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     

Acid-catalyzed rearrangements of tricyclo[4.3.2]Propellane derivatives

The acid-catalyzed rearrangements of three model tricyclo[4.3.2] propellane derivatives have been explored. In each case the observed products are proposed to arise via a concerted 1,2-shift of the cyclobutane bond having an antiperiplanar alignment with the leaving group (i.e., stereoelectronic control).     

Horizontal bridges in polar dielectric liquids

When a high-voltage direct-current is applied to two beakers filled with polar liquid dielectrica like water or methanol, a horizontal bridge forms between the two beakers. By repeating a version of Pellat’s experiment, it is shown that a horizontal bridge is stable by the action of electrohydrodynamic pressure. Thus, the static and dynamic properties of the phenomenon called a ‘floating water bridge’ can be explained by the gradient of Maxwell pressure, replenishing the liquid within the bridge against any drainage mechanism. It is also shown that a number of liquids can form stable and long horizontal bridges. The stability of such a connection, and the asymmetry in mass flow through such bridges caused by the formation of ion clouds in the vicinity of the electrodes, is also discussed by two further experiments.     

Determination of plasma lactic acid concentration and specific activity using high-performance liquid chromatography.

Assessment of lactate metabolism is of particular interest during exercise and in disease states such as diabetes, shock, and absorptive abnormalities of short-chain fatty acids by the colon. We describe an analytical method that introduces radio-active tracers and high-performance liquid chromatography (HPLC) to simultaneously analyze concentrations and specific activities (SAs) of plasma lactate. The HPLC conditions included separation on a reversed-phase column (octadecylsilane) and an isocratic buffer (30% acetonitrile in water). [3H]Acetate served as an internal standard. Lactate and acetate were extracted from plasma samples with diethyl ether following a pH adjustment to less than 1.0 and back-extracted into a hydrophilic phase with sodium carbonate (2 mM, pH greater than 10.0). Lactate is detected in the ultraviolet range (242 and 320 nm) by derivatization with alpha-bromoacetophenone. Control plasma samples were studied after an overnight fast for precision and analytical recovery. Calibration curves were linear in the range 0.18-6.0 mM (r = 0.92). The precision was 3% and the analytical recovery was 87%. The detection limit of the method was 36 pmol. Determination of lactate metabolism was performed in a patient with chronic congestive heart failure who was administered primed-continuous L-[U-14C]lactate (10 microCi bolus and 0.3 microCi/min continuously) during a 60-min rest period. Mean arterial lactate concentration and SA were 1.69 +/- 0.2 mM and 253.8 +/- 22 dpm/mumol, respectively. Systemic lactate turnover was 25.65 mumol/kg per min. Lactic acid systemic turnover, organ uptake and release rates can be accurately determined by isocratic HPLC.     

Densities and apparent molar volumes of atmospherically important electrolyte solutions. 1. The solutes H2SO4, HNO3, HCl, Na2SO4, NaNO3, NaCl, (NH4)2SO4, NH4NO3, and NH4Cl from 0 to 50 °C, including extrapolations to very low temperature and to the pure liquid state, and NaHSO4, NaOH, and NH3 at 25 °C

Calculations of the size and density of atmospheric aerosols are complicated by the fact that they can exist at concentrations highly supersaturated with respect to dissolved salts and supercooled with respect to ice. Densities and apparent molar volumes of solutes in aqueous solutions containing the solutes H(2)SO(4), HNO(3), HCl, Na(2)SO(4), NaNO(3), NaCl, (NH(4))(2)SO(4), NH(4)NO(3), and NH(4)Cl have been critically evaluated and represented using fitted equations from 0 to 50 °C or greater and from infinite dilution to concentrations saturated or supersaturated with respect to the dissolved salts. Using extrapolated densities of high-temperature solutions and melts, the relationship between density and concentration is extended to the hypothetical pure liquid solutes. Above a given reference concentration of a few mol kg(-1), it is observed that density increases almost linearly with decreasing temperature, and comparisons with available data below 0 °C suggest that the fitted equations for density can be extrapolated to very low temperatures. As concentration is decreased below the reference concentration, the variation of density with temperature tends to that of water (which decreases as temperature is reduced below 3.98 °C). In this region below the reference concentration, and below 0 °C, densities are calculated using extrapolated apparent molar volumes which are constrained to agree at the reference concentrations with an equation for the directly fitted density. Calculated volume properties agree well with available data at low temperatures, for both concentrated and dilute solutions. Comparisons are made with literature data for temperatures of maximum density. Apparent molar volumes at infinite dilution are consistent, on a single ion basis, to better than ±0.1 cm(3) mol(-1) from 0 to 50 °C. Volume properties of aqueous NaHSO(4), NaOH, and NH(3) have also been evaluated, at 25 °C only. In part 2 of this work (ref 1 ) an ion interaction (Pitzer) model has been used to calculate apparent molar volumes of H(2)SO(4) in 0-3 mol kg(-1) aqueous solutions of the pure acid and to represent directly the effect of the HSO(4)(-) ? H(+) + SO(4)(2-) reaction. The results are incorporated into the treatment of aqueous H(2)SO(4) density described here. Densities and apparent molar volumes from -20 to 50 °C, and from 0 to 100 wt % of solute, are tabulated for the electrolytes listed in the title and have also been incorporated into the extended aerosol inorganics model (E-AIM, http://www.aim.env.uea.ac.uk/aim/aim.php) together with densities of the solid salts and hydrates.     

Durability investigation of graphene-supported Pt nanocatalysts for PEM fuel cells

We report graphene nanosheets as a durable alternative support material for Pt nanoparticle catalysts for oxygen reduction in proton exchange membrane (PEM) fuel cells and compared them to XC-72. The materials were characterized by X-ray diffraction and transmission electron microscopy. Electrochemical surface oxidation of XC-72 and graphene, and of Pt/XC-72 and Pt/graphene has been compared following treatments for up to 120 h. The electrochemical performance of the specimens was evaluated by cyclic voltammetry and linear sweep voltammetry at different surface oxidation time intervals. Electrochemical measurements indicate that the graphene exihibits greatly enhanced electrochemical durability. It is suggested that graphene nanosheet is a promising, low-cost, and durable electrocatalyst support for oxygen reduction in the PEM fuel cell.     

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.