Water nucleation : wave tube experiments and theoretical considerations

This work is an experimental and theoretical study of the condensation of water. Condensation consists of nucleation – the formation of droplets – and the subsequent growth of those droplets. In our expansion tube setup, these processes are separated in time with the nucleation pulse principle, in the following manner. First, a mixture of water vapour and a carrier gas is cooled down by means of an adiabatic expansion. Nucleation then takes place during a period of constant pressure, temperature, and supersaturation; this period is called the nucleation pulse. At the end of the pulse, the gas is slightly recompressed, which ends the formation of new droplets. A state of supersaturation is maintained, so that the existing droplets grow until they become large enough be detected. The number density of droplets is inferred from the extinction of a laser beam and the scattered light from the droplets. The ratio of the number density of detected droplets and the pulse duration yields the nucleation rate: the number of macroscopic droplets that are formed per unit of space and time. The fraction of droplets that is detected ater use of the nucleation pulse method has been analysed theoretically by two condensation models. The first is based on the kinetic master equation, which describes the growth of molecular clusters of arbitrary size by collisions withmonomers. The second model is based on the general dynamic equation (GDE), which is often used in aerosol science. It was found that the gde is inaccurate for small droplets, whereas it agrees with the kinetic equation for large droplets. The nucleation pulse analysis shows that ater short pulses, a signiicant number of droplets evaporate, resulting in a systematic underestimation of the nucleation rate. In contrast, for our experimental pulse length, the number of droplets that evaporate ater the pulse is negligible. The nucleation rates of water have been measured with helium as a carrier gas, at a nucleation pressure of 1 bar and nucleation temperatures between 200 and 240 K. Our nucleation rates agree with accurate measurements by Wölk and Strey in the temperature and nucleation rate range of overlap. The results provide an extension of nucleation rate measurements to high supersaturations and low temperatures. Classical nucleation theory predicts an incorrect temperature dependence of the nucleation rate; this is well known. Contrary to what is usually assumed, our results demonstrate that the supersaturation dependence of the classical rate is incorrect as well. As the temperature dependence of the experimental rates is smooth, we assume that down to 200 K water condenses as supercooled liquid drops, which remain liquid during ourmeasurement time (15ms). Supercooled water does not normally exist below 233 K and its properties there are unknown, which makes the theoretical predictions more uncertain. Water nucleation has also been studied in a mixture of methane and carbon dioxide, a system that is important for the natural gas industry. To model nucleation, a description of the equilibrium composition in the water–methane–carbon dioxide system was required. Therefore, a suitable ‘cubic plus association’ (cpa) equation of state was selected and itted to experimental data. For that purpose, literature data on phase equilibrium in the three binary systems water–methane, water–carbon dioxide, and methane–carbon dioxide was summarized and reviewed. The literature data on water vapour fractions in the two binary systems with water is inaccurate and inconsistent, and the cpa prediction is accurate to 5%, at best. On the other hand, the solubility of methane or carbon dioxide in water is reproduced well. The validity range of the cpa equation of state fromthis work is 220–340K and 0–50 bar. Another quantity that is required for the prediction of the nucleation rate is the surface tension of water. For natural-gas-like systems, the inluence of methane and carbon dioxide on the surface tension should be known. Therefore, literature data were collected and are summarized by empirical its that are accurate to 0.5% in the range of experimental data. The its can be extrapolated down to 235 K, but the relative uncertainty of the surface tension is then about 5%, which strongly afects the prediction of nucleation rates. Water nucleation rates were measured at 235 K and 10 bar in pure methane, and also in two mixtures of methane and carbon dioxide. The nucleation rate inmethane was found to be about three orders ofmagnitude higher than the nucleation rate of water in helium at 1 bar, at equal temperature and supersaturation. The increase is likely caused by the reduction of the water surface tension by methane; the relative decrease of surface tension is estimated at 3.5 %. In our measurements with carbon dioxide we encountered problems in reproducing measurements on the long term.Within a measurement series, carried out in a few months, reproducibility of the nucleation rate was better than a factor of two, but we observed diferences of a factor of four between series performed in June and October 2007. The relative efect of carbon dioxide, however, is clear because experiments with and without carbon dioxide were performed consecutively. This allows drawing the following conclusions: The presence of 3% carbon dioxide beside methane increases the nucleation rate by one order of magnitude, compared to the rate in pure methane. Furthermore, 25% carbon dioxide increases the rate by four orders of magnitude, compared to pure methane. This efect is also explained by a decrease in surface tension. For 25% carbon dioxide, the estimated relative decrease of the surface tension is 13%, compared to the pure-water surface tension. In view of the large uncertainties at 235K in the predictions of the cpa equation of state and in the surface tension, a direct, quantitative comparison between experimental and theoretical nucleation rates in our systems is of limited value. The efect of carbon dioxide on the nucleation rate is qualitatively reproduced by the classical nucleation theory, however. The so-called nucleation theorem provides a way to deduce the properties of the critical cluster – the smallest stable molecular cluster – from experimental nucleation rate data. For water nucleation in methane at 235 K and 10 bar, the critical cluster consists of 22 watermolecules and 5 methanemolecules. The fraction of methane molecules in the cluster is a hundred times larger than the equilibrium fraction at those conditions, which indicates that the properties of small clusters strongly deviate from the macroscopic properties. Tesides nucleation rates, growth rates of water droplets were measured in methane and inmethane–carbon dioxide mixtures. At equal temperature, pressure and water vapour fraction, the growth rate of the squared droplet radius is about 20% lower in the mixture with 25% carbon dioxide than in pure methane. The lower growth rate is caused by a smaller difusion coeicient of water in the mixture with carbon dioxide; the diference of the difusion coeicients is qualitatively reproduced by the empirical Fuller correlation

