Agglomeration and aggregation of particles. Considerations based on the entropy of mixing using a stochastic approach

Abstract

It is well-known that larger quantities of fine powders, such as. nanoparticles, have the tendency to form larger clusters. These clusters may be stable aggregates or loosely bound agglomerates. These processes are of importance in the case of particle additions to rocket fuel. The formation of these secondary particles is a random process that can be described mathematically based on von-Smolukowski theory or by the application of appropriate statistical methods. In the context of this paper, a combination of Markov chains with Monte Carlo calculations was selected for the analysis. These calculations taught that the entropy is an important tool for describing the stability of the newly formed larger particles, stable aggregates, or loosely-bonded agglomerates. Another important and new result of these calculations was the finding that the maximum size of the aggregates is limited. This is not observed in the case of less stable bond agglomerates. In the case of dimensionless primary particles, the size distribution of the aggregates and agglomerates follows exactly an exponential function. In the case of agglomerates, this statement is valid for agglomerating objects with entropy values smaller than the maximum.This situation is different in cases where the real geometry of the particles is taken into account. In this case, the particle size distribution comes, in cases of larger numbers of interaction between the particles, close to a Poisson distribution. This is verified by comparing with the experimental data.