Bubble Oscillations in the Vicinity of a Nearly Plane Free Surface

The linear oscillation frequency of a bubble in the vicinity of a distorted plane free surface is calculated by a perturbation method. The approximate expression found is compared with numerical results valid for surface deformations of arbitrary magnitude. It is found that the approximate analytical result is quite good, provided that the deformation is small compared with the depth of immersion of the bubble. It is also shown that, unless the deformation of the free surface extends to distances at least of the order of an acoustic wavelength, the ‘‘image’’ bubble has the same source strength of the real bubble so that a dipolar acoustic emission can be expected in spite of the deformation of the surface

The natural frequency of oscillation of gas bubbles in tubes

A numerical study is presented of the natural frequency of the volume oscillations of gas bubbles in a liquid contained in a finite-length tube, when the bubble is not small with respect to the tube diameter. Tubes rigidly terminated at one end, or open at both ends, are considered. The open ends may be open to the atmosphere or in contact with a large mass of liquid. The numerical results are compared with a simple approximation in which the bubble consists of a cylindrical mass of gas filling up the cross section of the tube. It is found that this approximation is very good except when the bubble radius is much smaller than that of the tube. An alternative approximate solution is developed for this case. The viscous energy dissipation in the tube is also estimated and found generally small compared with the thermal damping of the bubble. This work is motivated by the possibility of using gas bubbles as actuators in fluid-handling microdevices

Bubble Oscillations in the Nearly Adiabatic Limit

Miksis and Ting [J. Acoust. Soc. Am. 81, 1331 (1987)] reported examples of a marked increase of the radius of an oscillating gas bubble as predicted by their nearly adiabatic model. They attributed this phenomenon to a process of rectified heat transfer into the bubble. By comparison with a more complete model which contains the nearly adiabatic one as an approximation, it is shown that the real cause of this result is instead the error inherent in the approximation. This error arises primarily from the failure of the approximation to capture the complex behavior of the gas temperature and manifests itself in a spurious growth of the mass of gas contained in the bubble. In addition to being more accurate, the more complete model is also found to be less computationally demanding than the approximate one

Examples of Air-Entraining Flows

Four examples of air?entraining flows at the free surface of a liquid are briefly considered: (a) the transient impact of a jet, (b) the application of an excess pressure, (c) two counter?rotating vortices below the surface, and (d) a disturbance on a vortex sheet

The oscillations of a small floating bubble

A simple model of a small bubble floating at the surface of a liquid before bursting is considered. The oscillations of this system are studied by means of a Lagrangian method. It is found that two fundamentally different modes exist. The surface mode has low frequency and does not change appreciably the volume of the immersed part of the bubble: As a consequence, its efficiency as a source of sound in the water is very limited. The volume mode has a much higher frequency and is a more efficient radiator in the water, although it may be hard to excite. Both modes behave as monopole sources in the air. It is therefore predicted that an oscillating floating bubble is a much more intense source of sound in the air than in the liquid. This conclusion seems to be supported by experimental observations

The hydrodynamic interaction of two slowly evaporating spheres

The Stokes flow induced by the slow evaporation or condensation of two spheres is studied. The phase?change velocity is prescribed and uniform over the surfaces of the spheres. Exact expressions are obtained for the streamfunction and the drag forces. Simpler expressions applicable to a variety of limit cases (distant spheres, a source and a sphere, and a sphere and a plane) are presented. When only one sphere is evaporating, depending on the distance from the other sphere, the flow may exhibit a variety of interesting behaviors such as smooth?boundary separation, closed recirculating eddies, and infinite open eddies

Mechanism of air entrainment by a disturbed liquid jet

It was shown in recent work that the crests of surface disturbances on a falling jet are a powerful agent for air entrainment at the free surface of a liquid pool. The paper explores the opposite case in which the jet is disturbed so as to form an axisymmetric trough, rather than a crest. It is found that no air is entrained in this case. The paper concludes with some considerations on the validity of a recently proposed model for air entrainment

Sound Emissions by a Laboratory Bubble Cloud

This paper presents the results obtained from a detailed study of the sound field within and around a cylindrical column of bubbles generated at the center of an experimental water tank. The bubbles were produced by forcing air through a circular array of hypodermic needles. As they separated from the needles the ‘‘birthing wails’’ produced were found to excite the column into normal modes of oscillation whose spatial pressure?amplitude distribution could be tracked in the vertical and horizontal directions. The frequencies of vibration were predicted from theoretical calculations based on a collective oscillation model and showed close agreement with the experimentally measured values. On the basis of a model of the column excitation, absolute sound levels were analytically calculated with results again in agreement with the measured values. These findings provide considerable new evidence to support the notion that bubble plumes can be a major source of underwater sound around frequencies of a few hundred hertz

(Physalis): A New (o) (N) method for the Numerical Simulation of Disperse Systems. Part I: Potential Flow of Spheres

This paper presents a new approach to the direct numerical simulation of potential problems with many spherical internal boundaries, e.g., many spheres in potential flow. The basic idea is to use a local analytic representation valid near the particle and to match it to an external field calculated by a standard finite-difference (or finite-element) method. In this way the geometric complexity arising from the irregular relation between the particle boundary and the underlying mesh is avoided and fast solvers can be used. The results suggest that the computational effort increases less than proportionally to the number of particles and, additionally, that meshes that would be excessively coarse as measured in terms of particle radius in a conventional calculation can be used without significant loss of accuracy. In separate (if preliminary) work the same approach has been extended to the simulation of viscous flow about spheres and cylinders at finite Reynolds numbers