On the Stability of Two Superposed Viscous-Viscoelastic (Walters B′) Fluids

2006 ◽  
Vol 129 (1) ◽  
pp. 116-119 ◽  
Author(s):  
Pardeep Kumar ◽  
Roshan Lal
Keyword(s):  
Viscous Fluid ◽  
Viscoelastic Fluid ◽  
Kinematic Viscosity ◽  
Taylor Instability ◽  
Stable Configuration ◽  
Stabilizing Effect ◽  
Unstable Configuration ◽  
Rayleigh Taylor Instability ◽  
Newtonian Viscous Fluid ◽  
The Stability

The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying Walters B′ viscoelastic fluid is considered. For the stable configuration, the system is found to be stable or unstable under certain conditions. However, the system is found to be unstable for the potentially unstable configuration. Further it is found numerically that kinematic viscosity has a destabilizing effect, whereas kinematic viscoelasticity has a stabilizing effect on the system.

scholarly journals Stability of two superposed viscous-viscoelastic fluids

2005 ◽  
Vol 9 (2) ◽  
pp. 87-95 ◽  
Author(s):  
Pardeep Kumar ◽  
Roshan Lal
Keyword(s):  
Dispersion Relation ◽  
Viscous Fluid ◽  
Kinematic Viscosity ◽  
Viscous Fluids ◽  
Stable Case ◽  
Stabilizing Effect ◽  
Unstable Case ◽  
Rayleigh Taylor Instability ◽  
Newtonian Viscous Fluid ◽  
Mode Technique

The Rayleigh-Taylor instability of a Newtonian viscous fluid overlying a Rivlin-Ericksen viscoelastic fluid is considered. Upon application of normal mode technique, the dispersion relation is obtained. As in both Newtonian viscous-viscous fluids the system is stable in the potentially stable case and unstable in the potentially unstable case, this holds for the present problem also. The behavior of growth rates with respect to kinematic viscosity and kinematic viscoelasticity parameters are examined numerically and it is found that both kinematic viscosity and kinematic viscoelasticity have stabilizing effect.

scholarly journals Rayleigh-Taylor instability of two superposed magnetized viscous fluids with suspended dust particles

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Dust Particles ◽  
Stable Configuration ◽  
Rayleigh Taylor Instability ◽  
Suspended Dust ◽  
The Stability

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.

scholarly journals Effect of Horizontal and Vertical Magnetic Fields on Rayleigh?Taylor Instability

1968 ◽  
Vol 21 (6) ◽  
pp. 923 ◽  
Author(s):  
RC Sharma ◽  
KM Srivastava
Keyword(s):  
Magnetic Fields ◽  
General Equation ◽  
Taylor Instability ◽  
Combined Effect ◽  
Physical Situation ◽  
Stable Case ◽  
Unstable Case ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
Superposed Fluids

A general equation studying the combined effect of horizontal and vertical magnetic fields on the stability of two superposed fluids has been obtained. The unstable and stable cases at the interface (z = 0) between two uniform fluids, with both the possibilities of real and complex n, have been. separately dealt with. Some new results are obtained. In the unstable case with real n, the perturbations are damped or unstable according as 2(k'-k~L2)_(<X2-<Xl)k is> or < 0 under the physical situation (35). In the stable case, the perturbations are stable or unstable according as 2(k2_k~L2)+(<Xl-<X2)k is > or < 0 under the same physical situation (35). The perturbations become unstable if HIlIH 1- (= L) is large. Both the cases are also discussed with imaginary n.

Observation of the stabilizing effect of a laminated ablator on the ablative Rayleigh-Taylor instability

2011 ◽  
Vol 83 (5) ◽  
Author(s):  
L. Masse ◽  
A. Casner ◽  
D. Galmiche ◽  
G. Huser ◽  
S. Liberatore ◽  
...  
Keyword(s):  
Taylor Instability ◽  
Stabilizing Effect ◽  
Rayleigh Taylor Instability

Magnetohydrodynamic Stability of Two Streaming Superposed Viscoelastic Conducting Fluids

2001 ◽  
Vol 56 (6-7) ◽  
pp. 416-439
Author(s):  
Mohamed Fahmy El
Keyword(s):  
Magnetic Field ◽  
Stable Configuration ◽  
Retardation Time ◽  
Horizontal Magnetic Field ◽  
Fluid Velocities ◽  
Unstable Configuration ◽  
The Stability ◽  
The Magnetic Field ◽  
Conducting Fluids ◽  
Alfven Velocity

