Journal ArticleDOI
Slow motion of two spheres in a shear field
C. J. Lin,K. J. Lee,N. F. Sather +2 more
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The exact solution of the Stokes equations for the creeping motion of two spheres of arbitrary size and arbitrarily oriented with respect to a shear field is obtained by use of spherical bipolar co-ordinates as mentioned in this paper.Abstract:
The exact solution of the Stokes equations for the creeping motion of two spheres of arbitrary size and arbitrarily oriented with respect to a shear field is obtained by use of spherical bipolar co-ordinates. Numerical results are given for two special cases: (1) the free motion of two equal-sized spheres in simple shear flow and (2) the free motion of a sphere near a wall in the rotational shear field between two parallel disks rotating at different rates. The sphere trajectories calculated for the first of these problems are found to agree fairly well with those observed experimentally.read more
Citations
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The determination of the bulk stress in a suspension of spherical particles to order c 2
G. K. Batchelor,J. T. Green +1 more
TL;DR: In this article, an exact formula for the term of order c2 in the expression for the bulk stress in a suspension of force-free spherical particles in Newtonian ambient fluid, where c is the volume fraction of the spheres and c [Lt ] 1.8.
Journal ArticleDOI
The hydrodynamic interaction of two small freely-moving spheres in a linear flow field
G. K. Batchelor,J. T. Green +1 more
TL;DR: In this article, the authors provide a systematic and explicit description of the interaction between two rigid spheres that are relevant in a calculation of the mean stress in a suspension of spherical particles subjected to bulk deformation.
Journal ArticleDOI
Dynamic simulation of sheared suspensions. I. General method
Georges Bossis,John F. Brady +1 more
TL;DR: In this article, a general method for simulating the dynamical behavior of a suspension of particles which interact through both hydrodynamic and non-hydrodynamic forces is presented, and two different procedures for computing the interactions among particles are used.
Journal ArticleDOI
The microrheology of colloidal dispersions VII. Orthokinetic doublet formation of spheres
T.G.M. van de Ven,S.G Mason +1 more
TL;DR: In this article, a theory for doublet formation in dilute dispersions of spheres subjected to a simple shear flow of gradient G when Brownian motion can be neglected but taking account of both hydrodynamic and interparticle interactions is developed.
Journal ArticleDOI
Shear-induced dispersion in a dilute suspension of rough spheres
F. R. Da Cunha,E. J. Hinch +1 more
TL;DR: In this article, the authors calculate the change between the initial and final streamlines caused by roughness, and calculate the shear-induced diffusivity for both self-diffusion and down-gradient diffusion.
References
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Journal ArticleDOI
The slow motion of a sphere through a viscous fluid towards a plane surface
TL;DR: In this paper, bipolar co-ordinates are employed to obtain exact solutions of the equations of slow viscous flow for the steady motion of a solid sphere towards or away from a plane surface of infinite extent.
Journal ArticleDOI
A sphere in contact with a plane wall in a slow linear shear flow
TL;DR: An exact solution of the linearised Stokes flow equations was derived for a viscous flow about a fixed sphere in contact with a fixed plane wall when the fluid motion in the absence of the sphere is assumed to be a uniform linear shear flow as mentioned in this paper.
Journal ArticleDOI
The Motion of Two Spheres in a Viscous Fluid
Margaret Stimson,G. B. Jeffery +1 more
TL;DR: In this paper, the authors determined the motion set up in a viscous fluid at rest at infinity by two solid spheres (equal or unequal) moving with equal small constant velocities parallel to their line of centres.
Journal ArticleDOI
A Slow motion of viscous liquid caused by a slowly moving solid sphere
TL;DR: In this paper, a slow steady motion of incompressible viscous liquid bounded by an infinite rigid plane is generated when a rigid sphere of radius a moves steadily without rotation in a direction parallel to, and at a distance d from, the plane.
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