  In this work, we develop a novel model describing the equilibrium shape of
sessile droplets on a wetted horizontal surface in a gravitational field. The
model takes into account the intermolecular Lenard-Jones forces between solid
and the liquid molecules using the standard disjoining pressure approximation.
These forces lead to the formation of a thin, non-removable fluid layer
covering the solid substrate. Balancing the disjoining pressure against the
surface tension and the gravitational force we calculate the smooth shape of
the surface of the liquid. We obtain a criterion when the gravitational forces
are so large that they level the droplets completely. We show that, in the case
of weak gravitational forces, the maximum height of the droplets is described
by the classical Quincke formula.
