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Unsteady motion of two solid spheres in Stokes flow
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10.1063/1.2363351
/content/aip/journal/pof2/18/10/10.1063/1.2363351
http://aip.metastore.ingenta.com/content/aip/journal/pof2/18/10/10.1063/1.2363351
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic of the problem and coordinate system.

Image of FIG. 2.
FIG. 2.

Comparison of the method of reflections and the exact solution for two solid particles moving steadily with equal constant velocities parallel to their line of centers.

Image of FIG. 3.
FIG. 3.

Two particles moving with the same velocity perpendicularly to their line of centers.

Image of FIG. 4.
FIG. 4.

The forces produced by the disturbed flow for the case of two particles moving perpendicularly to their line of centers compared with the forces due to the motion of an isolated sphere, , , and . In some of the plots, the dashed lines are indistinguishable from the solid line.

Image of FIG. 5.
FIG. 5.

Two particles moving with the same velocity along their line of centers.

Image of FIG. 6.
FIG. 6.

The forces produced by the disturbed flow for the case of two particles in the Stokes flow moving along their line of centers compared with the forces due to the motion of an isolated sphere, , , and . In some of the plots, the dashed lines are indistinguishable from the solid line.

Image of FIG. 7.
FIG. 7.

Sphere velocity for the problem of two spheres moving perpendicularly to their line of centers in a gravitational field compared with the motion of an isolated sphere, , , , and . Solid line: using the history and added mass terms for two spheres. Dashed-dotted line: using the Stokes drag for two spheres and the history and added mass terms for an isolated sphere. Dotted line: motion of an isolated sphere.

Image of FIG. 8.
FIG. 8.

Sphere velocity for the problem of two spheres moving along their line of centers in a gravitational field compared with the motion of an isolated sphere, , , , and . Solid line: using the history and added mass terms for two spheres. Dashed-dotted line: using the Stokes drag for two spheres and the history and added mass terms for an isolated sphere. Dotted line: motion of an isolated sphere.

Image of FIG. 9.
FIG. 9.

Complex plane contour for the calculation of the inverse Laplace transform.

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/content/aip/journal/pof2/18/10/10.1063/1.2363351
2006-10-27
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Unsteady motion of two solid spheres in Stokes flow
http://aip.metastore.ingenta.com/content/aip/journal/pof2/18/10/10.1063/1.2363351
10.1063/1.2363351
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