Version 1
: Received: 27 February 2021 / Approved: 1 March 2021 / Online: 1 March 2021 (13:19:28 CET)
How to cite:
Xie, M. Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium. Preprints2021, 2021030012. https://doi.org/10.20944/preprints202103.0012.v1
Xie, M. Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium. Preprints 2021, 2021030012. https://doi.org/10.20944/preprints202103.0012.v1
Xie, M. Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium. Preprints2021, 2021030012. https://doi.org/10.20944/preprints202103.0012.v1
APA Style
Xie, M. (2021). Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium. Preprints. https://doi.org/10.20944/preprints202103.0012.v1
Chicago/Turabian Style
Xie, M. 2021 "Particle Size Distribution of Smoluchowski Coagulation Equation for Brownian Motion at Equilibrium" Preprints. https://doi.org/10.20944/preprints202103.0012.v1
Abstract
The information entropy for Smoluchowski coagulation equation is proposed based on statistical mechanics. And the normalized particle size distribution is a lognormal function at equilibrium from the principle of maximum entropy and moment constraint. The geometric mean volume and standard deviation in the distribution function are determined as simple constant. The results reveal that the assumption that algebraic mean volume be unit in self-preserving hypothesis is reasonable in some sense. Based on the present definition of information entropy, the Cercignani’s conjecture holds naturally for Smoluchowski coagulation equation. Together with the proof that the conjecture is also true for Boltzmann equation, Cercignani’s conjecture will holds for any two-body collision systems, which will benefit the understanding of Brownian motion and molecule kinematic theory, such as the stability of the dissipative system, and the mathematical theory of convergence to thermodynamic equilibrium.
Keywords
Particle size distribution; population balance equation; information entropy; moment method
Subject
Physical Sciences, Acoustics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
