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  • 1
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    Target Preparation for Continuous Flow Accelerator Mass Spectrometry (1997)
    Cambridge University Press
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    Publication Date: 1997-01-01
    Description: For very small samples, it is difficult to prepare graphitic targets that will yield a useful and steady sputtered ion beam. Working with materials separated by preparative capillary gas chromatography, we have succeeded with amounts as small as 20 μg C. This seems to be a practical limit, as it involves 1) multiple chromatographic runs with trapping of effluent fractions, 2) recovery and combustion of the fractions, 3) graphitization and 4) compression of the resultant graphite/cobalt matrix into a good sputter target. Through such slow and intricate work, radiocarbon ages of lignin derivatives and hydrocarbons from coastal sediments have been determined. If this could be accomplished as an “online” measurement by flowing the analytes directly into a microwave gas ion source, with a carrier gas, then the number of processing steps could be minimized. Such a system would be useful not just for chromatographic effluents, but for any gaseous material, such as CO2 produced from carbonates. We describe tests using such an ion source.
    Print ISSN: 0033-8222
    Electronic ISSN: 1945-5755
    Topics: Archaeology , Energy, Environment Protection, Nuclear Power Engineering , Geosciences
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  • 2
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    Flow in a tube with non-uniform, time-dependent curvature: governing equations and simple examples (1996)
    Cambridge University Press
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    Publication Date: 1996-09-25
    Description: Motivated by the study of blood flow in the major coronary arteries, which are situated on the outer surface of the pumping heart, we analyse flow of an incompressible Newtonian fluid in a tube whose curvature varies both along the tube and with time. Attention is restricted to the case in which the tube radius is fixed and its centreline moves in a plane. Nevertheless, the governing equations are very complicated, because the natural coordinate system involves acceleration, rotation and deformation of the frame of reference, and their derivation forms a major part of the paper. Then they are applied to two particular, relatively simple examples: a tube of uniform but time-dependent curvature; and a sinuous tube, representing a small-amplitude oscillation about a straight pipe. In the former case the curvature is taken to be small and to vary by a small amount, and the solution is developed as a triple power series in mean curvature ratio δ0, curvature variation ε and Dean number D. In the latter case the Reynolds number is taken to be large and a linearized solution for the perturbation to the flow in the boundary layer at the tube wall is obtained, following Smith (1976a). In each case the solution is taken far enough that the first non-trivial effects of the variable curvature can be determined. Results are presented in terms of the oscillatory wall shear stress distribution and, in the uniform curvature case, the contribution of steady streaming to the mean wall shear stress is calculated. Estimation of the parameters for the human heart indicates that the present results are not directly applicable, but point the way for future work.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 3
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    The effects of wall inertia on flow in a two-dimensional collapsible channel (1998)
    Cambridge University Press
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    Publication Date: 1998-05-25
    Description: The effect of wall inertia on the self-excited oscillations in a collapsible channel flow is investigated by solving the full coupled two-dimensional membrane-flow equations. This is the continuation of a previous study in which self-excited oscillations were predicted in an asymmetric channel with a tensioned massless elastic membrane (Luo & Pedley 1996). It is found that a different type of self-excited oscillation, a form of flutter, is superposed on the original large-amplitude, low-frequency oscillations. Unlike the tension-induced oscillations, the flutter has high frequency, and grows with time from a small amplitude until it dominates the original slower mode. The critical value of tension below which oscillations arise (at fixed Reynolds number) is found to increase as the wall inertia is increased. The rate at which energy is (a) dissipated in the flow field and (b) transferred to the wall during the flutter is discussed, and results at different parameter values are compared with those of a massless membrane. There is also a discussion of whether the onset of flutter, or that of the slower oscillations, is correlated with the appearance of flow limitation, as is thought to be the case in the context of wheezing during forced expiration of air from the lungs.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 4
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    Systems of Conservation Laws 1: Hyperbolicity, Entropies, Shock Waves. By D. SERRE (translated by I. N. Sneddon). Cambridge University Press, 1999. 263 pp. ISBN 0 521 58233 4. £40. (1999)
