Caustics in turbulent aerosols

– Networks of caustics can occur in the distribution of particles suspended in a randomly moving gas. These can facilitate coagulation of particles by bringing them into close proximity, even in cases where the trajectories do not coalesce. The long-time morphology of these caustic patterns depends upon the Lyapunov exponents λ1, λ2 of the suspended particles, as well as the rate J at which particles encounter caustics. We develop a theory determining the quantities J , λ1, λ2 from the statistical properties of the gas flow, in the limit of short correlation times. Aerosols are usually unstable systems, in that the suspended particles eventually coagulate. Understanding the process giving rise to this coagulation, and determining the time scale over which it occurs are important questions in describing any aerosol system. If the gas phase does not have macroscopic motion, the coagulation may be effected by diffusion of the suspended particles, or (if the suspended particles are of a volatile substance) by Ostwald ripening. The coagulation process can be greatly accelerated if the aerosol undergoes macroscopic internal motion. Ultrasound, for example, has been used to accelerate coagulation in aerosols [1]. Turbulent flow could also play a role in the coagulation of suspended particles; this could be relevant in the coalescence of visible moisture into rain droplets [2]. If suspended particles are simply advected in an incompressible flow, their density remains constant. Inertial effects are therefore required for coagulation, unless the flow exhibits significant compressibility. In earlier work [3,4] we discussed the motion of inertial particles in a random velocity field. We showed that there is a phase where the trajectories of the particles coalesce, so that arbitrarily small particles coagulate. In the limit where the correlation time τ of the flow approaches zero, this path-coalescing phase only exists when the velocity field is predominantly potential flow (such as the flow due to sound waves) [4]. Turbulent fluid flow is, however, expected to be predominantly solenoidal, and it is of interest to find alternative mechanisms of coagulation which operate outside the path-coalescence phase. Here we describe an alternative mechanism facilitating coagulation, illustrated in Fig. 1: we show the distribution of particles suspended in a randomly moving gas (the equations of motion and statistics of the flow field are given by eqns. (1) to (3) below). The large