NUMERICALSIMULATION OF ELECTRO-OSMOTIC FLOW IN A MICRO-CHANNEL USING VELOCITY-VORTICITY FORMULATIOB

Abstract

The electro-osmotic induced flow by an applied electrostatic potential field through a rectangular micro-channel is analyzed numerically in this work. As the characteristic flow dimensions of these narrow channels decreases to micro ranges, the fluid flow behaviors are increasingly influenced by interfacial effects such as electric double layer (EDL). Because of the electric double layer (EDL) influence the micro-channel flows deviate from the predictions of the traditional channel flow problems. Mathematical modeling of flow through micro-channels has been carried out by taking into account the effect of applied electric potential as well as the effect of zeta potential generated due to electric double layer (EDL) near the surface of the channel. The vortex dominant flow field in the micro-channel can be easily studied by representing the Navier-Stokes equations in velocity-vorticity form. The force due to electric potential is represented by non-linear 2D Poisson-Boltzman equation. The velocity-vorticity form of Navier-Stokes equations, velocity Poisson equations, Poisson-Boltzmann equation and Laplace equation are used to represent the flow field, internal potential field and electrostatic potential fields in the micro-channel respectively. These equations are solved numerically by employing the Galerkin's weighted residual method. The final form of the discretized equations are represented in matrix form and the computational algorithm employed to solve the coupled equations is also discussed. Flow velocity distribution is plotted with and without the electro-osmotic effect for different Reynolds numbers. The effects of electrical double layer field and the electrostatic field on the fluid velocity distribution is discussed. Location of maximum velocity along the channel and the variation for different Reynolds numbers is also discussed. Flow with finite inlet velocity and with zero inlet velocity is analyzed to study the effect of electrostatic potential boundary conditions on the flow distribution.