Boltzmann Equation in Aggregation Kinetics

Brilliantov NV, Osinsky AI, Pöschel T (2022)

Publication Type: Book chapter / Article in edited volumes

Publication year: 2022

Publisher: Springer Science and Business Media Deutschland GmbH

Edited Volumes: Nonequilibrium Thermodynamics and Fluctuation Kinetics

Series: Fundamental Theories of Physics

Book Volume: 208

Pages Range: 191-216

ISBN: 978-3-031-04458-8

DOI: 10.1007/978-3-031-04458-8_10

Abstract

We consider the application of the Boltzmann equation to aggregation kinetics, where the transport mechanism is the ballistic motion of particles. This refers to molecular gases, granular gases, and, hypothetically, dark matter. Two aggregation models are analyzed—random and impact energy-dependent aggregation. The latter is associated with different interparticle forces responsible for agglomeration. We start from the Boltzmann equation governing the evolution of the mass–velocity distribution functions of different species—the agglomerates of different sizes and derive generalized Smoluchowski equations. These describe the time dependence of the agglomerates densities and their mean kinetic energy (partial temperatures). We obtain exact solutions to these equations for simplified cases and develop a scaling theory for the asymptotic behavior of the system. We explore numerically, the agglomeration kinetics and observe a very rich behavior of the system. We reveal new surprising regimes and construct the according kinetic phase diagram. The scaling theory is in excellent agreement with the simulation results.

Authors with CRIS profile

Thorsten Pöschel Lehrstuhl für Multiscale Simulation of Particulate Systems

Involved external institutions

Skolkovo Institute of Science and Technology RU Russian Federation (RU)

How to cite

APA:

Brilliantov, N.V., Osinsky, A.I., & Pöschel, T. (2022). Boltzmann Equation in Aggregation Kinetics. In Léon Brenig, Nikolai Brilliantov, Mustapha Tlidi (Eds.), Nonequilibrium Thermodynamics and Fluctuation Kinetics. (pp. 191-216). Springer Science and Business Media Deutschland GmbH.

MLA:

Brilliantov, Nikolai V., Alexander I. Osinsky, and Thorsten Pöschel. "Boltzmann Equation in Aggregation Kinetics." Nonequilibrium Thermodynamics and Fluctuation Kinetics. Ed. Léon Brenig, Nikolai Brilliantov, Mustapha Tlidi, Springer Science and Business Media Deutschland GmbH, 2022. 191-216.

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