Influence of surface interactions on spinodal decomposition

Abstract

Domain growth in a binary mixture, after a quench through its demixing critical point, near a boundary that attracts one of the components, is discussed. When mean-field theory is valid for equilibrium properties, a single domain may form at the substrate for much weaker surface interactions than those necessary for complete wetting in equilibrium. Prediction of a transition from such a ‘‘plating’’ configuration to ‘‘surface droplets’’ is verified using cell-dynamical simulations. At later times, if diffusion is the dominant transport process, simulations show the surface domain thickness to increase according to the bulk domain growth law R=${\mathit{t}}^{1/3}$—if there is not too much order near the boundary induced by the surface forces at early times. If a series of concentration oscillations is set up near the boundary at early times, surface domain thickening can be greatly slowed down. At still later times, the role that hydrodynamic flows play in changing the surface domain size is studied: the surface tension to viscosity ratio ${\mathit{v}}_0$=σ/η is an upper bound on interface velocities. This bound is obeyed by recent experiments that show ‘‘fast’’ growth of surface domains.