sec (red line).  0 100 200 300 400 500 600 700 800  0 500  1000  1500  2000    Chart count      t = 0.5 sec         t = 1 sec  Figure 5.8. Pressure profile of the flow imidiately after passing the gap across the line close to the leaflets, at t=0. 5 sec (blue line) and t=1 sec (red line).  0 50 100 150 200 250 300  0 0.1  0.2  0.3  0.4    Chart count 0.6  05       t = 0.5 sec         t = 1 sec  83  5.3.3 Velocity distribution around venting valve The air is considered to be incompressible flow with constant density due to Mach number = 0.3. The quantitative behavior of this type of flow is presented by Bernoulli's equation as follows:  𝑃 +12𝜌𝑉2 + 𝜌𝑔𝑧 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡. (26)  Based on this equation, the pressure drops in the regions where the flow velocity increases. This equation is valid for the steady state flow along a streamline at any arbitrary point, where there is no friction. The constant value in this equation depends only on the chosen streamline and varies from one streamline to another. As shown in Figure 5.6, the minimum pressure occurred within the gap between leaflets of valve #1, where the velocity was maximum. The velocity contour is shown in Figure 5.9. The velocity increased while the air passes through the gap and reached the maximum value of 4.42 m/s.           Figure 5.9. Velocity contour at t=1 sec. 84  Figure 5.10 shows the velocity change across the central axis at t=0.5 sec and t=1 sec. The velocity increased near the leaflets and decreased once the air left the gap.  As can be seen in Figure 5.10, the pressure change inside the gap was not stable. This phenomenon was due to the number of fluid mesh was so little and the fluid analysis was significanly affected by the fluid-strutural interface (i.e., no slip boundry). The fluctation was resluted from hindering the smooth transition from one mesh to another in the fluid mesh.  Similar to the post-processing for the vertical pressure distribtuion as shown in Figure 5.8, Figure 5.12 shows the velocity profile along the vertical line 3 mm away from the leaflets which is the location immediately after passing through the valve opening gap.                 5  Figure 5.10. Velocity change across the central axis at t = 0.5 sec (blue line) and t = 1 sec (red line).  0 100 200 300 400 500 600 700 800  0 1  2  3  4    Chart count 6  7  5       t = 0.5 sec          t = 1 sec   6 85              The same analysis for valves #2 and #3 has been conducted to investigate the effect of the thickness and curvature. These two valves were analyzed with the same settings as for valve #1. The same pressure was applied for 1 sec simulation. Similar graphs of pressure and velocity profiles were obtained. However, the maximum pressure of air close to the valve at 3 mm away from the leaflets at t = 1 sec for the valves #1, #2 and #3 are 0.52 Pa, 0.1 Pa and 0.4 Pa, respectively. The results revealed that by increasing the thickness the pressure drop decreased, which means that the leaflets are less affected by the pressure difference. In addition, by increasing the curvature (i.e., decreasing the curvature radius), the pressure drop decreased as well. These results are in agreement with the results of the steady-state simulation. The velocity change was also obtained for different valves. The maximum velocity on the defined line close to the leaflets for valve #1, #2 and #3 are 0.28  m/s2 , 0.04  m/s2  and 0.24  m/s2 , respectively. This trend shows that by Figure 5.11. The velocity change imidiately after passing the gap across the line close to the leaflets, at t=0.5 sec (blue line) and t=1 sec (red line).  0 50 100 150 200 250 300  0 0.05  0.1  0.15  0.2    Chart count 0.3  0.25       t = 0.5 sec         t = 1 sec  86  increasing the thickness or curvature, the leaflets movement due to the pressure change decreased, thus less gap was created between leaflets. The comparison between these results shows that the change in the thickness is more effective on the valve performance. Therefore, the thickness can be considered as the most effective parameter to optimize the valve performance.  5.4 Chapter summary Transient computational analysis is one of the best possible options to visualize physical phenomenon around the venting valve, since the valve leaflets are too small and there is no way to visualize airflow. To do that, a fluid-structure interaction (FSI) method was used, which requires the coupled analysis between computational fluid dynamics and structural mechanics. The model was set up in ANSYS and settings specific to the coupled analysis was then established in mechanical and fluent parts. The analysis used a flexible venting valve with a crosscut assembled with a closed bottle containing the fluid. Three geometries with different thickness and curvature were respectively analyzed: (i) t=1 mm and R=8.5mm, (ii) t=2 mm and R=8.5mm, and (iii) t=1 mm and R=7.5mm. The comparison between results shows that the change in the thickness is more effective on the valve performance. Therefore, the thickness can be considered as the most effective parameter to optimize the valve performance 87  Chapter 6: Conclusion and future work 6.1 Conclusion In this thesis, the prototype of a new venting valve for nursing-bottles was fabricated. Unlike all existing designs and patents, this new valve has a simple design, which provides fully-vented condition inside the bottle. The venting valve was tested under simulated feeding condition and results showed that the valve has a fast response to a small pressure change inside the bottle. The pressure inside the bottle controls the infant suction pressure. Therefore, it is important to adjust the pressure inside the bottle. In this research, venting valve bonded to the bottom of the bottle was used to control the inside pressure change. This valve prevents the pressure drop inside the bottle. FEM analysis proved that the valve was able to successfully respond to the pressure difference. In standing position of the bottles, the valve closed the air pass when the interior liquid touched the valve and exerted positive pressure over leaflets (passive condition). On the contrary, valve unlocked the crosscut and let the air enter the bottle (active condition).  