  We construct a novel model for the steady-state contact angles of liquid
droplets at the wetted substrate. The non-removable, thin liquid film covering
the substrate is governed by the intermolecular forces between molecules of
liquid and solid, which we describe using the standard disjoining pressure
approximation. Balancing the disjoining pressure against the surface tension we
find the smooth shape of the surface of the liquid. We show that we can extract
an effective contact angle from the region where the film and the droplet meet.
Crucially, we find that for large droplets the contact angle is independent of
the droplet size. Instead, the contact angle is determined by the surface
tension and the disjoining pressure parameters through a simple formula that
works for both small and large contact angles. We suggest that comparing
predictions of our model to experimentally measured contact angles will enable
constraining the parameters of the disjoining pressure models.
