PARTICLE MOTIONS IN SHEARED SUSPENSIONS III.: FURTHER OBSERVATIONS ON COLLISIONS OF SPHERES

1955 ◽  
Vol 33 (5) ◽  
pp. 763-773 ◽  
Author(s):  
R. St. J. Manley ◽  
S. G. Mason
Keyword(s):  
Particle Separation ◽  
Colloidal Dispersions ◽  
Mirror Image ◽  
Equal Size ◽  
Air Bubbles ◽  
Rigid Spheres ◽  
Glass Spheres ◽  
Velocity Gradients ◽  
Image Separation ◽  
Sheared Suspensions

Two-body interactions between glass spheres of diameters a1 and a2 caused by velocity gradients vary with a1/a2. When 1 < a1/a2 < 2, well-defined collisions similar to those previously reported for spheres of equal size can be observed. Fair agreement is found between the experimentally observed and calculated collision frequencies over a range of particle concentrations and velocity gradients. When a1/a2 > 2 the particles are separated at all times and the phenomena of interaction are more complex. Single air bubbles rotate at the same angular velocity as rigid spheres. When two air bubbles of equal size are brought into collision a doublet is formed; instead of the mirror-image separation observed with neutral rigid spheres, the doublet continues to rotate for as many as 60 rotations before coalescence occurs. Less frequently a doublet with distinct particle separation is observed. Periods of rotation of both types of doublet and certain details of the rotational orbit of a doublet of touching air bubbles have been measured and compared with values predicted from Jeffery's theoretical equations for rigid ellipsoids. Apart from their intrinsic interest, the phenomena described are of importance in theories of viscosity and coagulation of suspensions and colloidal dispersions.

Particle motions in sheared suspensions XXII: Interactions of rigid spheres (experimental)

1967 ◽  
Vol 6 (3) ◽  
pp. 273-284 ◽  
Author(s):  
C. L. Darabaner ◽  
S. G. Mason
Keyword(s):  
Rigid Spheres ◽  
Sheared Suspensions

Application of the Edwards Model to Steric Stabilization of Nanoparticles

2003 ◽  
Vol 17 (15) ◽  
pp. 2791-2820 ◽  
Author(s):  
Jiunn-Ren Roan
Keyword(s):  
Large Particle ◽  
Colloidal Particles ◽  
Particle Separation ◽  
Colloidal Dispersion ◽  
Colloidal Dispersions ◽  
Repulsive Force ◽  
Steric Stabilization ◽  
Conformational Entropy ◽  
Standard Picture ◽  
Edwards Model

The Edwards model for polymers with excluded-volume interaction has been used to study steric stabilization of colloidal dispersions since Dolan and Edwards' work in 1975. Following the standard picture of steric stabilization since 1950s, Dolan and Edwards solved the model by treating the surfaces of colloidal particles as plane surfaces. Consequently, their result was also consistent with the standard picture: Reduction of conformational entropy of the adsorbed homopolymers results in a purely repulsive force that stabilizes the colloidal dispersion. Recently the Edwards model was solved without treating the spherical particle surfaces as plane surfaces. It was found that, contrary to the standard picture, the conformational entropy indeed increases and the force between particles may be either purely attractive or attractive at large particle-particle separation, repulsive at intermediate separation, and again attractive at small separation. Thus, the standard picture of steric stabilization was challenged. This review summarizes this recent progress in the theory of steric stabilization of colloidal dispersions. Reconciliation between the standard picture and the recent result, and possible directions for further research are also discussed.

Dynamic simulation of suspensions of non-Brownian hard spheres

1996 ◽  
Vol 325 ◽  
pp. 53-77 ◽  
Author(s):  
D. I. Dratler ◽  
W. R. Schowalter
Keyword(s):  
Hydrodynamic Model ◽  
Short Range ◽  
Hard Spheres ◽  
Particle Separation ◽  
Repulsive Force ◽  
Stokesian Dynamics ◽  
Rigid Spheres ◽  
Dense Suspensions ◽  
Dynamics Simulations ◽  
Repulsive Forces

