Oscillating stationary distributions of nanoclusters in an open system

• Published in: Mathematical and computer modelling of dynamical systems Vol. 26; no. 6; pp. 562 - 575
• Main Authors: Matveev, S. A, Sorokin, A. A, Smirnov, A. P, Tyrtyshnikov, E.E.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 01-11-2020; Taylor & Francis Ltd
• Subjects: Agglomeration; Aggregation; Clusters; Collision dynamics; Kinetic coefficients; Kinetic equations; kinetic models; Mathematical models; Monomers; Nanoclusters; Nanoparticles; Nonlinear equations; numerical Analysis; Open systems; Oscillations; Population balance models
• ISSN: 1387-3954; 1744-5051
• DOI: 10.1080/13873954.2020.1793786

Steady-state oscillations of nanoparticle populations in the system of colliding monomers and seed-clusters are observed for the range of the seed-cluster source with diffusion and ballistic collision kernels. The dynamics of nanoparticles in this system is driven by monomer-cluster and cluster-cluster irreversible aggregation and described in terms of the number of primary monomers per nanoparticle based on solving the population balance equations as described by the classical system of Smoluchowski equations. The oscillations of particles' concentrations arise with growing power of the source of seed-clusters and can remain visible for several orders of magnitute of particle sizes
. For the case of constant kinetic coefficients the novel semi-analytial solution of the utilized aggregation model is found and results of numerical simulations with use of up to
non-linear kinetic equations agree excellently with proposed theory.