What Determines Size Distributions of Heavy Drops in a Synthetic Turbulent Flow?

We present results from an individual particle based model for the collision, coagulation and fragmentation of heavy drops moving in a turbulent flow. Such a model framework can help to bridge the gap between the full hydrodynamic simulation of two phase flows, which can usually only study few particles and mean field based approaches for coagulation and fragmentation relying heavily on parameterization and are for example unable to fully capture particle inertia. We study the steady state that results from a balance between coagulation and fragmentation and the impact of particle properties and flow properties on this steady state. We compare two different fragmentation mechanisms, size-limiting fragmentation where particles fragment when exceeding a maximum size and shear fragmentation, where particles break up when local shear forces in the flow exceed the binding force of the particle. For size-limiting fragmentation the steady state is mainly influenced by the maximum stable particle size, while particle and flow properties only influence the approach to the steady state. For shear fragmentation both the approach to the steady state and the steady state itself depend on the particle and flow parameters. There we find scaling relationships between the steady state and the particle and flow parameters that are determined by the stability condition for fragmentation.Comment: 14 pages, 7 figure

Aggregation and fragmentation dynamics of inertial particles in chaotic flows

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equation of motion with a new parameter. These particles can in turn fragment when they reach a certain size or shear forces become sufficiently large. The resulting system consists of a large set of coexisting dynamical systems with a varying number of particles. We find that the combination of aggregation and fragmentation leads to an asymptotic steady state. The asymptotic particle size distribution depends on the mechanism of fragmentation. The size distributions resulting from this model are consistent with those found in rain drop statistics and in stirring tank experiments.Comment: 4 pages, 4 figure

Coagulation and fragmentation dynamics of inertial particles

Inertial particles suspended in many natural and industrial flows undergo coagulation upon collisions and fragmentation if their size becomes too large or if they experience large shear. Here we study this coagulation-fragmentation process in time-periodic incompressible flows. We find that this process approaches an asymptotic, dynamical steady state where the average number of particles of each size is roughly constant. We compare the steady-state size distributions corresponding to two fragmentation mechanisms and for different flows and find that the steady state is mostly independent of the coagulation process. While collision rates determine the transient behavior, fragmentation determines the steady state. For example, for fragmentation due to shear, flows that have very different local particle concentrations can result in similar particle size distributions if the temporal or spatial variation of shear forces is similar.Comment: 8 pages, 7 figure