Hostname: page-component-848d4c4894-hfldf Total loading time: 0 Render date: 2024-05-06T18:44:35.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear adjustment of a thin annular film of viscous fluid surrounding a thread of another within a circular cylindrical pipe

Published online by Cambridge University Press:  20 April 2006

P. S. Hammond
P. S. Hammond
Affiliation:
Schlumberger-Doll Research, P.O. Box 307, Ridgefield, Connecticut 06877, U.S.A. Present address: Schlumberger Cambridge Research, P.O. Box 153, Cambridge CB2 3BE, England.
Get access Rights & Permissions [Opens in a new window]

Abstract

A nonlinear analysis, based on lubrication theory, is presented for the adjustment under surface tension of an initially uniform annular film of viscous fluid confined within a circular cylindrical pipe. The film surrounds a thread of another viscous fluid. Small axisymmetric interfacial disturbances of sufficiently long wavelength are found to grow, leading to the break-up of the initially continuous outer film into a number of isolated rings of fixed length on the pipe wall. The implications for the rupture of fluid threads surrounded by moderately thin films in confined geometries are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 137 , December 1983 , pp. 363 - 384
Copyright
© 1983 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

Chen, J. D. & Slattery, J. C. 1982 AIChE J. 28, 955.
Everett, D. H. & Haynes, J. M. 1972 J. Coll. Interface Sci. 38, 125.
Goldsmith, H. L. & Mason, S. G. 1963 J. Coll. Interface Sci. 18, 237.
Goren, S. L. 1962 J. Fluid Mech. 12, 309.
Hall, G. & Watt, J. M. (eds.) 1976 Modern Numerical Methods for Ordinary Differential Equations. Oxford University Press.
Hammond, P. S. 1982 Flows driven by surface tension with nearby rigid boundaries. PhD dissertation, Cambridge University.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Hickox, C. E. 1971 Phys. Fluids 14, 251.
Jones, A. F. & Wilson, S. D. R. 1978 J. Fluid Mech. 87, 263.
Koplik, J., Wilkinson, D. & Willemsen, J. F. 1983 Percolation and capillary fluid displacement. Presented at the Workshop on the Mathematics and Physics of Disordered Media, University of Minnesota, February 1983.
Larson, R. G., Scriven, L. E. & Davis, H. T. 1981 Chem. Engng Sci. 36, 57.
Mohanty, K. K. 1981 Fluids in porous media: two phase distribution and flow. PhD dissertation, University of Minnesota.
Rayleigh, Lord 1892 Phil. Mag. 34, 145.
Taylor, G. I. 1934 Proc. R. Soc. Lond. A, 146, 501.
Taylor, G. I. 1961 J. Fluid Mech. 10, 161.
Tomotika, S. 1935 Proc. R. Soc. Lond. A, 150, 322.
Williams, M. B. & Davis, S. H. 1982 J. Coll. Interface Sci. 90, 220.
Wu, R. & Weinbaum, S. 1982 J. Fluid Mech. 121, 315.