The stationary single vortex Marangoni convection in an axially symmetricalsessile drop of capillary size is considered. The detailed description of thefluid flows is presented for a wide range of contact angles, which takes intoaccount the boundary conditions and the mass balance equation, withoutexplicitly solving the Navier--Stokes equations. The analytical approachdeveloped is compared with the results of numerical simulations anddemonstrated to describe reasonably well the single-vortex Marangoni flows.This indicates the substantial role of the boundary conditions in the problem.
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