Diffusion-Controlled Bubble Growth

A new macroscopic traffic system is devised that observes the transition distance between the vehicles and driver sensitivity during traffic evolution. The driver sensitivity in this system is based on the traversed time over a 200 m road section and speed (velocity). In addition, the proposed system considers the safe distance headway as the distance between vehicles changes. An analogy system for vehicle flow behavior is devised from a spring–mass system with changes in traffic. The proposed system can characterize traffic evolution for small and large changes in density. Furthermore, the changes in the travel of traffic rearwards during congestion and forward during smooth flow are dependent on driver sensitivity, transition distance, and safe distance headway. The proposed traffic system is hyperbolic. The Payne Whitham traffic system is based on uniform constant velocity for different conditions, which characterizes traffic evolution unrealistically. The proposed traffic system and the Payne Whitham system are assessed over a 2000 m circular road for large changes in density in two examples. Both the Payne Whitham and proposed traffic systems are numerically implemented with the first order centered scheme in Matlab. The discretization stability of both systems is enforced with the Courant–Friedrich–Levy (CFL) condition. The proposed system with lower driver sensitivity evolves with larger changes, whereas the proposed system with larger density has smaller changes in density and velocity. The simulation results showed that the traffic evolution with the proposed system is more appropriate than with the Payne Whitham system.

In this paper, by using the synchrotron radiation real-time imaging, the growth of gas bubbles on solid-liquid interface during the soldering process was investigated. It was proved that the formation and growth of the bubbles was a process of heterogeneous nucleation. During the soldering heating insulation stage, the bubbles volume increased first and remained unchanged afterwards. When there were more than one bubbles, the annexation process was happened among the adjacent bubbles, the larger bubbles were pulled to the smaller ones. The bubbles volume remained unchanged during the cooling stage. At the same time, the dissolution of the Cu substrate and the growth of the IMCs were influenced by the bubbles.

On the low-temperature nucleation and growth of bubbles by helium bombardment of metals

A simple Excel or Quattro Pro spreadsheet method for the accurate and rapid determination of concentration distributions in zone refined and zone levelled ingots is described and illustrated. Only a fundamental understanding of the solidification process is needed with no requirement for complex mathematical equations or techniques. The spreadsheet method is applicable for any zone length, any value of distribution coefficient, and any number of zone passes. The assumption of an initial uniform concentration distribution is not necessary and therefore any initial concentration distribution can be used. Further, the effect of an initial transient on the concentration distribution is easily accommodated. The graphical capabilities of the spreadsheets provide the means for rapid and simple visual presentation of the results.

Bubble growth processes in magma surrounded by an elastic medium

Kinetics and physical mechanisms of the growth of helium bubbles at dislocations

We develop a model to describe the spreading of a reacting liquid which is injected at a steady rate into a permeable rock. We focus on the case in which there is a density difference between the host reservoir fluid and the injected liquid. We examine reactions which lead to precipitation and a decrease in permeability or dissolution and an increase in permeability. In both cases, we assume the reaction is rapid compared to the speed of the flow. As the current spreads under gravity, we show that the interface between the injected fluid and the original fluid and also the reaction front, may be described by similarity solutions. The morphology of the two interfaces is controlled by two parameters: the permeability ratio across the reaction front, k, and the speed of the reaction front as a fraction of the interstitial speed, λ. For a precipitation reaction, the reaction front lags some distance behind the leading edge of the region occupied by the injected fluid, and tends to terminate in a sharp vertical front. In contrast, for a dissolution reaction, the reaction front migrates as a gravity-driven finger along the base of the formation. In the case of large changes in permeability, kλ > 1, this finger advances to the front of the flow, whereas for smaller increases in permeability, kλ < 1, the finger is overrun with injected fluid which has already reacted and passed through the reaction front. We illustrate how these results are affected if the density of the reacting fluid decreases across the reaction zone. In the case of precipitation, small changes in density smooth out the leading edge of the reaction front, whereas large changes in density lead to slumping of the reaction front along the base of the current, and ultimately it extends to the nose of the flow. For dissolution reactions, the decrease in density across the reaction front causes the lateral extent of the finger to increase. As a result the critical value of the permeability ratio, k, for which the reaction front reaches the nose of the current decreases.

