Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T21:22:21.840Z Has data issue: false hasContentIssue false
  • English
  • Français

Creeping flow in two-dimensional channels

Published online by Cambridge University Press:  21 April 2006

C. Pozrikidis
C. Pozrikidis
Affiliation:
Research Laboratories, Eastman Kodak Company, Rochester, NY 14650, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Creeping flow in two-dimensional periodic channels of arbitrary geometry is considered. The problem is formulated using the boundary-integral method for Stokes flow, presently adapted for periodic flows with special geometrical characteristics. Numerical calculations for steady flow in channels constricted by a plane and a sinusoidal wall are performed. Detailed streamline patterns are presented and criteria for flow reversal are established. It is shown that for narrow channels the mechanism driving the flow has a strong effect on the structure of the flow. The results are discussed with reference to lubrication, coating and molecular-convective processes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 180 , July 1987 , pp. 495 - 514
Copyright
© 1987 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

Blake, J. R. 1971 A note on the image system for a stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303–310.Google Scholar
Caponi, E. A., Fornberg, B., Knight, D. D., Mclean, J. W., Saffman, P. G. & Yuen, H. C. 1982 Calculations of laminar viscous flow over a moving wavy surface. J. Fluid Mech. 124, 347–362.Google Scholar
Deiber, J. A. & Schowalter, W. R. 1979 Flow through tubes with sinusoidal axial variations in diameter. AIChE J. 25, 638–645.Google Scholar
Fraenkel, L. E. 1962 Laminar flow in symmetrical channels with slightly curved walls. I. On the Jeffery-Hamel solutions for flow between plane walls. Proc. Roy. Soc. Lond. A 267, 119–138.Google Scholar
Hall, P. 1974 Unsteady viscous flow in a pipe of slowly varying cross-section. J. Fluid Mech. 64, 209–226.Google Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Noordhoff.
Hasegawa, E. & Izuchi, H. 1983 On steady flow through a channel consisting of an uneven and a plane wall. Part 1. Case of no relative motion in two walls. Bull. JSME 26 (214), 514–520.Google Scholar
Hasegawa, E. & Izuchi, H. 1984 On steady flow through a channel consisting of an uneven and a plane wall. Part 2. Case of walls with a relative velocity. Bull. JSME 27 (230). 1631–1636.Google Scholar
Hasimoto, H. & Sano, O 1980 Stokeslets and eddies in creeping flow. Ann. Rev. Fluid Mech. 12, 335–363.Google Scholar
Higdon, J. J. L. 1985 Stokes flow in arbitrary two-dimensional domains: shear flow over ridges and cavities. J. Fluid Mech. 159, 195–226.Google Scholar
Jeffrey, D. J. & Sherwood, J. D. 1980 Streamline patterns and eddies in low-Reynolds-number flow. J. Fluid Mech. 96, 315–334.Google Scholar
Ladyzhenskaya, O. A. 1969 The Mathematical Theory of Viscous Incompressible Flow. Gordon & Breach.
Langlois, W. E. 1964 Slow Viscous Flow. Macmillan.
Lee, S. H. & Leal, L. G. 1986 Low-Reynolds-number flow past cylindrical bodies of arbitrary cross-sectional shape. J. Fluid Mech. 164, 401–427.Google Scholar
Moffatt, H. K. 1964 Viscous and resistive eddies near a sharp corner. J. Fluid Mech. 18, 1–18.Google Scholar
Munson, B. R., Rangwalla, A. A. & Mann, J. A. 1985 Low Reynolds number circular couette flow past a wavy wall. Phys. Fluids 28, 2679–26.Google Scholar
Pan, F. & Acrivos, A. 1967 Steady flow in rectangular cavities. J. Fluid Mech. 28, 643–655.Google Scholar
Pozrikidis, C. 1987 A study of peristaltic flows. J. Fluid Mech. 180, 515–527.Google Scholar
Sobey, I. J. 1980 On flow through furrowed channels. Part 1. Calculated flow patterns. J. Fluid Mech. 96, 1–26.Google Scholar
Sobey, I. J. 1983 The occurrence of separation in oscillatory flow. J. Fluid Mech. 134, 247–257.Google Scholar
Taylor, G. I. 1971 A model for the boundary condition of a porous material. Part 1. J. Fluid Mech. 49, 319–326.Google Scholar
Wang, C. Y. 1978 Drag due to a striated boundary in slow Couette flow. Phys. Fluids 21, 697–698.Google Scholar