Contact angle of a hemispherical bubble: an analytical approach

We have calculated the equilibrium shape of the axially symmetric Plateau border along which a spherical bubble contacts a flat wall, by analytically integrating Laplace’s equation in the presence of gravity, in the limit of small Plateau border sizes. This method has the advantage that it provides closed-form expressions for the positions and orientations of the Plateau border surfaces. Results are in very good overall agreement with those obtained from a numerical solution procedure, and are consistent with experimental data. In particular we find that the effect of gravity on Plateau border shape is relatively small for typical bubble sizes, leading to a widening of the Plateau border for sessile bubbles and to a narrowing for pendant bubbles. The contact angle of the bubble is found to depend even more weakly on gravity.

Speculative bubble spillovers across regional housing markets

In this paper we determine whether speculative bubbles in one region in the United States can lead bubbles to form in others. We first apply a regime-switching model to determine whether speculative bubbles existed in the U.S. regional residential real estate markets. Our findings suggest that the housing markets in five of the nine census divisions investigated were characterized by speculative bubbles. We then examine the extent to which bubbles spill over between neighboring and more distant regions, finding that the transmission of speculative bubbles and nonfundamentals between regions is multidirectional and does not depend on contiguity or distance

Technical note: how accurate can stalagmite formation temperatures be determined using vapour bubble radius measurements in fluid inclusions?

Stalagmites are natural archives containing detailed information on continental climate variability of the past. Microthermometric measurements of fluid inclusion homogenisation temperatures allow determination of stalagmite formation temperatures by measuring the radius of stable laser-induced vapour bubbles inside the inclusions. A reliable method for precisely measuring the radius of vapour bubbles is presented. The method is applied to stalagmite samples for which the formation temperature is known. An assessment of the bubble radius measurement accuracy and how this error influences the uncertainty in determining the formation temperature is provided. We demonstrate that the nominal homogenisation temperature of a single inclusion can be determined with an accuracy of ±0.25 °C, if the volume of the inclusion is larger than 105 μm3. With this method, we could measure in a proof-of-principle investigation that the formation temperature of 10–20 yr old inclusions in a stalagmite taken from the Milandre cave is 9.87 ± 0.80 °C, while the mean annual surface temperature, that in the case of the Milandre cave correlates well with the cave temperature, was 9.6 ± 0.15 °C, calculated from actual measurements at that time, showing a very good agreement. Formation temperatures of inclusions formed during the last 450 yr are found in a temperature range between 8.4 and 9.6 °C, which corresponds to the calculated average surface temperature. Paleotemperatures can thus be determined within ±1.0 °C.

Replacing fat and sugar with inulin in cakes: bubble size distribution, physical and sensory properties

The replacement of fat and sugar in cakes is a challenge as they have an important effect on the structural and sensory properties. Moreover, there is the possibility to incorporate an additional value using novel replacers. In this work, inulin and oligofructose were used as fat and sugar replacers, respectively. Different combinations of replacement levels were investigated: fat replacement (0 and 50 %) and sugar replacement (0, 20, 30, 40 and 50 %). Simulated microbaking was carried out to study bubble size distribution during baking. Batter viscosity and weight loss during baking were also analysed. Cake characteristics were studied in terms of cell crumb structure, height, texture and sensory properties. Fat and sugar replacement gave place to batters with low apparent viscosity values. During heating, bubbles underwent a marked expansion in replaced cakes if compared to the control cake. The low batter stability in fat-replaced samples increased bubble movement, giving place to cakes with bigger cells and less height than the control. Sugar-replaced samples had smaller and fewer cells and lower height than the control. Moreover, sugar replacement decreased hardness and cohesiveness and in- creased springiness, which could be related with a denser crumb and an easily crumbled product. Regarding the sensory analysis, a replacement up to 50 % of fat and 30 % of sugar, separately and simultaneously, did not change remarkably the overall acceptability of the cakes. However, the sponginess and the sweetness could be improved in all the replaced cakes, according to the Just About Right scales.

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface, by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semi-analytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a shallow flat bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.

Are mortgage lenders guilty of the housing bubble? A UK perspective

Existing theoretical models of house prices and credit rely on continuous rationality of consumers, an assumption that has been frequently questioned in recent years. Meanwhile, empirical investigations of the relationship between prices and credit are often based on national-level data, which is then tested for structural breaks and asymmetric responses, usually with subsamples. Earlier author argues that local markets are structurally different from one another and so the coefficients of any estimated housing market model should vary from region to region. We investigate differences in the price–credit relationship for 12 regions of the UK. Markov-switching is introduced to capture asymmetric market behaviours and turning points. Results show that credit abundance had a large impact on house prices in Greater London and nearby regions alongside a strong positive feedback effect from past house price movements. This impact is even larger in Greater London and the South East of England when house prices are falling, which are the only instances where the credit effect is more prominent than the positive feedback effect. A strong positive feedback effect from past lending activity is also present in the loan dynamics. Furthermore, bubble probabilities extracted using a discrete Kalman filter neatly capture market turning points.

