Time-Dependent Diffusion Coefficient in Pressure-Decay Experiments

Among all of the indirect methods of measuring the diffusion coefficient, the pressure-decay experiment has gained considerable attention due to its convenience, simplicity, and accuracy. In this study, mathematical modeling of a pressure-decay experiment based on the one-dimensional diffusivity equation with time-dependent molecular diffusion coefficients is developed. The available experimental data have been interpreted qualitatively and quantitatively by making use of the analytical solution in terms of a time-dependent diffusion coefficient that initially is greater and then gradually decreases. Diffusion process is much faster at the initial contact of the liquid and gas, and then gradually slows down. Therefore, we expect a larger value for the initial diffusion coefficient than that of the final diffusion coefficient. Results of the proposed time-dependent model excellently match all the experimental data sets, and this close agreement will confirm that the model is quite capable for the prediction of the diffusion coefficient