Nanoscale Poiseuille flow of charged particles

We consider the convection-diffusion process of charged particles in a fluid which is described by the Navier-Stokes equations. Assuming a Hagen-Poiseuille flow profile, a one-dimensional model is derived. For stationary cases, the positivity of the concentrations is proven. Unique equilibrium solutions are shown to exist for a certain range of Dirichlet boundary data. Based on the one-dimensional model and their analytical solution, numerical simulations are presented for several test cases.