Solution of hollow fibre bioreactor design equations: the case of power-law fluids
01 Oct 1994-The Chemical Engineering Journal and The Biochemical Engineering Journal (Elsevier)-Vol. 55, Iss: 3
TL;DR: In this article, a methodology for solving the hollow fiber bioreactor design equations for a power-law-type velocity profile in the lumen is presented, which can be applied to any non-Newtonian fluid with an arbitrary velocity profile.
Abstract: A methodology for solving the hollow fibre bioreactor design equations for a power-law-type velocity profile in the lumen is presented. The algorithm presented in this communication can be applied to any non-Newtonian fluid with an arbitrary velocity profile.
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TL;DR: A numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
Abstract: The behavior of an immobilized enzyme reactor utilizing asymmetric hollow fibers is simulated using a theoretical model. In this reactor, an enzyme solution contained within the annular open-cell porous support structure of the fiber is separated from a substrate flowing through the fiber lumen by an ultrathin dense membrane impermeable to enzyme but permeable to substrate and product. The coupled set of model equations describing the behavior of this reactor represents an extended Graetz problem in the fiber lumen, with diffusion through the ultrathin fiber skin and reaction in the microporous sponge region. Exact analytic expressions for substrate concentration profiles throughout an idealized fiber which incorporate the membrane and hydrodynamic mass transfer resistances are obtained for a first-order enzyme reaction, and numerical techniques for their evaluation are given. This analysis is extended to yield a numerical finite difference solution for nonlinear Michaelis-Menten reaction kinetics, which is shown to agree with the analytic solution, as Km/C0, the ratio of the Michaelis constant to the initial substrate concentration, becomes large (> 100).
107 citations
TL;DR: A methodology for simplifying the solution procedure for hollow fiber bioreactor design equations has been described, which facilitates decoupling of membrane and spongy matrix equations from the tube side equations.
Abstract: A methodology for simplifying the solution procedure for hollow fiber bioreactor design equations has been described. Such a procedure facilitates decoupling of membrane and spongy matrix equations from the tube side equations. The equivalence between the reduced equations and the hemodialyzer problem has been explicitly obtained.
18 citations