Ionic diffusion through confined geometries: From langevin equations to partial differential equations

Various aspects of ionic diffusion through confined geometries were discussed. The motion of the ions depended on the nanoscale geometry and charge distribution in and near the domain. A stochastic molecular model was made for the diffusive motion of ions in an external field using partial differential equations. It was observed that the force term depended on the conditional densities and the finite size of ions, and contained the dielectric boundary force.