In this work, we investigate the suitability of models based solely on continuum hydrodynamics for Stokesian Dynamics simulations of sheared suspensions of non-Brownian hard spheres. The suspensions of interest consist of monolayers of uniform rigid spheres subjected to a linear shear field. Areal fractions ranged from ϕa = 0.2 to 0.6. For these suspensions, two sets of Stokesian Dynamics simulations were performed. For the first set, particle interactions were assumed to be strictly hydrodynamic in nature. These simulations are analogous to those of Brady & Bossis (1985) and Chang & Powell (1993). For the second set of simulations, particles were subjected to both hydrodynamic and short-range repulsive forces. The repulsion serves as a qualitative model of non-hydrodynamic effects important when particle separation distances are small. Results from both sets of simulations were found to be within the range of established experimental data for viscosities of suspensions. However, simulations employing the pure hydrodynamic model lead to very small separation distances between particles. These small separations give rise to particle overlaps that could not be eliminated by time-step refinement. The instantaneous number of overlaps increased with density and typically exceeded the number of particles at the highest densities considered. More critically, for very dense suspensions the simulations failed to approach a long-time asymptotic state. For simulations employing a short-range repulsive force, these problems were eliminated. The repulsion had the effect of preventing extremely small separations, thereby eliminating particle overlaps. At high concentrations, viscosities computed using the two methods are significantly different. This suggests that the dynamics of particles near contact have a significant impact on bulk properties. Furthermore, the results suggest that a critical aspect of the physics important at small particle separation distances is missing from the pure hydrodynamic model, making it unusable for computing microstructures of dense suspensions. In contrast, simulations employing a short-range repulsive force appear to produce more realistic microstructures, and can be performed even at very high densities.

Ordered aggregates of particles in shear flow

1967 ◽  
Vol 300 (1463) ◽  
pp. 421-441 ◽  
Keyword(s):  
Physical Models ◽  
Low Velocity ◽  
Rigid Spheres ◽  
Motion Equations ◽  
Velocity Gradients ◽  
Rigid Rods ◽  
Particle Aggregates ◽  
High Gradients ◽  
Gap Width ◽  
Creeping Motion

A theoretical and experimental investigation was made into the behaviour of ordered aggregates of rigid spheres, disks and rods in plane Couette flow. Chains of spheres formed in an electric field behaved like rigid rods, a result which was predicted theoretically on the basis of the creeping motion equations and lubrication theory. However, such chains broke at high velocity gradients possibly from cavitation of the liquid between the spheres. For chains with non-zero gap width between spheres it was shown theoretically that one would expect periodic stretching and progressive bending. This periodic stretching was observed experimentally. Chains of spheres held together by liquid menisci behaved like flexible threads and formed disordered aggregates at high gradients. Aggregates of disks (rouleaux) behaved like deformable rods and were easily broken as the disks slid apart. Symmetrical but non-linear aggregates of spheres rotated like single spheres at low velocity gradients. The particle aggregates considered in this paper provide interesting physical models of threads, rouleaux of red blood cells and other flexible particles.

Particle motions in sheared suspensions XXI: Interactions of rigid spheres (theoretical)

1967 ◽  
Vol 6 (3) ◽  
pp. 264-273 ◽  
Author(s):  
S. Wakiya ◽  
C. L. Darabaner ◽  
S. G. Mason
Keyword(s):  
Rigid Spheres ◽  
Sheared Suspensions

Air entrainment during impact of droplets on liquid surfaces

2013 ◽  
Vol 726 ◽  
Author(s):  
Tuan Tran ◽  
Hélène de Maleprade ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Impact Velocity ◽  
Air Entrainment ◽  
Solid Surfaces ◽  
Short Time Scale ◽  
Air Bubbles ◽  
Rigid Spheres ◽  
Short Time ◽  
The Impact ◽  
Energy Argument ◽  
Liquid Surfaces

AbstractWe study drop impact on a deep pool of the same fluid, with an emphasis on the air layer trapped under the droplets from its formation to its rupture. The penetration velocity of the air layer at a very short time scale prior to its rupture is shown, using an energy argument and experimental verification, to be one-half of the impact velocity. We then deduce the dependence of the rupture position on the liquid viscosity and the impact velocity. We show that the volume of the resulting air bubbles can be related to both those resulting from droplets impacting on solid surfaces and those resulting from rigid spheres impacting on liquid surfaces.

Mirror-image stimulation.

1968 ◽  
Vol 70 (6, Pt.1) ◽  
pp. 782-793 ◽  
Author(s):  
Gordon G. Gallup
Keyword(s):  
Mirror Image
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