The lattice Boltzmann modeling of two-phase electroosmotic flow in microchannels

Abstract

In this paper, a numerical framework based on the lattice Boltzmann method is presented for modeling two-phase electroosmotic flow within microchannels. In the model, lattice Boltzmann schemes are designed for all the governing equations involved such as Navier-Stokes equations for momentum transport, Nernst-Planck equations for ion transport, the Cahn-Hilliard equation for the immiscible fluid interface motion, and Poisson equation for the electric potential referring the model proposed in Shao’s work [6]. Related boundary schemes are also proposed to modeling the slip effect on the microchannel surfaces. The theoretical analysis shows that the model has second order accuracy.