Spreading of thin volatile liquid droplets on uniformly heated surfaces

Abstract

We develop a mathematical model for the spreading of a thin volatile liquid droplet on a uniformly heated surface. The model accounts for the effects of surface tension, evaporation, thermocapillarity, gravity and disjoining pressure for both perfectly wetting and partially wetting liquids. Previous studies of non-isothermal spreading did not include the effects of disjoining pressure and therefore had to address the difficult issue of imposing proper boundary conditions at the contact line where the droplet surface touches the heated substrate. We avoid this difficulty by taking advantage of the fact that dry areas on the heated solid surface are typically covered by a microscopic adsorbed film where the disjoining pressure suppresses evaporation. We use a lubrication-type approach to derive a single partial differential equation capable of describing both the time-dependent macroscopic shape of the droplet and the microscopic adsorbed film; the contact line is then defined as the transition region between the two. In the framework of this model we find that both evaporation and thermocapillary stresses act to prevent surface-tension-driven spreading. Apparent contact angle, defined by the maximum interfacial slope in the contact-line region, decays in time as a droplet evaporates, but the rate of decay is different from that predicted in earlier studies of evaporating droplets. We attribute the difference to nonlinear coupling between different physical effects contributing to the value of the contact angle; previous studies used a linear superposition of these effects. We also discuss comparison of our results with experimental data available in the literature.