Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8395Research ArticleMathematical Modeling of Fluid Dynamics in Evaporating Drop with Taking into Account Capillary and Gravitational ForcesKolegovK SAstrakhan State University 20a, Tatischev str., Astrakhan, Russia, 414056k_k_s_87@mail.ruLobanovA IMoscow Physics Technical Institute (State University) 9, Institutskiy per., Dolgoprudny, Moscow region, Russia, 141700 Kabardino-Balkarian State University 173, Chernyshevskogo st., Nal’chik, Russia, 360004alexey.i.lobanov@gmail.comCaspian Institute of Sea and River TransportMoscow State Academy of Water Transport15022014237538008092016Copyright © 2014,2014An 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.evaporating dropstate equationgravitational and capillary forcesradial flowevolution of drop shapeиспаряющаяся капляуравнение состояниягравитационные и капиллярные силырадиальное течениеэволюция формы капли