Static and dynamic contact angles of evaporating liquids on heated surfaces

We studied both static and dynamic values of the apparent contact angle for gravity-driven flow of a volatile liquid down a heated inclined plane. The apparent contact line is modeled as the transition region between the macroscopic film and ultra-thin adsorbed film dominated by disjoining pressure effects. Four commonly used disjoining pressure models are investigated. The static contact angle is shown to increase with heater temperature, in qualitative agreement with experimental observations. The angle is less sensitive to the details of the disjoining pressure curves than in the isothermal regime. A generalization of the classical Frumkin-Derjaguin theory is proposed to explain this observation. The dynamic contact angle follows the Tanner's law remarkably well over a range of evaporation conditions. However, deviations from the predictions based on the Tanner's law are found when interface shape changes rapidly in response to rapid changes of the heater temperature. The Marangoni stresses are shown to result in increase of the values of apparent contact angles.