Wetting laws for polymer solutions

We measure the contact angle $\theta(\phi)$ of polymer solutions (polymer volume fraction ϕ) 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 we could expect a wetting transition at the concentration $\phi_{\rm w}$ such that $S(\phi_{\rm w})$ vanishes. We show here that $\theta(\phi)$ has a plateau $(\theta=\theta_{\rm L})$ for ϕ below a critical value $\phi_{\rm L}$ larger than $\phi_{\rm w}$. For $\phi > \phi_{\rm L}$, $\theta(\phi)$ increases monotonously. In the plateau regime, the solution droplet is in equilibrium with a precursor film of pure solvent. At $\phi_{\rm L}$, we have a “leak-out transition”, and the value of $\phi_{\rm L}$ 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