Abstract The stability of the plane interface separating two Oldroydian viscoelastic superposed moving fluids of uniform densities when immersed in a uniform horizontal magnetic field has been in­ vestigated. The stability analysis has been carried out, for mathematical simplicity, for two highly viscous fluids of equal kinematic viscosities. It is found that the potentially stable configuration remains stable if the fluids are at rest, while it becomes unstable if the fluids move. The stability criterion is found to be independent of the viscosity and viscoelasticity, and to be dependent on the orientation of the magnetic field and the magnitudes of the fluids and Alfven velocities. It is also found that the potentially unstable configuration remains unstable in the absence of average fluid velocities, or in the presence of fluid velocities and absence of a magnetic field. The magnetic field is found to stabilize a certain wavenumbers range of the unstable configuration even in the presence of the effects of viscoelasticity. The behaviour of growth rates with respect to the stress relaxation time, strain retardation time, fluid and Alfven velocity parameters is examined analytically, and the stability conditions are obtained and discussed. -Pacs: 47.20.-k; 47.50.+d; 47.65.+a.

The Rayleigh–Taylor instability of viscous fluid layers

1997 ◽  
Vol 9 (6) ◽  
pp. 1635-1649 ◽  
Author(s):  
A. Elgowainy ◽  
N. Ashgriz
Keyword(s):  
Viscous Fluid ◽  
Taylor Instability ◽  
Fluid Layers ◽  
Rayleigh Taylor Instability

Rayleigh-Taylor Instability of a Stratified Magnetized Medium in the Presence of Suspended Particles

1984 ◽  
Vol 39 (10) ◽  
pp. 939-944 ◽  
Author(s):  
R. K. Chhajlani ◽  
R. K. Sanghvi ◽  
P. Purohit
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Suspended Particles ◽  
Frequency Parameter ◽  
Relaxation Frequency ◽  
Taylor Instability ◽  
Horizontal Magnetic Field ◽  
Rayleigh Taylor Instability ◽  
The Stability ◽  
The Magnetic Field

Abstract The hydromagnetric Rayleigh-Taylor instability of a composite medium has been studied in the presence of suspended particles for an exponentially varying density distribution. The prevalent horizontal magnetic field and viscosity of the medium are assumed to be variable. The dispersion relation is derived for such a medium. It is found that the stability criterion is independent of both viscosity and suspended particles. The system can be stabilized for an appropriate value of the magnetic field. It is found that the suspended particles can suppress as well as enhance the growth rate of the instability in certain regions. The growth rates are obtained for a viscid medium with the inclusion of suspended particles and without it. It has been shown analytically that the growth rate is modified by the inclusion of the relaxation frequency parameter of the suspended particles.

scholarly journals Magneto-Rayleigh–Taylor instability in an elastic finite-width medium overlying an ideal fluid

2019 ◽  
Vol 867 ◽  
pp. 1012-1042 ◽  
Author(s):  
S. A. Piriz ◽  
A. R. Piriz ◽  
N. A. Tahir
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Ideal Fluid ◽  
Taylor Instability ◽  
Finite Width ◽  
Unexpected Result ◽  
Magnetic Field Effects ◽  
Linear Elastic ◽  
Rayleigh Taylor Instability ◽  
The Stability

We present the linear theory of two-dimensional incompressible magneto-Rayleigh–Taylor instability in a system composed of a linear elastic (Hookean) layer above a lighter semi-infinite ideal fluid with magnetic fields present, above and below the layer. As expected, magnetic field effects and elasticity effects together enhance the stability of thick layers. However, the situation becomes more complicated for relatively thin slabs, and a number of new and unexpected phenomena are observed. In particular, when the magnetic field beneath the layer dominates, its effects compete with effects due to elasticity, and counteract the stabilising effects of the elasticity. As a consequence, the layer can become more unstable than when only one of these stabilising mechanisms is acting. This somewhat unexpected result is explained by the different physical mechanisms for which elasticity and magnetic fields stabilise the system. Implications for experiments on magnetically driven accelerated plates and implosions are discussed. Moreover, the relevance for triggering of crust-quakes in strongly magnetised neutron stars is also pointed out.

Rayleigh-Taylor Instability of Newtonian and Oldroydian Viscoelastic Fluids in Porous Medium

1994 ◽  
Vol 49 (10) ◽  
pp. 927-930
Author(s):  
R. C. Sharma ◽  
V. K. Bhardwaj
Keyword(s):  
Porous Medium ◽  
Interfacial Tension ◽  
Viscoelastic Fluids ◽  
Taylor Instability ◽  
Horizontal Boundary ◽  
Wave Numbers ◽  
Unstable Configuration ◽  
Rayleigh Taylor Instability

AbstractThe Rayleigh-Taylor instability of viscous and viscoelastic (Oldroydian) fluids, separately, has been considered in porous medium. Two uniform fluids separated by a horizontal boundary and the case of exponentially varying density have been considered in both viscous and viscoelastic fluids. The effective interfacial tension succeeds in stabilizing perturbations of certain wave numbers (small wavelength perturbations) which were unstable in the absence of effective interfacial tension, for unstable configuration/stratification.

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