Electrified viscous thin film flow over topography

Abstract

The gravity-driven flow of a liquid film down an inclined wall with periodic indentations in the presence of a normal electric field is investigated. The film is assumed to be a perfect conductor, and the bounding region of air above the film is taken to be a perfect dielectric. In particular, the interaction between the electric field and the topography is examined by predicting the shape of the film surface under steady conditions. A nonlinear, non-local evolution equation for the thickness of the liquid film is derived using a long-wave asymptotic analysis. Steady solutions are computed for flow into a rectangular trench and over a rectangular mound, whose shapes are approximated with smooth functions. The limiting behaviour of the film profile as the steepness of the wall geometry is increased is discussed. Using substantial numerical evidence, it is established that as the topography steepness increases towards rectangular steps, trenches, or mounds, the interfacial slope remains bounded, and the film does not touch the wall. In the absence of an electric field, the film develops a capillary ridge above a downward step and a slight depression in front of an upward step. It is demonstrated how an electric field may be used to completely eliminate the capillary ridge at a downward step. In contrast, imposing an electric field leads to the creation of a free-surface ridge at an upward step. The effect of the electric field on film flow into relatively narrow trenches, over relatively narrow mounds, and down slightly inclined substrates is also considered.

Inertialess multilayer film flow with surfactant: Stability and traveling waves

“…Repeating with initial condition (52), the solution returns to the same travelling-wave profile for k = 0.7. Computing again using initial condition (52) but now taking two wave-periods over twice the domain size with L c = L 0 = 2π/0.35, we find that the solution diverges from the k = 0.7 travelling wave and the wave profiles develop to closely resemble the k = 0.35 travellingwave solution with a clean region on the interface, as in upper panel of figure 10. The simulation fails to capture the profiles accurately because of the sharp variations in gradient in the profiles discussed in section IV A.…”

“…[51]) and in flow over topography (e.g. [37], [52]). In some cases, shocks develop in the surfactant profiles as a clean region appears over part of a wave period.…”

Thin film flow over flexible membranes containing surface texturing: Bio-inspired solutions

“…While previous research considering the simpler two-dimensional problem of thin film flow over span-wise topography has shown that Marangoni stress [20] and electric fields [21] can be used to promote planarisation, the more general three-dimesional case considered here reveals that substrate flexibility can be similarly exploited. Indeed, in the context of mimicking naturally occurring biological surfaces for engineering applications, substrate compliance may turn out to be an added unexpected benefit in determining and hence controlling the flow of thin films on delicate tribological textured surfaces.…”

Electrohydrodynamics Instability of Three Periodic Streaming Fluids through Porous Media

“…The unit vectors î and ĵ are in x-and y-directions. The equations governing two-dimensional motion of an incompressible fluid through porous medium are given by the phenomenological Darcy equation, which comes from the combination of the momentum equation and Darcy's law [11]- [14]:…”

“…The long wave linear stability analysis is performed within the generic OrrSommerfeld framework for both perfect and leaky dielectrics. The approach proposed in paper [11] is limited to study the gravity-driven flow of a liquid film below an inclined wall with periodic indentations in the presence of a normal electric field. Espn et al [12] have analyzed the effect of viscoelasticity on the electrohydrodynamic instabilities in thin liquid films under the influence of AC and DC electric fields.…”