Effect of inertia on electrified film flow over a wavy wall

Abstract

The effect of inertia on the steady flow of a liquid layer down a wavy wall in the presence of an electric field is investigated. Both the liquid film and the region above it are assumed to act as perfect dielectrics. A linearised perturbation analysis is performed for flow down a wall with small-amplitude sinusoidal corrugations, and the freesurface amplitude and phase shift are computed numerically for a broad range of flow conditions. It is shown that the electric field can be used to manipulate the phase shift between the free surface and the wall. In particular, when the Reynolds number lies below a threshold value, an electric field of sufficient strength will bring the free surface precisely into phase with the wall. An electric field can also be used to mitigate the resonance effect identified by previous workers, in which the free surface suffers significant amplification in comparison to the height of the wall corrugations at a particular Reynolds number. Working on the basis of the lubrication approximation, a nonlinear equation for the film thickness is derived featuring a non-local term due to the electric field. Numerical solutions for flow over a wavy wall of finite amplitude reveal that the effect of inertia on the free-surface characteristics depends on the electrical properties of the fluid layer and the strength of the imposed electric field.

Electrified free-surface flow of an inviscid liquid past topography

“…[1][2][3][4][5][6][7][8][9][10][11][12][13]. These studies have looked at the effects of electric fields on both viscous and inviscid flows in the contexts of capillary waves on fluid sheets, 1,3,4 axisymmetric capillary waves, 2 gravity-capillary waves on a liquid layer, 5,6 rupture of an electric sheet, 7 and flow of a viscous layer over a topographic substrate.…”

“…These studies have looked at the effects of electric fields on both viscous and inviscid flows in the contexts of capillary waves on fluid sheets, 1,3,4 axisymmetric capillary waves, 2 gravity-capillary waves on a liquid layer, 5,6 rupture of an electric sheet, 7 and flow of a viscous layer over a topographic substrate. [8][9][10][11][12][13] The central theme of this research has been to investigate the interplay between the Maxwell stress induced by the electric field at the free surface of a liquid layer and the capillary force present due to surface tension. Of particular interest has been to see how this balance of forces can be exploited to manipulate the film shape, to influence the progression of surface waves, or to mitigate instability.…”

A Perturbation Analysis of the Fully Developed Convective Heat Transfer inside a Longitudinal Corrugation Channel

“…have been obtained for a long time [1]. But for another complex cross-sectional shape channels, analytic solution could not be easily obtained and most of the cases are being coped with experimental study [2] or numerical simulation [3] . However, analytical solutions to many situations could be obtained by using techniques such as perturbation expanding or variational principle [4,5] .…”