Calculation of the coupled system of PNP and NS equations in curvilinear coordinates

• Main Authors: Sheng-Tzung Yuan, 袁聖宗
• Other Authors: 許文翰
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/01027646844511303974

碩士 === 國立臺灣大學 === 工程科學及海洋工程學研究所 === 101 === 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.