Spinodal decomposition in a two-dimensional fluid model: Heat, sound, and universality

Abstract

Spinodal decomposition after a critical quench in a fluid system is studied through the use of a Langevin model in which pressure and thermal fluctuations are coupled to the currents giving rise to thermal diffusion and sound modes. The model would reduce to the standard model H (in the notation of Halperin and Hohenberg) if the coupling to the pressure fluctuations were dropped. Results are compared to those previously obtained in the absence of sound modes and emphasis is put on the question of universality. The results obtained here imply that, in a model with thermal diffusion, sound modes play only a minor role in domain formation and growth, just as they do in the dynamics of second-order phase transitions. The qualitative behavior of the model studied is the same as that found experimentally for three-dimensional fluids: there are two different time regimes each governed by a power law l(t)∼${\mathit{t}}^{\mathit{n}}$ for the domain size l(t). At earlier times the exponent n≊0.3, and there is later a well-defined crossover to a considerably faster growth law. We find that n reaches n=0.65±0.03 at the latest times studied. We conclude that there is a ‘‘universality class’’ for fluid models with thermal diffusion.