Transient behavior of a zeolite membrane under non-linear conditions

A simplified mathematical model is proposed to provide an analytic solution for the transient behavior of a Langmuirian zeolite membrane subjected to a step increase in sorbate pressure at the upstream surface at time zero. The concentration profiles derived from the simplified model agree with those calculated by numerical solution of the governing partial differential equation. The model is used to investigate the validity of the classical time-delay method of measuring diffusion in the adsorbed phase. Under non-linear conditions the time delay depends on the degree of non-linearity as well as on the diffusional time constant. Under highly non-linear conditions application of the classical linear model yields apparent diffusivity values that are about four times larger than the limiting value (D₀).The new model is used to reanalyze experimental permeation diffusivity data for p-xylene in a single crystal zeolite membrane. The resulting D₀ values are shown to be consistent with the values determined by other experimental techniques.