Approximate solutions for the structure of shock waves

Approximate solutions of the B-G-K model equation are obtained for the structure of a plane shock, using various moment methods and a least squares technique. Comparison with available exact solution shows that while none of the methods is uniformly satisfactory, some of them can provide accurate values for the density slope shock thickness delta n . A detailed error analysis provides explanations for this result. An asymptotic analysis of delta n for largeMach numbers shows that it scales with theMaxwell mean free path on the hot side of the shock, and that their ratio is relatively insensitive to the viscosity law for the gas.

Composition of aqueous solutions in equilibrium with sulfides and oxides of iron at 3500°C

Solutions of potassium chloride (pH-buffered and 1-molat) equilibrated at 350°C with pyrrhotite, pyrite, and magnetite contained approximately 1 millimole of reduced sulfur and less than 0.1 millimole of oxidized sulfur per kilogram. Similar solutions equilibrated with pyrite, magnetite, and hematite contained approximately 1 millimole of reduced sulfur, but 3 to 6 millimoles of oxidized sulfur per kilogram. Both types of solutions contained less than 0.1 millimole of iron per kilogram at pH ≥ 6 and approximately 100 millimoles per kilogram at pH 2.

Selective Homonuclear Decoupling in H-1 NMR: Application to Visualization of Enantiomers in Chiral Aligning Medium and Simplified Analyses of Spectra in Isotropic Solutions

The proton NMR spectral complexity arising due to severe overlap of peaks hampers their analyses in diverse situations, even by the application of two-dimensional experiments. The selective or complete removal of the couplings and retention of only the chemical shift interactions in indirect dimension aids in the simplification of the spectrum to a large extent with little investment of the instrument time. The present study provides precise enantiodiscrimination employing more anisotropic NMR parameters in the chiral liquid crystalline medium and differentiates the overlapped peaks of many organic molecules and peptides dissolved in isotropic solvents.

A novel fibre-coated sorbent for rapid removal of heavy metals from wastewater. Sorption of Zinc(II) from dilute aqueous solutions in the presence of high concentrations of common salts

The commercial acrylic fibre "Cashmilon" was partially hydrolyzed to convert a fraction of its nitrile (-CN) groups to carboxylic acid (-COOH) groups and then coated with polyethylenimine (PEI) resin and cross-linked with glutaraldehyde to produce a novel gel-coated fibrous sorbent with multiple functionalities of cationic, anionic and chelating types, and significantly faster sorption kinetics than bead-form sorbents. The sorption properties of the fibrous sorbent were measured using Zn(II) in aqueous solution as the sorbate to determine the effects of pH and the presence of common ions in the solution on the sorption capacity. The rate of sorption on the gel-coated fibre was measured in comparison with that on Amberlite IRA-68 weak-base resin beads, to demonstrate the marked difference between fibre and bead-form sorbents in their kinetic behaviour.

Coherent quasiparticle approximation cQPA and nonlocal coherence

We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum mechanical coherence evolution with a well defined collision integral giving rise to decoherence. Several applications of the method are given, for example to the coherent particle production, electroweak baryogenesis and study of decoherence and thermalization.

Reactions with disulphur monoxide solutions obtained by the reduction of cupric oxide by elemental sulphur

When the products of reaction between elemental sulphur and copper oxide at elevated temperature in vacuum are bubbled through chilled inert organic solvents like carbontetrachloride, orange-yellow solutions were obtained indicating the presence of lower oxide of sulphur. This lower oxide has been found to be disulphur monoxide as shown by three different types of reactions; (1) Mercury decomposition, (2) Reaction with hydrogen iodide and hydrolytic reaction in an alkaline homogeneous medium.

Compressibilities of some electrolyte solutions in relation to their stepwise dissociation

The compressibilities of some electrolytic solutions at low concentrations have been determined by employing Carstensen's phase-comparison pulse method for measuring the ultrasonic velocity differences and by simultaneously measuring their densities with a Weld-type pyknometer. The apparent molal compressibilities φ(χ̄2) of NaHSO4, KHSO 4, NaP2PO4 and Na-HPO4 have been plotted against the square root of the molarities c. The observations are explained in terms of incomplete dissociation.

