Multiphase flow modeling of spinodal decomposition based on the cascaded lattice Boltzmann method

A new multiphase lattice Boltzmann model based on the cascaded collision operator is developed to study the spinodal decomposition of critical quenches in the inertial hydrodynamic regime. The proposed lattice Boltzmann model is able to investigate simulations of multiphase spinodal decomposition with a very high Reynolds number. The law governing the growth of the average domain size, i.e. L ∝ t α , is studied numerically in the late-time regime, when multiple immiscible fluids are considered in the spinodal decomposition. It is found numerically that the growth exponent,  α , is inversely proportional to the number,  N , of immiscible fluids in the system. In fact, α = 6 / ( N + 7 ) is a simple law that matches the numerical results very well, even up to N = 20 . As the number of immiscible fluids increases, the corresponding drop in the connectivity of the various fluid domains is believed to be the main factor that drives and slows down the growth rate. Various videos that accurately demonstrate spinodal decomposition with different transport mechanisms are provided (see Appendix A). The remarks and statement made in this research are based on the analysis of 5120 numerical simulations and the postprocessing of about 3.5 TB of data.