Research Colloquium — Wednesday, September 27, 2006

When a liquid droplet is spreading on a horizontal solid substrate, the line where its surface comes into apparent contact with the substrate is referred to as a moving contact line. Imposing proper physical boundary conditions at such contact lines is essential for an accurate description of the overall dynamics of the droplet surface, regardless of the numerical method used to solve the equations for liquid flow inside the droplet. While isothermal contact lines have been studied extensively, the effect of evaporation on contact line motion has not been fully understood. We propose a mathematical model that describes the coupled effects of viscous flow, evaporation, and surface tension in the vicinity of a contact line. The case of a thin axisymmetric droplet is used to illustrate the model and carry out comparison with experimental data. The approach is then applied to other situations such as the growth of dry patches in evaporating liquid films and the coating of a heated solid surface with a film of viscous liquid.