Nonlinear stability, rupture and morphological phase separation of thin fluid films on the apolar and polar substrates

Abstract

The total free energy (per unit area) of a thin film on a substrate depends on the film thickness, and the apolar (Lifshitz-van der Waals) and polar (acid-base) spreading coefficients for the system. The free interface of the film becomes unstable and deforms when the second derivative of the free energy (i.e., force per unit volume) is negative. The film stability, kinetics of surface deformation, and the resulting morphology are investigated based on numerical solutions of a nonlinear, dynamic equation for the film thickness. A true rupture of the film always occurs when both the apolar (S^LW) and polar (S^P) components of the spreading pressure, S are negative; i.e., the equilibrium contact angle of the corresponding macroscopic drop is finite. However, the true time of rupture evaluated from the nonlinear formalism may be several orders of magnitude larger or smaller than the results of the linear stability analysis, depending on the mean film thickness, relative magnitudes of the apolar and polar forces, and amplitude and wavelength of initial perturbations. When one of the components of the total force is repulsive (either S^LW or S^P is positive), the film breakup occurs only if some localized, narrow regions of the film develop sufficient pent-up kinetic energy to penetrate the (positive) force barrier. Failing this, the thin film undergoes a "morphological phase separation," where nanodrops of the fluid attain equilibrium with relatively flat thin films. Some of the interesting observations that emerge are: (a) Films thicker than a certain critical thickness show true breakup, whereas thinner films may merely undergo a morphological phase separation, but a true dewetting of the substrate does not occur; (b) a thin film may be unstable to the extent of rupturing, even when a macroscopic drop of the same system is predicted to be completely wetting from the Young equation; and (c) a thin film may be stable despite a finite contact angle for the corresponding macrodrop. The underlying physics of observations is constructed by selective use of numerical simulations. Comparisons with predictions of the linear theory reveal that the latter fails, both qualitatively and quantitatively, in accounting for the stability and dynamics of thin films.