Slow evaporation of a small sessile liquid drop: new solutions based on the electrostatic analogy

Abstract

Evaporating sessile drop of liquid deposited on horizontal surface is an important object of applications and theoretical investigations. The evaporating flow density dramatically depends on contact angle of the droplet. Previously, the dependence of the flux density on the polar angle was established for arbitrary contact angles. The expression has the form of an integral and is rather complicated for use in modelling algorithms. In this paper, we propose new exact solutions for the set of some specific contact angles (135-180 degrees). The analogy of the drop evaporation problem with a similar problem from the field of electrostatics of equipotential surfaces, which has been solved in general terms before us, was used. The results of British mathematician H.M. Macdonald and Soviet scientist G.A. Grinberg were used in the derivation. Thus, relatively simple expressions for the evaporation flux density were found.