Membrane permeation under continuous elution of the sink side of the membrane

Abstract

Equations are presented which describe the kinetics of solute permeation through a membrane separating two compartments—donor and receiver—under the condition that the receiver compartment is continuously eluted. Their analytic solution reveals the following. Two processes are involved; permeation and elution. In the initial stage permeation through the membrane is dominant and in a later stage elution effects become dominant. Thus the solute concentration in the receiver as a function of time exhibits a maximum. Also, a time range is found over which the solute concentrations in the donor and the receiver vary almost linearly with time. The effect of elution can be considered equivalent to enlarging the receiver volume. A simple experimental system is proposed. The results are found to be well described with our model. Especially, agreement between theory and experiment is surprisingly good with respect to the location of the concentration maximum in the receiver when concentration is plotted as a function of time, in spite of the fact that our theory contains no adjustable parameter.