Monte Carlo simulations of drop growth by coalescence and collision-induced breakup

A Monte Carlo framework that simulates the evolution of raindrop spectra by coalescence and collision-induced breakup is presented. The stochastic algorithm of Gillespie for chemical reactions (Gillespie, 1976. J. Comp. Phys. 22:403-434) in the formulation proposed by Laurenzi and Diamond (1999) was used to simulate the kinetic behavior of the drop population. For pure coalescence, by using the solutions of Scott (1965) for the quasi-stochastic collection equation, the time evolution of total droplet concentration for the sum kernel, product kernel and constant kernel with bidisperse initial conditions were calculated and compared with the results of the stochastic algorithm. For the three cases, were obtained the same results as the analytical solutions of the stochastic collection equation.

Within Gillespie's framework, the collision-induced breakup is introduced by considering the breakup probability as a new reaction channel. The results for the pure collision-induced breakup case were compared with the analytical solution of the collection/ breakup equation founded by Feingold et al. (1988) for an exponential fragment distribution of satellite drops, and constant collection and breakup kernels. A good correspondence between the analytical and the stochastic algorithm was found for this case.