Персона: Лебедев-Степанов, Петр Владимирович
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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.
Evaporation of Small Sessile Drop Deposited on a Horizontal Solid Surface: New Exact Solutions and Approximations
Evaporating a liquid sessile drop deposited on a horizontal surface is an important object of applications (printing technologies, electronics, sensorics, medical diagnostics, hydrophobic coatings, etc.) and theoretical investigations (microfluidics, self-assembly of nanoparticles, crystallization of solutes, etc.). The arsenal of formulas for calculating the slow evaporation of an axisymmetric drop of capillary dimensions deposited on a flat solid surface is reviewed. Characteristics such as vapor density, evaporation flux density, and total evaporation rate are considered. Exact solutions obtained in the framework of the Maxwellian model, in which the evaporation process of the drop is limited by vapor diffusion from the drop surface to the surrounding air, are presented. The summary covers both well-known results obtained during the last decades and new results published by us in the last few years, but practically unknown to the wider scientific community. The newest formulas, not yet published in refereed publications, concerning exact solutions for a number of specific contact angles are also presented. In addition, new approximate solutions are presented (total evaporation rate and mass loss per unit surface area per unit time in the whole range of contact angles Оёв€€[0, ПЂ), drop lifetime in constant contact radius evaporation regime and constant contact angle mode), which can be used in modeling without requiring significant computational resources.