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.

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.

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.

Foldback current control for a DG to achieve Fast Arc Extinction in a distribution network

The distribution network reliability can be increased if distributed generators (DGs) are allowed to operate in both grid-connected and islanded operations when the network has a high DG penetration level. However, the current utility regulations do not allow for the islanded operation. The arc faults are the one of the major issues preventing the islanded operation, since the arc will not extinguish if the DGs are not disconnected. In this paper, the effect of a converter interfaced DG on an arc fault is investigated by considering different control strategies for the converter. The foldback current control characteristic is proposed to a converter interfaced DG to achieve quick arc extinction and self-restoration without disconnecting the DG in the event of an arc fault. The results are validated through PSCAD/EMTDC simulations.

Bubble geometry and chaotic pricing behaviour

This paper is a deductive theoretical enquiry into the flow of effects from the geometry of price bubbles/busts, to price indices, to pricing behaviours of sellers and buyers, and back to price bubbles/busts. The intent of the analysis is to suggest analytical approaches to identify the presence, maturity, and/or sustainability of a price bubble. We present a pricing model to emulate market behaviour, including numeric examples and charts of the interaction of supply and demand. The model extends into dynamic market solutions myopic (single- and multi-period) backward looking rational expectations to demonstrate how buyers and sellers interact to affect supply and demand and to show how capital gain expectations can be a destabilising influence – i.e. the lagged effects of past price gains can drive the market price away from long-run market-worth. Investing based on the outputs of past price-based valuation models appear to be more of a game-of-chance than a sound investment strategy.

The organic fraction of bubble-generated, accumulation mode Sea Spray Aerosol (SSA)

Recent studies have detected a dominant accumulation mode (~100 nm) in the Sea Spray Aerosol (SSA) number distribution. There is evidence to suggest that particles in this mode are composed primarily of organics. To investigate this hypothesis we conducted experiments on NaCl, artificial SSA and natural SSA particles with a Volatility-Hygroscopicity-Tandem-Differential-Mobility-Analyser (VH-TDMA). NaCl particles were atomiser generated and a bubble generator was constructed to produce artificial and natural SSA particles. Natural seawater samples for use in the bubble generator were collected from biologically active, terrestrially-affected coastal water in Moreton Bay, Australia. Differences in the VH-TDMA-measured volatility curves of artificial and natural SSA particles were used to investigate and quantify the organic fraction of natural SSA particles. Hygroscopic Growth Factor (HGF) data, also obtained by the VH-TDMA, were used to confirm the conclusions drawn from the volatility data. Both datasets indicated that the organic fraction of our natural SSA particles evaporated in the VH-TDMA over the temperature range 170–200°C. The organic volume fraction for 71–77 nm natural SSA particles was 8±6%. Organic volume fraction did not vary significantly with varying water residence time (40 secs to 24 hrs) in the bubble generator or SSA particle diameter in the range 38–173 nm. At room temperature we measured shape- and Kelvin-corrected HGF at 90% RH of 2.46±0.02 for NaCl, 2.35±0.02 for artifical SSA and 2.26±0.02 for natural SSA particles. Overall, these results suggest that the natural accumulation mode SSA particles produced in these experiments contained only a minor organic fraction, which had little effect on hygroscopic growth. Our measurement of 8±6% is an order of magnitude below two previous measurements of the organic fraction in SSA particles of comparable sizes. We stress that our results were obtained using coastal seawater and they can’t necessarily be applied on a regional or global ocean scale. Nevertheless, considering the order of magnitude discrepancy between this and previous studies, further research with independent measurement techniques and a variety of different seawaters is required to better quantify how much organic material is present in accumulation mode SSA.

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.

Bubble rise velocity and trajectory in xanthan gum crystal suspension

An experimental set-up was used to visually observe the characteristics of bubbles as they moved up a column holding xanthan gum crystal suspensions. The bubble rise characteristics in xanthan gum solutions with crystal suspension are presented in this paper. The suspensions were made by using different concentrations of xanthan gum solutions with 0.23 mm mean diameter polystyrene crystal particles. The influence of the dimensionless quantities; namely the Reynolds number, Re, the Weber number, We, and the drag co-efficient, cd, are identified for the determination of the bubble rise velocity. The effect of these dimensionless groups together with the Eötvös number, Eo, the Froude number, Fr, and the bubble deformation parameter, D, on the bubble rise velocity and bubble trajectory are analysed. The experimental results show that the average bubble velocity increases with the increase in bubble volume for xanthan gum crystal suspensions. At high We, Eo and Re, bubbles are spherical-capped and their velocities are found to be very high. At low We and Eo, the surface tension force is significant compared to the inertia force. The viscous forces were shown to have no substantial effect on the bubble rise velocity for 45 < Re < 299. The results show that the drag co-efficient decreases with the increase in bubble velocity and Re. The trajectory analysis showed that small bubbles followed a zigzag motion while larger bubbles followed a spiral motion. The smaller bubbles experienced less horizontal motion in crystal suspended xanthan gum solutions while larger bubbles exhibited a greater degree of spiral motion than those seen in the previous studies on the bubble rise in xanthan gum solutions without crystal.

