100 research outputs found
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
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
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
Predicting the Characteristics of Defect Transitions on Curved Surfaces
The energetically optimal position of lattice defects on intrinsically curved
surfaces is a complex function of shape parameters. For open surfaces, a simple
condition predicts the critical size for which a central disclination yields
lower energy than a boundary disclination. In practice, this transition is
modified by activation energies or more favorable intermediate defect
positions. Here it is shown that these transition characteristics (continuous
or discontinuous, first or second order) can also be inferred from analytical,
general criteria evaluated from the surface shape. A universal scale of
activation energy is found, and the criterion is generalized to predict
transition order as symmetries such as that of the shape are broken. The
results give practical insight into structural transitions to disorder in many
cellular materials of technological and biological importance
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
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