  Theoretical description and numerical simulation of an evaporating sessile
drop are developed. We jointly take into account the hydrodynamics of an
evaporating sessile drop, effects of the thermal conduction in the drop and the
diffusion of vapor in air. A shape of the rotationally symmetric drop is
determined within the quasistationary approximation. Nonstationary effects in
the diffusion of the vapor are also taken into account. Simulation results
agree well with the data of evaporation rate measurements for the toluene drop.
Marangoni forces associated with the temperature dependence of the surface
tension, generate fluid convection in the sessile drop. Our results demonstrate
several dynamical stages of the convection characterized by different number of
vortices in the drop. During the early stage the street of vortices arises near
a surface of the drop and induces a non-monotonic spatial distribution of the
temperature over the drop surface. The initial number of near-surface vortices
in the drop is controlled by the Marangoni cell size which is similar to that
given by Pearson for flat fluid layers. This number quickly decreases with
time, resulting in three bulk vortices in the intermediate stage. The vortices
finally transform into the single convection vortex in the drop, existing
during about 1/2 of the evaporation time.
