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. and Kendon et al. We find a late-stage scaling exponent consistent with the inertial regime. However, as observed with the previous lattice-gas model of Appert et al. our data does not fall in the same range of reduced length and time as that of Kendon et al. For off-critical binary spinodal decomposition we observe a reduction of the effective exponent with the volume fraction of the minority phase. However, the n=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 behaviour 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 a stretched exponential growth law provides the best fit to the data.