Electric field induced instability and pattern formation in thin liquid films

Abstract

Electrostatic field induced instability, morphology, and patterning of a thin liquid film confined between two electrodes with an air gap are studied on the basis of nonlinear 3D simulations, both for spatially homogeneous and heterogeneous fields. In addition to the spinodal flow resulting from the variation of field because of local thickness changes, a heterogeneous imposed field also moves the liquid from the regions of low field to high field, thus allowing a more precise control of pattern. Hexagonal packing of liquid columns is observed for a spatially homogeneous electric field, which is in accord with the e-field experiments on thin polymer films (Schaffer et al. Nature 2000, 403, 874). For a large liquid volume fraction in the gap, φ ≥ 0.75, the coalescence of columns causes a phase inversion, leading to the formation of air columns or cylindrical holes trapped in the liquid matrix (air-in-liquid dispersion). Locally ordered aligned patterns are formed by imposing a spatial variation of the electrostatic field by using a topographically patterned electrode. For example, multiple rows/lines of liquid columns are formed near the edge of a steplike heterogeneity of the electrode and annular rings of ordered columns or concentric ripples are formed around a heterogeneous circular patch. Simulations predict that the electrode pattern is replicated in the film only when the pattern periodicity, L_p, exceeds the instability length scale on the basis of the minimum interelectrode separation distance, L_p ≥ λ_m-dmin. Thus, the formation of secondary structures can be suppressed by employing an electrode with deep grooves and stronger field gradients, which produces almost ideal templating. The number density of the electric field induced patterns can be altered by tuning the mean film thickness (or the volume fraction of liquid in the gap), periodicity and depth (amplitude) of the grooves on the top electrode, and the applied voltage. The implications are in electrostatic lithography, pattern replication in soft materials, and the design and interpretation of thin film experiments involving electric fields.