DIFFUSIVE GROWTH OF PHASE-SEPARATING DOMAINS NEAR A SURFACE - THE EFFECT OF REDUCED DIMENSIONALITY

Recent experiments on phase separation in quenched binary liquid mixtu res confined between closely spaced quartz surfaces have uncovered tha t the growth of domains near the surfaces is considerably faster than the growth of domains in the bulk. While the domains in the bulk coars en in time as t1/3, those near the surfaces coarsen as t(x), where alp ha ranges from about 1.1 to 1.5 depending on the quench depth. Though it has yet to be determined whether this accelerated growth correspond s to the domains containing the more wetting or less wetting phase, it seems clear that both surface forces and reduced dimensionality can a ffect growth near a surface. To focus on the effect of dimensionality, we have developed a simplified model for the two-dimensional growth o f a wetting domain. The model describes the wetting domain as a circul ar disk which remains at constant thickness and is fed by the diffusio n of species from a three-dimensional supersaturated mixture. Numerica l solution of the diffusion equation reveals that the radius of the di sk increases linearly in time when the concentration field surrounding the disk equilibrates faster than the disk grows. At long times, howe ver, when the concentration field cannot equilibrate at the rate of di sk growth, the disk radius increases exponentially in time. Including the effect of other disks competing for the bulk species, as well as l oosening the restriction of constant thickness, will slow the exponent ial growth, but the transition from linear to faster-than-linear growt h will still occur. We draw favorable comparison between our theoretic al results and experimental findings for both the growth at small quen ches and the transition from linear to faster growth.