    Cambridge University Press
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    Publication Date: 1999-12-25
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 5
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    Oscillatory flow in a tube of time-dependent curvature. Part 1. Perturbation to flow in a stationary curved tube (1999)
    Cambridge University Press
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    Publication Date: 1999-03-25
    Description: Motivated by the study of blood flow in the coronary arteries, this paper examines the flow of an incompressible Newtonian fluid in a tube of time-dependent curvature. The flow is driven by an oscillatory pressure gradient with the same dimensionless frequency, α, as the curvature variation. The dimensionless governing parameters of the flow are α, the curvature ratio δ0 a secondary streaming Reynolds number Rs and a parameter Rt representing the time-dependence of curvature. We consider the parameter regime δ0 ≪ Rt ≪ 1 (Rs and α remain O(1) initially) in which the effect of introducing time-dependent curvature is to perturb the flow driven by an oscillatory pressure gradient in a fixed curved tube. Flows driven by low- and high-frequency pressure gradients are then considered. At low frequency (δ0 ≪ Rt ≪ α ≪ 1) the flow is determined by using a sequence of power series expansions (Rs = O(1)). At high frequency (δ0 ≪ Rt ≪ 1/α2 ≪ 1) the solution is obtained using matched asymptotic expansions for the region near the wall (Stokes layer) and the region away from the wall in the interior of the pipe. The behaviour of the flow in the interior is then determined at both small and intermediate values of Rs. For both the low and high frequency cases, we find the principal corrections introduced by the time-varying curvature to the primary and secondary flows, and hence to the wall shear stress. The physiological application to flow in the coronary arteries is discussed.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 6
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    Bioconvection in suspensions of oxytactic bacteria: linear theory (1996)
    Cambridge University Press
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    Publication Date: 1996-10-10
    Description: When a suspension of the bacterium Bacillus subtilis is placed in a chamber with its upper surface open to the atmosphere, complex bioconvection patterns form. These arise because the cells (a) are denser than water, and (b) swim upwards on average so that the density of an initially uniform suspension becomes greater at the top than at the bottom. When the vertical density gradient becomes large enough an overturning instability occurs which evolves ultimately into the observed patterns. The cells swim upwards because they are oxytactic, i.e. they swim up gradients of oxygen, and they consume oxygen. These properties are incorporated in conservation equations for the cell and oxygen concentrations, which, for the pre-instability stage of the pattern formation process, have been solved in a previous paper (Hillesdon, Pedley & Kessler 1995). In this paper we carry out a linear instability analysis of the steady-state cell and oxygen concentration distributions. There are intrinsic differences between the shallow-and deep-chamber cell concentration distributions, with the consequence that the instability is non-oscillatory in shallow chambers, but must be oscillatory in deep chambers whenever the critical wavenumber is non-zero. We investigate how the critical Rayleigh number for the suspension varies with the three independent parameters of the problem and discuss the most appropriate definition of the Rayleigh number. Several qualitative aspects of the solution of the linear instability problem agree with experimental observation.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 7
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    Bacterial bioconvection: weakly nonlinear theory for pattern selection (1998)
    Cambridge University Press
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    Publication Date: 1998-09-10
    Description: Complex bioconvection patterns are observed when a suspension of the oxytactic bacterium Bacillus subtilis is placed in a chamber with its upper surface open to the atmosphere. The patterns form because the bacteria are denser than water and vim upwards (up an oxygen gradient) on average. This results in an unstable density distribution and an overturning instability. The pattern formation is dependent on depth and experiments in a tilted chamber have shown that as the depth increases the first patterns formed are hexagons in which the fluid flows down in the centre. The linear stability of this system was analysed by Hillesdon & Pedley (1996) who und that the system is unstable if the Rayleigh number Γ exceeds a critical value, which depends on the wavenumber k of the disturbance as well as on the values of other parameters. Hillesdon & Pedley found that the critical wavenumber kc, could be either zero or non-zero, depending on the parameter values. In this paper we carry out a weakly nonlinear analysis to determine the relative ability of hexagon and roll patterns formed at the onset of bioconvection. The analysis is different in the two cases kc ≠ 0 and kc = 0. For the kc ≠ 0 case (which appears to be more relevant experimentally) the model does predict down hexagons, but only for a certain range of parameter values. Hence the analysis allows us to refine previous parameter estimates. For the kc = 0 case we carry out a two-dimensional analysis and derive an equation describing the evolution of the horizontal planform function.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 8
