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Fokker-Planck-Poisson kinetics: multi-phase flow beyond equilibrium

Published online by Cambridge University Press:  16 June 2021

Mohsen Sadr Open the ORCID record for Mohsen Sadr [Opens in a new window] ,
Marcel Pfeiffer Open the ORCID record for Marcel Pfeiffer [Opens in a new window]  and
M. Hossein Gorji Open the ORCID record for M. Hossein Gorji [Opens in a new window]
Mohsen Sadr*
Affiliation:
Applied and Computational Mathematics, RWTH Aachen University, Schinkestrasse 2, D-52062Aachen, Germany
Marcel Pfeiffer
Affiliation:
Institute of Space Systems, University of Stuttgart, Pfaffenwaldring 29, D-70569Stuttgart, Germany
M. Hossein Gorji
Affiliation:
Laboratory of Multiscale Studies in Building Physics, Empa, Swiss Federal Laboratories for Materials Science and Technology, Dübendorf, Switzerland
*
†Email address for correspondence: [email protected]
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Abstract

Multi-phase phenomena remain at the heart of many challenging fluid dynamics problems. Molecular fluxes at the interface determine the fate of neighbouring phases, yet their closure far from the continuum needs to be modelled. Along the hierarchy of kinetic approaches, a multi-phase particle method is devised in this study. This approach is built closely upon the previous studies on the kinetic method development for dense gases [Phys. Fluids, vol. 29 (12), 2017] and long-range interactions [J. Comput. Phys., vol. 378, 2019]. It is on this background that the current work on Fokker-Planck-Poisson modelling of multi-phase phenomena is initiated. Molecular interactions are expressed via stochastic forces driven by the white noise, coupled to the long-range attractions. The former is local and pursues diffusive approximation of molecular collisions, whereas the latter takes a global feature owing to mean-field forces. The obtained Fokker-Planck-Poisson combination provides an efficient work flow for physics-driven simulations suitable for multi-phase phenomena far from the equilibrium. Besides highlighting the computational efficiency of the method, various archetypical and complex problems ranging from inverted temperature gradients between droplets to spinodal decomposition are explored. Detailed discussions are provided on different characteristics of the droplets dispersed in low/high density background gases; including the departure of heat fluxes from Fourier's law as well as droplets growth in spinodal phases.

JFM classification

Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Multiphase flow Micro-/Nano-fluid dynamics: Non-continuum effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A46
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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