Segregation of inertial particles in turbulence via the Full Lagrangian Approach

Suspensions of small heavy particles in turbulent flows are found in a variety of natural and industrial applications such as droplets in clouds [1], soot particles in post combustion devices and reacting particles in chemical processs facilities [2]. It is well known from experimental results [3], numerical simulations [4] and theoretical studies [5] that particles in turbulent flows tend to concentrate preferentially due to inertia. This non-trivial behavior is associated with a nonlinear dynamical system that is far from equilibrium, which combines properties of kinetics and hydrodynamics and has caustics superimposed on a multifractal structure. Inertial particles are generally ejected from regions of high vorticity and accumulate in regions of high strain rate, thereby inducing non-zero gradients occur in the particle number density, n(x, t), i.e. the number of particles situated inside an infinitesimally small volume located around position x at time t. It is associated with a non-zero compressibility of the particle velocity field (PVF) v(x, t) which is defined as the mean velocity of particles at a certain position x at time t. Indeed, it is well-known [?] that the particle velocity field may be compressible even if the turbulent carrier flow is incompressible. Local gradients of n(x, t) and v(x, t) control the rates of inter-particle collisions, coalescence, break-up and possibly sedimentation and resuspension