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

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 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

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

The Action of Pressure-Radiation Forces on Pulsating Vapor Bubbles

The action of pressure-radiation (or Bjerknes) forces on gas bubbles is well understood. This paper studies the analogous phenomenon for vapor bubbles, about which much less is known. A possible practical application is the removal of boiling bubbles from the neighborhood of a heated surface in the case of a downward facing surface or in the absence of gravity. For this reason, the case of a bubble near a plane rigid surface is considered in detail. It is shown that, when the acoustic wave fronts are parallel to the surface, the bubble remains trapped due to secondary Bjerknes force caused by an "image bubble." When the wave fronts are perpendicular to the surface, on the other hand, the bubble can be made to slide laterally

PHYSALIS: a new method for particle simulation: Part II: two-dimensional Navier–Stokes flow around cylinders

This paper presents a new approach to the direct numerical simulation of particle flows. The basic idea is to use a local analytic representation valid near the particle to “transfer” the no-slip condition from the particle surface to the adjacent grid nodes. 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 very slowly with the number of particles so that the method is efficient for large-scale simulations. The focus here is on the two-dimensional case (cylindrical particles), but the same procedure, to be developed in forthcoming papers, applies to three dimensions (spherical particles). Several extensions are briefly discussed.\u