Showing papers on "Critical radius published in 2009"

Motion and shape of bubbles rising through a yield-stress fluid

Abstract: We study the velocity and shape of air bubbles rising through a transparent yield-stress fluid. The bubbles are small enough compared to the experimental vessel that effects of walls are weak. We find that the terminal rise velocity of the bubbles increases approximately linearly with bubble radius over the range of volumes accessible in our experiments. We observe bubble motion only when the bubbles are larger than a certain critical radius. In terms of a dimensionless yield parameter Y, the ratio between the force due to the yield stress and the buoyant force, we observe bubble motion only for Y ≲ 0.50 ± 0.04 . The bubbles are non-spherical, having the shape of an inverted teardrop with a rounded head and a cusp-like tail. The cusps may be an indication that elasticity plays a significant role in this system. By fitting the cross-sectional radius of the bubble as a function of the axial coordinate to an empirical function, we study the dependence of the bubble shape on volume and the yield stress of the material.

Maximum size of drops levitated by an air cushion

Abstract: Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath, as it is observed for water drops on a heated plate, kept aloft by a stream of water vapor. We investigate the limit of small flow rates, for which the size of the gap between the drop and the substrate becomes very small, to obtain a full analytical description of stationary drop states and their stability. Above a critical drop radius no stationary drops can exist, below the critical radius two solutions coexist. However, only the solution with the smaller gap width is stable, the other is unstable. We compare to experimental data and use boundary integral simulations to show that unstable drops develop a gas “chimney” that breaks the drop in its middle.

The definition of "critical radius" for a collection of nanoparticles undergoing Ostwald ripening.

Abstract: An improved, exact analysis of surface Ostwald ripening of a collection of nanoparticles is presented in an effort to redefine the critical radius involved in the kinetic models of ripening. In a collection of supported particles of different sizes, the critical radius is the size of the particle that is in equilibrium with the surrounding adatom concentration. Such a particle neither grows nor shrinks due to Ostwald ripening, whereas larger particles grow and smaller particles shrink. We show that previous definitions of critical radius are applicable only for limiting regimes where the Kelvin equation has been linearized. We propose a more universally applicable definition of critical radius that satisfies the constraints of mass balance.

Critical thickness and radius for axial heterostructure nanowires using finite-element method.

Abstract: Finite-element methods are used to simulate a heterostructured nanowire grown on a compliant mesa substrate. The critical thickness is calculated based on the overall energy balance approach. The strain field created by the first pair of misfit dislocations, which offsets the initial coherent strain field, is simulated. The local residual strain is used to calculate the total residual strain energy. The three-dimensional model shows that there exists a radius-dependent critical thickness below which no misfit dislocations could be generated. Moreover, this critical thickness becomes infinity for a radius less than some critical values. The simulated results are in good agreement with the experimental data. The critical radius from this work is smaller than that obtained from previous models that omit the interaction between the initial coherent strain field and the dislocation-induced strain field.

The effect of fluid inclusion size on determination of homogenization temperature and density of liquid-rich aqueous inclusions

Abstract: Homogenization temperature variations of several degrees Celsius or more are often observed within a group of fluid inclusions that appear to have all trapped the same homogeneous fluid at the same time and presumably at the same PTX conditions. For inclusions that homogenize at T≤ ≈230 °C, much of the observed variation can be attributed to the size of the inclusions. Larger inclusions homogenize at higher temperatures compared to smaller inclusions with the same density. The relationship between inclusion size and observed homogenization temperature is predicted by the Young-Laplace equation that relates the stability of a vapor bubble to the surface tension and pressure differential across the vapor-liquid interface. Vapor bubbles instantaneously collapse when the vapor bubble radius becomes less than the critical radius. During heating the critical radius of the vapor bubble is achieved at a lower temperature in the smaller inclusions. The critical vapor bubble radius varies from about 0.01 to ∼3 μm for low-temperature aqueous fluid inclusions. The Gibbs surface free energy associated with the growth and collapse of vapor bubbles in pure H 2 O inclusions with critical radii ranging from 0.01 to 1 μm ranges from about 10 -18 to 10 -13 J/m 2 and increases with both increasing critical vapor bubble radius and homogenization temperature. As a result of surface tension effects, the highest measured homogenization temperature, obtained from the largest inclusion in the group of coeval inclusions, most closely approximate the homogenization temperature that would be expected based on the inclusion density. For inclusions ranging from a few to several tens of micrometers in diameter and having densities such that the homogenization temperatures are approximately <230 °C, homogenization temperatures may vary by about 1-3 °C, depending on the inclusion size.

