Comparison of two statistical models for the calculation of collisions of particles in isotropic turbulence

Two models are given for determining the collision rate of inertial particles in a homogeneous isotropic turbulence. The advantages and disadvantages of the known models of particle collisions are discussed. One of the models suggested by us is based on the assumption that the joint probability density function of gas and particle velocities is a Gaussian distribution. The second model follows from the kinetic equation for the probability density of the relative velocity of two particles. These two models are compared with each other and with the available data of direct numerical simulation.