Compressibility of dilute solutions of sulphuric acid

By employing Carstensen's phase-comparison pulse method for measuring ultrasonic velocity-differences, the compressibility of sulphuric acid has been studied anew, the special interest being in the low concentration region. Sulphuric acid is found to show at first a decrease in velocity with increasing concentration and then an increase. The curve representing the apparent molal compressibility Φ(κ̄2) against the square root of the molar concentration c, shows a maximum and a minimum. This anomalous behaviour is interesting in view of the extreme anomalies in other colligative properties of sulphuric acid. A qualitative explanation of the observed maximum and minimum has been suggested.

Free convection heat transfer between vertical parallel plates

A new mathematical model for the solution of the problem of free convection heat transfer between vertical parallel flat isothermal plates under isothermal boundary conditions, has been presented. The set of boundary layer equations used in the model are transformed to nonlinear coupled differential equations by similarity type variables as obtained by Ostrach for vertical flat plates in an infinite fluid medium. By utilising a parameter ηw* to represent the outer boundary, the governing differential equations are solved numerically for parametric values of Pr = 0.733. 2 and 3, and ηw* = 0.1, 0.5, 1, 2, 3, 4, ... and 8.0. The velocity and temperature profiles are presented. Results indicate that ηw* can effectively classify the system into (1) thin layers where conduction predominates, (2) intermediate layers and (3) thick layers whose results can be predicted by the solutions for vertical flat plates in infinite fluid medium. Heat transfer correlations are presented for the 3 categories. Several experimental and analytical results available in the literature agree with the present correlations.

Application of ultraspherical polynomials to non-linear autonomous systems

This paper deals with the approximate solutions of non-linear autonomous systems by the application of ultraspherical polynomials. From the differential equations for amplitude and phase, set up by the method of variation of parameters, the approximate solutions are obtained by a generalized averaging technique based on the ultraspherical polynomial expansions. The method is illustrated with examples and the results are compared with the digital and analog computer solutions. There is a close agreement between the analytical and exact results.

Distribution of products around a burning droplet: an analytical approach

A knowledge of the concentration distribution around a burning droplet is essential if accurate estimates are to be made of the transport coefficients in that region which influence the burning rate. There are two aspects of this paper; (1) determination of the concentration profiles, using the simple assumption of constant binary diffusion coefficients for all species, and comparison with experiments; and (2) postulation of a new relation for the therinal conductivity, which takes into account the variations of both temperature and concentrations of various species. First, the theoretical concentration profiles are evaluated and compared with experimental results reported elsewhere [5]. It is found that the agreement between the theory and experiment is fairly satisfactory. Then, by the use of these profiles and the relations proposed in the literature for the thermal conductivity of a mixture of nonpolar gases, a new relation for thermal conductivity: K = (A1 + B1 T) + (A2 + B2 T) xr (21). is suggested for analytical solutions of droplet combustion problems. Equations are presented to evaluate A1, A2, B1, and B2, and values of these terms for a few hydrocarbons are tabulated.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Micellar size and shape in solutions of calcium stearate in cetane from optical depolarization data

Observations at a series of temperatures of the changes in viscosities and depolarization factors of 1% and 18% solutions of calcium stearate in cetane to which varying amounts of water have been added can be interpreted in terms of the existence of anisometric micelles. In general, changes in the size of the micelles inferred from values of ρh agree with those deduced from the viscosity data. The correlation between anisometry of micelles from rheological and optical observations is much poorer in the case of ρν, presumably because of the difficulty in differentiating the contribution of anisometry and anisotropy to ρν.

Ultrasonic propagation through aqueous solutions of acetates

Using the pulse method in the range of 2 to 26Mc's the ultrasonic absorption, velocity and the adiabatic compressibility have been studied in eleven aqueous acetate solutions up to a concentration of 1 mole/litre. The substances studied are the acetates of lithium, sodium, potassium, ammonium, magnesium, calcium, strontium, barium, zinc, cadmium and lead. Absorption in mercuric acetate has been studied only at 2 and 6 Mc/s. Two regions of relaxation are noticed, one below 10 Mc/s and the other between 10 and 26 Mc/s. The first relaxation is ascribed to the dissociation reaction of the salt and the second one to the monomerdimer reaction of the acetic acid formed by the hydrolysis of the salt in water.