The oil/water interface has been of great importance in understanding the dynamics of oscillatory interfacial mass transfer phenomenon and other bio-oscillations in excitable membranes. The oscillatory mass transfer across the oil/water interface generates an oscillating interfacial potential, which is measurable with suitable experimental setup. A detailed and systematic experimental study on the CTAB/picric acid system is done and a diffusion model is studied using delay-differential equations. It is found that a two-variable model with delay in one of the variables is able to explain the observed phenomenon satisfactorily.