The equilibrium shape of an axisymmetric sessile drop subject to local stresses

The exact equation describing the shape of a fluid drop under the action of local surface stresses induced by colloidal interactions is derived withou t resorting to any of the approximations inherent in the profile equation c urrently employed in the literature. The exact equation implies, and numeri cal examples confirm, that repulsive external (i.e. positive) surface energ ies assist in stabilizing the drop against deformation, while attractive (i .e. negative) energies destabilize the drop, promoting or enhancing deforma tion. An inherent singularity in the governing differential equation (absen t from the approximate equations currently used) when the surface energy (s urface tension) is identically matched by an external attractive energy rep resents an instability limit. Explicit bounds are established for a further instability criterion and for the hydrostatic pressure difference across t he interface. An exact equation for the radial extent of the sessile drop a nd some numerical examples are also presented.