A finite solid cylinder rotates inside a larger, fluid-filled cylindrical casing. The Stokes equation is solved by an efficient method using domain decomposition, eigenfunction expansion, and collection. The resistive torque is found as a function of the geometric parameters. The torque due to the rotation of a finite cylinder in an infinite fluid is extrapolated.

1.
Brenner
H.
,
1962
, “
Effect of Finite Boundaries on the Stokes Resistance of an Arbitrary Particle
,”
Journal of Fluid Mechanics
, Vol.
12
, pp.
35
48
.
2.
Brenner
H.
, and
Sonshine
R. M.
,
1964
, “
Slow Viscous Rotation of a Sphere in a Circular Cylinder
,”
Quarterly Journal of Mechanics and Applied Mathematics
, Vol.
17
, pp.
55
63
.
3.
Chan
P. C.
,
Leu
R. J.
, and
Zargar
N. H.
,
1986
, “
On the solution for the rotational motion of an axisymmetric rigid body at low Reynolds number with application to a finite length cylinder
,”
Chemical Engineering Communications
, Vol.
49
, pp.
145
163
.
4.
Happel, J., and Brenner, H., 1986, Low Reynolds Number Hydrodynamics, Martinus Nijhoff, Dordrecht, The Netherlands.
5.
Jeffrey
G. B.
,
1915
, “
On the Steady Rotation of a Solid of Revolution in a Viscous Fluid
,”
Proceedings of London Mathematical Society
, Section 2, Vol.
14
, pp.
327
338
.
6.
Kanwal
R. P.
,
1961
, “
Slow Steady Rotation of Axially Symmetric Bodies in a Viscous Fluid
,”
Journal of Fluid Mechanics
, Vol.
10
, pp.
17
24
.
7.
Kim
M. U.
,
1981
, “
Slow Rotation of a Disk in a Fluid-Filled Circular Cylinder
,”
Journal of the Physical Society of Japan
, Vol.
50
, pp.
4063
4067
.
8.
Kobayashi
H.
,
Nashima
T.
,
Okamoto
Y.
, and
Kaminaga
F.
,
1991
, “
End effect in a coaxial cylindrical viscometer
,”
Review of Scientific Instruments
, Vol.
62
, pp.
2748
2750
.
9.
Landau, L. P., and Lifshitz, E. M., 1959, Fluid Mechanics, Addison-Wesley, Reading, MA.
10.
Oka, S., 1960, “The principles of theology,” Rheology, Theory and Applications, F. R. Eirich, ed. Academic Press, New York, Vol. 3, Chapter 2.
11.
Olver, F. W. J., 1967, “Bessel Functions of Integer Order,” Handbook of Mathematical Functions, M. Abramowitz and I. A. Stegun, eds., Dover, New York, Chapter 9.
12.
Schmieden
C.
,
1928
, “
U¨ber den Widerstand einer in einer Flu¨ssigkeit rotieren-den Scheibe
,”
Zeitschrift fu¨r Angewandete Mathematik und Mechanik
, Vol.
8
, pp.
460
479
.
13.
Trogden
S. A.
, and
Joseph
D. D.
,
1982
, “
Matched Eigenfunction Expansions for Slow Flow over a Slot
,”
Journal of Non-Newtonian Mechanics
, Vol.
10
, pp.
185
213
.
14.
Wang
C. Y.
,
1992
, “
Slow Rotation of a Disc in a Fluid-Filled Casing
,”
Acta Mechanica
, Vol.
94
, pp.
97
103
.
15.
Wang
C. Y.
,
1993
, “
Stokes Flow through a Two-Dimensional Filter
,”
Physics of Fluids-A
, Vol.
5
, pp.
1113
1116
.
16.
Weil
H.
,
1951
, “
On the Extrusion of a Very Viscous Liquid
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
18
, pp.
267
272
.
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