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    A perturbation study of particle dynamics in a plane wake flow (1999)
    Cambridge University Press
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    Publication Date: 1999-04-10
    Description: We analyse the dynamics of small, rigid, dilute spherical particles in the far wake of a bluff body under the assumption that the background flow field is approximated by a periodic array of Stuart vortices that can be considered to be a regularization of the von Kármán vortices street. Using geometric singular perturbation theory and numerical methods, we show that when inertia (measured by a dimensionless Stokes number) is not too large, there is a periodic attractor in the phase space of the dynamical system governing the particle motion. We argue that this provides a simple mechanism to explain the unexpected 'focusing' effect that has been observed both numerically and experimentally in the far-wake flow past a bluff body by Tang et al. (1992). Their results show that over a range of Reynolds numbers and intermediate values of the Stokes number, particles injected into the wake of a bluff body concentrate near the edges of the vortex structures downstream, thus tending to 'demix' rather than disperse homogeneously.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 9
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    Numerical solutions for unsteady gravity-driven flows in collapsible tubes: evolution and roll-wave instability of a steady state (1999)
    Cambridge University Press
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    Publication Date: 1999-10-10
    Description: Unsteady flow in collapsible tubes has been widely studied for a number of different physiological applications; the principal motivation for the work of this paper is the study of blood flow in the jugular vein of an upright, long-necked subject (a giraffe). The one-dimensional equations governing gravity- or pressure-driven flow in collapsible tubes have been solved in the past using finite-difference (MacCormack) methods. Such schemes, however, produce numerical artifacts near discontinuities such as elastic jumps. This paper describes a numerical scheme developed to solve the one-dimensional equations using a more accurate upwind finite volume (Godunov) scheme that has been used successfully in gas dynamics and shallow water wave problems. The adapatation of the Godunov method to the present application is non-trivial due to the highly nonlinear nature of the pressure-area relation for collapsible tubes. The code is tested by comparing both unsteady and converged solutions with analytical solutions where available. Further tests include comparison with solutions obtained from MacCormack methods which illustrate the accuracy of the present method. Finally the possibility of roll waves occurring in collapsible tubes is also considered, both as a test case for the scheme and as an interesting phenomenon in its own right, arising out of the similarity of the collapsible tube equations to those governing shallow water flow.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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  • 10
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    Thermocapillary flow with evaporation and condensation at low gravity. Part 1. Non-deforming surface (1995)
    Cambridge University Press
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    Publication Date: 1995-07-10
    Description: The problem of steady motion and thermal behaviour of a volatile, wetting liquid in an open cavity under low gravity is defined and examined. The domain geometrically approximates a two-phase pore of liquid on a wicking structure surface, and consists of a 1 to 102 μu wide rectangular cavity bounded by a saturated vapour and liquid reservoir on its upper and lower surfaces, respectively. Thermal non-equilibrium and convection are established by symmetrically superheating or subcooling the pore boundaries by ∼ 1 K relative to the vapour. Numerical analyses show that although thermocapillary flow competes with interfacial phase change in dictating the circulation and flow structure, it tends to reinforce the convective effects of evaporation and condensation on surface temperature and heat transport. In addition, highly wetting fluids with curved menisci are characterized by greater circulation intensities and dynamic pressure gradients than a flat surface. The magnitude of these gradients suggests that the fixed menisci shapes assumed in this study are unrealistic, and that the influence of convection on surface morphology should be considered. © 1995, Cambridge University Press. All rights reserved.
    Print ISSN: 0022-1120
    Electronic ISSN: 1469-7645
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
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