Unsteady Electrokinetic Flow in a Microcapillary: Effects of Periodic Excitation and Geometry

Abstract

Oscillatory electrokinetic flow is numerically examined in a rectangular annulus microtube under the influence of various wave forms. When the inner and outer walls of the capillary are oppositely charged, an instantaneous two-direction flow field is produced and consequently the resultant flow rate is relatively reduced. A zero or negative flow rate may be achieved by appropriate design of the channel geometrical characteristics (e.g., hydraulic diameter) as well as the walls charges. In the case of sufficiently low kinematic viscosity and/or high excitation frequency, a relatively thin transient frictional layer is established close to the walls while the bulk fluid lags behind the liquid motion in the electric double layer by a phase shift. If different waveforms are combined together, fascinating outcomes can be obtained depending on the frequency of each individual wave. Applied electric fields with equal- and unequal-frequency combined waves may have the advantages of a double velocity field and a net mass flow rate, respectively. Interestingly, a direct flow pattern may be achieved by appropriately combining various waveforms with unequal frequencies. The mass flow rate decreases, with the constancy of the electrokinetic diameter, with approximately the square of hydraulic diameter. The Poiseuille number exhibits various characteristics depending on the excitation frequency as well as the type of wave especially in combination.