A Depth-Averaged Model for Electrokinetic Flows in a Thin Microchannel Geometry

We have developed a generalized electrokinetic model suitable for the study of microchannel flows with conductivity gradients and shallow channel depths. An asymptotic analysis was performed with channel depth-to-width ratio as the smallness parameter, and three dimensional transport equations are reduced to a set to depth-averaged equations governing flow dynamics in the streamwise-spanwise plane of a shallow channel. The momentum equation uses a Darcy-Brinkman-Forchheimer type formulation, and the convective-diffusive transport of the conductivity field in the depth direction manifests itself as a dispersion effect on in-plane motion. Accuracy of the model was assessed by comparing the numerical results with direct numerical simulations. These depth-averaged equations provide the accuracy of three-dimensional modeling with a convenient quasi-two-dimensional equation set applicable to a fairly wide class of microfluidic devices.