The slow motion of two identical arbitrarily oriented spheres through a viscous fluid

Goldman, A.J.; Cox, R. G.; Brenner, Howard

doi:10.1016/0009-2509(66)85036-4

Cited by 200 publications

(139 citation statements)

References 15 publications

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“…The terminal velocity of an Isolated, horizontally oriented spheroid was used to scale both -U and -wya. In ., a both figures the solid line is indistinguishable from the result for , , spheres (Goldman, Cox and Brenner 1966). The dependence on the aspect ratio is qualitatively similar to that found In the previous subsection.…”

Section: Sedimentation Of Two Horizontally Oriented Spheroidssupporting

confidence: 78%

Sedimentation of Two Arbitrarily Oriented Spheroids in a Viscous Fluid.

Kim¹

1984

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Section: Sedimentation Of Two Horizontally Oriented Spheroidssupporting

confidence: 78%

Sedimentation of Two Arbitrarily Oriented Spheroids in a Viscous Fluid.

Kim¹

1984

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“…The Blake's Green function relates the flow at r i to a unit point force applied at r j in the bounded fluid medium. One notes that the no-slip boundary condition on the plane of the wall is satisfied by the image system [38][39][40][41][42][43][44], consisting of the original Stokeslet G(r), the image Stokeslet G(R), a Doublet G D (R) and a source Doublet G SD (R). If one uses the tensor G wall given by Eq.…”

Section: Hydrodynamic Interactions Near a No-slip Surfacementioning

confidence: 99%

Hydrodynamic effects in driven soft matter

et al. 2006

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Recent theoretical works exploring the hydrodynamics of soft material in non-equilibrium situations are reviewed. We discuss the role of hydrodynamic interactions for three different systems: i) the deformation and orientation of sedimenting semiflexible polymers, ii) the propulsion and force-rectification with a nano-machine realized by a rotating elastic rod, and iii) the deformation of a brush made of grafted semiflexible polymers in shear flows. In all these examples deformable polymers are subject to various hydrodynamic flows and hydrodynamic interactions. Perfect stiff nano-cylinders are known to show no orientational effects as they sediment through a viscous fluid, but it is the coupling between elasticity and hydrodynamic torques that leads to an orientation perpendicular to the direction of sedimentation. Likewise, a rotating stiff rod does not lead to a net propulsion in the Stokes limit, but if bending is allowed an effective thrust develops whose strength and direction is independent of the sense of rotation and thus acts as a rectification device. Lastly, surface-anchored polymers are deformed by shear flows, which modifies the effective hydrodynamic boundary condition in a non-linear fashion. All these results are obtained with hydrodynamic Brownian dynamics simulation techniques, as appropriate for dilute systems. Scaling analyses are presented when possible. The common theme is the interaction between elasticity of soft matter and hydrodynamics, which can lead to qualitatively new effects.

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“…The theory was subsequently applied to a pair of particles of various regular shapes [14][15][16][17][18][19][20] . To this one should add many earlier studies of the collective dynamics of suspensions made of ellipsoids [21][22][23][24][25] .…”

Section: Introductionmentioning

confidence: 99%