Abstract
The frequency dependent electroosmotic flow in a closed-end rectangular microchannel is analyzed in this study. Dynamic AC electroosmotic flow field is obtained analytically by solving the Navier-Stokes equation using the Green’s function formulation in combination with a complex variable approach. With the Debye-Hu¨ckel approximation, the electrical double layer potential distribution in the channel is obtained by analytically solving the linearized two-dimensional Poisson-Boltzmann equation. Additionally, the Onsager’s principle of reciprocity is demonstrated to be valid for AC electroosmotic flow. The effects of frequency-dependent AC electric field on the oscillating electroosmotic flow and the induced backpressure gradient are studied. Furthermore, the expression for the electroosmotic vorticity field is derived, and the characteristic of the vorticity field in AC electroosmotic flow is discussed. Based on the Stokes second problem, the solution of the slip velocity approximation is also presented for comparison with the results obtained from the analytical solution developed in this study.
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