  In this paper, a novel lattice Boltzmann (LB) model based on the Allen-Cahn
phase-field theory is proposed for simulating axisymmetric multiphase flows.
The most striking feature of the model is that it enables to handle multiphase
flows with large density ratio, which are unavailable in all previous
axisymmetric LB models. The present model utilizes two LB evolution equations,
one of which is used to solve fluid interface, and another is adopted to solve
hydrodynamic properties. To simulate axisymmetric multiphase flows effectively,
the appropriate source term and equilibrium distribution function are
introduced into the LB equation for interface tracking, and simultaneously, a
simple and efficient forcing distribution function is also delicately designed
in the LB equation for hydrodynamic properties. Unlike many existing LB models,
the source and forcing terms of the model arising from the axisymmetric effect
include no additional gradients, and consequently, the present model contains
only one non-local phase field variable, which in this regard is much simpler.
We further conducted the Chapman-Enskog analysis to demonstrate the
consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn
equation and hydrodynamic equations. A series of numerical examples, including
static droplet, oscillation of a viscous droplet, breakup of a liquid thread,
and bubble rising in a continuous phase, are used to test the performance of
the proposed model. It is found that the present model can generate relatively
small spurious velocities and can capture interfacial dynamics with higher
accuracy than the previously improved axisymmetric LB model. Besides, it is
also found that our present numerical results show excellent agreement with
analytical solutions or available experimental data for a wide range of density
ratios, which highlights the strengths of the proposed model.
