Kinetic modeling of multiphase flow based on simplified Enskog equation

A new kinetic model for multiphase flow was presented under the framework of the discrete Boltzmann method (DBM). Significantly different from the previous DBM, a bottom-up approach was adopted in this model. The effects of molecular size and repulsion potential were described by the Enskog collision model; the attraction potential was obtained through the mean-field approximation method. The molecular interactions, which result in the non-ideal equation of state and surface tension, were directly introduced as an external force term. Several typical benchmark problems, including Couette flow, two-phase coexistence curve, the Laplace law, phase separation, and the collision of two droplets, were simulated to verify the model. Especially, for two types of droplet collisions, the strengths of two non-equilibrium effects, $bar{D}_2^*$ and $bar{D}_3^*$, defined through the second and third order non-conserved kinetic moments of $(f - f ^{eq})$, are comparatively investigated, where $f$ ($f^{eq}$) is the (equilibrium) distribution function. It is interesting to find that during the collision process, $bar{D}_2^*$ is always significantly larger than $bar{D}_3^*$, $bar{D}_2^*$ can be used to identify the different stages of the collision process and to distinguish different types of collisions. The modeling method can be directly extended to a higher-order model for the case where the non-equilibrium effect is strong, and the linear constitutive law of viscous stress is no longer valid.