The dynamics of particles in flows ("flowing matter") is fundamental to understanding chemical and kinetic processes in the Natural Sciences. Often the fluid flow is turbulent ("turbulent aerosols"). It is at present very difficult to perform direct numerical simulations of such systems, because of the large range of time and length scales involved. We have therefore pursued an alternative approach: we analyse statistical models of turbulent aerosols. The resulting equations parallelise in an ideal way: different statistical realisations are farmed out on independent processors. This approach has allowed us to identify and characterise important fundamental mechanisms determining the dynamics of particles in flows [Gustavsson & Mehlig, Adv. Phys. (2016)]. We now apply for computer resources to answer the following questions that have resulted from our research summarised in this review article. 1.) Statistical models for the collision rate between particles in turbulent aerosols are commonly formulated for identical particles. This is an important special case. But it is necessary to find a parametrisation for the collision rate between particles of different sizes. In 2014 we obtained preliminary results for the distribution of relative velocities of different-sized particles that are close to each other. We need to perform statistical-model simulations to validate the theory. (Jan Meibohm, Kristian Gustavsson). 2.) Statistical models for turbulent suspensions of non-spherical particles (Barbara Schnitzer, Kristian Gustavsson). 3.) Rheology of dilute suspensions of non-spherical particles. The viscosity of such a suspension is determined by the competition between Brownian diffusion torques and those due to the macroscopic motion of the fluid. Our aim is to investigate how the suspension viscosity depends on the shape of tri-axial particles. To answer this question we need to run specialised C++ code that integrates the stochastic equations of motion for the orientational dynamics of tri-axial particles (Gino Aimondo). 4. Evaporation and condensation of cloud droplets in the turbulent air at the edge of a cumulus cloud. This is a direct numerical simulation of the problem, taking into account turbulent dynamics and thermodynamic processes (Johan Fries). This project uses a parallelised direct-numerical simulation algorithm that has been extensively tested.