Interfacial diffusion controlled reactions with time varying absorbing domains

A theoretical study for diffusional crossing of a tracer through a membrane, where the size of the adsorbing domain (receptor) is time dependent, is presented, A periodic array of absorbing and reflecting domains at the membrane surface was assumed. This model is described by a time-dependent diffusion equation with mixed boundary conditions, where the boundaries are themselves varying with time. Both analytical and numerical methods were employed in order to calculate the total flux of a tracer across the membrane as a function of the oscillation frequency (omega) and amplitude (epsilon) of the receptor site. The results show an increase in the absorption rate with frequency, reaching a plateau at very high values of omega. The space and time behavior of the diffusing tracer concentration was analyzed, evidencing dephasing effects at high omega which are common to many nonlinear systems where the dynamic response becomes time independent in the high frequency limit. This approach could be useful in studying the anomalous effect of an oscillating electric field on the membrane permeability. (C) 1996 American Institute of Physics.