A numerical investigation of transient electro-osmotic flow in rectangular microchannels: A comparison of different models

Abstract

Transient electro-osmotic flow in rectangular microchannels is investigated numerically in this article. The complete Poisson—Boltzmann equation along with the time-dependent momentum equation is solved using the finite-difference method. Moreover, linearized equations based on the Debye—Huckle assumption are also solved to compare with the available analytical approximate solutions. The effects of different parameters such as wall zeta potential, non-dimensional electrokinetic width, and channel aspect ratio are also studied. It is shown that the Debye—Huckle approximation is not only valid for small values of zeta potential, but also the channel hydraulic diameter should be large enough with respect to electrical double layer (EDL) thickness. In addition, the flow behaviour at higher values of zeta potential is shown to be completely different from what available analytical solutions predict. Effective parameters on the transition period from the start time to the steady-state condition are also discussed. On the other hand, a comparison between the present numerical solution and the results of slip velocity approximation reveals that the slip model could be only used for very large values of non-dimensional electro-kinetic width. Finally, velocity distributions in channels of different aspect ratios are provided and discussed.