A class of perfect fluids in general relativity

This thesis is concerned with exact solutions of Einstein's field equations of general relativity, in particular, when the source of the gravitational field is a perfect fluid with a purely electric Weyl tensor. General relativity, cosmology and computer algebra are discussed briefly. A mathematical introduction to Riemannian geometry and the tetrad formalism is then given. This is followed by a review of some previous results and known solutions concerning purely electric perfect fluids. In addition, some orthonormal and null tetrad equations of the Ricci and Bianchi identities are displayed in a form suitable for investigating these space-times. Conformally flat perfect fluids are characterised by the vanishing of the Weyl tensor and form a sub-class of the purely electric fields in which all solutions are known (Stephani 1967). The number of Killing vectors in these space-times is investigated and results presented for the non-expanding space-times. The existence of stationary fields that may also admit 0, 1 or 3 spacelike Killing vectors is demonstrated. Shear-free fluids in the class under consideration are shown to be either non-expanding or irrotational (Collins 1984) using both orthonormal and null tetrads. A discrepancy between Collins (1984) and Wolf (1986) is resolved by explicitly solving the field equations to prove that the only purely electric, shear-free, geodesic but rotating perfect fluid is the Godel (1949) solution. The irrotational fluids with shear are then studied and solutions due to Szafron (1977) and Allnutt (1982) are characterised. The metric is simplified in several cases where new solutions may be found. The geodesic space-times in this class and all Bianchi type 1 perfect fluid metrics are shown to have a metric expressible in a diagonal form. The position of spherically symmetric and Bianchi type 1 space-times in relation to the general case is also illustrated.

Remobilisation of uranium and thorium by ore-forming fluids: a mineralogical study. Available in 2 volumes.

Mineralogical investigations have determined the sites of u and Th associated with two radioelement-enriched granites from different geological settings. In the Ririwai ring complex, Nigeria, the u- and Th-bearing accessories have been greatly affected by post-magmatic alteration of the biotite granite. Primary thorite, zircon and monazite were altered to Zr(±Y)-rich thorite, partially metamict zircon (enriched in Th, U, Y, P, Fe, Mn, Ca) and an unidentified LREE-phase respectively, by pervasive fluids which later precipitated Zr-rich coffinite. More intense, localised alteration and albitisation completely remobilised primary accessories and gave rise to a distinctive generation of haematite- and uranothorite-enriched zircon with clear, Hi-enriched rims and xenotime overgrowths. In the Ririwai lode, microclinisation and later greisenisation locally remobilised or altered zircon and deposited Y-ricl1 coffinite and Y(±Zr)-rich thorite which was overgrown by traces of xenotime and LREE-phase(s) of complex and variable composition. Compositions indicating extensive solid-solution among thorite, coffinite, xenotime and altered zircon are probably metastable and formed at low temperatures. The widespread occurrence of REE-rich fluorite suggests that F-complexing aided the mobility of REE, Y, U, Th and Zr during late-magmatic to post-magmatic alteration, while uranyl-carbonate complexing may have occurred during albitisation. The Caledonian, Helmsdale granite in northern Scotland has undergone pervasive and localised hydrothermal alteration associated with U enrichment. Zircon xenocrysts, primary sphene and apatite contain a small.proportion of this U which is largely adsorbed on to secondary iron-oxide, TiOand phyllosilicates.Additional sites for U in the overlying, Lower Devonian Ousdale arkose include coffinite, secondary uranyl phosphates, hydrocarbon and traces of xenotime and unidentified LREE-phases. U may have been leached from the granite and deposited in the arkose, along channelways associated with the Helmsdale fault, by convecting, hydrothermal fluids

The effects of solid contamination in hydraulic fluids on axial piston pumps

The fluids used in hydraulic systems inevitably contain large numbers of small, solid particles, a phenomenon known as 'fluid contamination'. Particles enter a hydraulic system from the environment, and are generated within it by processes of wear. At the same time, particles are removed from the system fluid by sedimentation and in hydraulic filters. This thesis considers the problems caused by fluid contamination, as they affect a manufacturer of axial piston pumps. The specific project aim was to investigate methods of predicting or determining the effects of fluid contamination on this type of pump. The thesis starts with a theoretical analysis of the contaminated lubrication of a slipper-pad bearing. Statistical methods are used to develop a model of the blocking, by particles, of the control capillaries used in such bearings. The results obtained are compared to published, experimental data. Poor correlation between theory and practice suggests that more research is required in this area before such theoretical analysis can be used in industry. Accelerated wear tests have been developed in the U.S.A. in an attempt to predict pump life when operating on contaminated fluids. An analysis of such tests shows that reliability data can only be obtained from extensive test programmes. The value of contamination testing is suggested to be in determining failure modes, and in identifying those pump components which are susceptible to the effects of contamination. A suitable test is described, and the results of a series of tests on axial piston pumps are presented and discussed. The thesis concludes that pump reliability data can only be obtained from field experience. The level of confidence which can be placed in results from normal laboratory testing is shown to be too low for the data to be of real value. Recommendations are therefore given for the ways in which service data should be collected and analysed.

