Simulation of defects in bubble clusters

Topological defects in foam, either isolated (disclinations and dislocations) or in pairs, affect the energy and stress, and play an important role in foam deformation. Surface Evolver simulations were performed on large finite clusters of bubbles. These allow us to evaluate the effect of the topology of the defects, and the distance between defects, on the energy and pressure of foam clusters of different sizes. The energy of such defects follows trends similar to known analytical results for a continuous medium.

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. (C) 2009 Elsevier Inc. All rights reserved.

Effect of the number of shells on the pressure and energy of two-dimensional free bubble clusters

We have performed Surface Evolver simulations of two-dimensional hexagonal bubble clusters consisting of a central bubble of area lambda surrounded by s shells or layers of bubbles of unit area. Clusters of up to twenty layers have been simulated, with lambda varying between 0.01 and 100. In monodisperse clusters (i.e., for lambda = 1) [M.A. Fortes, F Morgan, M. Fatima Vaz, Philos. Mag. Lett. 87 (2007) 561] both the average pressure of the entire Cluster and the pressure in the central bubble are decreasing functions of s and approach 0.9306 for very large s, which is the pressure in a bubble of an infinite monodisperse honeycomb foam. Here we address the effect of changing the central bubble area lambda. For small lambda the pressure in the central bubble and the average pressure were both found to decrease with s, as in monodisperse clusters. However, for large,, the pressure in the central bubble and the average pressure increase with s. The average pressure of large clusters was found to be independent of lambda and to approach 0.9306 asymptotically. We have also determined the cluster surface energies given by the equation of equilibrium for the total energy in terms of the area and the pressure in each bubble. When the pressures in the bubbles are not available, an approximate equation derived by Vaz et al. [M. Fatima Vaz, M.A. Fortes, F. Graner, Philos. Mag. Lett. 82 (2002) 575] was shown to provide good estimations for the cluster energy provided the bubble area distribution is narrow. This approach does not take cluster topology into account. Using this approximate equation, we find a good correlation between Surface Evolver Simulations and the estimated Values of energies and pressures. (C) 2008 Elsevier B.V. All rights reserved.

Size distribution of polycyclic aromatic hydrocarbons in a roadway tunnel in Lisbon, Portugal

Atmospheric aerosols of four aerodynamic size ranges were collected using high volume cascade impactors in an extremely busy roadway tunnel in Lisbon (Portugal). Dust deposited on the tunnel walls and guardrails was also collected. Average particle mass concentrations in the tunnel atmosphere were more than 30 times higher than in the outside urban background air, revealing its origins almost exclusively from fresh vehicle emissions. Most of the aerosol mass was concentrated in submicrometer fractions (65%), and polycyclic aromatic hydrocarbons (PAH) were even more concentrated in the finer particles with an average of 84% of total PAH present in sizes smaller than 0.49 mu m. The most abundant PAH were methylated phenanthrenes, fluoranthene and pyrene. About 46% of the total PAH mass was attributed to lower molecular weight compounds (two and three rings), suggesting a strong influence of diesel vehicle emissions on the production of local particulate PAH. The application of diagnostic ratios confirmed the relevance of this source of PAH in the tunnel ambient air. Deposited dust presented PAH profiles similar to the coarser aerosol size range, in agreement with the predominant origin of coarser aerosol particles from soil dust resuspension and vehicle wear products. (c) 201 1 Elsevier Ltd. All rights reserved.

Size-segregated chemical composition of aerosol emissions in an urban road tunnel in Portugal

An atmospheric aerosol study was performed in 2008 inside an urban road tunnel, in Lisbon, Portugal. Using a high volume impactor, the aerosol was collected into four size fractions (PM0.5, PM0.5-1, PM1-2.5 and PM2.5-10) and analysed for particle mass (PM), organic and elemental carbon (OC and EC), polycyclic aromatic hydrocarbons (PAH), soluble inorganic ions and elemental composition. Three main groups of compounds were discriminated in the tunnel aerosol: carbonaceous, soil component and vehicle mechanical wear. Measurements indicate that Cu can be a good tracer for wear emissions of road traffic. Cu levels correlate strongly with Fe, Mn, Sn and Cr, showing a highly linear constant ratio in all size ranges, suggesting a unique origin through sizes. Ratios of Cu with other elements can be used to source apportion the trace elements present in urban atmospheres, mainly on what concerns coarse aerosol particles. (C) 2013 Elsevier Ltd. All rights reserved.

Longitudinal versus polar wrinkling of core-shell fibers with anisotropic size mismatches

We consider a fiber made of a soft elastic material, encased in a stiff elastic shell (core-shell geometry). If the core and shell dimensions are mismatched, e.g., because the core shrinks while the shell does not, but the two remain attached, then an elastic instability is triggered whereby wrinkles may appear on the shell. The wrinkle orientation may be longitudinal (along the fiber axis), polar (along the fiber perimeter), or a mixture of both, depending on the fiber's geometrical and material parameters. Here we investigate under what conditions longitudinal or polar wrinkling will occur.

On the choice of posittioning and cluster size for fixed relay stations in a LTE network

The long term evolution (LTE) is one of the latest standards in the mobile communications market. To achieve its performance, LTE networks use several techniques, such as multi-carrier technique, multiple-input-multiple-output and cooperative communications. Inside cooperative communications, this paper focuses on the fixed relaying technique, presenting a way for determining the best position to deploy the relay station (RS), from a set of empirical good solutions, and also to quantify the associated performance gain using different cluster size configurations. The best RS position was obtained through realistic simulations, which set it as the middle of the cell's circumference arc. Additionally, it also confirmed that network's performance is improved when the number of RSs is increased. It was possible to conclude that, for each deployed RS, the percentage of area served by an RS increases about 10 %. Furthermore, the mean data rate in the cell has been increased by approximately 60 % through the use of RSs. Finally, a given scenario with a larger number of RSs, can experience the same performance as an equivalent scenario without RSs, but with higher reuse distance. This conduces to a compromise solution between RS installation and cluster size, in order to maximize capacity, as well as performance.

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 semianalytical 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 flat, shallow bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.