Simulation of hydrodynamics in a liquid evaporating from a cylindrical microcell using the thin layer approximation and a kinematic approach

The evaporation of a droplet in a cell attracts considerable attention due to the development of new applications, such as organic light-emitted displays. After complete evaporation, a deposit of particles that make up the solution remains on the substrate. The sediment geometry largely depends on the direction of the flows in the drop. These flows can be controlled by various factors, including changing the type of solvent or the substrate material. A physical model is presented that makes it possible to study the influence of thermal effects arising from cooling during liquid evaporation on hydrodynamic flows in the drop placed in a micrometer-sized cylindrical cell. The model takes into account the temperature dependence of the surface tension of the liquid and describes the diffusion of vapor in air, the distribution of heat in the cell and liquid due to thermal conduction, the thermocapillary flow of the liquid, the motion of the two-phase liquid-air interface, and the evaporation-driven compensation flow of the liquid. The mathematical model is based on the laws of conservation of matter and energy, the vapor diffusion equation, as well as on the fluid dynamics equation in the thin layer approximation in combination with a kinematic approach. The results of calculating the flow velocity in an ethylene glycol drop according to the obtained analytical formula are in good agreement with the literature experimental data.