Unsteady electrohydrodynamic flow of immiscible liquids in channels

An unsteady electrohydrodynamic flow of two viscous immiscible liquids in a channel is theoretically investigated. The flow is caused by an oscillating electric field whose intensity vector has both normal and tangential components on the interface between the liquids. The velocity profile and flow rates of the liquids are found for steady-state oscillatory flows. The limiting cases of constant and high-frequency fields are discussed.

Figure 1

Setting of the problem.

Figure 2

Evolution of the velocity profile for ${\eta }_2/{\eta }_1=1$, $h_2/h_1=1$, $\omega /{\omega }_{\mathrm{e}}=0.1$, (a) ${\delta }_1/h_1=0.1$, ${\delta }_2/h_2=0.5$; (b) ${\delta }_1/h_1=1$, ${\delta }_2/h_2=5$, (c)${\delta }_1/h_1=0.05$, ${\delta }_2/h_2=0.1$.