Non-existence of Mean-Field Models for Particle Orientations in Suspensions

被引:2
|
作者
Hoefer, Richard M. [1 ]
Mecherbet, Amina [2 ]
Schubert, Richard [3 ]
机构
[1] Univ Regensburg, Fac Math, Regensburg, Germany
[2] Univ Paris Cite, Inst Math Jussieu Paris Rive Gauche, CNRS, Paris, France
[3] Univ Bonn, Inst Appl Math, Bonn, Germany
关键词
Mean-field limit; Doi model; oriented particles; suspensions; EINSTEINS EFFECTIVE VISCOSITY; NONLINEAR FOKKER-PLANCK; GLOBAL WELL-POSEDNESS; ROD-LIKE; POLYMERIC FLUID; DOI MODEL; SEDIMENTATION; SIMULATIONS; EXISTENCE;
D O I
10.1007/s00332-023-09959-1
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a suspension of spherical inertialess particles in a Stokes flow on the torus 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 Doimodels and similarmodels 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.
引用
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页数:20
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