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

Abstract

The dynamics of thin liquid films on surfaces whose wettability changes in a time-periodic manner are examined in this work. A nonlinear evolution equation based on the lubrication approximation is used to describe the film height, and attractions due to van der Waals forces are incorporated. Film wettability is varied through an imposed sinusoidal modulation of the Hamaker constant. A linear stability analysis predicts that if the mean Hamaker constant is negative, disturbances at the film surface will eventually decay regardless of the amplitude and frequency of the oscillation. However, numerical solution of the evolution equation shows that the film can rupture at a given frequency if the amplitude is sufficiently large. The associated characteristic wavelength can be predicted from results for constant-wettability surfaces if an appropriate effective Hamaker constant is used. For positive mean Hamaker constants, film rupture can be accelerated, delayed, or prevented depending on how the Hamaker constant changes early in the oscillation cycle. The effects of spatial gradients in wettability are also considered, and it is found that oscillation can delay but not prevent rupture. Inclusion of short-range repulsive forces leads to the formation of droplet-like structures separated by ultra-thin films, but this can be prevented by sufficiently large and slow oscillations of the Hamaker constant. The results of this work may find use in applications that make use of surfaces whose wettability can be controlled by external stimuli.