Critical humidities of homogeneous and heterogeneous ice nucleation: Inferences from extended classical nucleation theory

Abstract: [1] A generalization of classical ice nucleation theory is used to derive analytical expressions for the critical (threshold) humidities of homogeneous and heterogeneous freezing. The critical radius and energy of an ice embryo and nucleation rates were derived previously by the authors as functions of temperature, pressure, water saturation ratio, and radii of freezing particles. Here we invert the analytical expressions for the nucleation rates and solve them relative to the critical water and ice saturation ratios (or critical relative humidities). The critical humidities are expressed as analytical functions of temperature, pressure, nucleation or cooling rates, radius of freezing particles and their physico-chemical properties, misfit strain, and activation energy. Calculations of critical ice relative humidities are made using these equations over an extended temperature range down to −75°C and are compared with previous empirical parameterizations and experimental data, and differences are interpreted in the context of variation of the other parameters. It is shown that the critical humidities for heterogeneous ice nucleation are lower than those for homogeneous nucleation; however, this difference is not constant but depends substantially on the temperature and properties of freezing aerosol. Some simple parameterizations for cloud and climate models are suggested.

A Confined Hydrogen Atom in Higher Space Dimensions

Abstract: We compute ground state energies for the N-dimensional hydrogen atom confined in an impenetrable spherical cavity. The obtained results show their dependence on the size of the cavity and the space dimension N. We also examine the value of the critical radius of the cavity in different dimensions. Furthermore, the number of bound states was found for a given radius S, in different space dimensions.

Dipole of edge misfit dislocations and critical radius conditions for buried strained cylindrical inhomogeneity

Abstract: A theoretical model is proposed for elastic stress relaxation of a buried strained cylindrical inhomogeneity, which assumes the edge misfit dislocation dipole formation in the soft matrix at some distance from the interface. The critical radius of the inhomogeneity for the formation of the edge misfit dislocation dipole is given and the influence of various parameters on the critical radius is evaluated. The result indicates that the critical radius decreases with increasing misfit strain and core radius of the misfit dislocation. It is also found that, compared to the edge misfit dislocation dipole formation in the interface, the critical radius of the inhomogeneity decreases when the location of an edge misfit dislocation dipole formation is in the soft matrix at some distance from the interface.

Size distribution of CuCl nanoparticles in glass in various stages of nucleation

Abstract: Variations in the size distribution of CuCl particles in the glass formed at different temperatures are studied via the temperature-dependent exciton spectra (the exciton-thermal analysis). The kinetics of melting of CuCl nanocrystals is measured via changes in the strength of exciton absorption during linear heating of the sample. Then, using the known dependence of the melting temperature of CuCl nanoparticles on their size, the size distribution of the CuCl nanocrystals is found. During the first, second, and early third stages of nucleation, the width δ of the size distribution grows with an increase in the mean radius of the nanoparticles Rm. During the first nucleation stage, when Rm = 1.2 nm, which is just above the critical radius, the ratio δ/Rm is about 0.2. While the mean radius of the distribution increases to 8 nm, the ratio δ/Rm varies only slightly in the range 0.20−0.35. A further increase in the mean radius of the distribution to 16 nm is accompanied by a twofold increase in the δ/Rm ratio. The shape of the distribution is close to Gaussian both at the initial and later stages of the growth of CuCl particles in glass.

Effect of Mn and Cu on Spheroidized Process of Mg-Zn-Y-Based Icosahedral Quasicrystal Phase

Abstract: In-situ spherical icosahedral quasicrystal phase (I-phase) was fabricated in Mg-Zn-Y-based alloys by metal mold casting route. The effects of Mn and/or Cu on spheroidized process, morphology and microhardness of primary I-phase were studied in this paper. The results showed that the solidified morphology of I-phase depended on the stability of spherical I-phase during the subsequent growth and critical radius Rr of the spherical I-phase. Only when actual radius smaller than critical radius Rr can spherical IQC be formed. The effects of the fourth component and degree of undercooling on Rr were studied for the first time. Amazing spherical minisize IQC had been produced by improving cooling rate using a water-cooled copper mold. Multicomponent spherical IQC is hopeful of being strengthening phase to novel metal composites.

Transformations of the distribution of nuclei formed in a nucleation pulse: Interface-limited growth

Abstract: A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r∗− and is allowed to nucleate during a finite time interval tn, after which the supersaturation is abruptly reduced to a fixed value with a larger critical radius r∗+. The size-distribution of nucleated particles f(r,t) further evolves due to their deterministic growth and decay for r larger or smaller than r∗+, respectively. A general analytic expressions for f(r,t) is obtained, and it is shown that after a large growth time t this distribution approaches an asymptotic shape determined by two dimensionless parameters, λ related to tn, and Λ=r∗+/r∗−. This shape is strongly asymmetric with an exponential and double-exponential cutoffs at small and large sizes, respectively, and with a broad near-flat top in case of a long pulse. Conversely, for a short pulse the distribution acquires a distinct maximum at r=rmax(t) and approaches a universal shape exp[ζ−eζ], with ζ∝r−rmax, indep...

