Fractal Substructures due to Fragmentation and Reagglomeration

TL;DR

This paper investigates how repeated fragmentation and reagglomeration of cohesive powders lead to fractal substructures with distinct scale-invariant dust and characteristic-sized fragments, using two different models.

Contribution

It introduces and compares two models of fragmentation-reagglomeration cycles to explain the development of fractal structures in powders.

Findings

Development of fractal substructures with robust statistical properties.

Identification of scale-invariant dust and characteristic-sized fragments.

Analysis of fragment size distribution and structural evolution.

Abstract

Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under gravity. If this fragmentation-reagglomeration cycle is repeated sufficiently often, the powder develops a fractal substructure with robust statistical properties. The structural evolution is discussed for two different models: The first one is an off-lattice model, in which a fragment does not stick to the surface of other fragments that have already settled, but rolls down until it finds a locally stable position. The second one is a simpler lattice model, in which a fragment sticks at first contact with the agglomerate of fragments that have already settled. Results for the fragment size distribution are shown as well. One can distinguish scale invariant dust and fragments of a characteristic size. Their role in the process of structure formation will be addressed.