A numerical study of fluid flow and mass transport in a microchannel bioreactor

A NUMERICAL STUDY OF FLUID FLOW AND MASS TRANSPORT IN A MICROCHANNEL BIOREACTOR ZENG YAN NATIONAL UNIVERSITY OF SINGAPORE 2006 A NUMERICAL STUDY OF FLUID FLOW AND MASS TRANSPORT IN A MICROCHANNEL BIOREACTOR ZENG YAN (B.Eng., M.Eng., Xi’an Jiaotong University, China) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2006 ACKNOWLEDGEMENTS I would like to express my deepest gratitude to my Supervisors, Assoc Prof Low H.T and Assoc Prof Lee T.S for introducing me into the exciting field of biofluids and giving me good suggestions that contributed much towards the formation and completion of this thesis I really appreciate their invaluable guidance, supervision, encouragement, patience and support throughout my Ph.D studies Moreover, I would like to thank all the technical staffs in the Fluid Mechanics Laboratory for their valuable assistance during my research work I also wish to express my gratitude to the National University of Singapore for awarding me a Research Scholarship and an opportunity to pursue a Ph.D degree My sincere appreciation will go to my dear family: my husband Yu Peng, my parents, my sister and brother Their love, concern, support and continuous encouragement really help me conquer much difficulty throughout this work Finally, I would like to thank all my friends who have helped me in different ways during my whole Ph.D studies! Their friendship will benefit me in my whole life! i TABLE OF CONTENTS ACKNOWLEDGEMENTS i TABLE OF CONTENTS ii SUMMARY vi NOMENCLATURE viii LIST OF FIGURES xii LIST OF TABLES xix Chapter Introduction 1.1 Background 1 1.1.1 Cell culture 1.1.2 Bioreactors 1.2 Literature Review 1.2.1 Development of bioartificial liver (BAL) bioreactors 1.2.2 Liquid flows in microchannels 1.2.3 Mass transport in microchannel bioreactors 10 1.2.4 Shear stress in microchannel bioreactors 15 1.2.5 Surface roughness effects in microchannel bioreactors 19 1.3 Research objectives and scope 22 1.4 Organization of the thesis 24 Chapter Numerical Method 2.1 Bioreactor model and governing equations 25 26 ii 2.2 CFD commercial software: FLUENT 27 2.2.1 User Defined Function (UDF) 27 2.2.2 User Defined Scalar (UDS) 28 2.2.3 Numerical method and code verification 29 2.3 Grid generation in complex domain and Finite Volume Method in curvilinear coordinate 31 2.3.1 Grid generation 31 2.3.2 Computational method 33 2.3.3 Code validation 42 2.4 Summary Chapter Mass Transport and Shear Stress for Single-culture 3.1 Analysis 49 51 52 3.1.1 Boundary conditions 52 3.1.2 Non-dimensional parameters 53 3.2 Results and discussion 57 3.2.1 Mass transport 57 3.2.2 Shear stress 63 3.2.3 Application of the generalized results 65 3.3 Conclusions Chapter Mass Transport for Randomly Mixed Co-culture 4.1 Analysis 69 71 72 4.1.1 Boundary conditions 72 4.1.2 Non-dimensional parameters 73 iii 4.2 Results and discussion 77 4.2.1 Species concentration distribution 77 4.2.2 Correlation of results for decreasing axial-concentration 80 4.2.3 Applications of the generalized results 85 4.3 Conclusions Chapter Mass Transport for Micropatterned Co-culture 5.1 Analysis 89 91 92 5.1.1 Boundary conditions 92 5.1.2 Non-dimensional parameters 93 5.2 Results and discussion 97 5.2.1 Species concentration distribution 97 5.2.2 Correlation of mass transport results 99 5.2.3 Mass transfer effectiveness 102 5.2.4 Applications of the generalized results 106 5.3 Conclusions Chapter Surface Roughness Effects for Single-culture 108 111 6.1 Geometry configuration and grid 112 6.2 Boundary conditions 112 6.3 Non-dimensional parameters 114 6.4 Results and discussion 115 6.4.1 Velocity field 116 6.4.2 Pressure gradient 119 iv 6.4.3 Shear stress 119 6.4.4 Mass transfer 121 6.5 Conclusions Chapter Conclusions and Recommendations 7.1 Conclusions 125 127 127 7.1.1 Single-culture system 128 7.1.2 Randomly mixed co-culture system 128 7.1.3 Micropatterned co-culture system 129 7.1.4 Surface roughness effects in single-culture system 130 