Homogenization of a non-linear strongly coupled model of magnetorheological fluids

Silvia Jim\'enez Bola\~nos; Thuyen Dang; Yuliya Gorb

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Homogenization of a non-linear strongly coupled model of magnetorheological fluids

Thuyen Dang, Yuliya Gorb, Silvia Jiménez Bolaños

Analysis of PDEs · Submitted 21 Dec 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim As the size of the particles approaches zero, it is shown that the suspension's behavior is governed by a generalized magnetohydrodynamic system, where the fluid is modeled by a stationary Navier-Stokes system, while the magnetic field is modeled by Maxwell equations.

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arXiv ID2112.11550 (version 2)

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CitationSilvia Jim\'enez Bola\~nos, Thuyen Dang, Yuliya Gorb. "Homogenization of a non-linear strongly coupled model of magnetorheological fluids." arXiv:2112.11550 (2021). https://pith.science/paper/K7RQA5SV

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,375 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.08 · mentions code or data availability 0.01.

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This paper concerns the rigorous periodic homogenization for a non-linear strongly coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid. The fluid drags the particles, thus alters the magnetic field. Vice versa, the magnetic field acts on the particles, which in turn affect the fluid via the no-slip boundary condition. As the size of the particles approaches zero, it is shown that the suspension's behavior is governed by a generalized magnetohydrodynamic system, where the fluid is modeled by a stationary Navier-Stokes system, while the magnetic field is modeled by Maxwell equations. A corrector result from the theory of two-scale convergence allows us to obtain the limit of the product of several weakly convergent sequences, where the div-curl lemma, which is a typical tool in these types of problems, is not applicable.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	This paper concerns the rigorous periodic homogenization for a non-linear strongly coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid.	contribution 0.89	0.72	0.07	asserted 0.83
s1	The fluid drags the particles, thus alters the magnetic field.	background 0.98	0.13	0.02	asserted 1.00
s2	Vice versa, the magnetic field acts on the particles, which in turn affect the fluid via the no-slip boundary condition.	background 0.98	0.17	0.03	asserted 1.00
s3	As the size of the particles approaches zero, it is shown that the suspension's behavior is governed by a generalized magnetohydrodynamic system, where the fluid is modeled by a stationary Navier-Stokes system, while the magnetic field is modeled by Maxwell equations.	result 1.00	0.90	0.86	asserted 1.00
s4	A corrector result from the theory of two-scale convergence allows us to obtain the limit of the product of several weakly convergent sequences, where the div-curl lemma, which is a typical tool in these types of problems, is not applicable.	method 0.92	0.85	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Original abstract

This paper concerns the rigorous periodic homogenization for a non-linear strongly coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid. The fluid drags the particles, thus alters the magnetic field. Vice versa, the magnetic field acts on the particles, which in turn affect the fluid via the no-slip boundary condition. As the size of the particles approaches zero, it is shown that the suspension's behavior is governed by a generalized magnetohydrodynamic system, where the fluid is modeled by a stationary Navier-Stokes system, while the magnetic field is modeled by Maxwell equations. A corrector result from the theory of two-scale convergence allows us to obtain the limit of the product of several weakly convergent sequences, where the div-curl lemma, which is a typical tool in these types of problems, is not applicable.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Builds on 1 paper

This paper is a counterpart of our previous works [ref] , where we carried out the rigorous periodic homogenization of a weakly (one-way) coupled non-linear system modeling a non-dilute suspension of magnetizable particles in a viscous Newtonian fluid.

Global gradient estimate for a divergence problem and its application to the homogenization of a magnetic suspension · Introduction · 0.83

Uses the method or tool of 4 papers

Adapting the construction in [ref] (see also [ref] , [ref] , [ref] , [ref] ) and using <ref>, we obtain

Effective viscosity of random suspensions without uniform separation · Existence and a priori estimate for the fine-scale pressure · 0.96
Adapting the construction in [ref] (see also [ref] , [ref] , [ref] , [ref] ) and using <ref>, we obtain

Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains · Existence and a priori estimate for the fine-scale pressure · 0.96
Adapting the construction in [ref] (see also [ref] , [ref] , [ref] , [ref] ) and using <ref>, we obtain

Quantitative homogenization theory for random suspensions in steady Stokes flow · Existence and a priori estimate for the fine-scale pressure · 0.96

Cites as background 6 papers

For details and information about the manifestations of the one-way coupling (as well as of the full coupling), its applications, and further literature on the subject, we refer the reader to [ref] and references cited therein.

Global gradient estimate for a divergence problem and its application to the homogenization of a magnetic suspension · Introduction · 0.97
Starting with the seminal work of Einstein on the effective viscosity of a suspension [ref] , there have been numerous studies on this subject, ranging from formal asymptotic analysis such as [ref] to rigorous analysis, e.g. [ref] and references cited therein.

On Einstein's effective viscosity formula · Introduction · 1.00
Starting with the seminal work of Einstein on the effective viscosity of a suspension [ref] , there have been numerous studies on this subject, ranging from formal asymptotic analysis such as [ref] to rigorous analysis, e.g. [ref] and references cited therein.

Quantitative homogenization theory for random suspensions in steady Stokes flow · Introduction · 1.00

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