A mathematical model of an aqueous-organic partition-based controlled release system using microporous membranes

A mathematical model with an exact solution is presented for the membrane-controlled release of small molecules such as nicotine, caffeine, and benzoic acid initially present in solution in the reservoir of the device. Both hollow fiber and flat membrane device geometries are considered. The reservoir is bounded by a microporous membrane, the pores of which are filled with a pore liquid immiscible with the reservoir phase liquid. At the interface between the reservoir and the pore, the solute partitions between the reservoir and the pore liquid phases, before diffusing outward through the membrane pore. The model results compare well with experimental data. Parametric studies reveal the interaction between system parameters and the controlled release behavior. A high partition coefficient of the solute between the reservoir and pore phases is found to effect pseudo-zero order release for an extended time. Similarly, when the ratio of time constants for transport of the solute through the reservoir and membrane regions is small, a constant release rate is achieved for an extended time.