Sampling of fluids for analysis

Disclosed is a fluid sampling apparatus (12). The apparatus has a sample inlet port (14) in communication with a fluid space (10) containing the fluid to be sampled. An analysis port (16) is provided for communication with an analysis device such as a mass spectrometer. A dilution gas injection port (22) is provided to dilute fluid is sampled from the fluid space via the sample inlet port. The diluted sample fluid is then conducted to the analysis port. The sampling apparatus is intended particularly for use in analysing biomass pyrolysis processes.

Pattern formation in volumetrically heated fluids

Finite element simulations have been performed along side normal mode analysis on the linear stability that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Pattern competition in volumetricaly heated fluids

Finite element simulations have been performed along side Galerkin-type calculations that examined the development of volumetrically heated flow patterns in a horizontal layer controlled by the Prandtl number, Pr, and the Grashof number, Gr. The fluid was bounded by an isothermal plane above an adiabatic plane. In the simulations performed here, a number of convective polygonal planforms occurred, as Gr increased above the critical Grashof number, Grc at Pr = 7, while roll structures were observed for Pr < 1 at 2Grc.

Stability of anthracycline cytotoxic agents in solution and infusion fluids

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

The structure and dynamics of 2-dimensional fluids in swelling clays

The interlayer pores of swelling 2:1 clays provide an ideal 2-dimensional environment in which to study confined fluids. In this paper we discuss our understanding of the structure and dynamics of interlayer fluid species in expanded clays, based primarily on the outcome of recent molecular modelling and neutron scattering studies. Counterion solvation is compared with that measured in bulk solutions, and at a local level the cation-oxygen coordination is found to be remarkably similar in these two environments. However, for the monovalent ions the contribution to the first coordination shell from the clay surfaces increases with counterion radius. This gives rise to inner-sphere (surface) complexes in the case of potassium and caesium. In this context, the location of the negative clay surface charge (i.e. arising from octahedral or tetrahedral substitution) is also found to be of major importance. Divalent cations, such as calcium, eagerly solvate to form outer-sphere complexes. These complexes are able to pin adjacent clay layers together, and thereby prevent colloidal swelling. Confined water molecules form hydrogen bonds to each other and to the clays' surfaces. In this way their local environment relaxes to close to the bulk water structure within two molecular layers of the clay surface. Finally, we discuss the way in which the simple organic molecules methane, methanol and ethylene glycol behave in the interlayer region of hydrated clays. Quasi-elastic neutron scattering of isotopically labelled interlayer CH 3OD and (CH2OD)2 in deuterated clay allows us to measure the diffusion of the CH3- and CH2-groups in both clay and liquid environments. We find that in both the one-layer methanol solvates and the two-layer glycol solvates the diffusion of the most mobile organic molecules is close to that in the bulk solution.

Free energy functional expansion as the generalized approach to the equation of state of dense fluids

A version of the thermodynamic perturbation theory based on a scaling transformation of the partition function has been applied to the statistical derivation of the equation of state in a highpressure region. Two modifications of the equations of state have been obtained on the basis of the free energy functional perturbation series. The comparative analysis of the experimental PV T- data on the isothermal compression for the supercritical fluids of inert gases has been carried out. © 2012.

Functional educational characterisation of the utility of embalming fluids for anatomical education and research

