Theoretical Analysis of Diffusional Movement Through Heterogeneous Barriers*

A number of theoretical relations dealing with diffusion through heterogeneous barriers are presented and discussed. These are expected to be useful in predicting barrier behavior in formulations such as pharmaceutical and particularly protective ointments and films. A relationship has been derived which expresses the effective permeability constant, P_m, of a two phase mixture as a function of the volume fraction and the permeability of each phase. The effect of the shape of the particles on P_m is also considered. Where data are available, agreement with theory is satisfactory. The nonstationary state behavior of a two phase heterogeneous barrier is discussed in relation to the diffusion coefficient, partition coefficient, the volume fraction, and the particle size associated with each phase. It is shown that the effectiveness of one heterogeneous barrier may be greater than another for a given time of exposure while for a longer time of exposure the reverse may be the case. The effect of a “skin” or a coat of a third phase on the internal phase particle has also been examined. Finally, the situation in which simultaneous diffusion and absorption occur is discussed and an expression for the lag time has been derived for this case.