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Relationships between the medium-range structure of glasses and crystals
- P. H. Gaskell
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- Journal:
- Mineralogical Magazine / Volume 64 / Issue 3 / June 2000
- Published online by Cambridge University Press:
- 05 July 2018, pp. 425-434
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The known structure of a crystalline phase is almost always useful in investigating the unknown structure of the compositionally equivalent glass. For the local environment around elements like Si, B and P, the correspondence between site geometry and symmetry can be impressively close. Beyond near neighbours, any relationship becomes less obvious – at least in real-space data. Progress in understanding the medium-range structures of glasses has been painfully slow as a result. One essential clue is given by reciprocal-space features at low Q (scattering vector) in X-ray or neutron scattering data, which are clearly related to the medium-range structure. Interpretation of these features as ‘quasi-Bragg’ scattering allows direct comparison between the structures of the glass and equivalent crystalline phases. Applications of this method will be illustrated in borates and silicates, together with some chalcogenide glasses. Correspondence between low-Q features for these glasses and compositionally-equivalent crystals is qualitatively good. In some cases there is semi-quantitative agreement too. Thus the essential flavour of the medium-range structure of several typical glasses appears to be interpretable, rather easily.
Use of vaccines and factors associated with their uptake variability in dogs, cats and rabbits attending a large sentinel network of veterinary practices across Great Britain
- F. Sánchez-Vizcaíno, A. Muniesa, D. A. Singleton, P. H. Jones, P. J. Noble, R. M. Gaskell, S. Dawson, A. D. Radford
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- Journal:
- Epidemiology & Infection / Volume 146 / Issue 7 / May 2018
- Published online by Cambridge University Press:
- 11 April 2018, pp. 895-903
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Vaccination remains a mainstay of companion animal population health. However, how vaccine use at a population level complies with existing guidelines is unknown. Here we use electronic health records to describe vaccination in dogs, cats and rabbits attending a large sentinel network of UK veterinary practices. In total, 77.9% (95% CI: 77.6–78.1) of animals had recorded vaccinations. The percentage of animals with recorded vaccinations was higher in dogs, neutered animals, in insured dogs and cats and in purebred dogs. Vaccination rates varied in different regions of Great Britain in all species. Dogs and cats belonging to owners living in less deprived areas of England and Scotland were more likely to be recorded as vaccinated. In the vaccinated population, cats received more core vaccines per year of life (0.86) than dogs (0.75), with feline leukaemia vaccines almost as frequent as core vaccines. In dogs, leptospira vaccines were more frequent than core vaccines. This descriptive study suggests a substantial proportion of animals are not benefiting from vaccine protection. For the first time, we identify potential factors associated with variations in recorded vaccination frequency, providing a critical baseline against which to monitor future changes in companion animal vaccination and evidence to inform future targeted health interventions.
Stirring and transport enhancement in a continuously modulated free-surface flow
- MARK C. T. WILSON, J. L. SUMMERS, N. KAPUR, P. H. GASKELL
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- Journal:
- Journal of Fluid Mechanics / Volume 565 / 25 October 2006
- Published online by Cambridge University Press:
- 28 September 2006, pp. 319-351
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The transport of fluid from a recirculation region adjacent to a free surface is studied using a numerical method validated with experimental flow visualization. The flow is an example of a liquid film coating process, and consists of two counter-rotating rolls placed side-by-side and half-submerged in a bath of fluid. In the gap between the rolls a recirculation zone exists just below the free surface, around which the flow splits into two films. Fluid recirculating for long periods has been identified as a source of coating defects, so this paper considers a possible method of inducing stirring. The flow is modulated by driving one of the rolls through a Hooke's joint, which delivers a well-characterized periodic perturbation to the roll speed. In response to this speed modulation, the free surface undergoes a periodic change in position and shape which drives an exchange of fluid between the recirculation region and the surrounding flow. The amplitude of the free-surface motion is strongly dependent on modulation frequency.
The dynamics of the free surface preclude a quasi-steady approach, even in the small-frequency limit, and so a fully time-dependent analysis based on the finite element method is employed. Trigonometric temporal interpolation of the finite element data is used to make passive tracer advection calculations more efficient, and excellent agreement is seen between simulation and experiment. Computations of the stable and unstable invariant manifolds associated with periodic points on the free surface reveal that the exchange of fluid is governed by a self-intersecting turnstile mechanism, by which most fluid entrained during a modulation cycle is ejected later in the same cycle.
