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Research Papers

Mass Transport in a Microchannel Bioreactor With a Porous Wall

[+] Author and Article Information
Xiao Bing Chen1

Dynamics Lab., E1–02–01, Department of Mechanical Engineering, National University of Singapore, 1 Engineering Drive 2, Singapore 117576mpecx@nus.edu.sg

Yi Sui, Heow Pueh Lee, Hui Xing Bai, Peng Yu, S. H. Winoto

Department of Mechanical Engineering, National University of Singapore, Singapore 117576

Hong Tong Low

Department of Mechanical Engineering, Division of Bioengineering, National University of Singapore, Singapore 117576

1

Corresponding author.

J Biomech Eng 132(6), 061001 (Apr 16, 2010) (12 pages) doi:10.1115/1.4001044 History: Received November 24, 2009; Revised January 08, 2010; Posted January 19, 2010; Published April 16, 2010; Online April 16, 2010

A two-dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two-domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier–Stokes equation; for the porous medium region, the generalized Darcy–Brinkman–Forchheimer extended model was used. For the porous-fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Damkohler number is the ratio of consumption to diffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction-convection distance parameter, which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction-convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis–Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number. The generalized results could find applications for the design of bioreactors with a porous wall.

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Figures

Grahic Jump Location
Figure 1

Schematic of the reactor model (not to scale)

Grahic Jump Location
Figure 2

Contour of concentration field with Pep=0.25, Damp=0.5, Damf=0.025, h/H=0.5, Km=0.260, ε=0.9, β=0, and β1=0

Grahic Jump Location
Figure 4

Effects of different Pep and Pef; Damp=0.6, h/H=0.5, Km=0.260, ε=0.9, β=0, and β1=0: (a) interface line concentration; (b) bottom line concentration; (c) concentration difference

Grahic Jump Location
Figure 5

Effects of different Damf and Pef; Damp=1.0, Km=0.260, h/H=0.5, ε=0.9, β=0, and β1=0: (a) interface line concentration; (b) bottom line concentration; (c) concentration difference

Grahic Jump Location
Figure 6

Effects of different Damp and Damf; Km=0.260, h/H=0.5, ε=0.9, β=0, and β1=0: (a) interface line concentration; (b) bottom line concentration; (c) concentration difference

Grahic Jump Location
Figure 7

Concentration at the interface as a function of reaction-convection distance parameter with different Damf for Michaelis–Menten reaction; ε=0.9, β=0, and β1=0: (a) at different Damf_d; (b) at different Km

Grahic Jump Location
Figure 3

Effects of different stress jump coefficients; Pep=0.25, Damp=0.5, Damf=0.025, h/H=0.5, Km=0.260, ε=0.9, β=0, and β1=0: (a) concentration distribution along interface; (b) concentration profiles normal to interface at x/H=10.0; (c) velocity profiles

Grahic Jump Location
Figure 8

Concentration difference parameter as a function of reaction-convection distance parameter with different Damf for Michaelis–Menten reaction; ε=0.9, β=0, and β1=0: (a) at different Damp; (b) at different Km

Grahic Jump Location
Figure 9

Reaction effectiveness factor as a function of reaction-convection distance parameter with different Damf for Michaelis–Menten reaction; ε=0.9, β=0, and β1=0: (a) at different Damp; (b) at different Km

Grahic Jump Location
Figure 10

Reactor efficiency as a function of reaction-convection distance parameter with different Damf for Michaelis–Menten reaction; ε=0.9, β=0, and β1=0: (a) at different Damp; (b) at different Km

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