Human cadavers have long been used to teach human anatomy and are increasingly used in other disciplines. Different embalming techniques have been reported in the literature; however there is no clear consensus on the opinion of anatomists on the utility of embalmed cadavers for the teaching of anatomy. To this end, we aimed to survey British and Irish anatomy teachers to report their opinions on different preservation methods for the teaching of anatomy. In this project eight human cadavers were embalmed using formalin, Genelyn, Thiel and Imperial College London- Soft Preserving (ICL-SP) techniques to compare different characteristics of these four techniques. The results of this thesis show that anatomy teachers consider hard-fixed cadavers not to be the most accurate teaching model in comparison to the human body, although it still serves as a useful teaching method (Chapter 2). In addition, our findings confirm that joints of cadavers embalmed using ICL-SP solution faithfully mimics joints of an unembalmed cadaver compared to the other techniques (Chapter 3). Embalming a human body prevents the deterioration in the quality of images and our findings highlight that the influence of the embalming solutions varied with the radiological modality used (Chapter 4). The method developed as part of this thesis enables anatomists and forensic scientists to quantify the decomposition rate of an embalmed human cadaver (Chapter 5). Formalin embalming solution showed the strongest antimicrobial abilities followed by Thiel, Genelyn and finally by ICL-SP (Chapter 6). The overarching viewpoint of this set of studies show that it is inaccurate to state that one embalming technique is ultimately the best. The value of each technique differs based on the requirement of the particular education or research area. Hence we highlight how different embalming techniques may be better suited to certain fields of study.

Geochemical composition of calcite and aragonite, and characteristics of hydrothermal fluids of ODP Leg 168 sites

During Leg 168 a transect was drilled across the eastern flank of the Juan de Fuca Ridge in an area where the volcanic basement is covered by sediments of variable thickness. Samples of basement volcanic rocks were recovered from nine locations along the transect, where the basement sediment interface is presently heated to temperatures varying from 15° to 64°C. Altered rocks with secondary calcium carbonate were common at four of the sites, where present-day temperatures range from 38° to 64°C. Fluid inclusions in aragonite suggest that the mineral precipitated from an aqueous fluid of seawater salinity at temperatures well below 100°C. The chemical compositions of secondary calcite and aragonite were determined with both an electron microprobe and a laser-ablation inductively coupled plasma-mass spectroscopy (LA-ICP-MS) microprobe. These two techniques yielded consistent analyses of the same minor elements (Mg and Sr) in the same specimens. The combined results show that secondary aragonites contain very little Mg, Mn, Fe, Co, Ni, Cu, Zn, Rb, La, Ce, Pb, or U, yet they contain significant Sr. In contrast, secondary calcites contain significant Mg, Mn, Fe, Ni, Cu, Zn, and Pb, yet very little Co, Rb, Sr, La, Ce, or U. Secondary calcium carbonates provide subseafloor reservoirs for some minor and trace elements. Replacement of aragonite by calcite should result in a release of Sr, Rb, and Zn to solution, and it provides a sink for Mg, Mn, Ni, Cu, Zn, and Pb.

(Table 3) Geochemistry of borehole fluids of ODP Hole 137-504B

Circulation of seawater through basaltic basement for several million years after crustal emplacement has been inferred from studies of surface heat flow, and may play a significant role in the exchange of elements between the oceanic crust and seawater. Without direct observation of the fluid chemistry, interpretations regarding the extent and timing of this exchange must be based on the integrated signal of alteration found in sampled basalts. Much interest has thus been expressed in obtaining and analyzing fluids directly from basaltic formations. It has been proposed that open oceanic boreholes can be used as oceanic groundwater wells to obtain fluids that are circulating within the formation. Water samples were collected from the open borehole in Hole 504B prior to drilling operations on Leg 137, with the original intention of collecting formation fluids from the surrounding basaltic rocks. Past results have yielded ambiguous conclusions as to the origin of the fluids recovered-specifically, whether or not the fluids were true formation fluids or merely the result of reaction of seawater in the borehole environment. The chemistry of eight borehole fluid samples collected during Leg 137 is discussed in this paper. Large changes in major, minor, and isotopic compositions relative to unaltered seawater were observed in the borehole fluids. Compositional changes increased with depth in the borehole. The samples exhibit the effect of simple mixing of seawater, throughout the borehole, with a single reacted fluid component. Analysis and interpretation of the results from Leg 137 in light of past results suggest that the chemical signals observed may originate predominantly from reaction with basaltic rubble residing at the bottom of the hole during the interim between drilling legs. Although this endeavor apparently did not recover formation waters, information on the nature of reaction between seawater and basalt at the prevalent temperatures in Hole 504B (>160°C) has been gained that can be related to reconstruction of the alteration history of the oceanic crust. Isotopic analyses allow calculation of element-specific water/rock mass ratios (Li and Sr) and are related to the extent of chemical exchange between the borehole fluids and basalt.