This paper describes a modified manufacturing route involving a large change in density in auxetic negative Poisson's ratio (NPR) foams. Density change of auxetic foams after manufacturing is a common feature for this porous material. Samples of open cell PU–PE (i.e. the combination of polyurethane–polyethylene) foams with NPR are produced from two similar native materials using both the classical and the novel custom manufacturing methods. In the classical manufacturing route the cooling process is typically carried out with the foam in a confined state. Conversely, in the new manufacturing process it was substituted with a release process. Samples were subjected to both tensile and compressive loading, as well as density measurements. A thorough mechanical characterisation of the foams is described, linking the mechanical properties with their change in density after conversion into auxetic.

This paper is concerned with the determination of the distribution of stress in an infinite elastic solid when time-dependent body forces act upon certain regions of the solid. It is assumed throughout that the strains are small. In §2 a general solution of the equations of motion for any distribution of body forces is derived by the use of four-dimensional Fourier transforms, and from that is derived the general solution for an isotropic solid (§ 3). From the latter solution are deduced the general solution of the statical problem (§4) and the two-dimensional problem (§5). The solution of the equations of motion in the case in which the distribution of body forces is symmetrical about an axis is derived in §6. The remainder of the paper consists in deducing the solution of special problems from these general solutions. In §§7 to 13 some typical two-dimensional problems are considered and exact analytical expressions found for the components of the stress tensor. In §§14 to 16 examples are given of the use of the general non-symmetrical three-dimensional solution derived in § 3, and in §§17 to 19 examples are given to illustrate the use of the general solution of the axially symmetrical problem. A certain amount of numerical work (presented in graphical form) is quoted to give some idea of the physical nature of the solutions.

Over the past two decades, a considerable amount of effort has been centered on the experimental and theoretical investigation of liquid metals expanded by heating toward the liquid-vapor critical point. Much of the activity is motivated by the large number of current and potential applications of fluid metals as high temperature working fluids for advanced energy technologies. From the scientific point of view, the main object of this effort is to find out how the properties of metals vary with large changes in density, large enough to change the liquid metal into a nonmetal at large enough expansion. Figure I shows why such a metal to nonmetal transition must occur with decreasing density. The discontinuous liquid-vapor phase change of a metal at low temperatures near the triple point is obviously accompanied by a discontinuous metal(M)-insulator(I) transition. In such a situation the liquid metal is reasonably well described by the nearly-free-electron model, whereas in the dilute insulating vapor the great majority of the electrons are attached to their parent atoms occupying spatially localized atomic orbitals. It follows that the precise nature of the electronic interactions between atoms must change on going by a suitable combination of temperatures and pressures continuously along the dashed path round the critical point from the liquid-like (M) to vapor-like (I) densities. Somewhere along this line a transition range must exist where metallic properties evolve into those characteristic of non­ metals.

Copyright: © 2014 Kong CY. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. A supercritical fluid (SCF) is an adjustable solvent which is reached at a temperature and pressure higher than its critical point. It can diffuse through solids like a gas, and dissolve materials like a liquid. In addition, close to the critical point, small changes in pressure or temperature result in large changes in density or viscosity, allowing many properties to be tuned. SCFs are suitable as a substitute for organic solvents in a range of industrial processes. Furthermore, there is no surface tension in a SCF, as above the critical temperature there is no phase transition. The applications of SCF is still expanding in the fields of extraction [1,2], food [3], pharmaceutical [4,5], material [6-8] and chemical reaction [9]. The quantitative knowledge of mass transport phenomena such as diffusion coefficients of various compounds in SCF is of considerable important in the design and efficient operation of the newly proposed SCF processes. Experimental methods, compounds and SCFs employed to determine the diffusion coefficients are highlighted in this editorial.

