Note: Elongational Flows of a Dilute Suspension of Spheroidal Particles

1987 ◽  
Vol 31 (5) ◽  
pp. 423-424 ◽  
Author(s):  
Howard Brenner
Keyword(s):  
Elongational Flows ◽  
Dilute Suspension

Elongational Flows of a Dilute Suspension of Spheroidal Particles

1986 ◽  
Vol 30 (4) ◽  
pp. S75-S89 ◽  
Author(s):  
C. J. Goh ◽  
N. Phan‐Thien ◽  
J. D. Atkinson
Keyword(s):  
Elongational Flows ◽  
Dilute Suspension

Dilute suspension of high inertia particles in the turbulent flow near the wall

2002 ◽  
Vol 14 (3) ◽  
pp. 1042-1055 ◽  
Author(s):  
Y. A. Sergeev ◽  
R. S. Johnson ◽  
D. C. Swailes
Keyword(s):  
Turbulent Flow ◽  
Dilute Suspension

The stress generated in a non-dilute suspension of elongated particles by pure straining motion

1971 ◽  
Vol 46 (4) ◽  
pp. 813-829 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Theoretical Formula ◽  
Rigid Sphere ◽  
Cross Sectional ◽  
Outer Flow ◽  
Rigid Particles ◽  
Bulk Stress ◽  
Order Of Magnitude ◽  
Sectional Plane ◽  
Dilute Suspension ◽  
A Minor

In a pure straining motion, elongated rigid particles in suspension are aligned parallel to the direction of the greatest principal rate of extension, provided the effect of Brownian motion is weak. If the suspension is dilute, in the sense that the particles are hydrodynamically independent, each particle of length 2l makes a contribution to the bulk deviatoric stress which is of roughly the same order of magnitude as that due to a rigid sphere of radius l. The fractional increase in the bulk stress due to the presence of the particles is thus equal to the concentration by volume multiplied by a factor of order l2/b2, where 2b is a measure of the linear dimensions of the particle cross-section. This suggests that the stress due to the particles might be relatively large, for volume fractions which are still small, with interesting implications for the behaviour of polymer solutions. However, dilute-suspension theory is not applicable in these circumstances, and so an investigation is made of the effect of interactions between particles. It is assumed that, when the average lateral spacing of particles (h) satisfies the conditions b [Lt ] h [Lt ] l, the disturbance velocity vector is parallel to the particles and varies only in the cross-sectional plane. The velocity near a particle is found to have the same functional form as for an isolated particle, and the modification to the outer flow field for one particle is determined by replacing the randomly placed neighbouring particles by an equivalent cylindrical boundary. The resulting expression for the contribution to the bulk stress due to the particles differs from that for a dilute suspension only in a minor way, viz. by the replacement of log 2l/b by log h/b, and the above suggestion is confirmed. The relative error in the expression for the stress is expected to be of order (log h/b)−1. Some recent observations by Weinberger of the stress in a suspension of glass-fibre particles for which 2l/h = 7·4 and h/2b = 7·8 do show a particle stress which is much larger than the ambient-fluid stress, although the theoretical formula is not accurate under these conditions.

Hydrodynamic shielding induced stability of zipping macromolecules in elongational flows

1994 ◽  
Vol 100 (8) ◽  
pp. 6055-6061 ◽  
Author(s):  
U. S. Agarwal ◽  
R. A. Mashelkar
Keyword(s):  
Elongational Flows

Scaling behavior of dilute polymer solutions in elongational flows

1985 ◽  
Vol 55 (2) ◽  
pp. 201-203 ◽  
Author(s):  
Y. Rabin ◽  
F. S. Henyey ◽  
R. K. Pathria
Keyword(s):  
Polymer Solutions ◽  
Scaling Behavior ◽  
Dilute Polymer Solutions ◽  
Elongational Flows

scholarly journals Hydrodynamic diffusion of a sphere sedimenting through a dilute suspension of neutrally buoyant spheres

1992 ◽  
Vol 236 ◽  
pp. 513-533 ◽  
Author(s):  
Robert H. Davis ◽  
N. A. Hill
Keyword(s):  
Reasonable Agreement ◽  
Trajectory Analysis ◽  
Heavy Particle ◽  
Small Reynolds Number ◽  
Mean Velocity ◽  
Dilute Suspension ◽  
Explicit Formulae ◽  
The Mean ◽  
Neutrally Buoyant ◽  
Large Peclet Number

The motion of a heavy sphere sedimenting through a dilute background suspension of neutrally buoyant spheres is analysed for small Reynolds number and large Péclet number. For this particular problem, it is possible not only to calculate the mean velocity of the heavy particle, but also the variance of the velocity and the coefficient of hydrodynamic diffusivity. Pairwise, hydrodynamic interactions between the heavy sphere and the background sphere are considered exactly using volume integrals and a trajectory analysis. Explicit formulae are given for the two limiting cases when the radius of the heavy sphere is much greater and much less than that of the background spheres, and numerical results are given for moderate size ratios. The mean velocity is relatively insensitive to the ratio of the radius of the background spheres to that of the heavy sphere, unless this ratio is very large, whereas the hydrodynamic diffusivity increases rapidly as the radius ratio is increased. The predictions are in reasonable agreement with the results of falling-ball rheometry experiments.

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