On a PNP-NS mathematical and numerical models for simulating transport phenomenon in cell membrane ion channel

In this study a high order scheme based on the combined compact difference method is developed to compute the metric tensor terms between the Cartesian coordinate and curvilinear coordinate systems subject to the Space Conservation Law (SCL). A high order scheme for the pressure is also proposed to solve the nonlinear electrohydrodynamic system in different channel types. The system under investigation includes the Poisson equation for the external potential, the Poisson-Nerest-Planck (PNP) equation which describes the distribution of ion concentration and the incompressible Navier-Stokes (NS) equation driven by Coulomb force. The transformation terms are computed by the sixth-order accurate combined compact difference scheme subject to the Space Conservation Law. This scheme is applied to simulate the electroosmotic flow from physical domain to computational domain. The electroosmotic flow details in plannar and channels are revealed through this study with the emphasis an the formation of Coulomb force. The competition among the pressure gradient, diffusion and Coulomb forces leading to the convective electroosmotic flow motion is also investigated in detail. Finally, we also simulate the transport phenomenon in ion channel of cell membrane to observe its physical behavior.