  A three-dimensional color-fluid lattice Boltzmann model for immiscible
two-phase flows is developed in the framework of a three-dimensional
27-velocity (D3Q27) lattice. The collision operator comprises the D3Q27
versions of three sub-operators: a multiple-relaxation-time (MRT) collision
operator, a generalized Liu--Valocchi--Kang perturbation operator, and a
Latva-Kokko--Rothman recoloring operator. A D3Q27 version of an enhanced
equilibrium distribution function is also incorporated into this model to
improve the Galilean invariance. Three types of numerical tests, namely, a
static droplet, an oscillating droplet, and the Rayleigh--Taylor instability,
show a good agreement with analytical solutions and numerical simulations.
Following these numerical tests, this model is applied to liquid-jet-breakup
simulations. The simulation conditions are matched to the conditions of the
previous experiments. In this case, numerical stability is maintained
throughout the simulation, although the kinematic viscosity for the continuous
phase is set as low as $1.8\times10^{-4}$, in which case the corresponding
Reynolds number is $3.4\times10^{3}$; the developed lattice Boltzmann model
based on the D3Q27 lattice enables us to perform the simulation with parameters
directly matched to the experiments. The jet's liquid column transitions from
an asymmetrical to an axisymmetrical shape, and entrainment occurs from the
side of the jet. The measured time history of the jet's leading-edge position
shows a good agreement with the experiments. Finally, the reproducibility of
the regime map for liquid-liquid systems is assessed. The present lattice
Boltzmann simulations well reproduce the characteristics of predicted regimes,
including varicose breakup, sinuous breakup, and atomization.
