Competitive displacement of thin liquid films on chemically patterned substrates

Abstract

The behaviour of the interface between stratified thin liquid films bounded by parallel solid surfaces and subject to van der Waals forces which drive dewetting is studied in this work. Chemically homogeneous surfaces are considered first; this is followed by an investigation of chemically heterogeneous surfaces. The lubrication approximation is applied to obtain a single nonlinear evolution equation which describes the interfacial behaviour, and both the linear stability and nonlinear development of the interface are examined. The sensitivity of the interfacial rupture time to problem parameters such as the viscosity ratio, initial interfacial height, interfacial tension, and magnitude of the van der Waals forces is characterized in detail for the homogeneous case. This serves as a basis for a study of the heterogeneous case, where the strong dependence of the rupture time on the length scale of the heterogeneity is found to be relatively independent of changes in the remaining problem parameters. The mechanisms underlying the rupture-time behaviour are also explored in detail. The results suggest a route by which one liquid can become emulsified in the other, and may be beneficial to industrial processes such as lithographic printing which are based on wettability phenomena.

Dynamics of thin liquid films on surfaces with a time-periodic wettability

“…Random initial conditions generated by averaging a sum of sine waves with random phases and amplitudes (no larger than 0.01) were employed for cases with wettability gradients. When wettability gradients are present, knowing where film rupture occurs is just as important as knowing the rupture time itself, which justifies the use of random initial conditions [11]. When they are absent, the place where rupture occurs is less important, so a simpler initial condition is used here; rupture times obtained with this initial condition were found to be the same as those obtained with random initial conditions.…”

“…When the above scalings are substituted into the NavierStokes equations and appropriate boundary conditions (balance of shear and normal forces at the liquid-gas interface; no-slip and no-penetration at the substrate), and only the leading order terms are retained after suitable rescalings, a nonlinear evolution equation for the dimensionless interfacial height, H = h/ h 0 , can be derived. As very similar derivations have been given elsewhere [1,11], we simply quote the final result:…”

“…Equation (3) is solved by discretizing the spatial derivatives using fourth-order centered finite differences, applying periodic boundary conditions, and time-stepping with Gear's algorithm [11]. For cases where the substrate has no wettability gradients and film rupture occurs (A * independent of X; B * = 0), using 300 grid points is sufficient for obtaining accurate results.…”

“…Here, we briefly examine what happens when the Hamaker constant varies in both time and space; repulsive forces are again neglected. To model spatial gradients in wettability, we use the following form of A [11]:…”

“…As the literature in this area has been discussed extensively elsewhere [1] and continues to evolve (e.g., Refs. [9][10][11]), we do not provide a review here. Whereas prior works, to the best of our knowledge, have assumed a time-independent Hamaker constant, the distinguishing feature of the present work is the consideration of the time-periodic case.…”