(Table 1) Chemical and isotopic composition of pore fluids in cores TGC-1 and TGC-6

The role of sediment diagenesis in the marine cycles of Li and B is poorly understood. Because Li and B are easily mobilized during burial and are consumed in authigenic clay mineral formation, their abundance in marine pore waters varies considerably. Exchange with the overlying ocean through diffusive fluxes should thus be common. Nevertheless, only a minor Li sink associated with the low-temperature alteration of volcanic ash has been observed. We describe a low-temperature diagenetic environment in the Black Sea dominated by the alteration of detrital plagioclase feldspars. Fluids expelled from the Odessa mud volcano in the Sorokin Trough originate from shallow (~100-400 m deep) sediments which are poor in volcanic materials but rich in anorthite. These fluids are depleted in Na+, K+, Li+, B, and 18O and enriched in Ca2+ and Sr2+, indicating that anorthite is dissolving and authigenic clays are forming. Using a simple chemical model, we calculate the pH and the partial pressure of CO2 (PCO2) in fluids associated with this alteration process. Our results show that the pH of these fluids is up to 1.5 pH units lower than in most deep marine sediments and that PCO2 levels are up to several hundred times higher than in the atmosphere. These conditions are similar to those which favor the weathering of silicate minerals in subaerial soil environments. We propose that in Black Sea sediments enhanced organic matter preservation favors CO2 production through methanogenesis and results in a low pore water pH, compared to most deep sea sediments. As a result, silicate mineral weathering, which is a sluggish process in most marine diagenetic environments, proceeds rapidly in Black Sea sediments. There is a potential for organic matter-rich continental shelf environments to host this type of diagenesis. Should such environments be widespread, this new Li and B sink could help balance the marine Li and Li isotope budgets but would imply an apparent imbalance in the B cycle.

Seawater carbonate chemistry and conditions of Mytilus edulis extracellular body fluids and shell composition in a pH-treatment experiment: Acid-base status, trace elements and delta11B, 2012

Mytilus edulis were cultured for 3 months under six different seawater pCO2 levels ranging from 380 to 4000 µatm. Specimen were taken from Kiel Fjord (Western Baltic Sea, Germany) which is a habitat with high and variable seawater pCO2 and related shifts in carbonate system speciation (e.g., low pH and low CaCO3 saturation state). Hemolymph (HL) and extrapallial fluid (EPF) samples were analyzed for pH and total dissolved inorganic carbon (CT) to calculate pCO2 and [HCO3]. A second experiment was conducted for 2 months with three different pCO2 levels (380, 1400 and 4000 µatm). Boron isotopes (delta11B) were investigated by LA-MC-ICP-MS (Laser Ablation-Multicollector-Inductively Coupled Plasma-Mass Spectrometry) in shell portions precipitated during experimental treatment time. Additionally, elemental ratios (B/Ca, Mg/Ca and Sr/Ca) in the EPF of specimen from the second experiment were measured via ICP-OES (Inductively Coupled Plasma-Optical Emission Spectrometry). Extracellular pH was not significantly different in HL and EPF but systematically lower than ambient water pH. This is due to high extracellular pCO2 values, a prerequisite for metabolic CO2 excretion. No accumulation of extracellular [HCO3] was measured. Elemental ratios (B/Ca, Mg/Ca and Sr/Ca) in the EPF increased slightly with pH which is in accordance with increasing growth and calcification rates at higher seawater pH values. Boron isotope ratios were highly variable between different individuals but also within single shells. This corresponds to a high individual variability in fluid B/Ca ratios and may be due to high boron concentrations in the organic parts of the shell. The mean delta11B value shows no trend with pH but appears to represent internal pH (EPF) rather than ambient water pH.

Fiber-optic vibration sensing of cantilevers immersed in fluids

An all fiber-optical method to monitor densities and viscosities of liquids utilizing a steel cantilever (4 x 0.3 x 0.08 cm3) is presented. The actuation is performed by photothermally heating the cantilever at its base with an intensity-modulated 808 nm diode laser. The cantilever vibrations are picked up by an in-fiber Fabry Perot cavity sensor attached along the length of the cantilever. The fluid properties can be related to the resonance characteristics of the cantilever, e.g. a shift in the resonance frequency corresponds to a change in fluid density, and the width of the resonance peak gives information on the dynamic viscosity after calibration of the system. Aqueous glycerol, sucrose and ethanol samples in the range of 0.79–1.32 gcm−3 (density) and 0.89–702 mPas (viscosity) were used to investigate the limits of the sensor. A good agreement with literature values could be found with an average deviation of around 10 % for the dynamic viscosities, and 5–16 % for the mass densities. A variety of clear and opaque commercial spirits and an unknown viscous sample, e.g. home-made maple syrup, were analyzed and compared to literature values. The unique detection mechanism allows for the characterization of opaque samples and is superior to conventional microcantilever sensors. The method is expected to be beneficial in various industrial sectors such as quality control of food samples.