A coordinate transformation method for numerical solutions of the electric double layer and electroosmotic flows in a microchannel

The electric double layer (EDL) and electroosmotic flows (EOFs) constitute the theoretical foundations of microfluidics. Numerical solution is one of the effective means of analysis in microfluidics. In general, it is difficult to obtain an accurate numerical solution of complex EOFs because of multiphysical interactions and locally high gradients. In this paper, a new coordinate transformation method is proposed to numerically solve the Poisson–Boltzmann, Navier–Stokes and Nernst–Planck equations to study the EDL and complex EOFs in a microchannel. A series of numerical examples is presented including cases of a homogeneous, discontinous wall electric potential and a locally high wall potential. A systematic comparison of numerical solutions with and without the coordinate transformation is carried out. The numerical results indicate that the coordinate transformation effectively decreases the gradient of the electric potential, ion concentration and electroosmotic velocity in the vicinity of the solid wall, and greatly improves the stability and convergency of the solution. 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. Copyright © 2011 John Wiley & Sons, Ltd.