Transport over several cycles is explored by observation of the evacuation of passive tracers initially distributed uniformly in the recirculation zone. Results demonstrate the persistence of unmixed cores whose size is dependent on the modulation frequency. By considering the percentage of tracers remaining after a fixed number of cycles, contours in frequency–amplitude space show that for each modulation amplitude there is a frequency which produces the most effective transport, with up to 80 % of tracers removed by a modulation which produces only a 5 % change in film thickness. Finally it is shown how modulation of both rolls at slightly different phases can reduce the film thickness variation to about 1 % while maintaining the level of transport.
Modelling and analysis of meniscus roll coating
- P. H. Gaskell, M. D. Savage, J. L. Summers, H. M. Thompson
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- Journal:
- Journal of Fluid Mechanics / Volume 298 / 10 September 1995
- Published online by Cambridge University Press:
- 26 April 2006, pp. 113-137
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Three mathematical models are developed for meniscus roll coating in which there is steady flow of a Newtonian fluid in the narrow gap, or nip, between two contrarotating rolls in the absence of body forces.
The zero flux model predicts a constant pressure gradient within the central core and two eddies, each with an inner structure, in qualitative agreement with observation. The small flux model takes account of a small inlet flux and employs the lubrication approximation to represent fluid velocity as a combination of Couette and Poiseuille flows. Results show that the meniscus coating regime is characterized by small flow rates (λ [Lt ] 1) and a sub-ambient pressure field generated by capillary action at the upstream meniscus. Such flows are found to exist for small modified capillary number, Ca(R/H0)1/2 [lsim ] 0.15, where Ca and R/H0 represent capillary number and the radius to semi-gap ratio, respectively.
A third model incorporates the full effects of curved menisci and nonlinear free surface boundary conditions. The presence of a dynamic contact line, adjacent to the web on the upper roll, requires the imposition of an apparent contact angle and slip length. Numerical solutions for the velocity and pressure fields over the entire domain are obtained using the finite element method. Results are in accord with experimental observations that the flow domain consists of two large eddies and fluid transfer jets or ‘snakes’. Furthermore, the numerical results show that the sub-structure of each large eddy consists of a separatrix with one saddle point, two sub-eddies with centres, and an outer recirculation.
Finally finite element solutions in tandem with lubrication analysis establish the existence of three critical flow rates corresponding to a transformation of the pressure field, the emergence of a ‘secondary snake’ (another fluid transfer jet) and the disappearance of a primary snake.
Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography
- P. H. GASKELL, P. K. JIMACK, M. SELLIER, H. M. THOMPSON, M. C. T. WILSON
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- Journal:
- Journal of Fluid Mechanics / Volume 509 / 25 June 2004
- Published online by Cambridge University Press:
- 07 June 2004, pp. 253-280
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A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver.
Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography.
Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function.
An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion.
A model for deformable roll coating with negative gaps and incompressible compliant layers
- M. J. GOSTLING, M. D. SAVAGE, A. E. YOUNG, P. H. GASKELL
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- Journal:
- Journal of Fluid Mechanics / Volume 489 / 25 July 2003
- Published online by Cambridge University Press:
- 30 July 2003, pp. 155-184
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A soft elastohydrodynamic lubrication model is formulated for deformable roll coating involving two contra-rotating rolls, one rigid and the other covered with a compliant layer. Included is a finite-strip model (FSM) for the deformation of the layer and a lubrication model with suitable boundary conditions for the motion of the fluid. The scope of the analysis is restricted to Newtonian fluids, linear elasticity/viscoelasticity and equal roll speeds, with application to the industrially relevant highly loaded or ‘negative gap’ regime. Predictions are presented for coated film thickness, inter-roll thickness, meniscus location, pressure and layer deformation as the control parameters – load (gap), elasticity, layer thickness and capillary number, $\hbox{\it Ca}$ – are varied. There are four main results:
Hookean spring models are shown to be unable to model effectively the deformation of a compliant layer when Poisson's ratio $\nu\rightarrow 0.5$. In particular, they fail to predict the swelling of the layer at the edge of the contact region which increases as $\nu\rightarrow 0.5$; they also fail to locate accurately the position of the meniscus, $X_M$, and to identify the presence, close to the meniscus, of a ‘nib’ (constriction in gap thickness) and associated magnification of the sub-ambient pressure loop.
