在曲線座標下求解EHD方程

Abstract

本論文發展一有限差分方法並在非正交曲線座標下求解電液動之非線性動力系統方程，這包含了描述外加電場之Laplace方程、描述壁面所施加之電位分布以及離子濃度分布的Poisson-Nernst-Planck方程組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方程式Poisson-Nernst-Planck方程組，以描述電滲流模型，以觀察流速對離子分布的影響，及是否能描述受zeta電位所產生之電雙層，及描繪出靠近壁面之速度邊界層、電荷擴散層等物理行為。

In this study we aim to develop a high order scheme for approximating the spatial derivative terms shown in the Poisson-Nernst-Planck(PNP) as well as in the incompressible Navier-Stokes(NS) equations. To resolve sharp solution profiles near the wall, within the three-point stencil the combined compact difference scheme in applied to yield sixth-order accuracy for the second-order derivative terms while fifth-order accuracy for the first-order derivative terms, the differential set of PNP-NS equations has been transformed to the nonlinear coordinates so as to be able to know how the channel curvature can affect the electroosmotic flow motion in a wavy channel. In this study the scheme in developed in detail and is analyzed rigorously though the modified equation analysis. In addition, the developed method has been computationally verified through three problems available to exact solutions. The electroosmotic flow details in plannar and channels have been revealed through this study with the emphasis an the formation of Coulomb force. The competition among the pressure gradient, diffusion and Coulomb forces leadings to the convective electroosmotic flow motion is also investigated in detail.