Journal ArticleDOI
Stress moments of nearly touching spheres in low Reynolds number flow
M. R. Corless,David J. Jeffrey +1 more
TLDR
In this paper, it was shown that the reciprocal theorem requires unexpected relations between the newly found singularities and ones found previously, and that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets.Abstract:
If two spheres are nearly touching, and the flow around them is governed by the Stokes equations, the integral moments of the surface stress are singular functions of the gap width. The method used previously to calculate the singular terms in the zeroth moment (the force) and the antisymmetric first moment (the couple) is extended here to calculate the singular terms in the symmetric first moment (the stresslet) for motions perpendicular to the line of centres. It is shown that the reciprocal theorem requires unexpected relations between the newly found singularities and ones found previously. It is also shown that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets. The series expressions then become valid for all separations of the spheres.read more
Citations
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Journal ArticleDOI
The calculation of the low Reynolds number resistance functions for two unequal spheres
TL;DR: In this paper, a tabulation of all of the two-sphere resistance functions at present needed in investigations of the mechanics of suspensions is presented, where each function is calculated first as a series in inverse powers of the center-to-center separation and then, in order to handle the singular behavior caused by lubrication forces, the asymptotic form which the function takes when the spheres are close is combined with the series expansion into a single expression valid for all separations of the spheres.
Journal ArticleDOI
Image representation of a spherical particle near a hard wall
TL;DR: In this paper, the motion of a spherical colloidal particle suspended in a moving fluid near a planar hard wall or free surface is considered, and a general expression for the flow field is obtained in terms of a set of force multipoles induced on the particle and on its mirror image in the bounding surface.
Journal ArticleDOI
Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particles
Chingyi Chang,Robert L. Powell +1 more
TL;DR: In this paper, Stokesian dynamics is used to simulate the dynamics of a monolayer of a suspension of bimodally distributed spherical particles subjected to simple shearing flow.
Journal ArticleDOI
Dynamics of concentrated suspensions of non-colloidal particles in Couette flow
Kyongmin Yeo,Martin R. Maxey +1 more
TL;DR: In this paper, a simulation of concentrated suspensions of O(1000) particles in a Couette flow at zero Reynolds number is performed with the goal of determining the wall effects on concentrated suspensions.
Journal ArticleDOI
Stokesian dynamics simulations of particle trajectories near a plane
TL;DR: In this article, the trajectories of spherical particles close to a plane in shear flow are computed, taking into account lubrication forces and many body hydrodynamic interactions between spheres, and between spheres and the plane.
References
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Journal ArticleDOI
The stress system in a suspension of force-free particles
TL;DR: In this paper, the authors consider the properties of the bulk stress in a suspension of non-spherical particles, on which a couple (but no force) may be imposed by external means, immersed in a Newtonian fluid.
Journal ArticleDOI
Slow viscous motion of a sphere parallel to a plane wall—I Motion through a quiescent fluid
TL;DR: Asymptotic solutions of the Stokes equations are derived for both the translational and rotational motions of a sphere parallel to a plane wall bounding a semi-infinite, quiescent, viscous fluid in the limit where the gap width tends to zero as discussed by the authors.
Journal ArticleDOI
Slow viscous motion of a sphere parallel to a plane wall—II Couette flow
TL;DR: Using bipolar co-ordinates, an exact solution of Stokes equations was obtained for the translational and rotational velocities of a neutrally buoyant sphere moving in proximity to a single plane wall under the influence of a simple shearing flow as mentioned in this paper.
Journal ArticleDOI
Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow
David J. Jeffrey,Y. Onishi +1 more
TL;DR: Two unequal rigid spheres are immersed in unbounded fluid and are acted on by externally applied forces and couples, which can be described by a set of linear relations between, on the one hand, the forces and spouses exerted by the spheres on the fluid and the translational and rotational velocities of the spheres.
Journal ArticleDOI
On the slow motion of a sphere parallel to a nearby plane wall
M. E. O'Neill,Keith Stewartson +1 more
TL;DR: In this paper, a matched asymptotic expansion technique was used to obtain the Stokes flow solution for a rigid sphere of radius a moving uniformly in a direction parallel to a fixed infinite plane wall when the minimum clearance between the sphere and the plane is very much less than a.
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