建構在細胞膜離子通道內傳輸行為的PNP-NS數學與數值模型

Abstract

在有限差分法的架構下，本論文發展一高階數值方法來計算卡氏座標與曲線座標兩系統之間矩陣張量的項並且保持SCL之特性， 以求解在非正交座標之下電液動(EHD)之非線性動力系統方程， 此系統包含了描述外加電場電位勢之Laplace方程、描述壁面電位勢之Poisson方程、描述離子濃度分布之Nernst-Planck方程以及由庫倫力所驅動的不可壓縮Navier-Stokes方程組。 論文之內容主要是使用離子守恆Poisson-Nernst-Planck(PNP)方程組來描述電滲流模型，以觀察流速對離子分布的影響， 並描述受zeta電位所產生之電雙層及電荷擴散層等物理行為，以及模擬細胞膜離子通道內的傳輸行為。

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.