A variational procedure is applied to obtain upper bounds on and estimates of interphase transfer rates in random two-phase media. Results are expressed in terms of the void-size distribution as introduced by SCHEIDEGGER, the void size at a point being detined as the minimum distance of that point from the interface between the phases. Specific cases discussed are, tirst, the diffusion controlled adsorption, at the interface, of a solute present in one phase; here the bounds obtained are on the rate of decay of the mean solute concentration in the limit of long times. The second case is that of diffusion controlled adsorption at the interface balanced by a uniform and constant generation of solute throughout one phase; bounds and estimates are obtained for the ratio of the rate of generation to the mean concentration level maintained at the steady state.
In addition, the transfer of solute between two phases with identical properties is treated. If the solute is initially distributed uniformly over one phase and absent from the other, it is possible to derive an exact expression for the fraction of total solute present in either phase as a function of time. The geometry of the interface enters into this expression in the form of the probability g(p) that two randomly placed points a distance p apart will both fall within the phase which originally contains the solute.