Electrokinetic viscous rotating disk flow of Poisson-Nernst-Planck equation for ion transport

Abstract

The main features of the present numerical model is to explore the behavior of an ionic transport electroviscous boundary layer flow over a rotating disk. For this purpose, the Nernst-Planck equation and Poisson's equation together with the traditional Navier Stokes equations are simulated for the conservation of ionic species. The Poisson-Nernst-Planck (PNP) equation neglects sterile effects and ion-ion interactions, which is widely recognized by the electro-chemists community, leading to advancement of various mathematical models. The modeled governing equations of the fluid flow are transformed to dimensionless ordinary differential equations under Von Karman's approach. The Parametric Continuation Method (PCM) is applied, in order to analyzed the numerical simulation of the problem. For validity of the method the results are compared with another numerical method (bvp4c) and some previous published work, seem to be in a very good agreement to each other. It is found that the potential gradient becomes smaller as Debye length parameter K increases and exposing more counter-ions to the flow which results an increase in the fluid velocity. The physical constraints impact on radial, axial and tangential velocity and on both positive and negative charge profile are sketched and briefly discussed.