Analytical Solutions of Time Periodic Electroosmotic Flow in a Semicircular Microchannel


1 Department of Engineering Mechanics, Shandong University, 250061 Jinan, P.R. China

2 Geotechnical and structural engineering research center, Shandong University, Jinan 250061, P.R. China

3 School of Mathematical Sciences, University of Jinan, 250100 Jinan, P.R. China

4 School of Control Science and Engineering, University of Jinan, 250100 Jinan, P.R. China


The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.