Non-existence of mean-field models for particle orientations in suspensions

We consider a suspension of spherical inertialess particles in a Stokes flow on the torus \(\mathbb T^3\). The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientati...

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Bibliographic Details
Published in:arXiv.org 2022-10
Main Authors: Höfer, Richard M, Mecherbet, Amina, Schubert, Richard
Format: Article
Language:English
Subjects:
Angular velocity
Perturbation
Stokes flow
Toruses
Online Access:Get full text
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Summary:We consider a suspension of spherical inertialess particles in a Stokes flow on the torus \(\mathbb T^3\). The particles perturb a linear extensional flow due to their rigidity constraint. Due to the singular nature of this perturbation, no mean-field limit for the behavior of the particle orientation can be valid. This contrasts with widely used models in the literature such as the FENE and Doi models and similar models for active suspensions. The proof of this result is based on the study of the mobility problem of a single particle in a non-cubic torus, which we prove to exhibit a nontrivial coupling between the angular velocity and a prescribed strain.
ISSN:2331-8422