Three-dimensional hydrodynamic lattice-gas simulations of domain growth and self-assembly in binary immiscible and ternary amphiphilic fluids

We simulate the dynamics of phase assembly in binary immiscible fluids and ternary microemulsions using a three-dimensional hydrodynamic lattice-gas approach. For critical spinodal decomposition we perform the scaling analysis in reduced variables introduced by Jury et al. [Phys. Rev. E 59, R2535 (1999)] and by Bladon et al. [Phys. Rev. Lett. 83, 579 (1999)]. We find a late-stage scaling exponent consistent with the $R\sim t^{2/3}$ inertial regime. However, as observed with the previous lattice-gas model of Appert et al. [J. Stat. Phys. 81, 181 (1995)] our data do not fall in the same range of reduced length and time as those of Jury et al. and Bladon et al. For off-critical binary spinodal decomposition we observe a reduction of the effective exponent with decreasing volume fraction of the minority phase. However, the $n=\frac{1}{3}$ Lifshitz-Slyzov-Wagner droplet coalescence exponent is not observed. Adding a sufficient number of surfactant particles to a critical quench of binary immiscible fluids produces a ternary bicontinuous microemulsion. We observe a change in scaling behavior from algebraic to logarithmic growth for amphiphilic fluids in which the domain growth is not arrested. For formation of a microemulsion where the domain growth is halted we find that a stretched exponential growth law provides the best fit to the data.