Non-linear effects and shock formation in the focusing of a spherical acoustic wave : Numerical simulations and experiments in liquid helium

The focusing of acoustic waves is used to study nucleation phenomena in liquids. At large amplitude, non-linear effects are important so that the magnitude of pressure or density oscillations is difficult to predict. We present a calculation of these oscillations in a spherical geometry. We show that the main source of non-linearities is the shape of the equation of state of the liquid, enhanced by the spherical geometry. We also show that the formation of shocks cannot be ignored beyond a certain oscillation amplitude. The shock length is estimated by an analytic calculation based on the characteristics method. In our numerical simulations, we have treated the shocks with a WENO scheme. We obtain a very good agreement with experimental measurements which were recently performed in liquid helium. The comparison between numerical and experimental results allows in particular to calibrate the vibration of the ceramics used to produce the wave, as a function of the applied voltage.Comment: 20 pages, 26 figures. Submitted to The European Physical Journal

Freezing of He-4 and its liquid-solid interface from Density Functional Theory

We show that, at high densities, fully variational solutions of solid-like type can be obtained from a density functional formalism originally designed for liquid 4He. Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased DF methods to study highly non-homogeneous systems, like 4He interacting with strongly attractive impurities/substrates, or the nucleation of the solid phase in the metastable liquid.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Detecting vapour bubbles in simulations of metastable water

International audienceThe investigation of cavitation in metastable liquids with molecular simulations requires an appropriate definition of the volume of the vapour bubble forming within the metastable liquid phase. Commonly used approaches for bubble detection exhibit two significant flaws: first, when applied to water they often identify the voids within the hydrogen bond network as bubbles thus masking the signature of emerging bubbles and, second, they lack thermodynamic consistency. Here, we present two grid-based methods, the M-method and the V-method, to detect bubbles in metastable water specifically designed to address these shortcomings. The M-method incorporates information about neighbouring grid cells to distinguish between liquid- and vapour-like cells, which allows for a very sensitive detection of small bubbles and high spatial resolution of the detected bubbles. The V-method is calibrated such that its estimates for the bubble volume correspond to the average change in system volume and are thus thermodynamically consistent. Both methods are computationally inexpensive such that they can be used in molecular dynamics and Monte Carlo simulations of cavitation. We illustrate them by computing the free energy barrier and the size of the critical bubble for cavitation in water at negative pressure

Cavitation pressure in liquid helium

Recent experiments have suggested that, at low enough temperature, the homogeneous nucleation of bubbles occurs in liquid helium near the calculated spinodal limit. This was done in pure superfluid helium 4 and in pure normal liquid helium 3. However, in such experiments, where the negative pressure is produced by focusing an acoustic wave in the bulk liquid, the local amplitude of the instantaneous pressure or density is not directly measurable. In this article, we present a series of measurements as a function of the static pressure in the experimental cell. They allowed us to obtain an upper bound for the cavitation pressure P_cav (at low temperature, P_cav < -2.4 bar in helium 3, P_cav < -8.0 bar in helium 4). From a more precise study of the acoustic transducer characteristics, we also obtained a lower bound (at low temperature, P_cav > -3.0 bar in helium 3, P_cav > - 10.4 bar in helium 4). In this article we thus present quantitative evidence that cavitation occurs at low temperature near the calculated spinodal limit (-3.1 bar in helium 3 and -9.5 bar in helium 4). Further information is also obtained on the comparison between the two helium isotopes. We finally discuss the magnitude of nonlinear effects in the focusing of a sound wave in liquid helium, where the pressure dependence of the compressibility is large.Comment: 11 pages, 9 figure

Anomaly in the stability limit of liquid helium 3

We propose that the liquid-gas spinodal line of helium 3 reaches a minimum at 0.4 K. This feature is supported by our cavitation measurements. We also show that it is consistent with extrapolations of sound velocity measurements. Speedy [J. Phys. Chem. 86, 3002 (1982)] previously proposed this peculiar behavior for the spinodal of water and related it to a change in sign of the expansion coefficient alpha, i. e. a line of density maxima. Helium 3 exhibits such a line at positive pressure. We consider its extrapolation to negative pressure. Our discussion raises fundamental questions about the sign of alpha in a Fermi liquid along its spinodal.Comment: 5 pages, 3 figure

Quantum cavitation in liquid 3^3He: dissipation effects

We have investigated the effect that dissipation may have on the cavitation process in normal liquid $^3$He. Our results indicate that a rather small dissipation decreases sizeably the quantum-to-thermal crossover temperature $T^*$ for cavitation in normal liquid $^3$He. This is a possible explanation why recent experiments have not yet found clear evidence of quantum cavitation at temperatures below the $T^*$ predicted by calculations which neglect dissipation.Comment: To be published in Physical Review B6

Effect of dissolved salt on the anomalies of water at negative pressure

Adding salt to water at ambient pressure affects its thermodynamic properties. At low salt concentration, anomalies such as the density maximum are shifted to lower temperature, while at large enough salt concentration they cannot be observed any more. Here we investigate the effect of salt on an anomaly recently observed in pure water at negative pressure: the existence of a sound velocity minimum along isochores. We compare experiments and simulations for an aqueous solution of sodium chloride with molality around $1.2\,\mathrm{mol\,kg^{-1}}$, reaching pressures beyond $-100\,\mathrm{MPa}$. We also discuss the origin of the minima in the sound velocity and emphasize the importance of the relative position of the temperatures of sound velocity and density anomalies.Comment: 10 pages, 13 figures, 1 appendix. Added minor simulation detail