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