Closed-form solutions of transient electro-osmotic flow driven by AC electric field in a microannulus

Boundary value problems

Shaowei Wang¹  Moli Zhao² 

[1] Department of Engineering Mechanics, School of Civil Engineering, Shandong University, Jinan, P.R. China;Geotechnical and Structural Engineering Research Center, Shandong University, Jinan, P.R. China

关键词: transient flow;    electro-osmosis flow;    integral transform;    velocity distribution;   

DOI  :  10.1186/s13661-014-0215-2

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

The time-periodic electro-osmotic flow of Newtonian fluids through a microannulus is studied in the Debye-Hückel approximation. Analytical series solutions for velocity and flow rate are presented with the help of an integral transform. The expression for the distribution of the velocity profile consists of a time-dependent oscillating part and a time-dependent generating or transient one, and the normalized velocity function is independent of the Reynolds number, which is very different from previous results. Then the effects of the electrokinetic width K, the wall zeta potential ratio β, and the frequency of applied external electric field ω on the distribution of the velocity profiles and flow rates are discussed numerically and theoretically. Some new physical and chemical phenomena are found theoretically. We point out that the electro-osmotic 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 the external electric field.

【 授权许可】

CC BY