Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-18T22:59:33.845Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximum dissipation resulting from lift in a slow viscous shear flow

Published online by Cambridge University Press:  28 March 2006

E. Y. Harper  and
I-Dee Chang
E. Y. Harper
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, California Now at Lockhead Palo Alto Research Laboratory.
I-Dee Chang
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, California
Get access Rights & Permissions [Opens in a new window]

Abstract

The lift tensor for any three-dimensional body moving in a linear shear flow at low Reynolds numbers has been calculated by asympototic methods. The tensor is applied to the problem of the motion of a dumb-bell shaped particle. The particle is shown to have a preferred periodic orbit which corresponds to maximum dissipation. The dissipation is calculated and the intrinsic viscosity of a dilute suspension of such particles is predicted. Experiments conducted with a single particle tend to confirm the stability of the predicted orientation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 33 , Issue 2 , 12 August 1968 , pp. 209 - 225
Copyright
© 1968 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brenner, H. 1958 Phys. Fluids, 1, 338.
Brenner, H. 1961 J. Fluid Mech. 11, 604.
Chang, I-DEE 1960 J. Fluid Mech. 9, 473.
Chang, I-DEE & Finn, R. 1961 Arch. Ratl Mech. Anal. 7, 388.
Chester, W. 1962 J. Fluid Mech. 13, 557.
Childress, W. S. 1964 J. Fluid Mech. 20, 305.
Christopherson, D. G. & Dowson, D. 1959 Proc. Roy. Soc. A, 251, 550.
Cox, R. G. 1965 J. Fluid Mech. 23, 273.
Einstein, A. 1905 Investigations on the Theory of the Brownian Movement. New York: Dover.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics, p. 83. New York: Prentice-Hall.
Jeffery, G. B. 1922 Proc. Roy. Soc. A, 102, 161.
Kaplun, S. 1967 Fluid Mechanics and Singular Perturbations, p. 47. Academic Press.
Mason, S. G., Karnes, A. & Goldsmith, H. L. 1963 Nature, Lond. 200, 159.
Saffman, P. G. 1956 J. Fluid Mech. 1, 540.
Saffman, P. G. 1965 J. Fluid Mech. 22, 385.
Saffman, P. G. 1968 J. Fluid Mech. 31, 624.
Taylor, G. I. 1923 Proc. Roy. Soc. A, 102, 58.