Scaling arguments suggest that layer thickness and elasticity may have similar effects on the field variables. It is shown that for positive gaps this is true, whereas for negative gaps they have similar effects on the pressure profile and flow rate yet quite different effects on layer swelling (deformation at the edge of the contact region) and different effects on $X_M$.
For negative gaps and $\hbox{\it Ca}\,{\sim}\,O(1)$, the effect of varying either viscosity or speed and hence $\hbox{\it Ca}$ is to significantly alter both the coating thickness and $X_M$. This is contrary to the case of fixed-gap rigid roll coating.
Comparison between theoretical predictions and experimental data shows quantitive agreement in the case of $X_M$ and qualitive agreement for flow rate. It is shown that this difference in the latter case may be due to viscoelastic effects in the compliant layer.
Stagnation–saddle points and flow patterns in Stokes flow between contra-rotating cylinders
- P. H. GASKELL, M. D. SAVAGE, H. M. THOMPSON
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- Journal:
- Journal of Fluid Mechanics / Volume 370 / 10 September 1998
- Published online by Cambridge University Press:
- 16 July 2002, pp. 221-247
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The steady flow is considered of a Newtonian fluid, of viscosity μ, between contra-rotating cylinders with peripheral speeds U1 and U2. The two-dimensional velocity field is determined correct to O(H0/2R)1/2, where 2H0 is the minimum separation of the cylinders and R an ‘averaged’ cylinder radius. For flooded/moderately starved inlets there are two stagnation–saddle points, located symmetrically about the nip, and separated by quasi-unidirectional flow. These stagnation–saddle points are shown to divide the gap in the ratio U1[ratio ]U2 and arise at [mid ]X[mid ]=A where the semi-gap thickness is H(A) and the streamwise pressure gradient is given by dP/dX =μ(U1+U2)/H2(A). Several additional results then follow.
(i) The effect of non-dimensional flow rate, λ: A2=2RH0(3λ−1) and so the stagnation–saddle points are absent for λ<1/3, coincident for λ=1/3 and separated for λ>1/3.
(ii) The effect of speed ratio, S=U1/U2: stagnation–saddle points are located on the boundary of recirculating flow and are coincident with its leading edge only for symmetric flows (S=1). The effect of unequal cylinder speeds is to introduce a displacement that increases to a maximum of O(RH0)1/2 as S→0.
Five distinct flow patterns are identified between the nip and the downstream meniscus. Three are asymmetric flows with a transfer jet conveying fluid across the recirculation region and arising due to unequal cylinder speeds, unequal cylinder radii, gravity or a combination of these. Two others exhibit no transfer jet and correspond to symmetric (S=1) or asymmetric (S≠1) flow with two asymmetric effects in balance. Film splitting at the downstream stagnation–saddle point produces uniform films, attached to the cylinders, of thickness H1 and H2, where
formula here
provided the flux in the transfer jet is assumed to be negligible.
(iii) The effect of capillary number, Ca: as Ca is increased the downstream meniscus advances towards the nip and the stagnation–saddle point either attaches itself to the meniscus or disappears via a saddle–node annihilation according to the flow topology.
Theoretical predictions are supported by experimental data and finite element computations.
