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

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.

evaporating drop, state equation, gravitational and capillary forces, radial flow, evolution of drop shape