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Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: Sphere–wall and sphere–sphere interactions
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10.1122/1.4798625
/content/sor/journal/jor2/57/3/10.1122/1.4798625
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/3/10.1122/1.4798625

Figures

Image of FIG. 1.
FIG. 1.

Steady shear viscosity of the Newtonian fluid and shear-thinning PIB/PB/TD polymer solution. Solid curve is from Eq. (1) with η = 7.0 Pa s, λ = 0.36 s, and n = 0.59.

Image of FIG. 2.
FIG. 2.

Storage (G′, upper) and loss (G″, lower) moduli for the PIB/PB/TD polymer solution. Solid curves show results from the fit to Eqs. (2) and (3) with the parameters given in Table II .

Image of FIG. 3.
FIG. 3.

Sphere velocity versus sphere-to-wall separation for (a) titanium, (b) stainless steel, and (c) tungsten carbide spheres moving away from a wall. The suspending fluid is Newtonian. The solid curve is the solution to Stokes' equations derived by .

Image of FIG. 4.
FIG. 4.

Sphere velocity versus sphere-to-wall separation for (a) titanium, (b) stainless steel, and (c) tungsten carbide spheres moving toward a wall. The suspending fluid is Newtonian. The solid curve is the solution to Stokes' equations derived by .

Image of FIG. 5.
FIG. 5.

Sphere velocity versus sphere-to-wall separation for (a) titanium, (b) stainless steel, and (c) tungsten carbide spheres away from a wall. The suspending fluid is the PIB solution. The solid curve is the solution to Stokes' equations derived by .

Image of FIG. 6.
FIG. 6.

Sphere velocity versus sphere-to-wall separation for (a) titanium, (b) stainless steel, and (c) tungsten carbide spheres moving toward a wall. The suspending fluid is the PIB solution. The solid curve is the solution to Stokes' equations derived by .

Image of FIG. 7.
FIG. 7.

Vector plots of the velocity field around a 0.318 cm tungsten carbide sphere moving away from the top, solid surface at when the distance from the sphere center to the top is (a) 3.6 diameters, (b) 5.8 diameters, and (c) 12.6 diameters. The suspending fluid is the PIB solution. The top surface is located at the top edge of the image.

Image of FIG. 8.
FIG. 8.

Vector plots of the velocity field around a 0.318 cm tungsten carbide sphere moving toward the bottom of the container when the distance from the sphere center to the bottom is (a) 11.3 diameters, (b) 5.7 diameters, and (c) 3.9 diameters. The suspending fluid is the PIB solution. The bottom surface is located at the bottom edge of the image.

Image of FIG. 9.
FIG. 9.

Rate of approach ΔU = U − U for two (a) stainless steel and (b) tungsten carbide spheres with diameter d = 0.318 cm separated by distance s in the shear-thinning PIB solution. Vertical error bars are standard deviations of velocities, and horizontal error bars are standard deviations of separation distances.

Image of FIG. 10.
FIG. 10.

Average velocity 〈U〉 = (U + U)/2 for two (a) stainless steel and (b) tungsten carbide spheres with diameter d = 0.318 cm separated by distance s in the shear-thinning PIB solution. Vertical error bars are standard deviations of velocities, and horizontal error bars are standard deviations of separation distances. Solid curve is the low-Reynolds-number Newtonian result of .

Image of FIG. 11.
FIG. 11.

Rate of approach ΔU = U − U for two (a) stainless steel and (b) tungsten carbide spheres with diameter d = 0.476 cm separated by distance s in the shear-thinning PIB solution. Vertical error bars are standard deviations of velocities, and horizontal error bars are standard deviations of separation distances.

Image of FIG. 12.
FIG. 12.

Average velocity 〈U〉 = (U + U)/2 for two (a) stainless steel and (b) tungsten carbide spheres with diameter d = 0.476 cm separated by distance s in the shear-thinning PIB solution. Vertical error bars are standard deviations of velocities, and horizontal error bars are standard deviations of separation distances. Solid curve is the low-Reynolds-number Newtonian result of .

Image of FIG. 13.
FIG. 13.

Rate of approach as shown in Figs. 9(a) and 11(a) , renormalized as shown in Eq. (12) . Solid curve is Eq. (13) , from .

Image of FIG. 14.
FIG. 14.

Vector plot of the axisymmetric velocity field around two 0.476 cm tungsten carbide spheres sedimenting in the PIB solution, when center-to-center separation is (a) 4 diameters and (b) 1 diameter.

Tables

Generic image for table
TABLE I.

Properties of spherical particles.

Generic image for table
TABLE II.

Relaxation spectrum.

Generic image for table
TABLE III.

Terminal velocities and Deborah numbers.

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/content/sor/journal/jor2/57/3/10.1122/1.4798625
2013-04-09
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Axisymmetric sedimentation of spherical particles in a viscoelastic fluid: Sphere–wall and sphere–sphere interactions
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/3/10.1122/1.4798625
10.1122/1.4798625
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