Self-diffusion of spheres in a concentrated suspension

Beenakker, C. W. J.; Mazur, Péter

doi:10.1016/0378-4371(83)90061-4

Cited by 195 publications

(139 citation statements)

References 21 publications

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“…85 In the companion paper, 50 we have successfully applied Eq. (61) to approximate the bidisperse partial hydrodynamic functions H α β (q) with the monodisperse δγ scheme 47,48 up to φ = 0.4.…”

Section: A Suspension Propertiesmentioning

confidence: 99%

“…There are two approaches to treat HIs: one is akin to the diagrammatic methods in liquid state theories. 46 For example, the δγ-scheme developed by Beenakker and Mazur [47][48][49] incorporates manybody HIs by resuming an infinite subset of the hydrodynamic scattering series from all particles in the suspension. In a companion paper, 50 we introduced a semi-empirical extension of the original monodisperse δγ-scheme to approximate the partial hydrodynamic functions of polydisperse suspensions.…”

Section: Introductionmentioning

confidence: 99%

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Short-time transport properties of bidisperse suspensions and porous media: A Stokesian dynamics study

Wang

Brady

2015

The Journal of Chemical Physics

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We present a comprehensive computational study of the short-time transport properties of bidisperse hard-sphere colloidal suspensions and the corresponding porous media. Our study covers bidisperse particle size ratios up to 4 and total volume fractions up to and beyond the monodisperse hard-sphere close packing limit. The many-body hydrodynamic interactions are computed using conventional Stokesian Dynamics (SD) via a Monte-Carlo approach. We address suspension properties including the short-time translational and rotational self-diffusivities, the instantaneous sedimentation velocity, the wavenumber-dependent partial hydrodynamic functions, and the high-frequency shear and bulk viscosities and porous media properties including the permeability and the translational and rotational hindered diffusivities. We carefully compare the SD computations with existing theoretical and numerical results. For suspensions, we also explore the range of validity of various approximation schemes, notably the pairwise additive approximations with the Percus-Yevick structural input. We critically assess the strengths and weaknesses of the SD algorithm for various transport properties. For very dense systems, we discuss in detail the interplay between the hydrodynamic interactions and the structures due to the presence of a second species of a different size. C 2015 AIP Publishing LLC. [http://dx

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Section: A Suspension Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Short-time transport properties of bidisperse suspensions and porous media: A Stokesian dynamics study

Wang

Brady

2015

The Journal of Chemical Physics

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“…For hard spheres, the well-established result is H 1 = -1.831 and H 2 = +0.71 [5,6,4]. Hard sphere suspensions can be considered to be dilute both with respect to particle hydrodynamics and microstructure as well.…”

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confidence: 99%

Enhanced structural correlations accelerate diffusion in charge-stabilized colloidal suspensions

1999

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Theoretical calculations for colloidal charge-stabilized suspensions and hard sphere suspensions show that hydrodynamic interactions yield a qualitatively different particle concentration dependence of the short-time self-diffusion coefficient. The effect, however, is numerically small and hardly accessible by conventional light scattering experiments.Applying multiple-scattering decorrelation equipment and a careful data analysis we show that the theoretical prediction for charged particles is in agreement with our experimental results from aqueous polystyrene latex suspensions.

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“…Indeed, two-and three-sphere interactions have been shown (in the context of diffusion) to give contributions of second power in the concentration of comparable magnitude. 15 …”

Section: Discussionmentioning

confidence: 99%

On the Smoluchowski paradox in a sedimenting suspension

Beenakker¹,

Mazur²

1985

The Physics of Fluids

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It is shown, by explicit calculation, that the influence of a plane wall supporting the Suspension on the Sedimentation velocity is such that the convergence problems of this quantity encountered in an unbounded Suspension do not occur-even in the limit of an infinitely distant wall. l. INTRODUCTIONThe motion of a particle in a viscous fluid causes a disturbance of the fluid flow which falls off very slowly with increasing distance to the particle, in fact only with the inverse first power of the distance. As a consequence, the influence of Container walls on properties of suspensions can in certain cases not be neglected, even if the Container is very large. An example, which forms a dramatic Illustration, is the divergency of the velocity of Sedimentation in an unbounded Suspension. This paradoxical Situation (which, first noticed in 1911 by Smoluchowski,' has been referred to äs the Smoluchowski paradox 2 ) has received considerable attention. 2 " 9 In 1972, Batchelor 6 introduced an ingenious argument to resolve the difficulties, which has since become generally accepted-although not without controversy. 10 The argument of Batchelor (to which we shall return) is based on general considerations of a physical nature and not on an explicit evaluation of the influence of Container walls. As a matter of fact, such an explicit calculation woulduntil recently-not have been possible, because not enough was known about the interaction of particles via the fluid (the so-called hydrodynamic interaction} in the presence of a boundary wall.It is the purpose of this note to present a explicit calculation of the Sedimentation velocity for the most simple case: a dilute homogeneous layer of spherical particles sedimenting towards a plane wall, in an otherwise unbounded fluid. Our calculation is based on results from a study by van Saarloos and the authors 11 of the hydrodynamic interactions between spheres and a wall. In the paper referred to, expressions for the mobility tensors of the spheres were obtained by an extension of a method developed previously for an unbounded fluid. 12 The results for the mobilities, äs far äs necessary for our purpose, are given in See. II. In See. III we then calculate the (average) Sedimentation velocity to linear order in the concentration of the suspended spheres, at a point sufficiently far from the wall supporting the fluid. A discussion follows in See. IV. II. RESULTS FROM THE HYDRODYNAMIC ANALYSISWe consider the motion of N identical spherical particles with radius a in an incompressible fluid with viscosity 77, which is bounded by an infinite wall in the plane z = 0. The centers of the spheres have positions R, (/ = l, 2,... ./V) and lie in the half-spacez > 0. We describe the motion of the fluid by the linear quasistatic Stokes equation, supplemented by stick boundary conditions on the surfaces of the spheres and on the wall.The velocity U, of sphere / can be expressed äs a linear combination of the forces K, , exerted by the fluid on each sphere./,(We have assumed here that the flu...

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Self-diffusion of spheres in a concentrated suspension

Cited by 195 publications

References 21 publications

Short-time transport properties of bidisperse suspensions and porous media: A Stokesian dynamics study

Short-time transport properties of bidisperse suspensions and porous media: A Stokesian dynamics study

Enhanced structural correlations accelerate diffusion in charge-stabilized colloidal suspensions

On the Smoluchowski paradox in a sedimenting suspension

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