A finite element formulation of frequency-dependent electro-osmosis

In this paper, we model frequency-dependent electro-osmosis in a capillary using the fully nonlinear Navier-Stokes equation (NSE) for viscous, incompressible, and homogeneous flow. We simulate the NSE using the finite element method, computing the solution for a closed capillary and compare it to the closed form solutions. It is confirmed that the second velocity zero crossing is dependent of the capillary radius. The distance of the zero velocity crossing decreases with decreasing capillary radius. It is also shown that the AC electro-osmosis causes a circulation of fluid within the capillary with low frequencies generating the greatest net flow.