| The role of the particle size distribution in coalescence was explored using a moving-pivot population balance approach. We examined coalescence induced by either simple shear flow or by Brownian motion. Particle collisions were assumed to be ideal with no inter-particle interactions. We considered how the evolution of the distribution shape was influenced by (1) the shape of the initial drop size distribution, and (2) the imperfect description of the distribution as provided by experimental measurement. The initial distribution shapes that were explored included monodisperse, lognormal, bimodal, polymodal and step distributions. It was found that the initial rate of coalescence was independent of average drop size and depended only upon the shape of the distribution. At long times, systems approached an asymptotic distribution, determined by the form of the collision kernel, that was characterized by a unique rate of coalescence. Brownian systems approached a bell-shaped distribution, while shear systems approached a distribution that was a monotonically decreasing function of drop size. Interestingly, even though all distributions approached the asymptotic shape characteristic of the governing collision kernel, fingerprints of the initial distribution persisted at long times. Overall, the rate of coalescence was bounded by the initial rate of coalescence, which was a function of the shape of the initial distribution, and the final rate of coalescence, a function of the shape of the asymptotic distribution. These results show that, since the rate of coalescence is a function of the shape of the distribution, differences between the 'measured' shape obtained from analysis of a given measurement, and the true underlying distribution, can significantly alter the perceived coalescence behavior. It was found that the rate of coalescence is significantly underestimated if the drops at the upper end of the size range are not measured. Surprisingly, this effect was significant even if over 99.95% of the dispersed phase was captured within the measurement window. It was also found that imposing a distribution shape upon the system during the measurement process, or during interpretation of results, can significantly alter the results obtained for the average particle size and the interpretation of the underlying coalescence mechanism. |
