Coupled aggregation and sedimentation processes: stochastic mean field theory

In this paper, we present a stochastic model for obtaining the time evolution of the cluster size distribution for systems following coupled aggregation and sedimentation processes. Both, diffusion-limited cluster aggregation conditions and reaction limited cluster aggregation conditions are studied under the effect of sedimentation. For this purpose, the master equation is adapted for considering several slices where cluster aggregation and mass transport through the boundaries are taken into account. Furthermore, the kernel needed to solve the stochastic equation is adapted for considering the sticking probability, P, and the Peclet number, Pe, as parameters. The obtained solutions are then compared with the time evolution of the cluster size distribution obtained by means of computer simulations in Leone et al. (Eur. Phys. J. E 7 (2002) 105), Odriozola et al. (Phys. Rev. E (2003) 031405).