The effect of predation by blue crabs and fishes on all species of infaunal macrobenthos of a subtidal sandy bottom in the York River, Virginia, was investigated by manipulative field experiments. Wire mesh cages were used both to exclude all large predators from and to confine different predators to small areas of the natural bottom. After 2 months, many species showed significant differences between the various treatments. There were similar patterns of species responses in three separate years. Species tended to fit one of two categories. Those species which had tough tubes, which lived deep in the sediment, or which could quickly retract deep into the sediment were shown experimentally not to change much in abundance regardless of whether predators were excluded or included. These species were generally the numerical dominants in the natural community—e.g.Peloscolex gabriellae, Heteromastus filiformis, Spiochaetopterus oculatus, andPhoronis psammophila. Other species which lived near the surface or exposed on the surface responded to experimentally altered predation intensity with large changes in density. These species were either uncommon or only sporadically abundant in the natural community—e.g.Polydora ligni, Streblospio benedicti, Mulinia lateralis, andLyonsia hyalina. This evidence indicates that the abundant species in the natural community are abundant because they avoid predators.

We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear deformations were carried out on glass samples of varying stability, determined by cooling rate, and at varying strain rates, at state points deep in the glass. Density changes up to and exceeding a factor of two were made. We investigated several different methods for generating isomorphs but none of the previously developed methods could generate sufficiently precise isomorphs given the large density changes and nonequilibrium situation. Instead, the temperatures for these higher densities were chosen to give state points isomorphic to the starting state point by requiring the steady-state flow stress for isomorphic state points to be invariant in reduced units. In contrast to the steady-state flow stress, we find that the peak stress on the stress strain curve is not invariant. The peak stress decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density. Analysis of strain profiles and nonaffine motion during the transient phase suggests that the root of the changes in peak stress is a varying tendency to form shear bands, with the largest tendency occurring at the lowest densities. We suggest that this reflects the effective steepness of the potential; a higher effective steepness gives a greater tendency to form shear bands.

Constraints on density as a function of pressure, temperature, and composition are crucial to understand isostatic movements during geodynamic processes. Here, we provide a systematic series of density diagrams extracted from thermodynamic calculations for a variety of crustal compositions within a wide P–T range. We quantify systematic density changes in collisional settings for relevant compositional variations and attempt to simplify the density–composition relationships. Rock densities depend strongly on pressure, temperature, and composition. Densities at some selected pressure–temperature conditions increase linearly with increasing Al2O3 as well as MgO/FeO contents in pelitic rocks. Al- and Fe-rich pelites yield the highest densities, which is mostly due to the formation of garnet but also depends on other minerals and changes of reactions. The effect of loading on densities is investigated, and we show that for deep burial, a meta-pelite rich in Fe and Mg yields much larger density changes than a dry basalt and that the burial of such a rock with a composition close to typical lower crust may result in significant negative buoyancy. Metamorphism of hydrous lower crust due to pressurization and heating thus leads to densification of thickened lower crust, while heating of dry crust leads to a decrease in density. Hence, water-loaded isostatic subsidence due to metamorphism of water-saturated lower crust is substantial and increases with the thickness and depth of the reacting layer, while dry compositions show much less or only transient densification and subsidence. The density change due to thermal expansion, an extensively used concept in geodynamic models, predicts uplift under the same P–T conditions and is an order of magnitude smaller than the density variation calculated from petrologically consistent diagrams.

Finite element analysis of thermoforming simulation based on isothermal as well as non-isothermal initial conditions has been applied successfully for predicating final thickness distributions. For these simulations, it is assumed that the initial sheet temperature is known and does not change significantly during forming at a rapid stretch rate. For a non-isothermal analysis, the temperature dependent material properties are necessary. In this paper sample results are presented for the so-called inverse thermoforming problem, where an initial temperature distribution is sought numerically that will result in a specific final thickness distribution. Thus, a finite element simulation is combined with an iterative algorithm to obtain inverse solutions for a thermoformed part. In this example, the required initial temperature distributions that result in a uniform final thickness are determined for a thermoformed part. It is shown that the calculated results are quite sensitive to perturbations in the specified initial temperature profile and thus the practical application of optimal temperature distributions may require high precision thermal sensors and controls. This initial temperature distribution can then be used for the determination of desired heating patterns on zone-controlled heaters of a thermoforming machine using transient heat transfer analysis.