An accurate reduced-dimension numerical model for evolution of electrical potential and ionic concentration distributions in a nano-scale thin aqueous film

The numerical modelling of ionic diffusive transport through a charged thin film of electrolyte is mathematically and computationally complex due to the strongly coupled hydrodynamics and electrochemical interactions. Generally, simulations are performed by solving the Poisson equation together with the Nernst-Planck flux formula to model electrochemical processes in electro-diffusion problems. One important application of these system of equations to study the interaction of ionic diffusion and thin film hydrodynamics in petroleum engineering. However, due to the highly nonlinear and coupled equations the computational costs are heavy and very often limited to simulations in two-dimensional geometries. In this article, we have developed an equivalent one-dimensional electro-diffusive transport model based on mathematical averaging of 2D equations to reduce the computational time. Doing so, the computational time is improved substantially and simulation of much larger domain sizes which are required to study and interpret the experimental results is shown to be feasible. We have shown the high accuracy of the developed model by comparing the electric potential and concentration profiles of the developed model against the original 2D simulations. The developed approach reduces the computational effort by over 200 times without losing accuracy.