Energy-Conserving Simulation of Incompressible Electro-Osmotic and Pressure-Driven Flow

A numerical model for electro-osmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier–Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences are second-order accurate and centered in space; however, the traditional second-order compact finite differencing of the Poisson equation for the pressure field is shown not to conserve energy in the inviscid limit. We have designed a non-compact finite differencing for the Laplacian in the pressure equation that allows exact energy conservation and affords second-order accuracy. The model also incorporates a new numerical method for passive scalar advection, called parcel advection, which accurately predicts the evolution of a passively traveling scalar pulse without requiring the addition of any artificial diffusion. The algorithm is used to confirm the experimentally observed asymmetric concentration profile that arises when an external pressure drop is imposed on electro-osmotic flow.