Cracks and fingers: dynamics of ductile fracture in an aqueous foam

Fracture of a quasi-two-dimensional aqueous foam by injection of air can occur via two distinct mechanisms, termed brittle and ductile, which are analogous to crack modes observed for crystalline atomic solids such as metals. In the present work we focus on the dynamics and morphology of the ductile process, in which no films between bubbles are broken. A network modeling approach allows detailed analysis of the foam morphology from individual bubbles to the shape of the propagating crack. This crack develops similarly to fingering instabilities in Hele–Shaw cells filled with homogeneous fluids. We show that the observed width and shape of the crack are compatible this interpretation, and that the discreteness of the bubble structure provides symmetry perturbations and limiting scales characteristic of anomalous fingering. The model thus bridges the gap between fracture of the solid foam lattice and instability growth of interfaces in a fluid system

Response of bubbles to diagnotic ultrasound:a unifying theoretical approach

The scattering of ultrasound from bubbles of $\sim 1~\mu$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

Bubble geometry

Droge schuim in rust evolueert naar een toestand waar de totale oppervlakte van de schuimbellen is geminimaliseerd. Dit proces veroorzaakt groei bij enkele luchtbellen en inkrimping bij andere. Vijftig jaar geleden toonde John von Neumann aan dat in tweedimensionaal schuim de groeiratio enkel afhangt van het aantal zijden van de polygonale schuimbel. Sascha Hilgenfeldt laat zien dat een goede indicator van de groeiratio in drie dimensies het aantal zijvlakken van de polyhedrale schuimbel is. De analytische theorie en de numerieke simulaties komen bovendien goed overeen

Sound radiation of 3 MHz driven gas bubbles

The sound radiation of 3 MHz acoustically driven air bubbles in liquid is analysed with respect to possible applications in second harmonic ultrasound diagnostics devices, which have recently come into clinical use. In the forcing pressure amplitude P_a = 1-10 atm and ambient radius R_0 = 0.5-5 \mu m parameter domain a narrow regime around the resonance radius R_0 \sim 1-1.5 \mu m and relatively modest P_a \sim 2-2.5 atm is identified in which optimal sound yield in the second harmonic is achieved while maintaining spherical stability of the bubble. For smaller P_a and larger R_0 hardly any sound is radiated; for larger P_a bubbles become unstable towards non-spherical shape oscillations of their surface. The computation of these instabilities is essential for the evaluation of the optimal parameter regime. A region of slightly smaller R_0 and P_a \sim 1-3 atm is best suited to achieve large ratios of the second harmonic to the fundamental intensity. Spherical stability is guaranteed in the suggested regimes for liquids with an enhanced viscosity compared to water, such as blood.Comment: 19 pages, 10 low resolution ps-figures; higher resolution figures can be retrieved from http://staff-www.uni-marburg.de/~hilgenfe/hires.htm

Analysis of Rayleigh-Plesset dynamics for sonoluminescing bubbles

Recent work on single bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can already be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. In this work we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is enlarged, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles against surface oscillations, we conclude that the ideal liquid for violently collapsing, surface stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (>40 times the viscosity of water) will again preclude collapses.Comment: 41 pages, 21 eps and ps figures; LaTeX stylefiles replaced because the PostScript file produced at the archive had misplaced and misscaled figure

Inert gas accumulation in sonoluminescing bubbles

In this paper we elaborate on the idea [Lohse et al., Phys. Rev. Lett. 78, 1359-1362 (1997)] that (single) sonoluminescing air bubbles rectify argon. The reason for the rectification is that nitrogen and oxygen dissociate and their reaction products dissolve in water. We give further experimental and theoretical evidence and extend the theory to other gas mixtures. We show that in the absence of chemical reactions (e.g., for inert gas mixtures) gas accumulation in strongly acoustically driven bubbles can also occur.Comment: J. Chem. Phys., in press (to appear in November 1997), 30 pages, 15 eps-figure