Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-28T06:28:07.876Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of a visco-elastic liquid film flowing down an inclined plane

Published online by Cambridge University Press:  28 March 2006

A. S. Gupta
A. S. Gupta
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur, India
Get access Rights & Permissions [Opens in a new window]

Abstract

The investigation concerns the stability of an incompressible second-order fluid (visco-elastic) film flowing down an inclined plane under gravity with respect to two-dimensional disturbances. When the elastic parameter is negative as in the case of a solution of polyisobutylene in cetane, surface disturbances (‘soft’ waves) are found to be unstable. The analysis in this case also reveals the existence of growing shear waves (‘hard’ waves) which are highly damped in ordinary Newtonian fluids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 28 , Issue 1 , 12 April 1967 , pp. 17 - 28
Copyright
© 1967 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

Benjamin, T. B. 1957 J. Fluid Mech. 2, 554.
Berg, J. C. & Acrivos, A. 1965 Chem. Engng Sci. 20, 737.
Binnie, A. M. 1957 J. Fluid Mech. 2, 551.
Coleman, B. D., Duffin, R. J. & Mizel, V. J. 1965 Arch. Rat. Mech. Anal. 19, 100.
Coleman, B. D. & Noll, W. 1960 Arch. Rat. Mech. Anal. 6, 355.
Levich, V. G. 1962 Physico-chemical Hydrodynamics. Englewood Cliffs, N.J.: Prentice-Hall.
Markovitz, H. & Coleman, B. D. 1964 Adv. Appl. Mech. New York: Academic Press.
Noll, W. 1958 Arch. Rat. Mech. Anal. 2, 197.
Rivlin, E. S. & Ericksen, J. L. 1955 J. Rat. Mech. Anal. 4, 681.
Truesdell, C. 1965 Phys. Fluids, 8, 1936.
Yih, C. S. 1955 Proc. Second U.S. Nat. Cong. Appl. Mech. pp. 623–628.
Yih, C. S. 1963 Phys. Fluids, 6, 321.
Yih, C. S. 1965 Phys. Fluids, 8, 1257.