Influence of boundary slip on the dynamics and stability of thermocapillary spreading with a significant gravitational counterflow

Abstract

Applied temperature gradients produce thermocapillary stresses that can force liquid films to spread along solid surfaces. These films are susceptible to a rivulet instability at the advancing solid-liquid-vapor contact line, which is linked to the development of a capillary ridge near the advancing front. The application of a sufficiently strong gravitational counterflow has been shown to drain fluid from the ridge and stabilize the film against rivulet formation and lead to interesting spreading dynamics. In this work, the dynamics and stability of thermocapillary driven films are analyzed for the entire range of drainage. Boundary slip is allowed at the solid-liquid interface, which introduces the static contact angle and slip coefficient as parameters that can typically be specified independently. The contact angle of the spreading film is allowed to depend on the velocity of the contact line, and the effects of this dependence on the film profile, linear stability, and transient response of perturbations are examined. Increasing the influence of gravitational drainage relative to the thermocapillary stress from zero has a stabilizing influence on the traveling wave solutions but is accompanied by an increase in the amplitude of the capillary ridge, which is contrary to stability results for spreading films with only one driving force. Results for the different spreading regimes are generally consistent with predictions based on the more extensively used precursor film model of the contact line, although some differences are observed due to the additional parameters in the slip model that are relevant to partially wetting fluids.