Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

Judge George W Paul's Japanese house : a case study

In the late 1880s a pre-fabricated Japanese house was shipped from Kobe, Japan, to Brisbane, Australia, and erected in the up-market suburb of New Farm by Japanese tradesmen. This paper is developed from a broader project researching the life of G W Paul, the man who had the house built and subsequently lived in it for the remainder of his life. Paul’s motivation in importing the house represented a unique, but unfulfilled effort to develop a future, hybrid culture for Queensland. This effort took the form of a commercial venture to construct Japanese houses as desirable and climatically suitable dwellings. Against the backdrop of this ambition, this paper presents new research to elucidate and extend previous knowledge, assesses the reception of the house by its nineteenth century Brisbane audience, and considers possible reasons for the limited response which signalled the cancellation of the commercial venture.

New exact solutions for Hele-Shaw flow in doubly connected regions

Radial Hele-Shaw flows are treated analytically using conformal mapping techniques. The geometry of interest has a doubly-connected annular region of viscous fluid surrounding an inviscid bubble that is either expanding or contracting due to a pressure difference caused by injection or suction of the inviscid fluid. The zero-surface-tension problem is ill-posed for both bubble expansion and contraction, as both scenarios involve viscous fluid displacing inviscid fluid. Exact solutions are derived by tracking the location of singularities and critical points in the analytic continuation of the mapping function. We show that by treating the critical points, it is easy to observe finite-time blow-up, and the evolution equations may be written in exact form using complex residues. We present solutions that start with cusps on one interface and end with cusps on the other, as well as solutions that have the bubble contracting to a point. For the latter solutions, the bubble approaches an ellipse in shape at extinction.

Et tu, George? Campaign journalism and the politics of compromise

There is a category of film about journalism in which journalism is not the star, but the supporting player, and journalists not the protagonists but the Greek chorus, commenting on and also changing the realities they report. In such films the news media are a structuring presence driving the plot, shaping the narrative, constructing what we might think of as a pseudo-reality. Like Daniel Boorstin’s notion of the pseudo-event (introduced in his still-relevant book The Image, 1962), this pseudo-reality is so-named because it would not exist were it not for the demands of the news media’s hunger for stories, and knowledge of the damage they can do with those stories, on the calculations and actions of the key actors. Pseudo-realities form as responses to what political actors think journalists and their organisations need and want, or as efforts to shape journalistic accounts in ways favourable to themselves. Films about politics often feature pseudorealities of this kind, in which the events and actions driving the plot have only a tenuous relationship with important things going on in the everyday world beyond the political arena. Everything we see is about image, perception, appearance.

Peggy Shaw's "RUFF"

Peggy Shaw has always had a host of crooners, lounge singers, movie stars, rock and roll bands, and eccentric family members living inside her. Ruff is a tribute to those who have kept Shaw company over the last 68 years, a lament for the absence of those who disappeared into the dark holes left behind by her recent stroke, and a celebration that her brain is able to fill the blank green screens with new insight. The original set and media environment for RUFF was conceived during a Split Britches residency hosted at QUT from June-August 2012, funded by Arts Queensland. After a preliminary season at Out North in Alaska RUFF premiered at Performance Space 122 2013 COIL festival, PS122 @ Dixon Place, New York in January 2013 and has since toured to the Chelsea Theatre in London and the Arches Festival in Glasgow. Co Written and Performed by Peggy Shaw, Co Written and Directed by Lois Weaver, Original Music Composed by Vivian Stoll, Choreography by Stormy Brandenburger, Set and Media Design by Matt Delbridge, Lighting Design by Lori E Said.

