Surface effects on spinodal decomposition in binary mixtures and the interplay with wetting phenomena

The phase separation of binary mixtures in a semi-infinite geometry is investigated both by a phenomenological theory and by numerical calculations using a discrete equivalent of the descriptive equations. In the framework of ‘‘model B’’ (which describes solid binary mixtures), attention is paid to a proper treatment of the boundary conditions at the free surfaces. We confine ourselves to short-range surface forces and consider parameter values that correspond to both nonwet and wet surfaces in thermal equilibrium. During the initial stages of spinodal decomposition, after a quench from considering an initial condition that corresponds to a completely random concentration distribution, one finds a rather rapid growth of a thin surface enrichment layer of the component that is energetically preferred by the surface. This layer stabilizes a growing concentration wave in the direction normal to the surface, whose oscillations are damped to zero as one goes into the bulk. Studying concentration correlations in the direction parallel to the surface at a distance z from it, one can define a length scale ${\mathit{l}}_{\mathrm{\parallel }}$(z,t) describing the coarsening of the growing domains. We find that ${\mathit{l}}_{\mathrm{\parallel }}$(z,t)≊A(z)+B(z)${\mathit{t}}^{\mathit{a}}$ for large t, with an amplitude B(z) that increases as z→0 and an exponent a which is close to that for Lifshitz-Slyozov growth, viz., a≊1/3. This increase is due to an orientation of the growing elongated domains parallel to the surface near z=0. There is surprisingly little influence of the wetting transition on these phenomena–even for a wet surface the growth of the wetting layer is only logarithmic in time for short-range surface forces, and hence does not significantly affect phenomena on the faster time scales of spinodal decomposition. Experimental findings on the interplay of spinodal decomposition and wetting are critically discussed.