Dynamics of a spreading thin film with gravitational counterflow using slip model

Abstract

Thin liquid films can be made to spread along a solid surface by application of temperature gradients at the liquid–gas interface. The surface tension of usual liquids decreases linearly with temperature thus producing the driving thermocapillary stresses due to the applied temperature gradient. These spreading films are susceptible to a fingering instability at the advancing solid–liquid–vapor contact line, which is linked to the development of a capillary ridge near the advancing front. A thin film climbing up on a vertical substrate against gravity shows interesting dynamics due to strong opposing gravitational counterflow. At the contact-line of the spreading film, slip-model is used to alleviate the stress-singularity due to more usual no-slip boundary condition. It is shown that depending upon the magnitude of a gravitational drainage parameter the steady-profiles of the spreading films show qualitatively different dynamics. The dynamics is in agreement with the experimentally observed profiles in the literature as well as computed profiles using precursor-film model at the contact-line in some earlier theoretical studies. Briefly, their stability behavior is also discussed.