On the stability of two superposed fluids

Willson, A. J.

doi:10.1017/s0305004100004163

Cited by 10 publications

(9 citation statements)

References 7 publications

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“…If one may judge from recent discussion of oscillations of two fluids separated by a plane interface, determining all of the significant features of droplet oscillation is scarcely likely to be a trivial matter. The work of Willson (1965) has shown, for example, that, contrary to the belief previously held by some workers, there are important aspects of wave propagation on and instability of plane interfaces which are not revealed by study of the special case of two fluids having equal kinematic viscosities. In particular, Willson established that if the two viscosities are equal but one fluid is of much greater density, there is a range of wavelengths in which only one mode of aperiodic decay exists although two modes are found when the fluids have equal kinematic viscosities.…”

Section: Behaviour When the Interface Is Freementioning

confidence: 65%

The oscillations of a fluid droplet immersed in another fluid

1968

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From an analysis of small oscillations of a viscous fluid droplet immersed in another viscous fluid a general dispersion equation is derived by which frequency and rate of damping of oscillations can be calculated for arbitrary values of droplet size, physical properties of the fluids, and interfacial viscosity and elasticity coefficients. The equation is studied for two distinct extremes of interfacial characteristics: (i) a free interface between the two fluids in which only a constant, uniform interfacial tension acts; (ii) an ‘inextensible’ interface between the two fluids, that is, a highly condensed film or membrane which, to first order, cannot be locally expanded or contracted. Results obtained are compared with those previously published for various special cases.When the viscosities of both fluids are low, the primary contribution to the rate of damping of oscillations is generally the viscous dissipation in a boundary layer near the interface, in both the free and inextensible interface situations. For this reason inviscid velocity profiles, which do not account for the boundarylayer flow, do not lead to good approximations to the damping rate. The two exceptions in which the approximation based on inviscid profiles is adequate occur when the interface is free and either the interior or exterior fluid is a gas of negligible density and viscosity.

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Section: Behaviour When the Interface Is Freementioning

confidence: 65%

The oscillations of a fluid droplet immersed in another fluid

1968

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“…Only the derivation of Eq. (3) was in question because comparisons have shown that the formula itself is an excellent approximation to the exact results [22,23]. In Ref.…”

Section: Dispersion Relationsmentioning

confidence: 99%

Viscous Rayleigh-Taylor instability in spherical geometry

Mikaelian

2016

Phys. Rev. E

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We consider viscous fluids in spherical geometry, a lighter fluid supporting a heavier one. Chandrasekhar [Q. J. Mech. Appl. Math. 8, 1 (1955)] analyzed this unstable configuration providing the equations needed to find, numerically, the exact growth rates for the ensuing Rayleigh-Taylor instability. He also derived an analytic but approximate solution. We point out a weakness in his approximate dispersion relation (DR) and offer a somewhat improved one. A third DR, based on transforming a planar DR into a spherical one, suffers no unphysical predictions and compares reasonably well with the exact work of Chandrasekhar and a more recent numerical analysis of the problem [Terrones and Carrara, Phys. Fluids 27, 054105 (2015)].

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“…We assume a small perturbation in the last system of eqs. (9)- (11) and consider the fluid to be arranged in horizontal strata, i.e., the density is a function of the vertical coordinate z only, and acted by gravity force g(0, 0, −g) and a homogeneous horizontal magnetic field H(H 0 , 0, 0). We put V = (u, v, w), H = (H x , H y , H z ); δρ and δp denote, respectively, the perturbations in density ρ and pressure p. Then the relevant linearized perturbations equations are…”

Section: Perturbation Equationsmentioning

confidence: 99%

“…here µ 1 , µ 2 are the viscosities of the lighter and heavier fluids, respectively, and T s is the surface tension at the interface. In the absence of surface tension equation (3), was proposed by Hide [8,9] and it was studied by Reid [10], Willson [11], and Plesset and Whipple [12]. Mikaelian [13] studied the effect of viscosity on RTI for two finite-thickness fluids in the presence of surface tension.…”

Section: Introductionmentioning

confidence: 99%

Study of the effect of viscosity and homogeneous horizontal magnetic field on Rayleigh-Taylor instability

Hoshoudy

El-Ansary

2003

Z. angew. Math. Mech.

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Rayleigh‐Taylor instability of a heavy fluid supported by a lighter one, in the presence of a homogeneous horizontal magnetic field pervading both the fluids is investigated. These fluids are considered to be incompressible, viscous, and infinitely conducting. In the lower region, z<0, the density is constant as well as in the upper region, z>0. The dispersion relation that defines the growth rate σ is derived as a function of the physical parameters of the system under the condition ky/kx=π and numerically analyzed. It is shown that the horizontal magnetic field helps to stabilize the instability. The growth rate depends on the relation between wave number components, where the instability increases with increasing π and thereby the role of horizontal magnetic field gradually declines.

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On the stability of two superposed fluids

Cited by 10 publications

References 7 publications

The oscillations of a fluid droplet immersed in another fluid

The oscillations of a fluid droplet immersed in another fluid

Viscous Rayleigh-Taylor instability in spherical geometry

Study of the effect of viscosity and homogeneous horizontal magnetic field on Rayleigh-Taylor instability

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