Turbulent aerosols are suspensions of heavy particles in a turbulent fluid. Examples are micron-sized water droplets or small ice crystals in turbulent clouds, virus-carrying droplets in the turbulent jet of exhaled air, or micron-sized dust grains in the turbulent gas around a growing star -- grain aggregation is thought to be the first stage of planet formation.
How do the particles grow or shrink in size by collisional aggregation or fragmentation, and in the case of droplets, by condensation or evaporation? Turbulence plays an essential role -- it may accelerate or slow down particle growth -- but the mechanisms are not understood because the analysis of these highly non-linear and multi-scale systems poses formidable challenges. Experiments resolving the motion of tiny particles in turbulence have only recently become possible, and direct numerical simulation of such systems is still immensely difficult.
Therefore we pursue a different approach: we derive idealised statistical models for turbulent aerosols that can be rigorously analysed using methods from non-equilibrium statistical physics and dynamical-systems theory. The turbulent velocity fluctuations are represented in terms of a stochastic synthetic turbulence model, and perturbation theory makes it possible to compute how the particles sample the turbulence, assuming that they do not directly interact. This allowed us to identify and describe key mechanisms that determine fractal spatial patterns of particles in dilute turbulent aerosols (Figure 1). See our review article  for a summary of recent progress.