Nonlinear Rayleigh–Taylor instability of two superposed magnetic fluids under parallel rotation and a normal magnetic field

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.     

Nonlinear theory of the ablative Rayleigh-Taylor instability

A fully nonlinear sharp-boundary model of the ablative Rayleigh-Taylor instability is derived and closed in a similar way to the self-consistent closure of the linear theory. It contains the stabilizing effect of ablation and accurately reproduces the results of 2D DRACO simulations. The single-mode saturation amplitude, bubble and spike evolutions in the nonlinear regimes, and the seeding of long-wavelength modes via mode coupling are determined and compared with the classical theory without ablation. Nonlinear stability above the linear cutoff is also predicted.     

Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: a magnetic levitation investigation and theoretical model

A magnetic field gradient was used to draw down a low density paramagnetic fluid below a more dense fluid in a Hele-Shaw cell. On turning off the field a Rayleigh-Taylor instability was observed in situ, and the growth of the most unstable wave vector was measured versus time. A theory for the instability that permits different viscosities for two immiscible fluids was developed, and good agreement was found with the experimental results. The technique of magnetic levitation promises to broaden significantly the accessible parameter space of gravitational interfacial instability experiments.     

Nonlinear analysis of the Rayleigh-Taylor instability at the charged interface

An asymptotic solution to the problem of analyzing the nonlinear stage of the Rayleigh-Taylor instability at the uniformly charged interface between two (conducting and insulating) immiscible ideal incompressible liquids is derived in the third order of smallness. It is found that the charge expands the range of waves experiencing instability toward shorter waves and decreases the length of the wave with a maximum growth rate. It turns out that the characteristic linear scale of interface deformation, which arises when the heavy liquid flows into the light one, decreases as the charge surface density increases in proportion to the square root of the Tonks-Frenkel parameter characterizing the stability of the interface against the distributed self-charge.     

A numerical study on Rayleigh-Taylor instability of aluminum plates driven by detonation

The authors,using elastic-plastic hydrodynamic code,present the Rayleigh-Taylor (RT) instability of Al plates driven by high-explosive detonation. Our numerical study assumes the material is fluid,or it is an elastic-plastic solid,and we compare the results of these simulations with the experimental data. For the numerical simulation of Rayleigh-Taylor instability of the metal driven by high-explosive detonation,the elastic-plastic effect must be assumed. The result of the simulation is different from the e...     

Bubble pulsations between parallel plates

The dynamic response of an acoustically driven spherical bubble between parallel plates is investigated in the linear approximation. For the case of rigid plates, explicit expressions are provided for the resonance frequency and damping, and the importance of including compressibility of the liquid is discussed. For wide channels, approximate results are presented that account for finite acoustic impedance of the plates.     

Hydromagnetic free convection flow through a porous medium between two parallel plates

Steady hydromagnetic free convective flow of a conducting fluid through a porous medium bounded by two parallel plates is considered and effects of G (Grashof number) and the K (permeability parameter) on the velocity field are discussed.     

Bubble acceleration in the ablative Rayleigh-Taylor instability

The highly nonlinear evolution of the single-mode Rayleigh-Taylor instability (RTI) at the ablation front of an accelerated target is investigated in the parameter range typical of inertial confinement fusion implosions. A new phase of the nonlinear bubble evolution is discovered. After the linear growth phase and a short constant-velocity phase, it is found that the bubble is accelerated to velocities well above the classical value. This acceleration is driven by the vorticity accumulation inside the bubble resulting from the mass ablation and vorticity convection off the ablation front. While the ablative growth rates are slower than their classical values in the linear regime, the ablative RTI grows faster than the classical RTI in the nonlinear regime for deuterium and tritium ablators.     

Resistive drift instability and Rayleigh-Taylor instability in a dusty plasma

The resistive drift instability and the Rayleigh-Taylor instability are studied self-consistently in a magnetized inhomogeneous dusty plasma. The effect of grain charge fluctuations is taken into consideration. It is found that the presence of the dust grains in the plasma can significantly affect the resistive drift instability but less significantly the Rayleigh-Taylor instability. Further, the grain charge fluctuation has a tendency to stabilize both instabilities.     

Rayleigh-Taylor instability in variable density swirling flows

Using linear instability theory and nonlinear dynamics, the Rayleigh-Taylor instability of variable density swirling flows is studied. It is found that the flow topology could be predicted, when the instability sets in, using a function χ dependent on density and axial and azimuthal velocities. It is shown that even when the inner axial-flow is heavier than the outer one (a favorable case for the development of the Rayleigh-Taylor instability thanks to the centrifugal force) the instability is not necessarily Rayleigh-Taylor-dominated. It is also shown that when the Rayleigh-Taylor instability develops, it is helical.     

