Kinetic toy model of disruption of binary collisional droplets

Abstract

The characteristics of a kinetic toy model representing the collective motion of droplets undergoing binary collisional disruption are investigated. To analyze the simplest case, the elastic Boltzmann equation with collisional disruption, where the differential collision cross section of the hard spherical (HS) droplets is symmetrized, is considered as the kinetic toy model. The thermal equilibrium distribution is derived from the kinetic toy model in accordance with the H-theorem. The kinetic toy model shows that the collisional moments corresponding to the diffusion flux and heat flux diverge. Furthermore, the validity of the H-theorem in the kinetic toy model is examined through numerical simulations using the direct simulation Monte Carlo (DSMC) method. To investigate the dissipation process described by the kinetic toy model, the time evolution of correlation functions of fluctuations in the pressure deviator, diffusion flux, and heat flux, and the shock layer around a triangular prism is numerically analyzed. The DSMC results demonstrate that the kinetic toy model reproduces features observed in the Boltzmann equation with a realistic differential collision cross section, including the decay of correlation functions associated with fluctuations in the pressure deviator, diffusion flux, and heat flux. In addition, the Maxwellian droplet model is introduced to support and complement the discussion of the HS droplet case.