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

A hollow-fiber reactor is a device within which a catalytically active material, generally comprising enzymes or cells, is retained by hollow-fiber membranes. In recent experimental work we examined the rate of transport of a non-reacting tracer through microbial cells contained within such a reactor, and obtained results that could not be described using a theoretical model in which the solute was assumed to be transported only by diffusion. This failure can be attributed to the fact that there is some convective fluid movement through the membranes and the catalytically active region in hollow-fiber reactors. We have developed two models that provide a quantitative description of the effect of this flow on the transport of either a non-reacting tracer or a solute that is consumed with first-order or Michaelis-Menten kinetics. The predictions of these models have been examined over a wide range of the applicable parameters, and show that convective transport can have a marked effect on the behavior of a reactor. Furthermore, the calculations show that under certain conditions the transport of a non-reacting solute can be adequately described by a reduced set of parameters. This finding considerably facilitates the analysis of experimental data to estimate the transport properties of cell aggregates confined within hollow-fiber reactors.