Statistical model for collisions and recollisions of inertial particles in mixing flows

摘要

Finding a quantitative description of the rate of collisions between smallparticles suspended in mixing flows is a long-standing problem. Here weinvestigate the validity of a parameterisation of the collision rate foridentical particles subject to Stokes force, based on results for relativevelocities of heavy particles that were recently obtained within a statisticalmodel for the dynamics of turbulent aerosols. This model represents theturbulent velocity fluctuations by Gaussian random functions. We find that theparameterisation gives quantitatively good results in the limit where the \lqghost-particle approximation' applies. The collision rate is a sum of twocontributions due to \lq caustics' and to \lq clustering'. Within thestatistical model we compare the relative importance of these two collisionmechanisms. The caustic formation rate is high when the particle inertiabecomes large, and we find that caustics dominate the collision rate as soon asthey form frequently. We compare the magnitude of the caustic contribution tothe collision rate to the formation rate of caustics.