Electro-Poiseuille Flow Modeling in Annular Geometry

The effect of geometry on the separation of ions in electrolytic solution is studied. The rectangular and cylindrical cases have already been derived as the result of previous work. For the case of steady-state flow in the annular region between two fixed, charged, concentric cylinders, the profiles of concentration, electric potential, and total mixture velocity have been obtained assuming the electrolytic fluid to be dilute in ion concentration. A decoupling technique is employed to handle the separation of the hydrodynamic problem from the electrostatics problem. For the electrostatics, the Debye-Huckel approximation is used, however a numerical method for improving this linearization of the Poisson-Boltzmann equation is discussed and shown to provide excellent convergence characteristics. Finally, the species continuity equation is stated (in terms of the electro-migration flux) and solved.