Rayleigh-Taylor/gravitational instability in dense magnetoplasmas

The Rayleigh-Taylor instability is investigated in a nonuniform dense quantum magnetoplasma. For this purpose, a quantum hydrodynamical model is used for the electrons whereas the ions are assumed to be cold and classical. The dispersion relation for the Rayleigh-Taylor instability becomes modified with the quantum corrections associated with the Fermi pressure law and the quantum Bohm potential force. Numerically, it is found that the quantum speed and density gradient significantly modify the growth rate of RT instability. In a dense quantum magnetoplasma case, the linear growth rate of RT instability becomes significantly higher than its classical value and the modes are found to be highly localized. The present investigation should be useful in the studies of dense astrophysical magnetoplasmas as well as in laser-produced plasmas.     

Nonlinear electrohydrodynamic instability conditions of an interface between two fluids under the effect of a normal periodic electric field. III

A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal periodic electric field is subjected to nonlinear deformations. We use the method of multiple scales in order to solve the nonlinear equations. In the first-order problem we obtained Mathieu's differential equation. For the second order, we obtain the nonhomogeneous Mathieu equation and we use the method of multiple scales to obtain a sequence of equations. In the third order we obtain the second-order differential equation of periodic coefficients. Also, we obtain a formula for surface elevation. The stability conditions are determined.     

Closed-form solution of mid-potential between two parallel charged plates with more extensive application

Efficient calculation of the electrostatic interactions including repulsive force between charged molecules in a biomolecule system or charged particles in a colloidal system is necessary for the molecular scale or particle scale mechanical analyses of these systems. The electrostatic repulsive force depends on the mid-plane potential between two charged particles. Previous analytical solutions of the mid-plane potential, including those based on simplified assumptions and modern mathematic methods, are reviewed. It is shown that none of these solutions applies to wide ranges of interparticle distance from 0 to 10 and surface potential from 1 to 10. Three previous analytical solutions are chosen to develop a semi-analytical solution which is proven to have more extensive applications. Furthermore, an empirical closed-form expression of mid-plane potential is proposed based on plenty of numerical solutions. This empirical solution has extensive applications, as well as high computational efficiency.     

Analytical and semi-analytical solutions to flows of two immiscible Maxwell fluids between moving plates

Unsteady flows of two immiscible Maxwell fluids in a rectangular channel bounded by two moving parallel plates are studied. The fluid motion is generated by a time-dependent pressure gradient and by the translational motions of the channel walls in their planes. Analytical solutions for velocity and shear stress fields have been obtained by using the Laplace transform coupled with the finite sine-Fourier transform. These analytical solutions are new in the literature and the method developed in this paper can be generalized to unsteady flows of n-layers of immiscible fluids. By using the Laplace transform and classical method for ordinary differential equations, the second form of the Laplace transforms of velocity and shear stress are determined. For the numerical Laplace inversion, two accuracy numerical algorithms, namely the Talbot algorithm and the improved Talbot algorithm are used.     

Rayleigh-Taylor instability of multi-fluid layers in cylindrical geometry

Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically.The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions. The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation. The two interfaces are decoupled for a larger mode number perturbation. The dependencies of the amplitudes of perturbation on different initial conditions are analyzed. The negative feedback effect from initially stable interface to another unstable interface is observed. In the limit of infinity inner radius and finite shell thickness, the results in planar geometry are recovered.     

Flow of low-density gases between parallel plates

The flow of inert gases, hydrogen, and deuterium was studied in a plane-parallel aperture 19 high formed by glass plates. A minimum volume flow rate is observed at a Knudsen number of 1. For Kn > 1, the volume flow rate increases without limit in the pressure range studied. The experimental results for the different gases differ greatly in the region of free molecular flow. Neon displays a behavior different from that of the other gases. The available theoretical results are compared with the experimental results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 9, pp. 105–111, September, 1969.     

Development of the Rayleigh-Taylor instability in a thin layer of a magnetic fluid subjected to an orthogonal magnetic field

A thin layer of a Newtonian magnetic fluid wetting the faced-down surface of a horizontal magnetized plate in a vertical magnetic field is considered. The lower boundary of the layer is the interface with a stationary gas. The effect of magnetic forces on the development of the Rayleigh-Taylor instability is considered in the linear formulation of the long-wave approximation of ferrohydrodynamic equations.