Can hybridization cause local extinction : the case for demographic swamping of the Australian native, Senecio pinnatifolius, by the invasive, S. madagascariensis?

The outcome of interspecific hybridization between native and invasive species depends on the relative frequencies of parental taxa and viability of hybrid progeny. We investigated individual and population level consequences of hybridization between the Australian native, Senecio pinnatifolius, and the exotic S. madagascariensis, with AFLP markers and used this information to simulate the expected outcome of hybridization.A high frequency (range 8.3-75.6 %) of hybrids was detected in open pollinated seeds of both species, but mature hybrids were absent from sympatric populations indicating that sympatric populations represent tension zones. A hybridization advantage was observed for S. madagascariensis,where significantly more progeny than expected were sired based on proportional representation of the two species in sympatric populations. Simulations indicated S. pinnatifolius could be replaced in sympatric populations if hybridization was density dependent.For this native-exotic pair, prezygotic isolating barriers are weak, but low hybrid viability maintains a strong postzygotic barrier to introgression. Due to asymmetric hybridization, S. pinnatifolius appears under threat from demographic swamping, and local extinction is possible where it occurs in sympatry with S. madagascariensis.

On the resistance to extinction of fear conditioned to angry faces

The present study investigated whether, like fear conditioned to pictures of snakes and spiders, fear conditioned to angry faces resists extinction even after verbal instruction and removal of the shock electrode. Participants were trained in a differential Pavlovian fear conditioning procedure with angry face or happy face conditional stimuli (CSs). Prior to extinction, half the participants in each group were informed that no more unconditional stimuli would be presented and the shock electrode was removed. In the absence of this manipulation, participants showed resistance to extinction after training with angry face CSs, but not after training with happy face CSs. Instructed extinction and electrode removal abolished fear conditioning regardless of the emotion expressed by the CS faces. This finding suggests that fear conditioned to angry faces, like fear conditioned to racial out-group faces, is more malleable than fear conditioned to snakes and spiders.

Rapid synthesis of porous honeycomb Cu/Pd through a hydrogen-bubble templating method

A rapid electrochemical method based on using a clean hydrogen-bubble template to form a bimetallic porous honeycomb Cu/Pd structure has been investigated. The addition of palladium salt to a copper-plating bath under conditions of vigorous hydrogen evolution was found to influence the pore size and bulk concentration of copper and palladium in the honeycomb bimetallic structure. The surface was characterised by X-ray photoelectron spectroscopy, which revealed that the surface of honeycomb Cu/Pd was found to be rich with a Cu/Pd alloy. The inclusion of palladium in the bimetallic structure not only influenced the pore size, but also modified the dendritic nature of the internal wall structure of the parent copper material into small nanometre-sized crystallites. The chemical composition of the bimetallic structure and substantial morphology changes were found to significantly influence the surface-enhanced Raman spectroscopic response for immobilised rhodamine B and the hydrogen-evolution reaction. The ability to create free-standing films of this honeycomb material may also have many advantages in the areas of gas- and liquid-phase heterogeneous catalysis.

The effect of electrode material on the electrochemical formation of porous copper surfaces using hydrogen bubble templating

The electrodeposition of copper onto copper, gold, palladium and glassy carbon (GC) electrodes via a hydrogen bubble templating method is reported. It is found that the composition of the underlying electrode material significantly influences the morphology of the copper electrodeposit. Highly ordered porous structures are achieved with Cu and Au electrodes, however on Pd this order is disrupted and a rough randomly oriented surface is formed whereas on GC a bubble templating effect is not observed. Chronopotentiograms recorded during the electrodeposition process allows bubble formation and detachment from the surface to be monitored where distinctly different potential versus time profiles are observed at the different electrodes. The porous Cu surfaces are characterised with scanning electron microscopy, X-ray diffraction and cyclic voltammetric measurements recorded under alkaline conditions. The latter demonstrates that there are active sites present on electrodeposited copper whose coverage and reactivity depend on the underlying electrode material. The most active Cu surface is achieved at a Pd substrate for both the hydrogen evolution reaction and the catalytic reduction of ferricyanide ions with thiosulphate ions. This demonstrates that the highly ordered porous structure on the micron scale which typifies the morphology that can be achieved with the hydrogen bubbling template method is not required in producing the most effective material.