The aim of this work is to provide operating data for biodegradable hollow fiber membrane bioreactors. The physicochemical cell culture environment can be controlled with the permeate flowrate, so this aim necessitates the provision of operating equations that enable end users to set the pressures and feed flowrates to obtain their desired culture environment. In this paper, theoretical expressions for the pure water retentate and permeate flowrates, derived using lubrication theory, are compared against experimental data for a single fiber poly(vinyl alcohol)-poly(lactide-co-glycolide) crossflow module to give values for the membrane permeability and slip. Analysis of the width of the boundary, layer region where slip effects are important, together with the sensitivity of the retentate and permeate equations to the slip parameter, show that slip is insignificant for these membranes, which have a mean pore diameter of 1.1 mu m. The experimental data is used to determine a membrane permeability, of k = 1.86 x 10(-16) m(2), and to validate the model. It was concluded that the operating equation that relates the permeate to feed ratio, c, lumen inlet flowrate, Q(1,in), lumen outlet pressure, P-1, and ECS outlet pressure, "P-0, is
P-1 - Po = Q(1,in)(Ac + B) (1)
where A and B are constants that depend on the membrane permeability and geometry (and are given explicitly). Finally, two worked examples are presented to demonstrate how a tissue engineer can use Equation (1) to specify operating conditions for their bioreactor.
- mathematical modeling
- tissue engineering
- permeability slip