E. Rolley

Equation of state of water under negative pressure

We report on the simultaneous measurements of the speed of sound and the density in liquid water under negative pressure. Application of a focused acoustic wave to the bulk liquid is able to generate negative pressures before nucleation of the vapor phase occurs. A method for time-resolved Brillouin scattering is developed to measure the speed of sound during the passage of a 1 MHz ultrasonic wave. This is coupled with a fiber optic probe hydrophone which allows the determination of the density. Together, these methods give an ambient temperature equation of state of metastable liquid water down to the acoustic cavitation threshold. Empirical equations of state of water are based on experimental data at positive pressure; the validity of their extrapolation to negative pressures had been tested only indirectly or with very weakly metastable liquid. We provide thermodynamic data that prove the fidelity of recent equations of state down to -26 MPa. However, this raises questions regarding the nature of the cavitation threshold observed in acoustic experiments, which is far less negative than expected.

The static and dynamic properties of vicinal surfaces on helium 4 crystals

We have studied melting-freezing waves propagating at low temperature (40<T<500mK) on vicinal surfaces of hep helium 4 crystals, which are tilted by a small angle ø with respect to c facets. We have first obtained the experimental evidence of a crossover angle øc≈ 2.5 °, where the surface properties change from stepped and anisotropic to rough and Isotropic. This result confirms our previous prediction1 that such a crossover should occur at the small angle where the large step width is comparable to the average distance between steps. It also confirms the hypothesis that crystal surfaces are weakly coupled to the lattice in helium. In the ø→ 0 limit, we observed a clear stepped behaviour: the longitudinal component of the surface stiffness vanishes while the transverse component diverges. A quantitative analysis of these two components allowed us to measure the step energy and the interactions between steps. Good agreement is found with the prediction that step interactions result from the combination of elastic and entropic effects. We also found evidence that helium 3 impurities adsorb on the liquid-solid interface and lower the step energy when ordinary helium 4 (130 ppb of3He) is used instead of an ultrapure sample (0.4ppb). Furthermore, from the damping of the waves, we could study the dynamics of vicinal surfaces, i.e. their mobility as a function of temperature, angle and frequency. Here too, a crossover is observed from stepped to rough behavior. The dynamics is sensitive to the existence of steps up to higher angles than the stiffness. We show that a true stepped behavior is observed only if two conditions are fulfilled: the distance between steps must be much larger than the step width, and also larger than the mean wavelength of thermal phonons. By changing the frequency, we could finally confirm that the surface mobility increases when the phonon mean free path becomes smaller than the wavelength of the melting-freezing waves. We conclude with some suggestions for further theoretical and experimental studies.

Width distribution of contact lines on a disordered substrate

We have studied the roughness of a contact line on a disordered substrate by measuring its width distribution, which characterizes the roughness completely. The measured distribution is in excellent agreement with the distribution calculated in previous works, extended here to the case of open boundary conditions. This type of analysis, which is performed here on experimental data, provides a strong confirmation that the Joanny-de Gennes model is not sufficient to describe the dynamics of the contact line at the depinning threshold.

The Surface Tension of B.c.c. 3He Crystals

We have measured the surface tension γ of b.c.c. solid helium-3 from the visual observation of large single crystals, in equilibrium with their liquid phase, between 0.1 and 0.4 K. This first direct measurement gives a much larger result (γ = (0.060 ± 0.011) erg/cm2) than previously estimated from the maximum temperature at which facets were observed on growing crystals (0.10 K). We propose that quantum fluctuations reduce the step energy and broaden the roughening transition, so that dynamic roughening may occur far below the static roughening temperature.

Dynamic Broadening of the Roughening Transition

By using an interferometric technique, we carefully studied the growth of hcp 4He crystals near the roughening transition of their (0001) surfaces, at TR = 1.28 K. We discovered an intermediate regime for the growth, at T TR, between an exponential behaviour due to the 2D nucleation of terraces in the smooth state (T TR). This intermediate regime takes place slightly below TR. Its temperature width increases with the applied driving force. All our experimental results are consistent with a new calculation based on the critical theory of roughening, which predicts a completely continuous or infinite-order transition. Precise values are deduced for the roughening temperature TR((1.28 ± 0.01) K) and the relative amplitude of the lattice potential (tc = 0.65 ± 0.15).

Optical measurement of contact angle of liquid helium on cesium

We have studied the wetting properties of helium-4 on a carefully prepared cesium substrate using an interferometric technique. Below the wetting temperature, which is 1.9 K in our experiment, we observe a striking hysteretic behaviour, which is due to the pinning of the contact line on defects of the substrate. We have measured the temperature dependence of the contact angle θa for an advancing meniscus. At low temperature, we find θa≈25°, in contrast with a previous result by Klier et al.

The growth rate of3He crystals

We have measured the relaxation of the shape of3He crystals under the effect of gravity and surface tension, close to the minimum in their melting curve atTmin=0.32 K. A growth rate is deduced, which is found to be at a maximum atTmin when the latent heat is zero. We interpret this maximum value (k=0.18±0.04 sec/m) as the intrinsic mobility of the liquid-solid interface and compare it with existing theories. We also consider on which side the latent heat is released during growth, and how it may cross the liquid-solid interface.

The First Roughening Transition of 3He Crystals

We have observed the appearance of (110) facets on b.c.c. 3He crystals at 0.08 K. This roughening temperature is consistent with an estimate of the surface stiffness and the universal relation from the critical theory of roughening. We also present a qualitative description of the various instabilities which occur in our experimental conditions (dendrites, needle and tip oscillating crystals, cellular instabilities) and discuss the effect of the roughening transition on these instabilities.

Defects at the Nanoscale Impact Contact Line Motion at all Scales.

The contact angle of a liquid drop moving on a real solid surface depends on the speed and direction of motion of the three-phase contact line. Many experiments have demonstrated that pinning on surface defects, thermal activation and viscous dissipation impact contact line dynamics, but so far, efforts have failed to disentangle the role of each of these dissipation channels. Here, we propose a unifying multiscale approach that provides a single quantitative framework. We use this approach to successfully account for the dynamics measured in a classic dip-coating experiment performed over an unprecedentedly wide range of velocity. We show that the full contact line dynamics up to the liquid film entrainment threshold can be parametrized by the size, amplitude and density of nanometer-scale defects. This leads us to reinterpret the contact angle hysteresis as a dynamical crossover rather than a depinning transition.

Thermally activated wetting dynamics in the presence of surface roughness.

From simple models of thermally activated contact line dynamics far below the depinning transition, one expects the velocity to depend exponentially on the applied force and the activation area to be the size of the defects on the surface. We study contact line motion on evaporated gold films and find that the dynamics are activated, but the activation area is not straightforwardly linked to the surface roughness. Surprisingly, the activation area can be significantly smaller than any features on the surface. Furthermore, it depends strongly on the liquid. We show that this indicates that the line is close to the depinning threshold at experimentally accessible velocities. A model based on independent defects is developed and used to show deviations from the purely exponential law. The dynamics are written entirely in terms of properties of the surface and partially wetting liquid. In addition, we are able to show that the region of validity of models of thermal activation on mesoscopically rough surfaces typically corresponds to velocities of less than 1 mm/s.