A procedure was proposed for computing the steady-state transport of charged particles based on the Nernst-Planck equation of electrodiffusion. To close the latter equation and to establish a relation between the concentration and electrochemical potential profiles, the local equilibrium Monte Carlo method was introduced. In this method, grand canonical Monte Carlo simulations were performed using the electrochemical potential specified for the distinct volume elements. An iteration procedure that self-consistently solved the Nernst-Planck equation and flux continuity equations with local equilibrium Monte Carlo was shown to converge quickly. This NP+LEMC technique could be used in systems with diffusion of charged or uncharged particles in complex three-dimensional geometries, including systems with low concentrations and small applied voltages that were difficult for other particle simulation techniques.

Steady-State Electrodiffusion from the Nernst-Planck Equation Coupled to Local Equilibrium Monte Carlo Simulations. D.Boda, D.Gillespie: Journal of Chemical Theory and Computation, 2012, 8[3], 824-9