‘Effective Interfacial Tension’ Effect On the instability of Streaming Rivlin-Ericksen Elastico-Viscous Fluids in Porous Mediu

‘Effective Interfacial Tension’ Effect on the Instability of Streaming Rivlin-Ericksen Elastico-Viscous Fluids in Porous Medium

Sanjeev Gangta¹* and Chanderbhan Mehta²

¹Department of Mathematics, Govt. Boys Sr. Secondary School, Kotkhai, Disstt Shimla. Himachal Pradesh

²Department of mathematics, center of excellence , Govt College Sanjauli, Shimla. Himachal Pradesh

*Corresponding Author E-mail: Sanjeev.gangta@yahoo.co.in; chanderbmehta@gmail.com

ABSTRACT:

The Instability of the plane interface between two uniform, superposed and streaming Rivlin-Ericksen elastico-viscous fluids through porous media, including ‘effective interfacial tension’ effect, is considered. In the absence of ‘effective interfacial tension’ stability/ instability of the system as well as perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored, whereas for perturbation in all other directions, there exists instability for a certain wave number range. The ‘effective interfacial tension’ is able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities.

KEYWORDS: elastic-viscous, porous media, effective interfacial tension, medium porosity and streaming velocities.

1. INTRODUCTION:

A detailed account of the Kelvin-Helmholtz instability of Newtonian fluids has been given by Chandrasekhar [1]. With the growing importance of non-Newtonian fluids in modern technology and industries, the investigations on such fluids are desirable. One important class of elastico-viscous fluids (sub-class of non-Newtonian fluids) is the Rivlin-Ericksen elastico-viscous fluid, the constitutive equation for which has been proposed by Rivlin and Ericksen [2].

4. REFERENCES:

[1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York 1981.

[2] R.S. Rivlin and J.L. Ericksen, J. Rational Mech. Anal. 4, 323 (1955)

[3] O.M. Phillips, Flow and Reaction in Permeable Rocks, Cambridge University Press, Cambridge 1991.

[4] R. L. Chuoke, P. Van Meurs and C. Van der Poel, Trans. AIME 216, 188 (1959)

[5] R.C. Sharma and T.J.T. Spanos, Canadian J. Phy. 60, 1391 (1982).

[6] R.C. Sharma, P. Kumar and S.Sharma, Int. J. Appl. Mech. Engng. 7, 433 (2002).

Received on 02.01.2014 Accepted on 28.01.2014

Int. J. Tech. 4(1): Jan.-June. 2014; Page 163-167