Thin films in partial wetting: stability, dewetting and coarsening

A uniform nanometric thin liquid film on a solid substrate can become unstable due to the action of van der Waals (vdW) forces. The instability leads to dewetting of the uniform film and the formation of drops. To minimize the total free energy of the system, these drops coarsen over time until one single drop remains. Here, using a thermodynamically consistent framework, we derive a new model for thin films in partial wetting with a free energy that resembles the Cahn-Hilliard form with a height-dependent surface tension that leads to a generalized disjoining pressure, and revisit the dewetting problem. Using both linear stability analysis and nonlinear simulations we show that the new model predicts a slightly smaller critical instability wavelength and a significantly (up to six-fold) faster growth rate than the classical model in the spinodal regime; this faster growth rate brings the theoretical predictions closer to published experimental observations. During coarsening at intermediate times, the dynamics become self-similar and model-independent; we therefore observe the same scalings in both the classical (with and without thermal noise) and new models. Both models also lead to a mean-field Lifshitz-Slyozov-Wagner (LSW)-type droplet-size distribution at intermediate times for small drop sizes. We, however, observe a skewed drop-size distribution for larger drops in the new model; while the tail of the distribution follows a Smoluchowski equation, it is not associated with a coalescence-dominated coarsening, calling into question the association made in some earlier experiments. Our observations point to the importance of the height dependence of surface tension in the early and late stages of dewetting of nanometric films and motivate new high-resolution experimental observations to guide the development of improved models of interfacial flows at the nanoscale.