Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

A further breakthrough in biphasic, rhodium-catalyzed hydroformylation: the use of Per(2,6-di-O-methyl)-β-cyclodextrin as inverse phase transfer catalyst

Solvent free biphasic hydroformylalion of various water-insoluble terminal olefins can be achieved in high yields and sclcctivitics by using a water-soluble rhodium/triphenylphosphine trisulfonate catalyst and per(2,6-di-o-mclhyl)-β-cyclodcxtrin as inverse phase transfer catalyst. The catalytic activities were up to ten times higher than those observed without pcr(2,6-di-o-methyl)-β-cyclodextrin.     

Methode calorimetrique de mesure des enthalpies de formation des alliages liquides a forte tension de vapeur

The heat effects corresponding to the dissolution of solid PbSe in liquid Pb-Se alloys starting from pure Pb were measured with a direct reaction calorimeter. The partial enthalpy of formation of PbSe in the melt and the integral enthalpy of formation of the Pb-PbSe system in the liquid state referred the liquid Pb and PbSe were deduced. Then, from a very simple change of reference state, and in the knowledge of the enthalpy of PbSe, the integral enthalpy of formation of Pb-Se liquid alloys with reference to pure liquid components could be derived. The results agreed very well with those obtained previously on the dissolution of Se in Pb. The method used can be applied whenever the component to be added to the bath has a high vapor pressure.

---

Zusammenfassung Die bei der Überführung von festem PbSe in flüssige Pb-Se-Legierungen auftretenden Wärmeeffekte wurden mittels direkter Reaktionskalorimetrie bestimmt. Die auf flüssiges Pb und PbSe bezogene partielle Bildungsenthalpie des Pb-PbSe-Systems im flüssigen Zustand wurde ermittelt. Durch eine geringfügige Veränderung des Referenzzustandes konnte bei Kenntnis der Enthalpie von PbSe die integrale Bildungsenthalpie von flüssigen Pb-Se-Legierungen in Bezug auf die reinen Komponenten abgeleitet werden. Die Ergebnisse stimmen gut mit denen überein, die früher für die Auflösung von Se in Pb erhalten wurden. Die Methode ist anwendbar, wenn dem Bade zuzugebende Komponenten einen hohen Dampfdruck haben.

---

Pb-Se Pb-Se, . Pb-Se Pb-PbSe Pb Pb-Se. PbSe, Pb-Se . , . , .

     

Ordre chimique dans les alliages metalliques liquides

Due to improvements of high temperature calorimetry, the quantity of liquid alloys showing large negative departures from ideality increased strongly during the last decades. Such a behaviour is now explained by the occurence of chemical short-range order (CSRO), the stoichiometry of which is often elucidated from direct structural determinations as well as from modelization of the thermodynamic functions. In some extreme cases, the destruction of CSRO by increasing temperature lead to a genuine second order transition. The short rewiev of experimental results concerning the variation of physical properties of some liquid alloysvs. temperature and concentration agrees well with CSRO. Some examples of structural determination of CSRO in metallic melts are given. Finally, links between CSRO and phase diagrams and between CSRO and glass-forming ability are also examined.     

Evaluation of temperature gradients within combusting droplets in linear stream using two colors laser-induced fluorescence

The scope of this paper concerns the heating process of fuel droplets injected in a hot gaseous environment. The two colors laser-induced fluorescence technique allows measuring the temperature distribution within a droplet by scanning the droplet volume by a sufficiently small probe volume compared to the droplet volume itself. The temperature field is reconstructed using two approaches which have been compared. One is based on a geometrical optics model and the other is based on the 3D calculation of the internal excitation field within the droplet, using the generalized Lorenz-Mie theory. Experimental results have been obtained on a combusting monodisperse ethanol droplet stream (diameter around 200 m).     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Mesure des capacites calorifiques et des enthalpies de la solution solide AIN-SiC

The AlN-SiC solid solution was prepared by a reaction of powdered silicon, carbon and aluminium nitride at 2000°C. In the molar ratio range from 1 AlN -0 SiC to about 0.5 AlN -0.5 SiC high purity phases with wurtzite structure were obtained.Heat capacities of some mixtures were measured at constant pressure between 313 and 533 K, and also the enthalpy changes between 298 and 453 K. It was observed that addition of small amounts of silicon carbide to aluminium nitride resultedC _p and H values close to those of silicon carbide.

---

Zusammenfassung Durch die Reaktion von pulverisiertem Silizium, Kohlenstoff und Aluminiumnitrid bei 2000°C wurden AlN-SiC- Mischkristalle hergestellt. Im Molverhältnisbereich von 1 AlN - 0 SiC bis 0.5 A1N - 0.5 SiC erhielt man reine Phasen mit Wurtzit-Struktur. Im Temperaturbereich 313–533 K wurden Wärmekapazitäten bei konstantem Druck und im Temperaturbereich 298–453 K auch die Enthalpieänderungen einiger Gemische gemessen. Es konnte festgestellt werden, daß geringe Zusätze von Siliziumcarbid zu AluminiumnitridC _p und H-Werte verursachen, die denen von Siliziumcarbid sehr nahe stehen.

     

The first regioselective metalation and functionalization of unprotected 4-halobenzoic acids

[reaction: see text] By treatment with s-BuLi, s-BuLi/TMEDA, or t-BuLi at approximately -78 degrees C, 4-fluoro- and 4-chlorobenzoic acids (1a,b) are metalated preferentially in the position adjacent to the carboxylate. A complete reversal in regioselectivity is observed for 1a when treated with LTMP; a sequential process involving a rapid intraaggregate lithiation through a quasi dianion complex "QUADAC" is postulated to explain the unusual reactivity of Me(2)S(2) and I(2).