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Mean field surrogate model of a dilute and chaotic particle suspension
Author(s) -
Vibe Alexander,
Marheineke Nicole
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900360
Subject(s) - particle (ecology) , physics , inertia , classical mechanics , momentum (technical analysis) , suspension (topology) , phase space , mechanics , distribution function , field (mathematics) , tensor (intrinsic definition) , cauchy stress tensor , convection–diffusion equation , mean field theory , statistical physics , thermodynamics , mathematics , quantum mechanics , geometry , oceanography , homotopy , pure mathematics , geology , finance , economics
We present a mean field approximation for a dilute suspension of small particles, which accounts for a non‐homogeneous particle distribution and small inertial effects of the particle phase. The model consists of the momentum equation for the fluid coupled to a transport equation for the probability density function on the particle phase space. Apart from the well‐known particle extra stress tensor first presented by Batchelor (1970), the fluid equation contains additional force terms resulting from inertia and hydrodynamic interaction of the particles. A brief sketch of the main derivation steps is presented.