Dynamics of coarsening foams: accelerated and self-limiting drainage

The evolution of a foam is determined by drainage flow of the continuous (liquid) phase and coarsening (aging) of the dispersed phase (gas bubbles). Free-drainage experiments with slow- and fast-coarsening gases show markedly different dynamics and elucidate the importance of the coupling of the two effects. Strong coarsening leads to drainage times that are shorter (accelerated drainage) and independent of the initial liquid content (self-limiting drainage). A model incorporating the physics of both drainage and diffusive coarsening shows quantitative agreement with experiment.     

Squeezing alcohols into sonoluminescing bubbles: the universal role of surfactants

We conduct an experimental study of the dependence of single bubble sonoluminescence intensity on the concentration of various alcohols. The light intensity is reduced by one-half at a molar fraction of ethanol of approximately 2.5x10(-5); butanol achieves the same reduction at a concentration 10 times smaller. We account for the results by a theoretical model in which the alcohols are assumed to be mechanically forced into the bubble at collapse, modifying the adiabatic exponent of the gas. The increasing hydrophobicities of the alcohols lead to decreasing effective adiabatic exponents, and thus to less heating and therefore less light. Support for this model is obtained by replotting the experimental light intensity values vs the calculated exponents, yielding a collapse of all data onto a universal curve.     

High-speed imaging of an ultrasound-driven bubble in contact with a wall: “Narcissus” effect and resolved acoustic streaming

We report microscopic observations of the primary flow oscillation of an acoustically driven bubble in contact with a wall, captured with the ultra high-speed camera Brandaris 128 (Chin et al. 2003). The driving frequency is up to 200 kHz, and the imaging frequency is up to 25 MHz. The details of the bubble motion during an ultrasound cycle are thus resolved, showing a combination of two modes of oscillations: a radius oscillation and a translation oscillation, perpendicular to the wall. This motion is interpreted using the theory of acoustic images to account for the presence of the wall. We conclude that the bubble is subjected to a periodic succession of attractive and repulsive forces, exerted by its own image. Fast-framing recordings of a tracer particle embedded in the liquid around the particle are performed. They fully resolve the acoustic streaming flow induced by the bubble oscillations. This non-linear secondary flow appears as a tiny drift of the particle position cycle after cycle, on top of the primary back and forth oscillation. The high oscillation frequency accounts for a fast average particle velocity, with characteristic timescales in the millisecond range at the lengthscale of the bubble. The features of the bubble motion being resolved, we can apply the acoustic streaming theory near a wall, which provides predictions in agreement with the observed streaming velocity.     

Response of bubbles to diagnostic ultrasound: a unifying theoretical approach

The scattering of ultrasound from bubbles of m radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and “active” emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scattering and absorption cross-sections. We show that several well-known formulas are recovered in the linear limit of this ansatz. In the case of strongly nonlinear oscillations, however, the cross-sections can be larger than those for linear response by several orders of magnitude. The major part of the incident sound energy is then converted into emitted sound, unlike what happens in the linear case, where the absorption cross-sections exceed the scattering cross-sections. Received: 26 February 1998 / Revised: 13 March 1998 / Accepted: 15 March 1998     

The acoustics of diagnostic microbubbles: dissipative effects and heat deposition

We discuss the effectively detectable scattered intensity of ultrasound from diagnostic microbubble suspensions, taking dissipative mechanisms in the liquid medium into account. In particular, we conclude that neither non-linear wave steepening of the incident (driving) wave nor of the outgoing (scattered) wave has a large effect on the scattered signal from typical bubbles. It is shown that, paradoxically, the far-field solution of the wave field is sufficient to compute the magnitude of expected temperature rises in the medium due to acoustic heat deposition, although appreciable heating is limited to intermediate-field distances from the bubble surface.     

Size-topology correlations in disk packings: terminal bidispersity in order–disorder transitions

Abstract

In random packings or tilings, the size distribution of individual elements (domains) and the statistics of numbers of neighbours of those domains are strongly correlated. In the case of circular disks forming a random packing in the plane, it has long been known empirically that a certain critical amount of bidispersity avoids crystallization of the packing. We demonstrate how the formalism of a simplified granocentric model allows for an analytical computation of the size-topology correlation as a function of both size ratio and frequency of small disks. The results, obtained without free parameters, are in excellent agreement with the empirical findings of packing simulations concerning critical (terminal) bidispersity. It is also shown that, at equal size variance, the discrete (bidisperse) disk size distributions induce stronger disorder than continuously polydisperse disks.