7.2 Recommendations 131 References 133 Tables 149 Figures 150 v SUMMARY Microchannel bioreactors have been used in many studies to manipulate and investigate the fluid microenvironment around cells The objective of this thesis was to develop a numerical model of the fluid flow and mass transport in a microchannel bioreactor for single-culture, randomly mixed co-culture and micropatterned co-culture First, the fluid flow and mass transfer in a three-dimensional flat-plate microchannel bioreactor for single-culture were studied A monolayer of absorption cells was assumed to attach to the base of the channel and consumes nutrients from culture medium flowing through the channel A three-dimensional numerical flow model, incorporating mass transport, was used to simulate the internal flow and mass transfer The computational fluid dynamics code (FLUENT), with its User Defined Functions, was used to solve the numerical model Two combined non-dimensional parameters were developed to correlate the numerical results of species concentration The correlations may be useful for general applications in microchannel bioreactor design, for example in the calculation of the critical channel length to avoid species insufficiency A generalized relationship between mass transport and shear stress was found Based on the generalized relationship and the condition of dynamic similarity, various means to isolate their respective effects on cells were considered Subsequently, the study was extended to a randomly mixed co-culture system Two types of cells were assumed to be adherent randomly to the base: absorption cells which only consume species, and release cells which secrete species to support the absorption cells Under the condition of decreasing axial-concentration and positive flux- vi parameter, combined parameters were proposed to correlate the numerical data of axial concentration The correlations may be useful for general applications in design of randomly mixed co-culture systems The micropatterned co-culture system has release and absorption parts arranged alternately, and each part has a single cell type Different combined parameters were developed for release and absorption parts to make the data collapse in each part Combination of the collapse data in release and absorption parts can be used to predict concentration distribution through the whole channel The mass transfer effectiveness was found to be higher with more numbers of units The optimal condition for micropatterned co-culture bioreactors is achieved when the product of the length ratio and the reaction ratio is equal to Furthermore, surface roughness effects in a microchannel bioreactor for singleculture were investigated by a numerical model based on Finite Volume Method in curvilinear coordinate, with two types of roughness elements on the bottom walls: semicircle and triangle The results showed non-uniform species concentration at the base, peaking at the apex of the roughness elements For the roughness size ratio of 0.2 and the spacing ratio of 5.0, with Peclet number of 50 and Damkohlar number of 0.6, the peak concentration is around 7% higher than that in a smooth mirochchannel, suggesting that the roughness element has some effect on the mass transport in a microchannel whose height is less than about times that of the roughness element vii NOMENCLATURE A cross-sectional area of the microchannel Ar Archimedes Number C species concentration Cin inlet concentration of the microchannel, which is uniform and specified C non-dimensional species concentration C dimensionless minimum concentration at the base in the rough channels C0 non-dimensional species concentration at the base D diffusivity of the species in culture medium DR spacing between the roughness elements Da Damkohler number for single-culture Daa Damkohler number of absorption cells in co-culture Dar Damkohler number of release cells in co-culture Df Stokes’ drag force on cells Dh hydraulic diameter of the microchannel d diameter of the circular