Stochastic transport of particles in straining flows.

Important features associated with the segregration of particles in turbulent flow are investigated by considering the statistical distribution (phase-space number density) of particles subject to the combined effects of straining flow and stochastic forcing. A Fokker-Planck model is used to obtain results for the phase-space distributions of particles that are entrained into straining flow fields. The analysis shows that, in marked contrast to the zero strain case, nonsingular steady-state distributions are generated, and also confirms that the diffusional effect resulting from stochastic forcing is sufficient to offset the otherwise singular distributions that would result from the indefinite accumulation of particles along stagnation lines. The influence of particle inertia (Stokes number) on the form of the resulting distributions is considered and several significant results are observed. The influence of strain rate on the attenuation of particle kinetic stresses is quantified and explained. The development of large third-order velocity moments is observed for Stokes numbers above a critical value. The mechanism underlying this phenomenon is seen to be a generic feature of particle transport in flows where vortex structures induce local counterflows of particles. The system therefore provides an ideal test for closure models for third-order moments of particle velocities, and here the standard Chapman-Enskog approximation is assessed.