Mathematical Modeling of Fluid Dynamics in Evaporating Drop with Taking into Account Capillary and Gravitational Forces

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Abstract


An one-dimensional mathematical model described evolution of drop shape and viscous fluid dynamics (vertically averaged radial flow of the liquid) as the result of evaporation from impermeable horizontal surface is presented in this work. The model considers the influence of volume and capillary forces. Non-steady-state approach has been used to describe the process mathematically. The continuity equation and the motion equation for the case of a system with a variable mass are solved numerically with using standard tools of mathematical package Maple. We carry out calculations for cases of different sizes of water drop volumes. Results of modeling have shown that profile of drop which is bigger in size of capillary length (Bond number is greater than unity) differs from shape of spherical segment. The surface of such drop is almost flat. We explain it by domination of the gravity over a surface tension force. The flow of compensation nature is present in evaporated drops of different volumes what is coordinated with experimental data of other authors. Thus radial fluid flow is result of work of both capillary and gravitational forces. The results which we have got will help to describe the coffee ring effect in macrodrops in future.

K S Kolegov

Caspian Institute of Sea and River Transport

Email: k_k_s_87@mail.ru
Astrakhan State University 20a, Tatischev str., Astrakhan, Russia, 414056

A I Lobanov

Moscow State Academy of Water Transport

Email: alexey.i.lobanov@gmail.com
Moscow Physics Technical Institute (State University) 9, Institutskiy per., Dolgoprudny, Moscow region, Russia, 141700 Kabardino-Balkarian State University 173, Chernyshevskogo st., Nal’chik, Russia, 360004

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Copyright (c) 2014 Колегов К.С., Лобанов А.И.

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