Fragmentation instability in aggregating systems

TL;DR

This paper introduces a new model for aggregation systems that incorporates an instability threshold, simplifying the complex interactions caused by fragmentation and revealing two distinct behavioral regimes.

Contribution

A novel model that includes an instability threshold to simplify the analysis of fragmentation in aggregating systems, capturing different dynamic regimes.

Findings

Model exhibits two distinct regimes

Simplifies the combinatorics of fragmentation

Provides insights into instability effects

Abstract

The inclusion of a fragmentation mechanism in population balance equations introduces complex interactions that make the analytical or even computational treatment much more difficult than for the pure aggregation case. This is specially true when variable sized fragments are allowed, because of the exponential growth in fragments size combinations with the number of monomers in the exchanges. In this contribution we present a new model that incorporates an instability threshold in the clusters, which induces arbitrary losses or gains of particles by fracture with a substantial simplification of the combinatorics of the process. The model exhibits two different regimes.