Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T01:22:22.798Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of an elastico-viscous liquid film flowing down an inclined plane

Published online by Cambridge University Press:  24 October 2008

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

Abstract

An analysis is made of the stability of a layer of an elastico-viscous liquid flowing down an inclined plane in the presence of two-dimensional disturbances. The modified Orr-Sommerfeld equation is solved by a regular perturbation technique for disturbances of large wavelengths. It is shown that in the absence of surface tension, the layer is more unstable as compared with that for an ordinary viscous liquid if Q1 > Q2, Q1 and Q2 being stress relaxation and strain retardation parameters respectively.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 527 - 536
Copyright
Copyright © Cambridge Philosophical Society 1967

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

REFERENCES

(1)Benjamin, T. B.J. Fluid Mech. 2 (1957), 554.CrossRefGoogle Scholar
(2)Binnie, A. M.J. Fluid Mech. 2 (1957), 551.CrossRefGoogle Scholar
(3)Ivanilov, I. P.Prikl. Mat. Mek. (English translation) 24 (1960), 549.Google Scholar
(4)Kapitza, P. L. Ž. Eksper. Teoret. Fiz. 18 (1948), 3.Google Scholar
(5)Oldroyd, J. G.Proc. Roy. Soc. London Ser. A 200 (1950), 523.Google Scholar
(6)Oldroyd, J. G.Proc. Roy. Soc. A 245 (1958), 291.Google Scholar
(7)Oldroyd, J. G., Strawbridge, D. J. and Toms, B. A.Proc. Phys. Soc. Sect. B 64 (1951), 44.CrossRefGoogle Scholar
(8)Yih, C. S.Proc. 2nd U.S. Nat. Cong. Appl. Mech. (American Soc. Mech. Engrs. New York, 1955), 623.Google Scholar
(9)Yih, C. S.Phys. Fluids 6 (1963), 321.CrossRefGoogle Scholar
(10)Yih, C. S.Phys. Fluids 8 (1965), 1257.CrossRefGoogle Scholar