cylinder (Chapter 2); the cell diameter (Chapter 6) FB buoyant force on cells f friction factor H height of the rough microchannel h height of the flat-plate microchannel jR absorption rate in the rough channels jS absorption rate in the smooth channels jab absorption flux viii Chapter Mass transport for micropatterned co-culture (a) K ave -2 -4 Daa = 0.1 Daa = 0.5 -6 -8 (b) K ave Daa = 0.1 Daa = 0.5 α Da α Da α Da α Da α Da α Da = 1.5 = 1.0 L = cm = 0.5 Release parts = 1.5 = 1.0 L = 4.5 cm = 0.5 10 Numbers of units Unit number α Da α Da α Da α Da α Da α Da 15 20 = 1.5 = 1.0 L = cm = 0.5 Absorption parts = 1.5 = 1.0 L = 4.5 cm = 0.5 -2 -4 -6 -8 10 15 20 Unit number Numbers of units Figure 5.14 Average effectiveness parameters as a function of numbers of units for different α Da at Daa = 0.1, 0.5; Pe = 10, K ma = 0.068 and α l = 1.0 : (a) release parts; (b) absorption parts 194 Chapter Mass transport for micropatterned co-culture (a) K ave Daa Daa Daa Daa Daa Daa Daa Daa = 0.1 = 0.5 = 0.1 = 0.5 = 0.1 = 0.5 = 0.1 = 0.5 α Da = 1.5 and α l = 1.0 α Da = 0.75 and α l = 2.0 α Da = 1.5 and α l = 1.0 α Da = 0.75 and α l = 2.0 Release parts Absorption parts -2 -4 -6 -8 10 15 20 Unit number Numbers of units (b) K ave Daa Daa Daa Daa Daa Daa Daa Daa = 0.1 = 0.5 = 0.1 = 0.5 = 0.1 = 0.5 = 0.1 = 0.5 10 12 α Da = 1.0 and α l = 1.0 α Da = 0.5 and α l = 2.0 α Da = 1.0 and α l = 1.0 α Da = 0.5 and α l = 2.0 Release parts Absorption parts -2 -4 -6 -8 14 16 18 20 Unit number Numbers of units Figure 5.15 Average effectiveness parameters as a function of numbers of units at release and absorption parts with Daa = 0.1, 0.5; Pe = 10, K ma = 0.068 : (a) α l ⋅ α Da = 1.5 ; (b) α l ⋅ α Da = 1.0 ; (c) α l ⋅ α Da = 0.5 195 Chapter Mass transport for micropatterned co-culture (c) Daa Daa Daa Daa Daa Daa Daa Daa K ave = 0.1 = 0.5 = 0.1 = 0.5 = 0.1 = 0.5 = 0.1 = 0.5 α Da = 1.0 and α l = 0.5 α Da = 0.5 and α l = 1.0 α Da = 1.0 and α l = 0.5 α Da = 0.5 and α l = 1.0 Release parts Absorption parts -2 -4 -6 -8 10 Numbers of units Unit number 15 20 Figure 5.15 (continued) 196 Chapter Surface roughness effects for single-culture L Um H DR R DR (a) DR R l=R DR (b) Figure 6.1 Schematic of the microchannel with surface roughness on the base wall: (a) semicircle roughness; (b) triangle roughness 197 Chapter Surface roughness effects for single-culture (a) H DR (b) H DR Figure 6.2 Grid generation in one unit of rough channels: (a) semicircle roughness; (b) triangle roughness 198 Chapter Surface roughness effects for single-culture (a) 1.7 1.8 0 (b) 75 1.65 Figure 6.3 Constant-velocity lines along axial and vertical directions for flow through rough channels at α = 0.2 and β = : (a) Constant axial velocity lines in semicircle rough channel; (b) Constant axial velocity lines in triangle rough channel; (c) Constant vertical velocity lines in semicircle rough channel; (d) Constant vertical velocity lines in triangle rough channel 199 Chapter Surface roughness effects for single-culture (c) 0.250 0.004 -0.250 -0.013 0.013 -0.004 (d) -0.250 0.250 0.00 0.004 -0.013 0.013 -0.004 -0.00 Figure 6.3 (continued) 200 Chapter Surface roughness effects for single-culture (a) 0.005 Ar Re DR R = 4.0 DR R = 5.0 DR R = 7.5 0.004 DR R = 10.0 R H = 0.1 R H = 0.2 0.003 R H = 0.3 0.002 0.001 0 0.05 0.1 0.15 d R (b) Ar Re 0.006 DR R = 4.0 DR R = 5.0 DR R = 7.5 DR R = 10.0 R H = 0.1 0.004 R H = 0.2 R H = 0.3 0.002 0 0.05 0.1 0.15 d R Figure 6.4 Ar/Re as a function of d/R in different rough microchanels at different rougness size ratio α and spacing ratio β : (a) semicircle rough microchannel; (b) triangle rough microchannel 201 Chapter Surface roughness effects for single-culture DR DR DR DR DR DR DR DR ∆P ∆X R = 4.0 R = 5.0 R = 7.5 R = 10.0 R = 4.0 R = 5.0 R = 7.5 R = 10.0 Semicircle roughness Triangle roughness 0 0.1 0.2 0.3 0.4 R H 0.5 Figure 6.5 Dimensionless pressure gradients in terms of the roughness size ratio α at different spacing ratio β in semicircle and triangle rough microchannels R/H=0.1 R/H=0.2 R/H=0.1 R/H=0.2 τ s ,R