Thermal Conductivity of Supercooled Water

The heat capacity of supercooled water, measured down to -37 {\deg}C, shows an anomalous increase as temperature decreases. The thermal diffusivity, i. e., the ratio of the thermal conductivity and the heat capacity per unit volume, shows a decrease. These anomalies may be associated with a hypothetical liquid-liquid critical point in supercooled water below the line of homogeneous nucleation. However, while the thermal conductivity is known to diverge at the vapor-liquid critical point due to critical density fluctuations, the thermal conductivity of supercooled water, calculated as the product of thermal diffusivity and heat capacity, does not show any sign of such an anomaly. We have used mode-coupling theory to investigate the possible effect of critical fluctuations on the thermal conductivity of supercooled water, and found that indeed any critical thermal-conductivity enhancement would be too small to be measurable at experimentally accessible temperatures. Moreover, the behavior of thermal conductivity can be explained by the observed anomalies of the thermodynamic properties. In particular, we show that thermal conductivity should go through a minimum as temperature is decreased, as Kumar and Stanley observed in the TIP5P model of water. We discuss physical reasons for the striking difference between the behavior of thermal conductivity in water near the vapor-liquid and liquid-liquid critical points.Comment: References added, typos corrected. Extrapolation for viscosity improved; results essentially unchange

Epicycles and Poincar\'{e} Resonances in General Relativity

The method of geodesic deviations provides analytic approximations to geodesics in arbitrary background space-times. As such the method is a useful tool in many practical situations. In this note we point out some subtleties in the application of the method related to secular motions, in first as well as in higher order. In particular we work out the general second-order contribution to bound orbits in Schwarzschild space-time and show that it provides very good analytical results all the way up to the innermost stable circular orbit.Comment: 24 pages, 4 figure

Comment on "The nucleation behavior of supercooled water vapor in helium"

In a recent paper Peeters et al. published new experimental data on nucleation rates of water in the temperature range of 200–235 K. They reported about a drastic change in the nucleation rate at 207 K. An error in their experimental procedure has been found. The data of Peeters et al. have been reinterpreted. The jump in nucleation rate disappears and the corrected nucleation rate data are in good agreement with data found by Wölk and Strey with a different experimental facility

Occlusion-related lateral connections stabilize kinetic depth stimuli through perceptual coupling

Local sensory information is often ambiguous forcing the brain to integrate spatiotemporally separated information for stable conscious perception. Lateral connections between clusters of similarly tuned neurons in the visual cortex are a potential neural substrate for the coupling of spatially separated visual information. Ecological optics suggests that perceptual coupling of visual information is particularly beneficial in occlusion situations. Here we present a novel neural network model and a series of human psychophysical experiments that can together explain the perceptual coupling of kinetic depth stimuli with activity-driven lateral information sharing in the far depth plane. Our most striking finding is the perceptual coupling of an ambiguous kinetic depth cylinder with a coaxially presented and disparity defined cylinder backside, while a similar frontside fails to evoke coupling. Altogether, our findings are consistent with the idea that clusters of similarly tuned far depth neurons share spatially separated motion information in order to resolve local perceptual ambiguities. The classification of far depth in the facilitation mechanism results from a combination of absolute and relative depth that suggests a functional role of these lateral connections in the perception of partially occluded objects

Tensor extension of the Poincar\'e algebra

A tensor extension of the Poincar\'e algebra is proposed for the arbitrary dimensions. Casimir operators of the extension are constructed. A possible supersymmetric generalization of this extension is also found in the dimensions $D=2,3,4$.Comment: 1+7 pages, LaTe

GRAIL, an omni-directional gravitational wave detector

A cryogenic spherical and omni-directional resonant-mass detector proposed by the GRAIL collaboration is described.Comment: 5 pages, 4 figs., contribution to proceedings GW Data Analysis Workshop, Paris, nov. 199