Instabilities and pattern formation under an applied non-uniform electric field

Hak Koon Yeoh, Purdue University

Abstract

Stresses induced by a spatially non-uniform electric field acting on an initially flat fluid-fluid interface can be exploited beneficially to pattern polymer microstructures without the use of photolithographical techniques, but they also cause undesirable non-uniformity in film thickness in precision coating processes. As contribution to fundamental understanding of the underlying physics, this work has uncovered, through theoretical studies on prototypical models, the heretofore unknown (i) static equilibrium, (ii) limits of stability, and (iii) dynamics in response to small-amplitude perturbations in the stable region, of a dielectric or conducting liquid film, overlaid by a dielectric gas, and sandwiched in between two horizontal, solid electrodes imposing non-uniform electric fields. Solutions at arbitrary non-uniform fields are computed using the Galerkin / Finite Element Method (G/FEM), coupled with turning point refinement and tracking methodologies for the static equilibrium computations, or adaptive time integration and Fourier mode analysis for the dynamic simulations. For non-uniform fields imposed through a sinusoidally varying potential along a boundary of the system, G/FEM computations of the equilibrium profiles are in excellent agreement with asymptotic results of the domain perturbation technique when the non-uniformity is weak. The rich and complex behavior exhibited by the system at static equilibrium can be rationalized by scrutinizing the balance of stresses due to the destabilizing normal component of the electric field and those due to the stabilizing tangential component. The effects of the field non-uniformity on the dynamics are examined for situations when the field is abruptly switched on or when the free surface is perturbed from its equilibrium. An integral part of the numerical schemes in this work is the linear stability analysis of an identical system under a uniform field, in which a new generalized dispersion relation is obtained, specific cases are exhaustively studied numerically, and a criterion for the transition between the viscous and inviscid limiting cases defined and charted in the parameter space of interest.

Degree

Ph.D.

Advisors

Basaran, Purdue University.

Subject Area

Chemical engineering

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