Semicircle Roughness Triangle Roughness 0 0.2 0.4 0.6 0.8 x Figure 6.6 Comparison of dimensionless shear stress τ s , R at base in one unit in different rough microchannels at the roughness size ratios α = 0.1, 0.2 and the spacing ratio β = 5.0 202 Chapter Surface roughness effects for single-culture (a) Roughness apex Flat-bed base τ s ,R,max DR R = 4.0 DR R = 5.0 DR R = 7.5 DR R = 10.0 (b) 0.1 10 0.2 0.3 0.4 0.3 0.4 R H 0.5 Roughness apex Flat-bed base τ s ,R,max DR R = 4.0 DR R = 5.0 DR R = 7.5 DR R = 10.0 0 0.1 0.2 0.5 R H Figure 6.7 Dimensionless maximum shear stress τ s , R ,max verses the roughness size ratio α at different spacing ratio β in different rough microchannels: (a) semicircle rough microchannel; (b) triangle rough microchannel 203 Chapter Surface roughness effects for single-culture (a) C/Cin (b) (c) 1.000 0.947 0.895 0.842 0.789 0.737 0.684 0.632 0.579 0.526 0.474 0.421 0.368 0.316 0.263 0.211 0.158 0.105 0.053 0.000 Figure 6.8 Comparison of the species concentration distributions in the smooth and rough channels at Pe = 50, Da = 1.2 and K m = 0.05: (a) smooth channel; (b) semicircle rough channel; (c) triangle rough channel 204 Chapter Surface roughness effects for single-culture (a) C0 Cin 0.8 0.6 Smooth Channel 0.4 α = 0.1 α = 0.2 α = 0.3 Semicircle Roughness 0.2 (b) C0 Cin 0.2 0.4 x/L 0.6 0.8 1.0 0.8 0.6 Smooth Channel 0.4 α = 0.1 α = 0.2 α = 0.3 Triangle Roughness 0.2 0 0.2 0.4 0.6 0.8 1.0 x/L Figure 6.9 Effect of the roughness size ratio α on the species concentration distributions at base; Pe = 50, Da = 0.6, K m = 0.05 and β = : (a) semicircle rough microchannel; (b) triangle rough microchannel 205 Chapter Surface roughness effects for single-culture (a) C0 Cin 0.8 0.6 0.4 Pe=10 Pe=50 Pe=10 Pe=50 0.2 Pe=10 Pe=50 (b) C0 Cin 0.2 Smooth Channel Semicircle Roughness Triangle Roughness 0.4 x/L 0.6 0.8 1.0 0.8 0.6 0.4 Da=0.6 Da=1.2 Da=0.6 Da=1.2 0.2 Da=0.6 Da=1.2 0 0.2 Smooth Channel Semicircle Roughness Triangle Roughness 0.4 x/L 0.6 0.8 1.0 Figure 6.10 Effects of the mass transfer parameters Pe and Da on the species concentration distributions at base; the roughness size ratio α = 0.2 , the spacing ratio β = and K m = 0.05: (a) different Pe at Da = 0.6; (b) different Da at Pe = 50 206 Chapter Surface roughness effects for single-culture (a) DR DR DR DR DR DR DR DR ∆j % 1.5 R = 4.0 R = 5.0 R = 7.5 R = 10.0 R = 4.0 R = 5.0 R = 7.5 R = 10.0 Semicircle roughness Triangle roughness 0.5 (b) 0.1 0.2 0.3 R H 0.4 C 0.8 0.6 DR DR DR DR DR DR DR DR 0.4 0.2 0 R = 4.0 R = 5.0 R = 7.5 R = 10.0 R = 4.0 R = 5.0 R = 7.5 R = 10.0 0.1 Semicircle roughness Triangle roughness 0.2 0.3 R H 0.4 Figure 6.11 Effects of the roughness size ratio α and spacing ratio β on dimensionless absorption rate ∆j % and minimum concentration at base C in semicircle and triangle rough channels; Pe = 50, Da = 0.6, K m = 0.05 for L/H = 100: (a) ∆j % ; (b) C 207 Chapter Surface roughness effects for single-culture (a) Pe = 50 Pe = 250 Pe = 50 ∆j % Pe = 250 Semicircle roughness Triangle roughness 1.5 0.5 (b) 0.3 0.6 0.9 1.2 Da 1.5 C 0.8 0.6 0.4 Pe = 50 Pe = 250 Pe = 50 0.2 Pe = 250 0 0.3 0.6 Semicircle roughness Triangle roughness 0.9 1.2 Da 1.5 Figure 6.12 Effects of the mass transfer Peclet number Pe and Damkohler number Da on dimensionless absorption rate ∆j % and minimum concentration at base C in semicircle and triangle rough channels; α = 0.2 , β = 5.0 , K m = 0.05 for L/H = 100: (a) ∆j % ; (b) C 208 ... theoretical information on mass transport A systematic study is needed to investigate the effects of various important parameters on the fluid flow and mass transport in microchannel bioreactors... increasing fluid- phase endocytosis; and they are capable of producing intracellular actin and myosin filaments that are oriented in the flow direction Eskin et al (1984) investigated the shear... governing equations and the numerical methods for the present simulations In Chapter 3, the numerical analysis of fluid flow and mass transfer in a threedimensional flat-plate microchannel bioreactor