Rayleigh-Taylor Model Research Articles

Atomization of viscous and non-newtonian liquids by a coaxial, high-speed gas jet. Experiments and droplet size modeling

This paper describes a collaborative theoretical and experimental research effort to investigate both the atomization dynamics of non-Newtonian liquids as well as the performance of coaxial atomizers utilized in pharmaceutical tablet coating. In pharmaceutically relevant applications, the coating solutions being atomized are typically complex, non-Newtonian fluids which may contain polymers, surfactants and large concentrations of insoluble solids in suspension. The goal of this investigation was to improve the understanding of the physical mechanism that leads to atomization of viscous and non-Newtonian fluids and to produce a validated theoretical model capable of making quantitative predictions of atomizer performance in pharmaceutical tablet coaters. The Rayleigh–Taylor model developed by Varga et al. has been extended to viscous and non-Newtonian fluids starting with the general dispersion relation obtained by Joseph et al. The theoretical model is validated using droplet diameter data collected with a Phase Doppler Particle Analyzer for six fluids of increasing rheological complexity. The primary output from the model is the Sauter Mean Diameter of the atomized droplet distribution, which is shown to compare favorably with experimental data. Critical model parameters and plans for additional research are also identified.

The Semiclassical Regime for Ablation Front Models

In this paper, we study two problems appearing in two-dimensional fluid mechanics in a constant gravity field $${g}=-g{e}_{\tilde x}$$ . These two problems—the Rayleigh convection problem and the ablation front problem—generalize the Rayleigh–Taylor model in compressible flows. The analysis of their stability relies on semiclassical techniques for the linearized system around a reference solution. We consider normal modes which are approximate solutions corresponding to large wave numbers associated with $$\tilde{y}$$ , and we discuss the existence or the non-existence of such normal modes. The results depend on the value of the dimensionless growth rate Γ compared with two relevant mathematical parameters, namely σ p (p standing for the model) and some effective semiclassical parameter h.

On the miscible Rayleigh–Taylor instability: two and three dimensions

We investigate the miscible Rayleigh–Taylor (RT) instability in both two and three dimensions using direct numerical simulations, where the working fluid is assumed incompressible under the Boussinesq approximation. We first consider the case of randomly perturbed interfaces. With a variety of diagnostics, we develop a physical picture for the detailed temporal development of the mixed layer: we identify three distinct evolutionary phases in this development, which can be related to detailed variations in the growth of the mixing zone. Our analysis provides an explanation for the observed differences between two- and three-dimensional RT instability; the analysis also leads us to concentrate on the RT models which (i) work equally well for both laminar and turbulent flows, and (ii) do not depend on turbulent scaling within the mixing layer between fluids. These candidate RT models are based on point sources within bubbles (or plumes) and their interaction with each other (or the background flow). With this motivation, we examine the evolution of single plumes, and relate our numerical results (for single plumes) to a simple analytical model for plume evolution.

Developments in Spray Modeling in Diesel and Direct-Injection Gasoline Engines

Developments in Spray Modeling in Diesel and Direct-Injection Gasoline Engines — In direct- injection engines the fuel spray characteristics influence the combustion efficiency and exhaust emissions. The performance of available spray models for predicting liquid and vapor fuel distributions, and their influence on combustion is reviewed for both diesel and gasoline direct injection engines. A phenomenological nozzle flow model is described for simulating the effects of diesel injector nozzle internal geometry on the fuel injection and spray processes. The flow model provides initial conditions for the liquid jet breakup model that considers wave instabilities due to Kelvin-Helmholtz (KH) and Rayleigh-Taylor (RT) mechanisms. A linearized instability analysis has also been extended to consider the breakup of liquid sheets for modeling pressure-swirl gasoline injectors. Diesel engine predictions have been compared with extensive data from in-cylinder laser diagnostics carried out in optically accessible heavy-duty, DI Diesel engines over a wide range of operating conditions. The results show that the nozzle flow model used in combination with the KH and RT models gives realistic spray predictions. In particular, the limited liquid fuel penetration length observed experimentally and the flame shape details are captured accurately. The liquid sheet breakup model has also been compared favorably with experimental spray penetration and drop size data for gasoline hollow-cone sprays. This model is currently being applied to study stratified charge combustion in GDI engines.

