A Mathematical Model for Kinetic Study of Analyte Permeation from Both Liquid and Gas Phases through Hollow Fiber Membranes into Vacuum

A mathematical model and a Matlab-5 computer code have been developed to study the dynamic response of the hollow fiber membrane probe. The depletion layer formation at the sample/membrane interface is taken into consideration by the mathematical model for the liquid mobile phase. The code produces concentration profiles within a sample feed stream and in the membrane. Flux values at the vacuum side of the membrane can also be calculated as a function of time. The method can be applied both for gas and liquid feed streams. Concentration profiles in a mobile phase and the flux of analytes through the hollow fiber membrane inlet have been studied with this simulation technique as a function of the liquid-phase flow rate. The influence of the formation of a layer of the analyte depletion during the dynamic response has been considered. The shape of the depleted layer and selectivity of permeation from a liquid mobile phase through the membrane into the vacuum are shown to be dependent on the mobile-phase flow rate. In addition, for studied conditions, formation of a depletion layer is demonstrated to be fast compared with membrane diffusion. Thus, if a homogeneous aqueous sample is coming through the inlet cross-section of a hollow fiber membrane containing pure water, the response time mostly depends on analyte diffusivity in the membrane. However, if the aqueous sample is coming through the inlet cross-section of a hollow fiber membrane containing clean air, response time also depends on equilibrium analyte concentration in the depletion layer.