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We study unsteady internal flows in a sessile droplet of capillary size evaporating in constant contact line mode on a heated substrate. Three-dimensional simulations of internal flows in evaporating droplets of ethanol and silicone oil have been carried out. For describing the Marangoni flows we find it necessary to account for the diffusion of vapor in air, the thermal conduction in all three phases and thermal radiation. The equations have been solved numerically by finite element method using ANSYS Fluent. As a result of the simulations, the nonstationary behavior of Bénard-Marangoni (BM) instabilities is obtained. At the first stage, a flower structure of BM cells near the triple line emerge. For smaller contact angles, the cells grow in size and occupy the central region of the droplet surface. Being closely connected with recent experimental and theoretical studies, the results obtained help to analyze and resolve the associated issues.

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We investigate numerically quasi-steady internal flows in an axially symmetrical evaporating sessile droplet depending on the ratio of substrate to fluid thermal conductivities, fluid volatility, contact angle and droplet size. Temperature distributions and vortex structures are obtained for droplets of 1-hexanol, 1-butanol and ethanol. To this purpose, the hydrodynamics of an evaporating sessile drop, effects of the thermal conduction in the droplet and substrate and diffusion of vapor in air have been jointly taken into account. The equations have been solved by finite element method using ANSYS Fluent. The phase diagrams demonstrating the number and orientation of the vortices as functions of the contact angle and the ratio of substrate to fluid thermal conductivities, are obtained and analyzed for various values of parameters. In particular, influence of gravity on the droplet shape and the effect of droplet size have been considered. We have found that the phase diagrams of highly volatile droplets do not contain a subregion corresponding to a reversed single vortex, and their single-vortex subregion becomes more complex. The phase diagrams for droplets of larger size do not contian subregions corresponding to a regular single vortex and to three vortices. We demonstrate how the single-vortex subregion disappears with a gradual increase of the droplet size.