Abstract
Knowledge of the fluid flow and mass transfer over circular strands is fundamental to the cell culture of tissue scaffolds in bio-reactors. This paper presents a study on the simulation of fluid flow and mass transfer over the circular strands of a tissue scaffold by using the multiple relaxation time lattice Boltzmann method for the low Reynolds number regime, with Re D = 0.01 and 0.1, respectively. The mass transfer problem approximates the transport of a scalar nutrient from the bulk fluid to the strand surface, such as is encountered in the flow through tissue scaffolds placed in bio-reactors. The circular geometry of the scaffold strand is treated and implemented by means of the interpolated bounce-back boundary condition formulation. Our simulation illustrates that the flow accelerates around the strand, resulting in the maximum shear stress at the shoulder of the strand and that diffusion mass transfer plays the dominant role in the scalar transport. The local Sherwood number varies significantly over the surface of the strand, with a peak value located on the upstream surface. Increasing the Schmidt number of the scalar and decreasing the blockage ratio results in higher mass transfer rates on the surface of the stand. Overall, the simulation results provide one with the insight into the fluid flow and mass transfer over the circular strands of a tissue scaffold in a bio-reactor, which would be impractical to obtain by experiments.
Similar content being viewed by others
References
Yan X, Chen XB, Bergstrom DJ (2011) Modeling of the flow within scaffolds in perfusion bio-reactors. Am J Biomed Eng 1(2):72–77
Hossain MS, Chen XB, Bergstrom DJ (2012) Investigation of the in vitro culture process for skeletal-tissue-engineered constructs using computational fluid dynamics and experimental methods. ASME J Biomech Eng 134:121003
Singh H, Hutmacher DW (2009) Bio-reactor studies and computational fluid dynamics. Adv Biochem Eng Biotechnol 112:231–249
Zdravkovich MM (1997) Flow around circular cylinders, vol 1: fundamentals, vol 1. Oxford University Press, New York
Thom A (1933) The flow past circular cylinders at low speeds. Proc R Soc Lond A 141:651–669
Takami H, Keller HB (1969) Steady two dimensional viscous flow of an incompressible fluid past a circular cylinder. Phys Fluids 12:II-51–II-56
Dennis SCR, Chang G-Z (1970) Numerical solutions for steady flow past a circular cylinder at Reynolds number up to 100. J Fluid Mech 42(3):471–489
Mandujano F, Peralta-Fabi R (2005) On the viscous steady flow around a circular cylinder. Rev Mex de Física 51(1):87–99
Ribeiro VM, Coelho PM, Pinho FT, Alves MA (2012) Three-dimensional effects in laminar flow past a confined cylinder. Chem Eng Sci 84:155–169
Yu D, Mei R, Luo L-S, Shyy W (2003) Viscous flow computations with the method of lattice Boltzmann equation. Prog Aerosp Sci 39:329–367
Premnath KN, Pattison MJ, Banerjee S (2009) Generalized lattice Boltzmann equation with forcing term for computation of wall-bounded turbulent flows. Phys Rev E 79:026703
Kang S (2008) An improved immersed boundary method for computation of turbulent flows with heat transfer. PhD Thesis, Stanford University
Mei R, Luo L-S, Shyy W (1999) An accurate curved boundary treatment in the lattice Boltzmann method. J Comput Phys 155:307–330
Filippova O, Hanel D (1998) Grid refinement for lattice-BGK models. J Comput Phys 147:219–228
He X, Doolen GD (1997) Lattice Boltzmann method on curvilinear coordinates system: vortex shedding behind a circular cylinder. Phys Rev E 56(1):434–440
Zhang J, Johnson PC, Poepl AS (2007) An immersed boundary lattice Boltzmann approach to simulate deformable liquid capsules and its application to microscopic blood flows. Phys Biol 4:285–295
Bouzidi M, Firdaouss M, Lallemand P (2001) Momentum transfer of a lattice Boltzmann fluid with boundaries. Phys Fluids 13:3452–3459
Flekkoy EG (1993) Lattice Bhatnagar–Gross–Krook models for miscible fluids. Phys Rev E 47(6):4247–4257
Sullivan SP, Sani FM, Johns ML, Gladden LF (2005) Simulation of packed bed reactors using lattice Boltzmann method. Chem Eng Sci 60:3405–3418
Schulenburg DAG, Pintelon TRR, Picioreanu C, Loosdrecht MCM, Johns ML (2008) Three-dimensional simulations of biofilm growth in porous media. AIChE J 55:494–504
Pintelon TRR, Picioreanu C, Loosdrecht MCM, Johns ML (2011) The effect of biofilm permeability on bio-clogging of porous media. Biotechnol Bioeng 109(4):1031–1042
Hossain MS, Bergstrom DJ, Chen XB (2014) Prediction of cell growth rate over scaffold strands inside the perfusion bioreactor. Biomech Model Mechanobiol. doi:10.1007/s10237-014-0606-4
Yoshida H, Nagaoka M (2010) Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation. J Comput Phys 229:7774–7795
d’Humières D, Ginzburg I, Krafczyk M, Lallemand P, Luo L-S (2002) Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos Trans R Soc Lond A 360:437–456
Li L, Mei R, Klausner JF (2013) Boundary conditions for thermal lattice Boltzmann equation method. J Comput Phys 237:366–395
Zhang T, Shi B, Guo Z, Chai Z, Lu J (2012) General bounce-back scheme for concentration boundary condition in the lattice Boltzmann method. Phys Rev E 85:016701
Sacco R, Causin P, Zunino P, Raomondi MT (2011) A multiphysics/multiscale 2D numerical simulation of scaffold-based cartilage regeneration under interstitial perfusion in a bioreactor. Biomech Model Mechanobiol 10:577–589
Yu H, Luo L-S, Girimaji SS (2006) LES of turbulent square jet flow using an MRT lattice Boltzmann method. Comput Fluids 35:957–965
Yang Y, Liao Q, Zhu X, Wang H, Wu R, Lee DJ (2011) Lattice Boltzmann simulation of substrate flow past a cylinder with PSB biofilm for bio-hydrogen production. Int J Hydrog Energy 36:14031–14040
Dani A, Cockx A, Guiraud P (2006) Direct numerical simulation of mass transfer from spherical bubbles: the effect of interface contamination al low Reynolds number. Int J Chem Reactor Eng 4:A2
Yan X, Bergstrom DJ, Chen XB (2012) Modeling of cell cultures in perfusion bio-reactors. IEEE Trans Biomed Eng 59(9):2568–2575
Gokaltun S, Dulikravich GS (2010) Lattice Boltzmann computations of incompressible laminar flow and heat transfer in a constricted channel. Comput Math Appl 59:2431–2441
Acknowledgments
The authors wish to acknowledge the financial support of the Natural Science and Engineering Research Council of Canada (NSERC) and the Saskatchewan Health Research Foundation (SHRF).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hossain, M.S., Chen, X.B. & Bergstrom, D.J. Fluid flow and mass transfer over circular strands using the lattice Boltzmann method. Heat Mass Transfer 51, 1493–1504 (2015). https://doi.org/10.1007/s00231-015-1514-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231-015-1514-6