  Multi-phase phenomena remain at the heart of many challenging fluid dynamics
problems. Molecular fluxes at the interface determine the fate of neighboring
phases, yet their closure far from the continuum needs to be modeled. Along the
hierarchy of kinetic approaches, a multi-phase particle method is devised in
this study. This approach is built closely upon the previous studies on the
kinetic method development for dense gasses [Phys. Fluids, 29 (12), 2017] and
long-range interactions [J. Comput. Phys, 378, 2019]. It is on this background
that the current work on Fokker-Planck-Poisson modeling of multi-phase
phenomena is initiated. Molecular interactions are expressed via stochastic
forces driven by the white noise, coupled with long-range attractions. The
former is local and pursues diffusive approximation of molecular collisions,
whereas the latter takes a global feature owing to mean-field forces. The
obtained Fokker-Planck-Poisson combination provides an efficient workflow for
physics-driven simulations suitable for multi-phase phenomena far from the
equilibrium. Besides highlighting the computational efficiency of the method,
various archetypical and complex problems ranging from
inverted-temperature-gradient between droplets to spinodal decomposition are
explored. Detailed discussions are provided on different characteristics of the
droplets dispersed in low/high density background gases; including the
departure of heat fluxes from Fourier's law as well as droplets growth in
spinodal phases.
