Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation

The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solutions with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. An unusual test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle

Reply to comments on "General analysis of the stability of superposed fluids"

Previous results by Plesset and Hsieh on the effects of compressibility for Rayleigh–Taylor instability are shown to be valid, and an alternative brief deduction is given

Flow of vapour in a liquid enclosure

A solution is developed for the flow of a vapour in a liquid enclosure in which different portions of the liquid wall have different temperatures. It is shown that the vapour pressure is very nearly uniform in the enclosure, and an expression for the net vapour flux is deduced. This pressure and the net vapour flux are readily expressed in terms of the temperatures on the liquid boundary. Explicit results are given for simple liquid boundaries: two plane parallel walls at different temperatures and concentric spheres and cylinders at different temperatures. Some comments are also made regarding the effects of unsteady liquid temperatures and of motions of the boundaries. The hemispherical vapour cavity is also discussed because of its applicability to the nucleate boiling problem

The Motion of a Charge Particle in a Uniform Magnetic Field

We study the motion of a classical (nonquantal) charged particle in a uniform magnetic field by means of i) the Abraham-Lorentz equation, ii) the Dirac relativistic equation and iii) the Caldirola nonrelativistic, finite-difference equation. In cases i) and iii) closed-form solutions are obtained. For case ii) we apply for the first time the twovariable asymptotic method which enables us to obtain a uniformly valid approximate solution free of the secular terms present in the results of previous authors

The average stress in incompresible disperse flow

An analysis of the average stress in a disperse flow consisting of equal spherical particles suspended in a fluid is presented. Other than incompressibility, no assumptions are made on the rheological nature of the fluid. In particular, the Reynolds number of the particle motion relative to the fluid is arbitrary. The use of ensemble averages permits the consideration of spatially non-uniform systems, which reveals features not identified before. In particular, it is shown that, in general, the average stress is not symmetric, even when there are no external couples acting on the particles. A quantity to be identified with the mixture pressure (including the particle contribution) is identified. The structure of the momentum equations for the fluid and particle phases is systematically derived. As an example, the case of particles suspended in a locally Stokes flow is considered

Nonlinear Oscillations of Gas Bubbles in Liquids: Steady State Solutions

The nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to the action of a sound field are investigated by means of an asymptotic method. Approximate analytical solutions for the steady?state oscillations are presented for the fundamental mode, for the first and second subharmonics, and for the first and second harmonics to second order in the expansion. These results are compared with some numerical ones and a very good agreement is found

Nonlinear Oscillations of Gas Bubbles in Liquids: Transient Solutions and the Connection Between Subharmonic Signal and Cavitation

The transient nonlinear oscillations of a spherical gas bubble in an incompressible, viscous liquid subject to the action of a sound field are investigated by means of an asymptotic method. Approximate analytical solutions are presented for the frequency regions of the fundamental resonance, the first and second subharmonic, and the first and second harmonic. Based on the results of this investigation, a new hypothesis to explain the connection between subharmonic signal and cavitation is put forward. It is suggested that bubbles emitting the subharmonic signal act primarily as monitors of cavitation events, and are smaller than resonance size. Finally, the free oscillations of the bubble are briefly considered

Thermal Effects and Damping Mechanisms in the Forced Radial Oscillations of Gas Bubbles in Liquids

A linearized theory of the forced radial oscillations of a gas bubble in a liquid is presented. Particular attention is devoted to the thermal effects. It is shown that both the effective polytropic exponent and the thermal damping constant are strongly dependent on the driving frequency. This dependence is illustrated with the aid of graphs and numerical tables which are applicable to any noncondensing gas–liquid combination. The particular case of an air bubble in water is also considered in detail

A new mechanism for sonoluminescence

It is argued that a pulsating acoustically levitated bubble cannot possibly maintain a spherical shape. A jet forms during compression, and the sound amplitude such that the jet first strikes the other side of the bubble with sufficient energy is hypothesized to be the threshold for sonoluminescence. It is proposed that the connection between jet impact and light emission is a fracturing of the liquid that cannot flow during the extremely short time scale over which pressure is applied. With this hypothesis, sonoluminescence would therefore be a manifestation of the non-Newtonian nature of water and other simple liquids when stressed with sufficient intensity and rapidity

Bubble-Related Ambient Noise in the Ocean

An analysis is presented of the mechanisms by which bubbles can generate ambient noise in the ocean and the resulting noise levels are estimated. Bubbles can be extremely efficient amplifiers of water turbulence noise up to 100–200 Hz. At higher frequencies, the Lagrangian spectral intensity of the turbulence is too poor for this mechanism to contribute. Above 1–2 kHz, however, the oscillations by which newly formed bubbles dispose of their initial energy is shown to lead to substantial noise levels. This same process cannot account for the noise in the frequency range intermediate between these two because it would require unrealistically large bubbles, with a diameter of 1 cm or more. A possible mechanism active in this intermediate range, in which relatively large levels of ambient noise are observed, is that of collective oscillations of bubble clouds. In all cases the results obtained by the formal derivations (which are based on an adaptation of Lighthill’s theory of aerodynamic noise) are substantiated by simple physical arguments. Other possible noise mechanisms in which bubbles are involved are also briefly considered