Driving force in first‐order phase transitions and its application to gas hydrate nucleation from a single phase

Abstract: Classical nucleation theories of general application are taken as starting point to analyze the driving force for multicomponent gas hydrate nucleation from a single homogeneous phase. It is shown that the ratio between the specific surface energy and the critical radius of nucleation has a single value irrespective of the analyzed driving force expression. From this result, two driving force expressions for multicomponent gas hydrate nucleation are derived in the context of the so-called generalized nucleation theory, and it is demonstrated that the driving force for gas hydrates can be estimated using the same information given for the determination of the incipient formation points of the dispersed phase from a saturated phase. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Role of radius on prewetting behavior in nematic liquid-crystal droplets.

Abstract: The prewetting phenomena in a nematic liquid crystal confined to a droplet embedded in a spherical solid surface are discussed. This paper is based on Landau-de Gennes theory and Nobili-Durand surface energy. By using a Maxwell construction, we find that the first-order boundary-layer transition inside of droplet which vanishes completely below a critical radius R c when bulk nematic isotropic transition temperature is approached from above. We obtain a narrow temperature interval above the bulk nematic-isotropic phase transition which corresponds to nematic boundary layer inside of droplet. The interval length depends on surface potential and droplet radius. We also find that there is no critical radius for boundary transition when the nematic-isotropic transition temperature is approached from below.

Critical Radius of Axial Magnetic-Field Contacts in Vacuum Interrupters

Abstract: Vacuum circuit breakers (VCBs) are widely used to protect medium-voltage (MV) power distribution circuits. Since SF6 gas is specified as a global warming gas, VCBs are stepping into a higher voltage sector to protect power transmission circuits. Axial magnetic field (AMF) contacts are widely used in vacuum interrupters. In this paper, we propose a concept of critical radius of AMF contacts. When coil width and coil height are fixed, the axial magnetic flux density increases first with increasing contact diameter. Then, it reaches a maximum value. Thereafter, the axial magnetic flux density decreases. The contact radius corresponding to the maximum axial magnetic flux density is critical radius. The concept of critical radius is validated by coil-type AMF contacts and slot-type AMF contacts in MV vacuum interrupters with finite-element analysis. Critical radius is only related to contact geometry parameters and the current has no influence on critical radius. Critical radius increases with increasing contact gap, coil width, coil height, and thickness of the contact plate. In high-voltage AMF vacuum interrupters, axial magnetic flux density per kiloampere increases with increasing contact diameter since the critical radius is typically high with a high contact gap and it is in the rising branch. In an MV AMF vacuum interrupter, interrupting capacity could increase with an increase of the contact diameter with a different rising rate before and after the critical radius. This is expected to be experimentally validated.

Crystal growth nucleation and equalization of Fermi energies of intrinsic nuclei and glass-forming melts

Abstract: The energy saving produced by the equalization of Fermi energies of a crystal and its melt is determined by adding a negative fraction sl(T) of the fusion heat to the Gibbs free energy change ?G2ls associated to a charged crystal formation in glass-forming melts. In bulk metallic glasses, ls(Tm) is larger than 1 at the melting temperature Tm and only determined by the knowledge of the free volume disappearance temperature. When the unmelted intrinsic crystals have a radius Rnm much smaller than the critical radius R*2ls, sl(T) is strongly reduced by the quantification of electronic levels in the large electrostatic potential created by the electron transfer from the crystal to the melt. The reduced value nm0 of sl(Tm) for Rnm=3.2E-10m in Zr41.2Ti13.8Cu12.5Ni10Be22.5 is determined by comparing the experimental Time-Temperature-Transformation diagram measured by electrostatic levitation to the calculated one. It exactly corresponds to the first energy level of one s state electron moving in the same spherical attractive potential and in vacuum in spite of the fact that, in a metal, the charge screening is built by many-body effects.

Relation between the critical detonation diameter of explosive charges with characteristics of their shock-wave sensitivity

Abstract: Correlation dependences between the critical diameter of high explosive (HE) charges and characteristics of their shock-wave sensitivity are theoretically justified. Relations for the critical radius of curvature of the detonation-wave front and for the critical detonation diameter are derived on the basis of the author’s theory of the critical diameter and the generalized kinetic characteristic of HE decomposition determined from the experimental dependence of the distance of transition of the initiating shock wave to the detonation wave on the wave amplitude. A qualitative analysis of these relations reveals good agreement with available experimental data. Key words: detonation, critical diameter, sensitivity, shock-wave initiation of detonation, HE decomposition kinetics.

