Dynamics of wetting transitions: A time-dependent Ginzburg-Landau treatment

The dynamic behavior at wetting transitions is studied for systems with short-range forces and nonconserved order parameter. From a continuum limit of a purely relaxational lattice model in mean-field approximation, a time-dependent Ginzburg-Landau equation with a time-dependent boundary condition at the surface is derived in the long wavelength approximation. The dynamics of relaxation close to stable and metastable states is treated in linear response. A divergence of the relaxation time occurs both for critical wetting and along the surface spinodal lines (in the case of first-order wetting), although the static surface layer susceptibilities ₁, ₁₁ stay finite at the surface spinodal in the non-wet region of the phase diagram.Also the highly nonlinear relaxation that occurs when a wetting layer forms out of an initially non-wet state is considered. For late times, the thickness of the wetting layer grows proportional to the logarithm of time. A comparison with recent Monte Carlo work shows that the present mean-field theory underestimates the prefactor in this growth law. For early times and states in the metastable region a distance H ₁ away from the first order wetting transition, the formation of the wet layer starts by heterogeneous nucleation of droplets at the surface. The droplets have the shape of (approximately) caps of a sphere and involve a free energy barrier proportional to (H ₁)^–2 as H ₁0. The generalization of this phenomenological approach for the nucleation barrier to the case of long range forces is also discussed and open problems are briefly outlined.