Mathemateg a Ffiseg / Mathematics & Physics
http://hdl.handle.net/2160/14
2015-03-06T04:30:06Z
2015-03-06T04:30:06Z
Polyamorphism and the universal liquid-liquid critical point in the supercooled state
Neville
http://hdl.handle.net/2160/26446
2015-01-08T09:49:46Z
2011-04-01T00:00:00Z
Polyamorphism and the universal liquid-liquid critical point in the supercooled state
Neville
The physics of critical phenomena is well established in systems as diverse as molecular fluids, crystalline alloys and magnetic materials. As the critical point is approached, the susceptibility increases anomalously and fluctuations give rise to dramatic opalescence. Evidence has recently emerged for the existence of a second critical point in the liquid state at supercooled temperatures, below which polyamorphic phases coexist differing in density but sharing the same composition. Whilst much attention has been paid to supercooled water, polyamorphic phases have been observed in many elemental and oxide liquids potentially offering routes to low-entropy glasses. Our recent direct observation of a polyamorphic phase transition in levitated molten yttria-alumina offers the first opportunity to study the associated critical point in a real supercooled system. In situ small-angle X-ray scattering records sharp rises in the average correlation length of density fluctuations and in the compressibility as the transition is approached. Both increases approximate to the universal power-law relations predicted by the three-dimensional Ising model in common with all critical point phenomena. The observation brings the second critical point predicted in liquids into line with other critical phenomena. 1. Introduction Supercooled liquids are antecedents of the vitreous and crystalline states and their vast application, which stretches from glass making and ceramic fabrication to steel production (Zarzycki 1991), derives from the increasingly complex structural behaviour that develops as liquids that are initially homogeneous cool below the melting point with rising viscosity and density (Greaves & Sen 2007). In particular, statistical fluctuations in density, which generally decrease in amplitude as the temperature falls and the bulk modulus rises (Landau & Lifshitz 1969), become non-ergodic in the supercooled state (Scopigno et al. 2003) with the emergence of slow processes which bifurcate from the fast processes of the thermodynamic liquid and influence the onset of the glass transition (Greaves & Sen 2007; Götze 1999).
2011-04-01T00:00:00Z
Analysis of a model for foam improved oil recovery
P.
E.
N.
S. J.
G.
W. R.
http://hdl.handle.net/2160/14173
2015-02-28T22:01:52Z
2014-07-01T00:00:00Z
Analysis of a model for foam improved oil recovery
P.; E.; N.; S. J.; G.; W. R.
During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ` pressure-driven growth'is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, `pressure-driven growth' is shown to correspond to a special case of the more general `viscous froth' model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such `inherent'singularities can be readily incorporated into these numerical schemes.
2014-07-01T00:00:00Z
Yttria-zirconia coatings studied by grazing-incidence small-angle X-ray scattering during in situ heating
Hoydalsvik, Kristin
Barnardo, Twilight
Winter, Rudolf
Haas, Sylvio
Tatchev, Dragomir
Hoell, Armin
http://hdl.handle.net/2160/14165
2014-10-23T03:02:33Z
2010-11-21T00:00:00Z
Yttria-zirconia coatings studied by grazing-incidence small-angle X-ray scattering during in situ heating
Hoydalsvik, Kristin; Barnardo, Twilight; Winter, Rudolf; Haas, Sylvio; Tatchev, Dragomir; Hoell, Armin
The morphology of sol–gel derived dip-coated yttria-doped zirconia ﬁlms containing variable amounts of yttria has been studied using in situ grazing-incidence small-angle X-ray scattering (GISAXS) whilst heated incrementally to 1000C. A procedure to analyse in situ GISAXS data has been devised which allows a quantitative analysis of time-dependent GISAXS data tracing processes such as chemical reactions or manufacturing procedures. To achieve this, the relative positions of the Yoneda peak and the through beam are used to ﬁx the vertical q scale when the sample thickness is subject to ﬂuctuations due to chemical reactions or deposition processes. A version of Beaucage’s uniﬁed model with a structure factor from Hosemann’s model for paracrystals describes the yttria-zirconia ﬁlm data best. It is interpreted in terms of particles forming from a polymeric gel network and subsequently agglomerating into larger units subject to Ostwald ripening as both size and average separation distance of the scattering objects increase. The sample with the highest yttria content shows progressive surface roughening from 850C which may indicate the onset of chemical segregation.
Hoydalsvik, K., Barnardo, T., Winter, R., Haas, S., Tatchev, D., Hoell, A. (2010). Yttria-zirconia coatings studied by grazing-incidence small-angle X-ray scattering during in situ heating. Physical Chemistry Chemical Physics, 12 (43), 14492-14500. Sponsorship: HEFCW, EPSRC, EU
2010-11-21T00:00:00Z
Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits
Marc
Andrew M.
Frank
Jos
Catherine
Simon
Shirin
François
http://hdl.handle.net/2160/14130
2015-01-31T22:01:47Z
2014-06-19T00:00:00Z
Statistical mechanics of two-dimensional shuffled foams: Geometry-topology correlation in small or large disorder limits
Marc; Andrew M.; Frank; Jos; Catherine; Simon; Shirin; François
Bubble monolayers are model systems for experiments and simulations of two-dimensional packing problems of deformable objects. We explore the relation between the distributions of the number of bubble sides (topology) and the bubble areas (geometry) in the low liquid fraction limit. We use a statistical model [M. Durand, Europhys. Lett. 90, 60002 (2010)EULEEJ0295-507510.1209/0295- 5075/90/60002] which takes into account Plateau laws. We predict the correlation between geometrical disorder (bubble size dispersity) and topological disorder (width of bubble side number distribution) over an extended range of bubble size dispersities. Extensive data sets arising from shuffled foam experiments, surface evolver simulations, and cellular Potts model simulations all collapse surprisingly well and coincide with the model predictions, even at extremely high size dispersity. At moderate size dispersity, we recover our earlier approximate predictions [M. Durand, J. Kafer, C. Quilliet, S. Cox, S. A. Talebi, and F. Graner, Phys. Rev. Lett. 107, 168304 (2011)PRLTAO0031-900710.1103/ PhysRevLett.107.168304]. At extremely low dispersity, when approaching the perfectly regular honeycomb pattern, we study how both geometrical and topological disorders vanish. We identify a crystallization mechanism and explore it quantitatively in the case of bidisperse foams. Due to the deformability of the bubbles, foams can crystallize over a larger range of size dispersities than hard disks. The model predicts that the crystallization transition occurs when the ratio of largest to smallest bubble radii is 1.4. © 2014 American Physical Society.
2014-06-19T00:00:00Z