PDMS and LRS were used to fabricate the valve. However, LSR was selected because it has several comparative advantages in terms of the fabrication process and mechanical properties. The mechanical properties of the LSR were measured with three different techniques and Young’s modulus calculated by compression test, i.e., E = 3.7 ± 0.32 MPa, was used for computational analysis. Different molds were employed to cure the valve with LSR. Finally, the aluminum mold was used in order to cure the valve at high temperature. Two different techniques, such as epoxy glue and thermal press, were used to bond the valve to the bottom part of the bottle. The bonded valve was screwed to the body of the bottle to assemble the whole system. The leaflets on hemispherical part of the valve respond to this pressure change and perform ventilation by opening the air pass.  88  Computational analysis was conducted to assess effects of different parameters, such as thickness and curvature, on the valve performance. Then, results were experimentally validated by simulating the actual feeding conditions. Different valves were bonded to the bottom of bottle and suction pressure was applied to the teat. Experimental analysis shows that this new design has a fast response to the air flow. Based on statistical data, a valve with 1.5 mm thickness, 8.5 mm radius of curvature and 3 mm crosscut has the best venting performance. Fluid solid interfaces (FSI) coupled simulation was also conducted to visualize the venting phenomena around the venting valve. To model the valve, mechanical transient structure system was set up. Fluid geometry was designed as a cylinder that encloses the valve. Surfaces inside the crosscut reservoir and both inside and outside of the hemispherical part of the valve were selected as fluid solid interfaces. These surfaces were defined as system coupling zone in dynamic mesh setting. The coupled simulation of the solid structural and fluid analysis systems was controlled by a system coupling. Results show that the leaflets were deformed more than other parts of the valve and the maximum deformation occurred where the meshes were closer to the center of the crosscut. In addition, the maximum pressure and velocity change occurred where the air passes though the gap between leaflets.  6.2 Limitations  In this project, only one cycle of infant’s actual suction, i.e., 1 sec, and the resultant negative pressure inside the bottle were simulated using transient computational analysis. For each venting valve, the simulation took 2 days, which limited simulation of multicycles. 89   The interior pressure was assumed to linearly decrease from zero to 2 kPa, which is not totally linear in real case. Also, the pump was set to apply the suction for two minutes which is about 30 minutes in actual feeing.   Water was used as the working liquid instead of formula for experimental investigations because of the similarity in their properties, e.g., density and viscosity.  Experiential analyses for cleaning and reliability of the valve were not performed. Also, results of pressure and velocity distributions were not experimentally validated, which is defined to be completed as future works.  6.3 Future works Several improvements can be considered as future works for this project as listed:  In this project, five different valves were experimentally/numerically tested. The best valve was selected amongst tested valves in terms of performance criterions such as minimum pressures and intake volume. Wide range of thicknesses and curvatures can be further tested. However, it requires different aluminum molds.   The teat of the bottle can be also optimized to help both infants feeding and natural flow inside the bottle. The material and the design of the teat can be modified. For instance, the ratio of the LSR components affects the stiffness of the cured teat. Different ratios can be tested to fabricate the teat, which is more comfortable for infants. Also, the geometry of the cut on top of the teat can be changed to optimize the flow rate.  The FSI simulation was performed to analyze the transient behavior of the fluid flow. The pressure was set to increase linearly from 0 to 2 kPa over the time. Based on our experimental results, the pressure change inside the bottle is not exactly linear. For the 90  future study, the exact template of the pressure change inside the bottle can be set as an inlet for the FSI simulation.    Results of computational simulation should be experimentally validated. Laser Doppler vibrometer (LDV) can be used to measure the displacement of leaflets. Also, particle image velocimetry (PIV) can measure the air velocity distribution inside the bottle.    One of the important issues regarding the nursing-bottles is the process of cleaning the bottle. During the cleaning, the venting valve bonded to the bottle may be damaged. Therefore, an appropriate cleaning process should be introduced.  The thermal bonding used to connect the valve to the bottom part of the bottle is resistant to the water. However, the robustness of the valve in long term operation should be tested.    91  Bibliography [1] C. E. Brown and B. Magnuson, “On the physics of the infant feeding bottle and middle ear sequela,” Int. J. Pediatr. 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