Hydrothermalism and diapirism in the Archean: gravitational instability constraints

In Archean granite–greenstone terrains, greenstone belts are interspersed between granitic plutons to form dome-and-basin structures. Although the hypothesis is widely debated, gravitational instabilities have been invoked to explain such structures, which are typical of Archean cratons. We used a numerical approach based on a Rayleigh-Taylor model to examine the possibility that these structures result from gravitational processes, giving a special emphasis to the alteration of the mafic–ultramafic volcanic rocks. We investigated (a) the influence of contemporaneous hydrothermal activity upon density and viscosity of mafic–ultramafic volcanics and (b) the perturbation of thermal conditions in the granitoid basement on its rheology. Variables included: (1) varying proportions of mafic–ultramafic volcanics and their thickness relative to a granitoid basement; (2) density and viscosity differences between fresh and altered rocks; (3) kinetics of alteration; and (4) thermal regime and viscosity of the basement. We adopted a multi-layer model with variable viscosity in which the upper layers represent an ultramafic–mafic volcanic pile and the underlying layers a granitic basement. We show that the high viscosities of fresh volcanic rocks and underlying basement granitoids normally prevent the development of gravity-driven deformation. The conditions required to produce the observed structures are realized only when: (a) a high proportion of the volcanic rocks are altered to a low-viscosity assemblage; and (b) the underlying granitic basement is moderately heated or migmatized.

Nonlinear magnetohydrodynamic detonation: Part I

The sudden release of magnetic free energy, as occurs in spectacular solar flare events, tokamak disruptions, and enigmatic magnetospheric substorms, has long defied any acceptable theoretical explanation. Usual attempts at explaining these explosive events invoke magnetic reconnection and/or ideal magnetohydrodynamic (MHD) instability. However, neither of these two mechanisms can explain the fast time scales without nonlinear destabilization. Recently, Cowley et al. [Phys. Plasmas 3, 1848 (1996)] have demonstrated a new mechanism for nonlinear explosive MHD destabilization of a line tied Rayleigh–Taylor model. In this paper, this picture is generalized to arbitrary magnetic field geometries. As an intermediate step, the ballooning equation in a general equilibrium is derived including the effects of magnetic field curvature, shear, and gravity. This equation determines the linear stability of the plasma configuration and the behavior of the plasma displacement along the magnetic field line. The nonlinear equation which determines the time and spatial dependence, transverse to the equilibrium magnetic field, of the plasma displacement is obtained in fifth order of the expansion. The equations show that explosive behavior is a natural and generic property of ballooning instabilities close to the linear stability boundary.

Calculations of R-T instability in liners based on the nonlinear Baker-Freeman model

We used the nonlinear Rayleigh-Taylor model of instabilities proposed by Baker and Freeman for studying instabilities in targets for inertial controlled thermonuclear synthesis for investigation of analogous problems arising upon implosion in liners. We give a description of the model as applied to the problem of acceleration of the liners by the internal magnetic field. We compare the given model with the familiar results of two-dimensional MHD calculations. We consider the problem of development of R-T instability in the linear upon passage of a 15–20 MA current pulse along it with a 200 nsec leading edge.

Electroviscoelastic Rayleigh-Taylor instability of Maxwell fluids: I. Effect of a constant tangential electric field

The stability of the Rayleigh-Taylor model for an electroviscoelastic Maxwell fluid are investigated. The method of multiple scales is used in order to obtain the stability conditions. A transcendental dispersion relation is obtained at zero-order. The special case, when the two fluids have the same kinematic viscosity, is considered to relax the complexity of the transcendental dispersion relation. The solvability conditions introduce a first-order differential equation. It is found that the increase in the relaxation time lambda has a destabilizing influence. Also the increase in the kinematic viscosity in the presence of the parameter lambda yields a destabilizing effect. The increase in the kinematic viscosity in the absence of elasticity (pure viscous fluids) has a stabilizing effect.

On the Rate of Growth of Disturbances in Rayleigh-Taylor Model

On the basis of the linear theory of stability, the present paper makes an attempt to investigate theoretically the bounds for the rate of growth of an arbitrary disturbance in the Rayleigh-Taylor configuration. A circle theorem is established in this direction which arrests the complex amplification rate of an arbitrary oscillatory perturbation inside a circle. Certain other results concerning the above bounds and the stability of the model are also given.