A detonation stability formulation for arbitrary equations of state and multi-step reaction mechanisms

A general normal-mode linear stability formulation of steady planar detonation waves is presented that is valid both for an arbitrary equation of state and for multi-step, multi-species chemical kinetics. The general formulation can be used for many purposes, including an examination of gaseous detonation stability with complex reaction kinetics in which the individual reacting species have variable thermochemical properties. In the present paper, we consider two cases that could not be obtained by previous one-step chemistry, polytropic gas formulations: the first concerns the effect of a difference in heat capacities between product and fuel species, as well as a possible mole change, in a single-step irreversible reaction. The second examines the effects of exothermic or endothermic heat release/absorption in the chain-initiation stage of a model three-step reaction.     

Shock-induced ignition of thermally sensitive explosives

The process of planar detonation ignition, induced by a constant-velocitypiston or equivalently by a shock reflected from a stationarywall, is investigated using high-resolution one-dimensionalnumerical simulations. The standard one-step model with Arrheniuskinetics, which models thermally sensitive explosives, is employed.Emphasis is on comparing and contrasting the results of thefinite activation temperature simulations with high activationtemperature asymptotic predictions and previous simulations.During the induction phase, it is shown that the asymptoticresults give qualitatively good predictions. However, for parametersrepresentative of gaseous explosives, subsequent to thermalrunaway at the piston and the formation of a reaction wave,the high activation temperature asymptotic theory is qualitativelyincorrect for moderately high activation temperatures. It isshown that the results are very sensitive to the value of theactivation temperature, especially the distance from the pistonat which a secondary shock forms and the degree of unsteadinessin the reaction wave which moves away from the piston. The dependenceof the ignition evolution on the other parameters (initial shockMach number, heat of reaction and polytropic index) is alsoinvestigated. It is shown that qualitative predictions regardingthe dependence of the ignition evolution on each of the parameterscan be elucidated from finite activation temperature homogeneousexplosion calculations together with the high activation temperatureasymptotic shock ignition results. It is found that for sufficientlystrong initiating shocks the ignition evolution is qualitativelydifferent from cases studied previously in that no secondaryshock forms. For a high polytropic index, corresponding to asimple equation of state model for condensed phase explosives,the results are in much better qualitative agreement with theasymptotic theory.     

Microplasma patterning of bonded microchannels using high-precision "injected" electrodes

A rapid, high-precision method for localised plasma-treatment of bonded PDMS microchannels is demonstrated. Patterned electrodes were prepared by injection of molten gallium into preformed microchannel guides. The electrode guides were prepared without any additional fabrication steps compared to conventional microchannel fabrication. Alignment of the "injected" electrodes is precisely controlled by the photomask design, rather than positioning accuracy of alignment tools. Surface modification is detected using a fluorescent dye (Rhodamine B), revealing a well-defined micropattern with regions less than 100 μm along the length of the microchannel.     

Hexaphenylbenzene-based polymers of intrinsic microporosity

Microporous polymers derived from the 1,2- and 1,4-regioisomers of di(3',4'-dihydroxyphenyl)tetraphenylbenzene have very different properties with the former being composed predominantly of cyclic oligomers whereas the latter is of high molar mass suitable for the formation of robust solvent-cast films of high gas permeability.     

Self-sustaining, weakly curved, imploding pathological detonation

We provide the first theoretical demonstration of the existence of quasi-one-dimensional, quasi-steady, self-sustaining convergent detonation waves. These occur in systems where, in the planar wave, the rate of heat release by chemical reaction reaches a maximum at a point of incomplete reaction. The case examined in the present paper is that for a two-step sequential reaction, with the second stage endothermic. We construct detonation velocity against curvature relationships for converging waves, and compare these theoretical curves with direct numerical simulations of imploding detonations in cylindrical and spherical geometries. We also comment on the one-dimensional stability of imploding and diverging detonation fronts governed by the two-step model.     

Hyperbolic Geometry and the Hillam–Thron Theorem

Every open ball within has an associated hyperbolic metric and Möbius transformations act as hyperbolic isometries from one ball to another. The Hillam–Thron Theorem is concerned with images of balls under Möbius transformation, yet existing proofs of the theorem do not make use of hyperbolic geometry. We exploit hyperbolic geometry in proving a generalisation of the Hillam–Thron Theorem and examine the precise configurations of points and balls that arise in that theorem.This work was supported by Science Foundation Ireland grant 05/RFP/MAT0003     

Reversible maps and composites of involutions in groups of piecewise linear homeomorphisms of the real line

An element of a group is reversible if it is conjugate to its own inverse, and it is strongly reversible if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be expressed as a composite of two involutions. In this paper the reversible maps, the strongly reversible maps, and those maps that can be expressed as a composite of involutions are determined in certain groups of piecewise linear homeomorphisms of the real line.     

Comparison of molecular images as defined by Raman spectra between normal mucosa and squamous cell carcinoma in the oral cavity

Raman spectroscopy has been effectively applied to clinically differentiate normal and cancerous mucosal tissues. Micro‐Raman spectroscopy provides a tool to better understand the molecular basis for the Raman clinical signal. The objective of the current study was to utilize micro‐Raman spectroscopy to define the molecular/spectral differences between normal and abnormal squamous cell carcinoma (SCC) in oral mucosa (in vitro). Understanding this may help in identifying unique spectra or may be useful for in vivo application of this technology. Micro‐Raman (confocal) spectroscopy was used to obtain molecular images of normal and SCC cells of human oral mucosa. Four fresh flashed‐frozen tumor and four matched normal tongue specimens were studied. The spectra covered a wavenumber range from 300 to 4000 cm⁻¹ with a spectral resolution of 8 cm⁻¹ and a spatial resolution of 1.0 µm. The cells were located within thin sections of tongue mucosa biopsies. The excitation wavelength of 515 nm was used. We were able to obtain Raman images with rich information about the spectroscopic and structural features within the cytoplasm, cell membrane, and cell nuclei. Significant spectral differences were observed between the Raman images of normal and malignant squamous cells. The heterogeneity of tumor cells within the abnormal tissue was also demonstrated. Spectral differences demonstrated between both tissue types have provided important information regarding the origins of specific signals within the cells of each tissue type. In our search for specific spectral biomarkers, we believe that a cell surface protein, greatly upregulated in SCC cells, was discovered at 1583 cm⁻¹. Copyright © 2010 John Wiley & Sons, Ltd.