Equilibrium shapes and stability of a liquid film subjected to a nonuniform electric field

Abstract

Stresses induced by a spatially nonuniform electric field acting on an initially flat fluid-fluid interface can (i) be exploited beneficially to pattern polymer microstructures without the use of resists, exposure, development, and etching, but (ii) cause undesirable nonuniformity in film thickness in precision coating processes. The equilibrium shape of an interface separating a liquid film from an ambient fluid subjected to a uniform electric field is flat so long as the field strength is below a critical value. A nonuniform electric field, however, results in the deformation of the interface no matter how small its strength, an important difference which previous theoretical studies have not addressed satisfactorily. Hence, whereas under a uniform field loss of stability occurs via a bifurcation from the flat film solution, under a nonuniform field destabilization may occur at a turning point at which the film profile already exhibits a finite-amplitude deformation. This deficiency in understanding is remedied here by analyzing a model problem in which a gas overlying a perfect dielectric liquid film is sandwiched between two electrodes wherein the top electrode is grounded and the electric potential of the bottom electrode varies sinusoidally with distance measured along it. The equilibrium shapes and stability of the liquid-gas interface are determined directly in the present work by simultaneously solving the augmented Young-Laplace equation governing the shape of the free surface and the Laplace equation governing electric potentials theoretically by domain perturbation analysis and numerically by finite element analysis. For small nonuniformities in the electric field, analytical solutions are reported for the profile of the free surface. The computational predictions are shown to be in excellent accord with these small-deformation results. Moreover, computations are used to extend the investigations into the nonlinear regime where nonuniformities in the electric field and deformations of the free surface are large, and loss of stability may occur. The variation of the equilibrium shapes and the limits of stability with the governing dimensionless groups are investigated thoroughly. It is shown that the rich response exhibited by the system can be rationalized by interrogating the computed solutions and scrutinizing the balance of stresses due to the normal component of the electric field, which are destabilizing, and those due to its tangential component, which are stabilizing.

Electro-osmosis of superimposed fluids in the presence of modulated charged surfaces in narrow confinements

“…Noting that c 3 (t) comes from the Maxwell stresses, we infer that the electrical stresses only induce a transient flow, which vanishes at steady state, inducing a permanent deformation in the process. In fact, previously Yeoh et al (2007) have shown that the Maxwell stresses can lead to a deformed equilibrium shape of a liquid-gas interface, in the presence of a modulated potential. We thus conclude that at O(Ca 2 ) of deformation (note that O(Ca) velocities lead to the O(Ca 2 ) deformation), both the components of the surface potential as well as the Maxwell stresses contribute, as claimed in the previous section.…”

“…Focusing particularly on the electrohydrodynamics of superimposed fluids in the presence of a modulated surface potential, such systems have been shown (Schäffer et al 2000(Schäffer et al , 2001Verma et al 2005;Yeoh, Xu & Basaran 2007;Esmaeeli & Reddy 2011) to cause interesting pattern formation. The pioneering work of Schäffer et al (2000) demonstrated that application of a non-uniform electric field can lead to the formation of pillar-like patterns replicating the shapes of the electrodes in thin polymeric films.…”

“…The pioneering work of Schäffer et al (2000) demonstrated that application of a non-uniform electric field can lead to the formation of pillar-like patterns replicating the shapes of the electrodes in thin polymeric films. Later, Yeoh et al (2007) theoretically predicted that the liquid interface always gets deformed when subjected to a non-uniform potential. Theoretical estimations of flows caused by imbalances in Maxwell stresses and the resulting deformation, in the presence of a patterned surface potential (Esmaeeli & Reddy 2011) and topography (Tseluiko et al 2008a,b), have been reported in the literature.…”

“…However, most of the theoretical studies on the electrohydrodynamics of superimposed fluids, in the presence of a patterned potential, either consider the leaky dielectric model (proposed by Melcher & Taylor 1969), without any imposed flow, or only study the equilibrium profile of the interface (Yeoh et al 2007). The aforementioned studies did not consider any axially applied electric field and hence no imposed electro-osmotic flow was present in these cases.…”

Thin liquid film morphology driven by electro-static field

“…A good deal of analytical efforts have been done to explore the mechanism for such amazing phenomena [4][5][6][7][8][9][10][11] . The linear stability analysis showed that the thickness ratio ξ of the air gap to the film layer is critical in determining the interfacial patterns [12][13][14] .…”