Kinetic regimes in aggregating systems with spontaneous and collisional fragmentation

TL;DR

This paper investigates how clusters grow and break apart in systems with both spontaneous and collision-induced fragmentation, revealing different behaviors in closed versus open systems and identifying dominant processes.

Contribution

It introduces a comprehensive analysis of aggregation systems with both spontaneous and collisional fragmentation, distinguishing behaviors in closed and open systems.

Findings

In closed systems, size distribution reaches a steady state influenced mainly by spontaneous fragmentation.

In open systems, collisional fragmentation dominates, leading to a quasi-stationary state with linearly growing cluster densities.

The size distribution in open systems matches the steady state of a similar system with only collisional fragmentation.

Abstract

We analyze systems of clusters and interacting upon colliding---a collision between two clusters may lead to merging or fragmentation---and we also investigate the influence of additional spontaneous fragmentation events. We consider both closed systems in which the total mass remains constant and open systems driven by a source of small-mass clusters. In closed systems, the size distribution of aggregates approaches a steady state. For these systems the relaxation time and the steady state distribution are determined mostly by spontaneous fragmentation while collisional fragmentation plays a minor role. For open systems, in contrast, the collisional fragmentation dominates. In this case, the system relaxes to a quasi-stationary state where cluster densities linearly grow with time, while the functional form of the cluster size distribution persists and coincides with the steady state size distribution of a system which has the same aggregation and fragmentation rates and only collisional fragmentation.