Rheology of a dilute suspension of axisymmetric Brownian particles

Brenner, Howard

doi:10.1016/0301-9322(74)90018-4

Cited by 568 publications

(418 citation statements)

References 52 publications

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“…(4.40) is a delicate matter. In [33] we demonstrated that in the limit of long times (that is in the limit ω → 0 used in this work) all random walks are asymptotically closed (that is, the Brownian trajectory in this limit becomes very much the same as known for ring polymers) 9 . Since the result, Eq.…”

Section: Reparametrization Invariance and Vortex-vortex Interactionsmentioning

confidence: 73%

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

Ballard¹,

Kholodenko²

2009

Physica A: Statistical Mechanics and its Applications

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Although in the case of polymer solutions the existence of hydrodynamic screening has been theoretically established some time ago, use of the same methods for suspensions of hard spheres thus far have failed to produce similar results. In this work we reconsider this problem. Using superposition of topological and London-style qualitative arguments we prove the existence of screening in hard sphere suspensions. Even though some of these arguments were employed initially for treatments of superconductivity and superfluidity, we find analogs of these phenomena in nontraditional settings such as in colloidal suspensions, turbulence, magnetohydrodynamics, etc. In particular, in suspensions we demonstrate that the hydrodynamic screening is an exact analog of Meissner effect in superconductors. The extent of screening depends on the volume fraction of hard spheres. The zero volume fraction limit corresponds to the normal state. The case of finite volume fractions-to the mixed state typical for superconductors of the second kind with such a state becoming fully "superconducting" at the critical volume fraction ϕ * for which the (zero frequency) relative viscosity η(relative) diverges. Brady and, independently, Bicerano et al using scaling-type arguments predicted that for ϕ close to ϕ * the viscosity η(relative) behaves as C(1−ϕ/ϕ * ) −2 with C being some constant. Their prediction is well supported by experimental data. In this work we explain such a behavior of viscosity in terms of a topological-type transition which mathematically can be made isomorphic to the more familiar Bose-Einstein condensation transition. Because of this, the results and methods of this work are not limited to suspensions. In the concluding section we describe other applications ranging from turbulence and magnetohydrodynamics to high temperature superconductors and QCD, etc.

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Section: Reparametrization Invariance and Vortex-vortex Interactionsmentioning

confidence: 73%

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

Ballard¹,

Kholodenko²

2009

Physica A: Statistical Mechanics and its Applications

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“…particles with the same density as the carrier uid, are convected with the uid velocity. Brenner [2] showed that only ve dimensionless material constants are required to fully describe the hydrodynamic e ects of inertia-free particles with axial and fore-aft symmetry. He tabulated these constants for spheroids, long slender axisymmetric bodies and dumbbells, all of which can be derived analytically.…”

Section: Constitutive Equations Of Ber Suspensionsmentioning

confidence: 99%

“…Brenner [2] provided analytical solutions for steady shear and extensional ows. Okagawa et al [3] gave analytical solution to dilute suspension of non-Brownian rigid rodlike and disklike particles subjected to a simple shear ow.…”

Section: Introductionmentioning

confidence: 99%

On the orientation dynamics and viscoelasticity of Brownian rigid disklike particles suspended in a shear flow

Moosaie

2017

Scientia Iranica

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Abstract. In this paper, numerical simulations are employed to study the orientation behavior of a dilute suspension of Brownian rigid disklike particles in a simple shear ow. Also, the viscoelasticity of such a suspension is analyzed by considering the stress budget of the two-phase material. A direct Monte-Carlo simulator as well as the moment approximation approaches with two di erent closure models are used to produce the data. Results are compared by available experimental and analytical data, and a very good agreement is established. After the validation of the simulators, the results are presented and discussed. Di erent P eclet numbers and shape factors of particles are considered and their e ects on various quantities are presented, e.g. particle orientations in space, viscous and elastic contributions to the non-Newtonian stress tensor, etc.

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“…This approach has begun with the seminal work of Einstein [17,18] in 1906 and 1911 on the effective viscosity of a dilute suspension of rigid spheres and, since then, it has been completed by numerous works (Batchelor [3,4], Brenner [9], Jeffrey & Acrivos [32], Russel [44], Davis & Acrivos [14]) related to the framework of dilute suspensions. From the prediction point of view, most of these works deal with weak solid concentrations in which pairwise interactions lead the behaviour of the suspensions.…”

Section: On the Determination Of The Behaviour Of Dilute And Dense Sumentioning

confidence: 99%

Towards the simulation of dense suspensions: a numerical tool

Faure¹,

Maury²,

Takahashi³

2009

ESAIM: Proc.

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Abstract. We present a numerical tool which aims at investigating the rheology of dense suspensions of entities such as spheres, red blood cells, polymer chains, or any kind of rigid or deformable bodies, in a viscous fluid. We shall pay a special attention to the short-range interactions between those entities (contact forces, lubrication forces). As for the fluid itself, our strategy consists in avoiding the direct and costly solution of the Stokes equations by integrating only the interaction forces which are likely to play a significant role in the overall behaviour of the suspension, in the spirit of Stokesian Dynamics. We present some preliminary results for suspensions of spheres, Red Blood Cells, and polymer-like chains.Résumé. Nous présentons un outil numérique permettant d'étudier la rhéologie de suspensions denses d'entités telles que des sphères, des globules rouges, des chaînes de polymère et, d'une manière générale, des objets rigides ou déformables dans un fluide visqueux. Nous portons une attention particulière aux interactionsà courte distance entre ces entités (forces de contact, forces de lubrification). En ce qui concerne le fluide lui-même, notre stratégie consisteàéviter le calcul direct (et coûteux) de la solution deséquations de Stokes, en déterminant uniquement les forces d'interaction qui jouent un rôle significatif dans le comportement général de la suspension, dans l'esprit de la méthode dite de Dynamique Stokesienne. Nous présentons quelques résultats préliminaires pour des suspensions de sphères, de globules rouges, et de chaînes de polymère.

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Rheology of a dilute suspension of axisymmetric Brownian particles

Cited by 568 publications

References 52 publications

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

Topological character of hydrodynamic screening in suspensions of hard spheres: An example of universal phenomenon

On the orientation dynamics and viscoelasticity of Brownian rigid disklike particles suspended in a shear flow

Towards the simulation of dense suspensions: a numerical tool

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