Bubble extinction in Hele-Shaw flow with surface tension and kinetic undercooling regularisation

We perform an analytic and numerical study of an inviscid contracting bubble in a two-dimensional Hele-Shaw cell, where the effects of both surface tension and kinetic undercooling on the moving bubble boundary are not neglected. In contrast to expanding bubbles, in which both boundary effects regularise the ill-posedness arising from the viscous (Saffman-Taylor) instability, we show that in contracting bubbles the two boundary effects are in competition, with surface tension stabilising the boundary, and kinetic undercooling destabilising it. This competition leads to interesting bifurcation behaviour in the asymptotic shape of the bubble in the limit it approaches extinction. In this limit, the boundary may tend to become either circular, or approach a line or "slit" of zero thickness, depending on the initial condition and the value of a nondimensional surface tension parameter. We show that over a critical range of surface tension values, both these asymptotic shapes are stable. In this regime there exists a third, unstable branch of limiting self-similar bubble shapes, with an asymptotic aspect ratio (dependent on the surface tension) between zero and one. We support our asymptotic analysis with a numerical scheme that utilises the applicability of complex variable theory to Hele-Shaw flow.

An accurate numerical scheme for the contraction of a bubble in a Hele-Shaw cell

We report on an accurate numerical scheme for the evolution of an inviscid bubble in radial Hele-Shaw flow, where the nonlinear boundary effects of surface tension and kinetic undercooling are included on the bubble-fluid interface. As well as demonstrating the onset of the Saffman-Taylor instability for growing bubbles, the numerical method is used to show the effect of the boundary conditions on the separation (pinch-off) of a contracting bubble into multiple bubbles, and the existence of multiple possible asymptotic bubble shapes in the extinction limit. The numerical scheme also allows for the accurate computation of bubbles which pinch off very close to the theoretical extinction time, raising the possibility of computing solutions for the evolution of bubbles with non-generic extinction behaviour.

An afternoon with Chopin and George Sand

An original edutainment piece written by Caroline Heim and Christian Heim. Frederic Chopin and George Sands' turbulent and fraught relationship is dramatised through Chopin's music and Sand's writings.

Mathematical models of bubble evolution in a Hele-Shaw Cell

This thesis concerns the mathematical model of moving fluid interfaces in a Hele-Shaw cell: an experimental device in which fluid flow is studied by sandwiching the fluid between two closely separated plates. Analytic and numerical methods are developed to gain new insights into interfacial stability and bubble evolution, and the influence of different boundary effects is examined. In particular, the properties of the velocity-dependent kinetic undercooling boundary condition are analysed, with regard to the selection of only discrete possible shapes of travelling fingers of fluid, the formation of corners on the interface, and the interaction of kinetic undercooling with the better known effect of surface tension. Explicit solutions to the problem of an expanding or contracting ring of fluid are also developed.

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.

Pimelea trichostachya poisoning (St George disease) in horses

A dense population of Pimelea trichostachya plants (Family Thymelaeaceae) in pasture poisoned a horse herd in southern inland Queensland in October-November 2005. Plant density was 2 to 45 g wet weight/m2 (mean 16 g/m2) from 5 to 69 plants/m2 (mean 38 plants/m2) representing 3 to 20% (mean 9%) of the volume of pasture on offer. Ten of 35 mares, fillies and geldings were affected. Clinical signs were loss of body weight, profound lethargy, serous nasal discharge, severe watery diarrhoea and subcutaneous oedema of the intermandibular space, chest and ventral midline. Pathological findings were anaemia, leucocytopenia, hypoproteinaemia, dilatation of the right ventricle of the heart, dilated hepatic portal veins and periportal hepatic sinusoids (peliosis hepatis), alimentary mucosal hyperaemia and oedema of mesenteric lymph nodes. Cattle grazing the same pasture were affected by Pimelea poisoning simultaneously. Removal of the horses to Pimelea-free pasture initiated recovery. The one other incident of this syndrome, previously only recognised in cattle in Australia, occurred in horses, in South Australia in 2002, with access to a dense Pimelea simplex population.

Portrait of George Louis Wolff (Gerd Ludwig Wolff) holding a mouse in his genetics laboratory; Little Rock, Arkansas.

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