Frequency-dependent velocity and vorticity fields of electro-osmotic flow in a closed-end cylindrical microchannel

The frequency-dependent electro-osmotic flow in closed-end cylindrical microchannels is analyzed in this study. A dynamic ac electro-osmotic flow field is obtained analytically by solving the Navier-Stokes equation using the Green function formulation in combination with a complex variable approach. Onsager's principle of reciprocity is demonstrated to be valid for transient and ac electro-osmotic flow. The effect of a frequency-dependent ac electric field on the oscillating electro-osmotic flow is studied. The induced pressure gradient is analyzed under the effects of the channel dimension and the frequency of electric field. Based on the Stokes second problem, the solution of the slip velocity approximation is presented for comparison with the results obtained from the analytical solution developed in this study. In addition, the expression for the electro-osmotic vorticity field is derived, and the characteristic of the vorticity field in ac electro-osmotic flow is discussed.