There exist, mainly, two different continuum approaches to calculate transient multi species ionic diffusion. One of them is based on explicitly assuming a zero current in the diffusing mixture together with an introduction of a streaming electrical potential in the constitutive equations for the mass density flow of ionic species. The other is based on using the Gauss’ law and assuming no polarization, in order to obtain an equation for the determination of the electrical field, together with adding the electrical field in the constitution of the ionic mass density flows. The important difference of the two types of potentials, that is, the streaming electrical potential and the electrical field is carefully examined. A novel numerical method based on the finite element approach is established for the zero current method case. The proposed numerical method uses the direct calculation of the coupled set of equation in favor of the staggering approach. A one step truly implicit time stepping scheme is adopted together with an implementation of a modified Newton-Raphson iterational scheme for search of equilibrium at each considered time step calculation. Results from the zero current case are compared with existing results from the solutions of the Gauss’ law method. For the studied case the calculated concentrations of the ionic species, using the two different methods, differed very little.