The main features of a numerical model aiming at predicting the drift of ions in an electrolytic solution upon a chemical potential gradient are presented. The mechanisms of ionic diffusion are described by solving the extended Nernst-Planck system of equations. The electrical coupling between the various ionic fluxes is accounted for by the Poisson equation. Furthermore, chemical activity effects are considered in the model. The whole system of nonlinear equations is solved using the finite-element method. Results yielded by the model for simple test cases are compared to those obtained using an analytical solution. Applications of the model to more complex problems are also presented and discussed.