  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.
