Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T18:43:11.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Stokes problems for moving half-planes

Published online by Cambridge University Press:  26 April 2006

Y. Zeng  and
S. Weinbaum
Y. Zeng
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, NY 10031, USA
S. Weinbaum
Affiliation:
Department of Mechanical Engineering, The City College of the City University of New York, NY 10031, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

New exact solutions of the Navier–Stokes equations are obtained for the unbounded and bounded oscillatory and impulsive tangential edgewise motion of touching half-infinite plates in their own plane. In contrast to Stokes classical solutions for the harmonic and impulsive motion of an infinite plane wall, where the solutions are separable or have a simple similarity form, the present solutions have a two-dimensional structure in the near region of the contact between the half-infinite plates. Nevertheless, it is possible to obtain relatively simple closed-form solutions for the flow field in each case by defining new variables which greatly simplify the r- and θ-dependence of the solutions in the vicinity of the contact region. These solutions for flow in a half-infinite space are then extended to bounded flows in a channel using an image superposition technique. The impulsive motion has application to the motion near geophysical faults, whereas the oscillatory motion has arisen in the design of a novel oscillating half-plate flow chamber for examining the effect of fluid shear stress on cultured cell monolayers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 287 , 25 March 1995 , pp. 59 - 74
Copyright
© 1995 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

Davis, S. H. 1976 The stability of time-periodic flows. Ann. Rev. Fluid Mech. 8, 57–74.Google Scholar
Dewey, C. F., Bussolari, S. R., Gimbrone, M. A. & Davies, P. F. 1981 The dynamic response of vascular endothelial cells to fluid shear stress. Trans. ASME K: J. Biomech. Engng 103, 177–181.Google Scholar
Hall, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347–367.Google Scholar
Kerczek, C. von & Davis, S. H. 1974 Linear stability theory of oscillating Stokes layers. J. Fluid Mech. 62, 753–773.Google Scholar
Stokes, G. G. 1851 On the effect of internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 8–106.Google Scholar
Weinbaum, S., Cowin, S. C. & Zeng, Y. 1994 A model for the excitation of osteocytes by mechanical loading induced bone fluid shear stress. J. Biomech. 27, pp. 339–360.Google Scholar