A Twyman-Green interferometer was used to study the selective transport of ethanol-water mixtures of various concentration across a nonporous homogeneous silicone rubber membrane at 25°C. The instrument developed enabled the measurement of the transient concentration profiles within the boundary layers bathing the membrane. Measurements as close as 5um from the membrane surface were possible. The majority of the reported interferometric studies of liquid/membrane transport have been limited to the observation of the fringes and stop short of a full theoretical analysis. Such analysis is complicated by the optical effects of light deflection and the computational burden involved in the transient solution of the mathematical models required to describe membrane transport. A rigorous treatment of light deflection was developed on the basis of Fermat's principle of least time. The transient numerical solution of the model equations was accomplished by the application of the method of lines. To decouple the equilibrium and kinetic phenomena in membrane transport requires the independent measurement of the sorption isotherm. Traditional techniques for measuring the extent and composition of the imbibed phase involve removing the membrane from the liquid and are therefore limited by the inherent difficulties of obtaining a 'clean' separation. This was circumvented by measuring the excess (relative) sorption isotherm without removing the membrane from the liquid. The data was analysed in terms of Flory-Huggins thermodynamics which was fitted to the measured excess isotherm across the entire concentration range. For a binary mixture, transport across a homogeneous membrane involves two simultaneous fluxes which can be coupled through kinetic and/or equilibrium interactions. A measure of the extent of coupling was obtained by comparing the results from a simplified 'decoupled' flux model with those based on a 'coupled' flux model allowing for equilibrium interactions. Such interactions were found to have little effect on the flux of ethanol but strongly influenced the flux of water across silicone rubber. In particular, coupling through equilibrium interaction was found to be responsible for as much as 75% of the total flux of water. The diffusion coefficients of both ethanol and water in silicone rubber were shown to decrease strongly with alcohol concentration.