Economic growth in Sweden, 2000-2010 : The dot-com bubble and the financial crisis

    Economic growth is the increase in the inflation-adjusted market value of the goods and services produced by an economy over time. The total output is the quantity of goods or servicesproduced in a given time period within a country. Sweden was affected by two crises during the period 2000-2010: a dot-com bubble and a financial crisis. How did these two crises affect the economic growth?     The changes of domestic output can be separated into four parts: changes in intermediate demand, final domestic demand, export demand and import substitution. The main purpose of this article is to analyze the economic growth during the period 2000-2010, with focus on the dot-com bubble in the beginning of the period 2000-2005, and the financial crisis at the end of the period 2005-2010. The methodology to be used is the structural decomposition method.     This investigation shows that the main contributions to the Swedish total domestic output increase in both the period 2000-2005 and the period 2005-2010 were the effect of domestic demand. In the period 2005-2010, financial crisis weakened the effect of export. The output of the primary sector went from a negative change into a positive, explained mainly by strong export expansion. In the secondary sector, export had most effect in the period 2000-2005. Nevertheless, domestic demand and import ratio had more effect during the financial crisis period. Lastly, in the tertiary sector, domestic demand can mainly explain the output growth in the whole period 2000-2010.

House price bubble estimations in Australia's capital cities with market fundamentals

This paper investigates the existence of house price bubbles in Australia's eight capital cities in recent years by using quantitative analyses including Johansen cointegration test, Granger causality test, impulse response and Chow forecast test. While interactions between house prices and market fundamentals are discussed in long-run and causal estimations, shocks from the market fundamentals to house prices are investigated in generalized impulse response analyses. Findings from estimating house price bubbles for eight capital cities suggest that there was an obvious house price bubble in Perth, while a slight house price bubble occurred in Sydney. In contrast, house prices in Adelaide and Darwin can be explained very well by market fundamentals, while house prices in Melbourne, Brisbane, Hobart and Canberra were undervalued in the study period.

Bubble-solid interactions in water and electrolyte solutions

Surface forces between an air bubble and a flat mica surface immersed in aqueous electrolyte solutions have been investigated using a modified surface force apparatus. An analysis of the deformation of the air bubble with respect to the mutual position of the bubble and the mica surface, the capillary pressure, and the disjoining pressure allows the air-liquid surface electrical potential to be determined. The experiments show that a long-range, double-layer repulsion acts between the mica (which is negatively charged) and an air bubble in water and in various electrolyte solutions at low concentration, thereby indicating that the air bubble surface is negatively charged. However, there is clear evidence that charge regulation occurs at the air-water interface to maintain a constant surface potential, and as a result of this, the charge at this interface changes from negative to positive as the bubble approaches the mica surface. Because of the attraction that arises as a result of the charge reversal, a finite force is required to separate the bubble from the mica, though the mica remains wetted by the aqueous phase. At the low concentrations investigated, the potential on the gas-liquid interface is independent of the electrolyte type within experimental uncertainty.

Stability of aqueous films between bubbles. Part 1. The effect of speed on bubble coalescence in purified water and simple electrolyte solutions

Film thinning experiments have been conducted with aqueous films between two air phases in a thin film pressure balance. The films are free of added surfactant but simple NaCl electrolyte is added in some experiments. Initially the experiments begin with a comparatively large volume of water in a cylindrical capillary tube a few millimeters in diameter, and by withdrawing water from the center of the tube the two bounding menisci are drawn together at a prescribed rate. Thismodels two air bubbles approaching at a controlled speed. In pure water, the results show three regimes of behavior depending on the approach speed; at slow speed (<1 μm/s) it is possible to form a flat film of pure water, ∼100 nm thick, that is stabilized indefinitely by disjoining pressure due to repulsive double-layer interactions between naturally charged air/water interfaces. The data are consistent with a surface potential of -57mV on the bubble surfaces. At intermediate approach speed (∼1-150 μm/s), the films are transiently stable due to hydrodynamic drainage effects, and bubble coalescence is delayed by ∼10-100 s. At approach speeds greater than ∼150 μm/s, the hydrodynamic resistance appears to become negligible, and the bubbles coalesce without any measurable delay. Explanations for these observations are presented that take into account Derjaguin-Landau-Verwey-Overbeek and Marangoni effects entering through disjoining pressure, surface mobility, and hydrodynamic flow regimes in thin film drainage. In particular, it is argued that the dramatic reduction in hydrodynamic resistance is a transition from viscosity-controlled drainage to inertia-controlled drainage associated with a change from immobile to mobile air/water interfaces on increasing the speed of approach of two bubbles. A simple model is developed that accounts for the boundaries between different film stability or coalescence regimes. Predictions of the model are consistent with the data, and the effects of adding electrolyte can be explained. In particular, addition of electrolyte at high concentration inhibits the near-instantaneous coalescence phenomenon, thereby contributing to increased foam film stability at high approach speeds, as reported in previous literature. This work highlights the significance of bubble approach speed as well as electrolyte concentration in affecting bubble coalescence.