坐标变换法数值求解微通道行波电场电渗流

采用坐标变换法数值求解了耦合的Poisson-Nernst-Planck (PNP)方程和Navier-Stokes(NS)方程, 研究二维狭窄微通道行波电场电渗流数值解. 数值结果表明,坐标变换法能有效降低电渗流解数值解在双电层的高梯度, 有效改善数值解的收敛性和稳定性. 坐标变换的电渗流数值解和原始坐标下的数值解完全一致. 坐标变换后采用简单的网格也能得到和原始坐标下复杂网格相同的解. 给出了滑移边界的近似解与完整的PNP-NS数值解的比较. 在双电层厚度与微通道深度比值(λ/H)很小的情况下(相对深通道), 两者的解基本一致. 但在λ/H较大时(相对浅通道)滑移边界的解高于电渗流速度. 

A COORDINATE TRANSFORMATION METHOD FOR NUMERICAL SOLUTIONS OF TRAVELING-WAVE ELECTROOMTIC FLOWS IN MICROCHANNEL

In this paper,a coordinate transformation method is employed to numerically solve the coupling Poisson-Nernst-Planck(PNP) equation and Navier-Stokes(NS) equations for studying the traveling-wave electroosmotic flow in two-dimensional microchannel.Numerical solutions indicate that the coordinate transformation effectively decreases the gradient of the solution in the electric double layer(EDL),and greatly improves the stability and convergence of the solution.The numerical solutions with and without the coordinate transformation are in good agreement.In a transformed coordinate system with a coarse grid,the numerical solutions can be as accurate as those in the original coordinate system with a refined grid.The approximate solutions of slip boundary are also presented for a comparison.It is found that the solutions of slip boundary agree with those of complete PNP-NS equations in the cases of small ratio of EDL thickness and channel depth(λ/H).In cases of largeλ/H,the solution of slip boundary over-predicts the electroosmotic flow velocity.