Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-14T16:37:38.611Z Has data issue: false hasContentIssue false
  • English
  • Français

The Stokes resistance of a spherical cap to translational and rotational motions in a linear shear flow

Published online by Cambridge University Press:  12 April 2006

J. M. Dorrepaal
J. M. Dorrepaal
Affiliation:
Department of Mathematical and Computing Sciences, Old Dominion University, Norfolk, Virginia 23508
Get access Rights & Permissions [Opens in a new window]

Abstract

Brenner's general results for the force and torque experienced by an arbitrary particle simultaneously translating and rotating in a linear shear flow are applied to the spherical cap. The cap's five fundamental resistance tensors are determined and the corresponding tensors for the sphere and circular disk are recovered as special cases. The problem of a freely moving cap in a linear shear is considered and the resulting translational and rotational motions are analysed. The cap's centre of free rotation is found and trajectories of this point are plotted in a few instances. The cap is also found to possess a ‘point of planar motion’ which always moves in a plane perpendicular to the vorticity vector of the undisturbed shear regardless of the initial orientation of the cap. It is shown that the motion of the cap actually serves as a model for the motions of all ‘oblate’ asymmetric bodies of revolution which are moving freely in a linear shear.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 2 , 30 January 1978 , pp. 265 - 279
Copyright
© 1978 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. 1963 Chem. Engng Sci. 18, 1–25.Google Scholar
Brenner, H. 1964a Chem. Engng Sci. 19, 599–629.Google Scholar
Brenner, H. 1964b Chem. Engng Sci. 19, 631–651.Google Scholar
Brenner, H. 1964c Chem. Engng Sci. 19, 703–727.Google Scholar
Brenner, H. 1964d Chem. Engng Sci. 19, 519–539.Google Scholar
Brenner, H. 1972 Prog. Heat Mass Transfer 6, 509–574.Google Scholar
Bretherton, F. P. 1962 J. Fluid Mech. 14, 284–304.Google Scholar
Collins, W. D. 1959 Quart. J. Mech. Appl. Math. 12, 232–241.Google Scholar
Collins, W. D. 1963 Mathematika 10, 72–79.Google Scholar
Dorrepaal, J. M. 1975 Ph.D. thesis, University of Toronto.Google Scholar
Dorrepaal, J. M. 1976 Z. angew. Math. Phys. 27, 739–748.Google Scholar
Dorrepaal, J. M., O'NEILL, M. E. & Ranger, K. B.1976 J. Fluid Mech. 75, 273–286.Google Scholar
Nir, A. & Acrivos, A. 1973 J. Fluid Mech. 59, 209–223.Google Scholar
Ranger, K. B. 1973 Z. angew. Math. Phys. 24, 801–809.Google Scholar