A Theoretical Investigation of Convective Transport in the Hollow-Fiber Reactor

Modeling of Axial-Flow Hollow Fiber Cell Culture Bioreactors

“…Their assumption is valid for cell densities in the early phase of a cell culture before cell mass approaches tissue-like density. They clearly illustrated, as did Salmon et al (1988) and Heath et al (1990), that for certain axial-flow hollow fiber bioreactor designs a significant secondary axial flow was induced within the ECS.…”

“…Figure 6 shows the streamlines calculated from the unobstructed flow model of Kelsey et al (1990), and it has the same qualitative feature as the ones generated with the porous medium model (Apelblat et al, 1974;Salmon et al, 1988;Heath et al, 1990). Although the streamlines have similar patterns for the two flow regimes, the actual axial and radial velocities can be very different.…”

“…The dimensionless length is scaled by the Peclet number, analogous to the use of the Graetz number. This concept is taken up later by Salmon et al (1988). The realization that, in cell bioreactors, criteria based on prevention of substrate depletion rather than high conversion are more applicable comes much later.…”

“…The resulting expression, divided by LπR s 2 , provides a fractional ECS volume, f ECS , Webster and Shuler (1978) x zero, first effectiveness factor in ECS x x zero, first effectiveness factor in ECS Webster and Shuler (1981) x first transient solution Davis and Watson (1985) x x parabolic Monod estimate effective diffusivity in ECS Kleinstreuer and Agarwal (1986) x x parabolic Monod general transient model Chresand et al (1988) x x parabolic zero optimal fiber spacing Heath and Belfort (1987) x plug-flow zero, first analytical axial and radial profiles Sardonini and DiBiasio (1992) x x zero growth of randomly distributed colonies x x parabolic zero oxygen transport limitations Schonberg and Belfort (1987) x 1-D (radial) first effect of radial convection; criterion for neglecting lumen resistance Salmon et al (1988) x 2-D (porous medium)…”

“…However, a more complete picture of bioreactor performance is provided by the coupling of the fluid dynamics to the substrate mass balance and to cellular growth kinetics. Salmon et al (1988) superimposed the porous medium velocity profiles derived by Apelblat et al (1974) on the substrate balance eq 7 in the ECS. They gave an in-depth report on the methodology for their solutions of reacting and nonreacting solutes and the effects of substrate kinetics and transport.…”