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

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED Journal of Nonlinear Science Pub Date : 2023-10-16 DOI:10.1007/s00332-023-09959-1

Richard M. Höfer, Amina Mecherbet, Richard Schubert

引用次数: 3

Abstract

Abstract We consider a suspension of spherical inertialess particles in a Stokes flow on the torus $$\mathbb {T}^3$$ 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.

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悬架中粒子取向的平均场模型的不存在性

摘要:我们考虑环状面上$$\mathbb {T}^3$$ t3的Stokes流中球形无惯性粒子的悬浮。粒子由于其刚性约束而扰动线性拉伸流。由于这种扰动的奇异性，粒子取向行为的平均场极限是无效的。这与文献中广泛使用的模型，如FENE和Doi模型以及类似的主动悬架模型形成对比。这一结果的证明是基于对非三次环面中单个粒子的迁移率问题的研究，我们证明了角速度与规定应变之间存在非平凡耦合。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.