This paper presents an application of the Cosserat spectrum theory in elasticity to the solution of low Reynolds number (Stokes flow) problems. The velocity field is divided into two components: a solution to the vector Laplace equation and a solution associated with the discrete Cosserat eigenvectors. Analytical solutions are presented for the Stokes flow past a sphere with uniform, extensional, and linear shear freestream profiles.

Issue Section:
Brief Notes
Topics:
Creeping flow, Eigenvalues, Elasticity, Laplace equations, Reynolds number, Shear (Mechanics)
1.
Chwang
A. T.
, and
Wu
T. Y.
,
1975
, “
Hydromechanics of Low-Reynolds-Number Flow. Part 2. Singularity Method for Stokes Flows
,”
Journal of Fluid Mechanics
, Vol.
67
, No.
4
, pp.
787
–
815
.
2.
Cosserat
E.
, and
Cosserat
F.
,
1898
, “
Sur les equations de la theorie de l’elasticite
,”
C. R. Acad. Sci. Paris
, Vol.
126
, pp.
1089
–
1091
.
3.
Hill
E. L.
,
1954
, “
The Theory of Vector Spherical Harmonics
,”
American Journal of Physics
, Vol.
22
, pp.
211
–
214
.
4.
Liu, W., 1998, “The Cosserat Spectrum Theory and its Applications,” Ph.D. dissertation, Joint Doctoral Program in Engineering Sciences/Applied Mechanics, University of California, San Diego and San Diego State University.
5.
Markenscoff
X.
, and
Paukshto
M. V.
,
1998
, “
The Cosserat Spectrum in the Theory of Elasticity and Applications
,”
Proc. R. Soc. Lond.
, Vol.
A454
, pp.
631
–
643
.
1.
Mikhlin
S. G.
,
1973
, “
The Spectrum of a Family of Operators in the Theory of Elasticity
,”
Uspekhi Mat. Nauk
, (in Russian), Vol.
28
, No.
3
, pp.
43
–
82
; English translation in
2.
Russian Math Surveys
, Vol.
28
, No.
3
, pp.
45
–
88
.
This content is only available via PDF.
Copyright © 1999
 by The American Society of Mechanical Engineers
You do not currently have access to this content.