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The Navier-Stokes equations and boundary conditions for viscous fluids ofcapillary size are formulated in curvilinear coordinates associated with ageometry of the fluid-gas interface. As a result, the fluid dynamics of dropsand menisci can be described taking into account an influence of gravitationalforces and flows on the surface shape. This gives a convenient basis forrespective numerical studies. Estimations of the effects are presented for thecase of an evaporating sessile drop.

Influence of gravitational forces and fluid flows on a shape of surfaces of a viscous fluid of capillary size