Comparison of Nucleation Site Density for Pool Boiling and Gas

Abstract: It has been well established that the rate of heat transfer associated with boiling systemsis strongly dependent on the nucleation site density. Over many years attempts have beenmade to predict nucleation site density in boiling systems using a variety of techniques.With the exception of specially prepared surfaces, these attempts have met with littlesuccess. This paper presents an experimental investigation of nucleation site densitymeasured on roughly polished brass and stainless steel surfaces for gas nucleation andpool boiling over a large parameter space. A statistical model used to predict the nucle-ation site density in saturated pool boiling is also investigated. The fluids used for thisstudy, distilled water and ethanol, are moderately wetting and highly wetting, respec-tively. Using distilled water it has been observed that the trends of nucleation site densityversus the inverse of the critical radius are similar for pool boiling and gas nucleation.The nucleation site density is higher for gas nucleation than for pool boiling. An unex-pected result has been observed with ethanol as the heat transfer fluid, which casts doubton the general assumption that heterogeneous nucleation in boiling systems is exclusivelyseeded by vapor trapping cavities. Due to flooding, few sites are active on the brasssurface and at most two are active on the stainless steel surface during gas nucleationexperiments. However, nucleation sites readily form in large concentration on both thebrass and stainless steel surfaces during pool boiling. The pool boiling nucleation sitedensities for ethanol on rough and mirror polished brass surfaces are also compared. Itshows that there is not a significant difference between the measured nucleation sitedensities on the smooth and rough surfaces. These results suggest that, in addition tovapor trapping cavities, another mechanism must exist to seed vapor bubble growth inboiling systems.

Critical Coating Radius of Spherical Particle in Thermal Radiation Environment

Abstract: Bi = Biot number, hri=k h = heat transfer coefficient outside the coating, W=m K k = coating thermal conductivity,W=mK Q = dimensionless total heat transfer Qc = dimensionless convection heat transfer Qk = dimensionless conduction heat transfer Qmax = dimensionless maximum heat transfer Qr = dimensionless radiation heat transfer q = total heat transfer, W R = dimensionless coating outer radius, ro=ri Rcr = dimensionless critical radius coating outer radius, ro;cr=ri ri = inner coating radius, m ro = outer coating radius, m Ti = temperature at the inner surface of coating, K To = temperature at the outer surface of coating, K T1 = temperature of the surroundings, K

Nonlinear Singular Kelvin Modes in a Columnar Vortex

Abstract: This paper considers the propagation of helical neutral modes within a cylindrical vortex and the subsequent formation of nonlinear critical layers around the radius where the mean-flow angular velocity and the mode frequency are comparable. Analogy can be done with the stratified critical layers. We formulate a steady-state theory valid when the analogous Richardson number is small at the critical radius. The apparent singularity is removed by retaining nonlinear terms in the critical-layer equations of motion. The result from the interaction is the emergence ofmultipolar vortices whose poles are located around the critical radius, spiral along the basic vortex axis and are embedded in a distorted mean flow caused by a slow diffusion of the three-dimensional vorticity field from the critical layer.

On the stability of electrostatic orbits

Abstract: We analyze the stability of two charged conducting spheres orbiting each other. Due to charge polarization, the electrostatic force between the two spheres deviates significantly from 1∕r2 as they come close to each other. As a consequence, there exists a critical angular momentum, Lc, with a corresponding critical radius rc. For L>Lc two circular orbits are possible: one at r>rc that is stable and the other at r

The kinetics of negative 2D-islands on Si (111) surface during sublimation

Abstract: Kinetics of two dimensional islands on Si(111) was investigated by in situ ultrahighvacuum reflection electron microscopy during sublimation. The temperature dependences of critical radius of the terrace for nucleation of new island were measured. On the base of the obtained data the adatom diffusion length on the Si(111) surface was estimated at temperature range 1000 – 1300°C.

Atomic scale phenomena - Nucelation and growth

Abstract: Solidification is the result of the formation of stable clusters of solid in the liquid (nucleation), followed by their growth. These are phenomena occurring at the atomic scale (nano meter) level. The present understanding of the beginning of formation of solid crystals from their liquid is based on the classical theory of homogeneous nucleation. This theory uses macroscopic concepts and classic thermodynamics to describe the appearance of the first microscopic crystals in the melt.