In Fig. 11 we illustrate the case of a critical
A = ½ mA = mB).
The value of the "quench depth" equals
G = 0.537 and the reduced
Periodic boundary conditions are employed in this LB calculation
to minimize wall effects.
Figure 12 shows separation after a later time,
= 17.8. The pattern is similar in geometric form to Fig. 11, but the characteristic scale of the pattern is larger after longer times, geometrically illustrating the notion of dynamic similarity in the phase separation coarsening process. A study of the time dependence of the growth of the phase separation shows that the pattern scale grows slowly in the early stage of the phase separation process, as the local composition builds up to its coexisting composition value (one of the coexisting phases, B, has been rendered transparent in Fig. 11). At a later stage of phase separation, the pattern scale growth is roughly linear in time [96,97]. Other LB studies have recently focused on modeling the kinetics of phase separation so we do not dwell on this well known phenomena in the present paper [11,97,98,99,100]. We next illustrate the qualitative change in the phase separation morphology that occurs under off-critical conditions. Fig. 13 shows the phase separation morphology for a quench depth, G = 0.133. The rendered composition A is taken to have the off-critical value, A = 0.1. The phase separation then occurs through droplet formation rather then the formation of a bicontinuous "spinodal" phase separation pattern. At a later time, we observe the droplets to coarsen by coalescence in a normal manner for off-critical fluids . In future work we plan to explore the conditions (e.g. quench depth, viscosity mismatch, etc.) that determine the crossover between the droplet and bicontinuous phase separation patterns observed in the early stages of phase separation. Even this basic aspect of fluid phase separation remains poorly understood so that materials scientists must rely on engineering correlations .