Boltzmann cellular automata studies of the spinodal decomposition

A nonlinear, Galilean invariant 2-color Boltzmann cellular automaton is used to study spinodal decomposition in 2-dimensional systems. The initial conditions for the process correspond to a well mixed state of two fluids, present in equal proportions. We specify two types of such initial conditions—corresponding to a correlated quench and to a deep quench. In the former case, a specific color is assigned randomly to each site. In the latter, individual states on each site are populated by the two colors about evenly, with small fluctuations. In the correlated quench situation, the domain growth exponent is initially equal to 0.33 ± 0.06 and for the late time stage it is equal to 0.66 ± 0.06. In the deep quench situation, on the other hand, the effective exponent from initial value of 0.33 takes on the value of 0.82 ± 0.05 for intermediate time scales and only at later times it crosses over to the exponent corresponding to the correlated quench. Spinodal decomposition taking place in a porous medium is slower and the effective exponents are nonuniversal. Inadequacies in the existing models of the surface tension in cellular automata are pointed out