A number of papers have been published on the computational approaches to electrokinetic flows. Nearly all of these decoupled approaches rely on the assumption of the Poisson-Boltzmann equation and do not consider the effect of velocity field on the electric double layers. By means of a charge continuity equation, we present here a numerical model for the simulation of pressure driven flow with electrokinetic effects in parallel-plate microchannels. Our approach is similar to that given by van Theemsche et al. [Anal. Chem., 74, 4919 (2002)] except that we assumed liquid conductivity to be constant and allows simulation to be performed in experimental dimension. The numerical simulation requires the solution of the Poisson equation, charge continuity equation and the incompressible Navier-Stokes equations. The simulation is implemented in a finite-volume based Matlab code. To validate the model, we measured the electrical potential downstream along the channel surface. The simulated results were also compared with known analytical solutions and experimental data. Results indicate that the linear potential distribution assumption in the streaming direction is in general not valid, especially when the flow rate is large for the specific channel geometry. The good agreement between numerical simulation and experimental data suggests that the present model can be employed to predict pressure-driven flow in microchannels.
Heuristic derivation of Casimir effect in minimal length theories
