  Several dynamical stages of the Marangoni convection of an evaporating
sessile drop are obtained. 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. The stages are characterized by different number of
vortices in the drop and the spatial location of vortices. During the early
stage the array of vortices arises near a surface of the drop and induces a
non-monotonic spatial distribution of the temperature over the drop surface.
The number of near-surface vortices in the drop is controlled by the Marangoni
cell size, which is calculated similar to that given by Pearson for flat fluid
layers. The number of vortices quickly decreases with time, resulting in three
bulk vortices in the intermediate stage. The vortex structure finally evolves
into the single convection vortex in the drop, existing during about 1/2 of the
evaporation time.
