Cluster-size dynamics: A phenomenological model for the interaction between coagulation and fragmentation processes

We present a novel phenomenological modeling approach to describe the growth of clusters as the result of the interaction between cluster coagulation and fragmentation. The cluster-size growth (CSG) model tracks the evolution of cluster-sizes rather than the concentrations of clusters with different sizes as in the Smoluchowski and Becker-Döring coagulation-fragmentation equations. Our modeling perspective allows for a description of cluster growth in realistic systems by using a significantly smaller number of differential equations to describe their dynamics. We used dynamical system tools (phase-plane analysis) and numerical simulations to investigate the CSG model dynamics and to understand how the model parameters describing the coagulation and fragmentation processes determine balances between these two processes that create non-zero stationary cluster size distributions.