Wetting laws for polymer solutions

We measure the contact angle theta(phi) of polymer solutions (polymer volume fraction phi) on a solid surface. The polymer is repelled at both solid and air interfaces. The pure solvent wets the solid, but the polymer does not. Thus the spreading coefficient S(phi) is positive for phi = 0 and negative for phi = 1. Naively rye could expect a wetting transition at the concentration phi(w) such that S(phi(w)) vanishes. We show here that theta(phi) has a plateau (theta = theta(L)) for phi below a critical value phi(L) larger than phi(w). For phi > phi(L), theta(phi) increases monotonously. In the plateau regime, the solution droplet is in equilibrium with a precursor film of pure solvent. At phi(L), we have a ''leak-out transition'', and the value of phi(L) results from a balance between the osmotic pressure of the polymer solution and the disjoining pressure of the solvent film. These ideas can be extended to other liquid mixtures. again assuming that the solute does not adsorb at the interfaces and, more precisely, that the thickness of the depletion layers is larger than the natural thickness of the solvent film.