Long-time evolution of a drop size distribution by coalescence in a linear flow

The growth of spherical drops by coalescence in simple shear and axisymmetric straining flows has been numerically investigated, and the long-time scaling behavior of the system was explored. It is shown that hydrodynamic interactions qualitatively modify the the collision kernel in the population balance equation and thus alter the evolution of the drop size distribution at long times. In the presence of hydrodynamic interactions, the number of drops in the system decays as t(-1), and the average drop size grows as e(sqrt[t]); in the absence of hydrodynamic interactions, these quantities evolve exponentially at long times. Hydrodynamic interactions lead to broader drop size distributions, and cause the influence of initial conditions to decay with time. Drops undergoing thermocapillary migration are shown to exhibit similar features. Our results are shown to be consistent with the established theory for the scaling behavior of aggregating systems. It is shown that the theory applies even in certain cases where the binary collision kernel does not have the assumed form. In the presence of hydrodynamic interactions, the scaling regime is attained slowly (logarithmically).