No abstract

Recent measurements have shown1 that the compressions of benzene and a number of its monosubstituted derivatives over considerable ranges of pressure may be well represented by the Tait equation2where k is the decrease in volume per unit volume when the pressure is raised from Pq to P kilobars. B, a function of the temperature, is a constant characteristic of the liquid or liquid mixture, and C is a constant independent of temperature and the same for all the derivatives of benzene we have examined. In this paper we shall give data on the thermal expansions of the liquids mentioned in the title, give more complete compressibility data, and discuss some of the thermodynamic quantities derivable from these measurements, including the pressure-temperature coefficient {dP/dT')v which, following Hildebrand,3 4we shall denote as y, and especially the energy-volume coefficient (dE/d V)T. ExperimentalThe compressions of the liquids to various pressures up to 1000 bars were measured at 25,45, 65 and 85°in vitreous silica piezometers in our latest pressure apparatus,1 and depend on the same constants for vitreous silica and mercury that were employed in the investigation of benzene.5The specific volumes of the liquids at atmospheric pressure were measured at intervals of 10°between 25 and 85°in a weight dilatometer of the type used by Burlew8 and by Pesce and Holeraann.' The dilatometer, made of vitreous silica, is shown diagrammatically in Fig. 1. Its chief merits are simplicity and ease of manipulation. By following Bttrlew's design of having the open end of the capillary above the dilatometer, we were able to avoid the complicated thermostat used by Pesce and Holeinann, and by having an opening at the top of the dilatometer bulb we were able to fill it readily with solutions whose (1) R, E. Gibson and O. H, Loeffler, J. phys. Chem.t 43, 207 (1939).(2) This equation in the differential form was proposed by Tait in 1881 to fit the compressibility data for water. It was rederived by A. Wohl [Z. physik. Chem., 99, 234 (1921)], who applied it to some organic liquids, and it was later applied successfully to the existing data on a large number of liquids by H. Carl [ibid., 101, 238 (1922)]. who showed that the constant C did not depend on the temperature.(3) W.

Ground penetrating radar (GPR) is a non-destructive method which, over the past 10 years, has been successfully used not only to estimate the water content of soil, but also to detect and monitor the infiltration of pollutants on sites contaminated by light nonaqueous phase liquids (LNAPL). We represented a model water table aquifer (72 cm depth) by injecting water into a sandbox that also contains several buried objects. The GPR measurements were carried out with shielded antennae of 900 and 1200 MHz, respectively, for common mid point (CMP) and constant offset (CO) profiles. We extended the work reported by Loeffler and Bano by injecting 100 L of diesel fuel (LNAPL) from the top of the sandbox. We used the same acquisition procedure and the same profile configuration as before fuel injection. The GPR data acquired on the polluted sand did not show any clear reflections from the plume pollution; nevertheless, travel times are very strongly affected by the presence of the fuel and the main changes are on the velocity anomalies. We can notice that the reflection from the bottom of the sandbox, which is recorded at a constant time when no fuel is present, is deformed by the pollution. The area close to the fuel injection point is characterized by a higher velocity than the area situated further away. The area farther away from the injection point shows a low velocity anomaly which indicates an increase in travel time. It seems that pore water has been replaced by fuel as a result of a lateral flow. We also use finite-difference time-domain (FDTD) numerical GPR modelling in combination with dielectric property mixing models to estimate the volume and the physical characteristics of the contaminated sand. To cite this article: M. Bano et al., C. R. Geoscience 341 (2009). # 2009 Published by Elsevier Masson SAS on behalf of Académie des sciences. RésuméImagerie géoradar et modélisation en domaine temporel par différences-finies (FDTD) d'une infiltration de gasoil dans un bac à sable. Le géoradar (GPR) est une méthode non destructive qui, au cours des dix dernières années, a été utilisée avec succès pour estimer la teneur en eau du sol ; mais aussi pour détecter et suivre l'infiltration de polluants en phase liquide non aqueuse (LNAPL) sur des sites contaminés. Nous avons simulé une nappe libre (dont le toit est à 72 cm de profondeur) en injectant de l'eau dans une cuve remplie de sable qui contient également plusieurs objets. Les mesures GPR ont été réalisées à l'aide d'une antenne blindée à 900 et 1200 MHz, respectivement, en dispositif point milieu commun (CMP) et en profils à offset constant (CO). Nous présentons ici une extension du travail publié par Loeffler et Bano qui consiste à injecter 100 L de gasoil dans la cuve, depuis la surface du sable. Les données GPR acquises sur le sable pollué ne montrent pas de réflexions claires dues à la présence du panache

Ground penetrating radar (GPR) is a nondestructive method, which, as with other geophysical methods, has been successfully used to estimate the water content or hydraulic properties of soils. We performed GPR measurements to calibrate and compare water content estimates with actual water contents in a sand box. A vadose zone was simulated by injecting water in a sand box. We obtained four GPR data sets: for dry sand, for sand with water tables at 72‐ and 48‐cm depths, and for sand after drainage. Using the reflections (or diffractions) from the bottom of the sand box (or objects buried in the sand), mean relative dielectric permittivities were determined at several depths in the sand box. These relative dielectric permittivities were used to calculate “real” mean relative dielectric permittivities of a sand box made up of three layers (dry sand, unsaturated sand, and fully saturated sand), knowing that a layer can be subdivided into more layers depending on the depth of the reflections (or diffractions) recorded. We used three relationships between relative dielectric permittivity and the water content to estimate the mean water content for each layer. From these water contents and the known volume of sand considered, we estimated the amount of water in the sand box for each water table. Subtracting the volume obtained for dry sand from the volume obtained for the different water tables gave estimates of the variations in water quantities in the sand box; these were compared with the quantities injected in the sand box. Despite uncertainties in the determination of the mean relative dielectric permittivities, the calculated variations in water quantities were very similar to those injected in the sand box.