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Modelling of fluid flow and protein transport in hollow-fibre bioreactors Labecki, Marek

Abstract

A mathematical model (the Porous Medium Model, PMM) was developed to predict the fluid flow and solute transport in hollow-fibre devices, with a particular emphasis on hollowfibre bioreactors (HFBRs). In the PMM, both the extracapillary space (ECS) and the lumen side are treated as interpenetrating porous regions with a continuous source or sink of fluid. The hydrodynamic equations of the PMM are based on Darcy's law and continuity considerations while the transport of the ECS protein is described by the time-dependent convective-diffusion equation. Compared to the earlier Krogh Cylinder Model (KCM), in which the fluid flow and protein transport are assumed to be the same for each fibre, the PMM represents an improved approach in which the spatial domain corresponds to the real dimensions of the hollow-fibre module. Thus, it can be applied to operating conditions where macroscopic radial pressure and concentration gradients exist, such as in open-shell operations. It was demonstrated that, in the absence of radial gradients, the PMM becomes mathematically equivalent to the one-dimensional KCM. The PMM also takes into account the osmotic pressure dependence on the ECS protein concentration, which causes a coupling of the hydrodynamic and protein transport equations. The Porous Medium Model was tested by applying it to one- and two-dimensional closed-shell operations. Both confirmed that a significant polarization of the ECS protein occurs in the direction of the existing pressure gradients under dominant convective transport conditions. The downstream polarization of protein affects HFBR hydrodynamics by virtually shutting down the flow in a significant portion of the ECS due to locally high osmotic pressures. It can also facilitate harvesting of the product protein by increasing its concentration near the downstream ECS port. Modelling studies of the hydrodynamics of hollow-fibre devices in the partial and full filtration modes of operation were carried out for a wide range of membrane permeabilities (10"14

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