Flow in a double-film-fed fluid bead between contra-rotating rolls Part 1: equilibrium flow structure
- M. C. T. WILSON, P. H. GASKELL, M. D. SAVAGE
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- Journal:
- European Journal of Applied Mathematics / Volume 12 / Issue 3 / June 2001
- Published online by Cambridge University Press:
- 06 August 2001, pp. 395-411
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In multiple-roll coaters thin liquid films are transferred from roll to roll by means of liquid ‘beads’ which occupy the small gaps between adjacent rolls. Double-Film-Fed (DFF) beads are those which feature two ingoing films instead of the usual one, and arise in the intermediate stages of certain types of roll coater. One of the ingoing films, h1, is supplied from the previous inter-roll gap while the other, h2, ‘returns’ from the subsequent gap. Such a flow is investigated here under the conditions of low flow rate, small capillary number and negligible gravity and inertia, using lubrication theory and finite element analysis. The thickness of film h1 is fixed independently, while that of h2 is specified as a fraction, ζ, of the film output on the same roll. This simple approach allows a degree of feedback between the output and input of the bead, and enables one to simulate different conditions in the subsequent gap. Predictions of outgoing film thicknesses made using the two models agree extremely well and show that, for each value of ζ < 1, one outgoing film thickness decreases monotonically with speed ratio, S, while the other features a maximum. Good agreement is also seen in the pressure profiles, which are entirely sub-ambient in keeping with the small capillary number conditions. The finite element solutions reveal that in the ‘zero-flux’ case (when ζ = 1) the flow structures are very similar to those seen in an idealized cavity problem. In the more general (ζ < 1) situation, as in single-film-fed meniscus roll coating, several liquid transfer-jets occur by which liquid is conveyed through the bead from one roll to the other. The lubrication model is used to calculate several critical flow rates at which the flow is transformed, and it is shown that when the total dimensionless flow rate through the bead exceeds 1/3, the downstream flow structure is independent of the relative sizes of the ingoing films.
An experimental investigation of meniscus roll coating
- P. H. GASKELL, G. E. INNES, M. D. SAVAGE
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- Journal:
- Journal of Fluid Mechanics / Volume 355 / 25 January 1998
- Published online by Cambridge University Press:
- 25 January 1998, pp. 17-44
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A two-roll apparatus is used to explore experimentally the detailed fluid mechanics of meniscus roll coating in which inlets are starved and flow rates are small. Both forward and reverse modes of operation (with contra- and co-rotating rolls) are investigated using optical sectioning combined with dye injection and particle imaging techniques. That part of parameter space where meniscus coating occurs is identified by varying the roll separation and roll speeds and hence flow rate and capillary number.
Key features of the flow structures identified in the forward mode include two large eddies (each with saddle point, separatrix and sub-eddies), a primary fluid transfer jet and the existence of two critical flow rates associated with the switching-on of a second fluid transfer jet and the switching-off of the primary transfer jet followed by a change in the flow structure. In the reverse mode, the key features are a single large eddy consisting of two sub-eddies, a saddle point and separatrix, a primary fluid transfer jet and once again two critical flow rates. These correspond to (i) the switching-on of a secondary transfer jet and (ii) the disappearance of a saddle point at the nip resulting in the merger of the primary and secondary transfer jets.
Measurements of film thickness and meniscus location made over a range of speed ratios and capillary numbers are compared with theoretical predictions. A plate–roll apparatus is used to confirm the presence, for very small flow rates, of a sub-ambient, almost linear, pressure profile across the bead. Investigated also is the transition from inlet-starved to fully flooded roll coating as flow rate is increased and the changes in flow structure and pressure profile are observed.
Stokes flow in a half-filled annulus between rotating coaxial cylinders
- P. H. GASKELL, M. D. SAVAGE, M. WILSON
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- Journal:
- Journal of Fluid Mechanics / Volume 337 / 25 April 1997
- Published online by Cambridge University Press:
- 25 April 1997, pp. 263-282
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A model is presented for viscous flow in a cylindrical cavity (a half-filled annulus lying between horizontal, infinitely long concentric cylinders of radii Ri, Ro rotating with peripheral speeds Ui, Uo). Stokes' approximation is used to formulate a boundary value problem which is solved for the streamfunction, ω, as a function of radius ratio R¯= Ri/Ro and speed ratio S=Ui/Uo.
Results show that for S>0 (S<0) the flow domain consists of two (one) large eddies (eddy), each having a stagnation point on the centreline and a potentially rich substructure with separatrices and sub-eddies. The behaviour of the streamfunction solution in the neighbourhood of stagnation points on the centreline is investigated by means of a truncated Taylor expansion. As R¯ and S are varied it is shown that a bifurcation in the flow structure arises in which a centre becomes a saddle stagnation point and vice versa. As R¯→1, a sequence of ‘flow bifurcations’ leads to a flow structure consisting of a set of nested separatrices, and provides the means by which the two-dimensional cavity flow approaches quasi-unidirectional flow in the small gap limit. Control-space diagrams reveal that speed ratio has little effect on the flow structure when S<0 and also when S>0 and aspect ratios are small (except near S=1). For S>0 and moderate to large aspect ratios the bifurcation characteristics of the two large eddies are quite different and depend on both R¯ and S.