Spinodal instability and pattern formation in thin liquid films confined between two plates

Abstract

The instability, morphology and pattern formation engendered by the van der Waals force in a thin liquid film of thickness h confined between two closely placed solid surfaces (at distance d>h) are investigated based on nonlinear 3D simulations. The initial and the final stages of dewetting and pattern formation are found to be crucially dependent on the volumetric (thickness) ratio of air and liquid and its deviation from the location of the maximum of the spinodal parameter versus volumetric ratio curve. On a low energy surface, relatively thinner films and wider air gaps favor initial dewetting of the lower plate by the formation of holes, whereas thicker films with thinner air gaps initially evolve by the formation of columns/bridges that join the upper plate. In the later stage of evolution, the initial holes in thinner films evolve into columns/drops, while a rapid coalescence of columns in the thicker films eventually causes formation of holes. Thus, a phase inversion, either from liquid-in-air to air-in-liquid dispersion or vice versa, occurs during the final stages of evolution. A thin film confined between two high-energy solid surfaces forms columns (bridges) only when its mean thickness, h₀, is greater than a critical thickness (h_c) or the air gap is smaller than a critical distance. The patterns can be aligned by using a topographically patterned confining surface. Conditions on pattern periodicity, amplitude, and the volumetric ratio of air and liquid in the gap are explored for the formation of various types of ordered patterns including annular rings of columns, concentric ripples, parallel channels and a rectangular array of complex features. The results are of significance in soft lithographies such as LISA, soft stamping and capillary force lithography.