The electroosmotic flow in a microchannel packed with microspheres under both direct and alternating electric fields is analyzed. In the case of the steady DC electroosmosis in a packed microchannel, the so-called “capillary model” is used, in which it is assumed that a porous medium is equivalent to a series of intertwined tubules. The interstitial tubular velocity is obtained by analytically solving the Navier-Stokes equation and the complete Poisson-Boltzmann equation. Then using the volume averaging method, the solution for the electroosmotic flow in a single charged cylindrical tubule is applied to estimate the electroosmosis in the overall porous media by introducing the porosity and tortuosity. Assuming uniform porosity, an exact solution accounting for the electrokinetic wall effect is obtained by solving the modified Brinkman momentum equation. For the electroosmotic flow under alternating electric fields in a cylindrical microchannel packed with microspheres of uniform size, two different conditions regarding the openness of channel ends are considered. Based on the capillary model, the time-periodic oscillating electroosmotic flow in an open-end microchannel in response to the application of an alternating electric field is obtained using the Green’s function approach to the Navier-Stokes equation. When the two ends of the channel are closed, a backpressure is induced to generate a counter flow, resulting in a new zero flow rate. Such induced backpressure associated with the counter-flow in a closed-end microchannel is obtained analytically by solving the transient modified Brinkman momentum equation.
An exact solution of the 3-D Navier–Stokes equation