Simulation of the temperature field of evaporating drops on a solid substrate

S. Z. Dunin, O. V. Nagornov, V. P. Trifonenkov

National Research Nuclear University MEPhI, Moscow, Russian Federation

Abstract: We studied the free evaporation of a non-isothermal sessile liquid drop on a horizontal solid substrate. We derived exact expressions for the temperature and vapor-concentration fields as functions of the dimensionless thermodynamic parameters of the drop, the vapor, and the substrate. The non-uniform temperature distribution along the drop surface generates thermocapillary (Marangoni) stresses whose direction changes in the vicinity of stagnation points. We determined the directions of these stresses and the locations of the stagnation points as functions of the contact angle and the thermodynamic parameters of the model. We established the conditions under which stagnation points appear and derived the maximum contact angle at which they can exist. We compared the calculated temperature field with experimental measurements. We also computed the time evolution of the contact angle and the evaporative mass loss of the drop.

Keywords: drop evaporation, Marangoni force, stagnation points.