AC electroosmosis in microchannels packed with a porous medium

Abstract

This paper presents a theoretical study on ac-driven electroosmotic flow in both open-end and closed-end microchannels packed with uniform charged spherical microparticles. The time-periodic oscillating electroosmotic flow in an open-end capillary in response to the application of an alternating (ac) electric field is obtained using the Green function approach. The analysis is based on the Carman–Kozeny theory. The backpressure associated with the counter-flow in a closed-end capillary is obtained by analytically solving the modified Brinkman momentum equation. It is demonstrated that in a microchannel with its two ends connected to reservoirs and subject to ambient pressure, the oscillating Darcy velocity profile depends on both the pore size and the excitation frequency; such effects are coupled through an important aspect ratio of the tubule radius to the Stokes penetration depth. For a fixed pore size, the magnitude of the ac electroosmotic flow decreases with increasing frequency. With increasing pore size, however, the magnitude of the maximum velocity shows two different trends with respect to the excitation frequency: it gets higher in the low frequency domain, and gets lower in the high frequency domain. In a microchannel with closed ends, for a fixed excitation frequency, use of smaller packing particles can generate higher backpressure. For a fixed pore size, the backpressure magnitude shows two different trends changing with the excitation frequency. When the excitation frequency is lower than the system characteristic frequency, the backpressure decreases with increasing excitation frequency. When the excitation frequency is higher than the system characteristic frequency, the backpressure increases with increasing excitation frequency.