Cracking particles: a simplified meshfree method for arbitrary evolving cracks

A new approach for modelling discrete cracks in meshfree methods is described. In this method, the crack can be arbitrarily oriented, but its growth is represented discretely by activation of crack surfaces at individual particles, so no representation of the crack's topology is needed. The crack is modelled by a local enrichment of the test and trial functions with a sign function (a variant of the Heaviside step function), so that the discontinuities are along the direction of the crack. The discontinuity consists of cylindrical planes centred at the particles in three dimensions, lines centred at the particles in two dimensions. The model is applied to several 2D problems and compared to experimental data. Copyright © 2004 John Wiley & Sons, Ltd.     

Mixing of particles in apparatuses with a circulating fluidized bed

A phenomenological model of mixing of particles in a circulating fluidized bed has been formulated; a distinctive feature of the model is allowance for convective particle fluxes in the radial direction that ensure a substantial decrease observed in practice in the concentration of the particles over the risers height. As a result of a comparison of experimental and calculated mixing curves it has been established that the value of the coefficient of radial dispersion of the particles lies in the interval 0.0006–0.006 m²/sec.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 77, No. 6, pp. 148–158, November–December, 2004.     

The effect of the surface state of particles on pair interaction in a magnetic suspension

The dynamics of a pair of spherical magnetically soft particles suspended in a fluid under the action of a rotating field is studied experimentally and theoretically. Hydrodynamic interaction of the particles and repulsion in the surface layer are taken into consideration in the theory and the magnetic field is described in a dipole-dipole approximation. Experiments confirm the important role of surface roughness, which limits the increase in viscous friction between the particles that are coming closer together. The effect of roughness-induced stochastization of the dynamics of the pair is found in the frequency range near the cutoff frequency of rotation synchronous with the field. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 2, pp. 179–183, March–April, 1997.     

Pairwise interaction of drops of magnetic emulsion under the action of rotating field

Consideration is given to the dynamics of a pair of drops of a magnetic liquid that are suspended in a normal liquid with relatively low viscosity under the action of a rotating field. Account is taken of hydrodynamic and dipole-dipole interactions as well as of the electrodynamic torque due to the finite relaxation time of magnetization of the magnetic liquid. It is shown that hydrodynamic interaction leads to the formation of a rigid pair in the rotating field and the electrodynamic moment of forces governs its dynamics at large frequencies, leading to a growth that is linear in the field frequency in the rotational velocity for the pair of drops, whereas a pair of solid particles loses sensitivity to the field. Academic Scientific Complex “A. V. Luikov Institute of Heat and Mass Transfer of the Academy of Sciences of Belarus,” Minsk, Belarus. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 1, pp. 98–102, January–February, 1996.     

A revisited generalized self-consistent polycrystal model following an incremental small strain formulation and including grain-size distribution effect

A generalized self-consistent approach, recently proposed by Jiang and Weng (2004) [B. Jiang, G.J. Weng, A generalized self-consistent polycrystal model for the yield strength of Nanocrystalline materials, Journal of the Mechanics and Physics of Solids 52 (2004a) 1125-1149; B. Jiang, G.J. Weng, A theory of compressive yield strength of nano-grained ceramics, International Journal of Plasticity 20 (2004b) 2007-2056.] for investigating the so-called “breakdown” of the Hall-Petch law in the case of nanocrystalline (NC) materials, is revisited and reformulated following an incremental small strain scheme. The NC material is modelled as a composite material that takes each oriented grain and its immediate grain boundary to form a pair, which in turn is embedded in the infinite effective medium with a property representing the average orientation of all these pairs. The plastic deformation of the inclusion phase takes into account the dislocation glide mechanism whereas boundary phase is modelled as an amorphous material. As an application, the model’s parameters are identified under an optimization code with respect to data stated from pure copper submitted to tensile load. The aggregate is composed of spherical randomly distributed grains with a grain-size distribution following a log-normal statistical function.     

Surface and Size Effects on the Specific Heat Capacity of Nanoparticles

Extending the elastic continuum model for fine particles, a theoretical model was proposed to include the different contributions of interior and surface atoms for the specific heat capacity. The effect of size and temperature and the softening of surface atom vibrations were studied, and a dimensionless variable was proposed to characterize the effect of particle size and temperature on the specific heat capacity of nanoparticles. The proposed model was used to fit experimental data for copper oxide nanoparticles.Paper presented at the Seventh Asian Thermophysical Properties Conference, August 23–28, 2004, Hefei and Huangshan, Anhui, P. R. China     

Nonuniform absorption of thermal radiation in semitransparent spherical particles under conditions of arbitrary illumination of a disperse system

Different methods of calculating the nonuniform absorption of radiation in spherical particles are treated. An approximate representation of asymmetric illumination of a particle is used in application to heat transfer problems characterized by diffuse radiation in a wide spectral range. In each spectral range, the illumination of the particle is assumed to be uniform but varying in intensity from the front and rear hemispheres (with respect to the spectral radiation flux). The Mie theory is used to solve the problem, and the modified differential approximation is used in the case of symmetric illumination of large particles. Approximate analytical relations are obtained for the distribution of the power of absorbed radiation in the volume of a large semitransparent particle. Calculation data are given for droplets of water and diesel fuel.Translated from Teplofizika Vysokikh Temperatur, Vol. 42, No. 6, 2004, pp. 961–971.Original Russian Text Copyright © 2004 by I. A. Dombrovsky.     

Quartet Structures of Particles and Quasiparticles in the BCS Model

We study the possibility of multiple paring for more than two particles or two quasiparticles in terms of the BCS model. We consider the multiple pairs of particles in terms of the BCS Hamiltonian for two different ground states: in a quiescent Fermi sea model and in the BCS ground state. In case of quasiparticles, we consider the multiple quasiparticle pairs in terms of the BCS ground state only. Although there is no interaction between Cooper’s type pairs in terms of the BCS Hamiltonian, yet we have shown that four particles or two/four quasiparticles can be paired and form a bound state in the singlet state with just twice the bound state energy of a single Cooper’s pair. In the case of a pair of quasiparticles, the bound state exists as a result of the large quasiparticle density of states and the residual interaction between two quasiparticles which is described by the off-diagonal terms in the BCS Hamiltonian written in terms of quasiparticles. In the case of four particles, the bound state exists only as a result of the Pauli principle and the sharp Fermi edge. In the BCS model, a quartet of bound fermions indeed represents a boson, and the many-particle system of the composite of bosons can undergo the conventional Bose condensation of a boson gas. The temperature of the Bose condensation corresponds to the conventional temperature of Bose condensation for non-interacting bosons where each boson has quadruple mass (4m) and the boson density is one-quarter (n/4) of fermions density. A similar conclusion remains valid in the case of the particle–hole resonance in a quiescent Fermi sea. We have shown that in the particle–hole channel there exists the multiple particle–hole resonance for four particles and four holes in a quiescent Fermi sea model similar to the case of two particles and two holes resonance. We have shown that there is no particle–hole resonance in the case of the BCS ground state because there is no hole-type of excitations in the BCS ground state. Nevertheless we have shown that in the BCS ground state quasiparticle pairs can form bound pairs similar to the Cooper’s pair of particles due to the off-diagonal terms in the BCS Hamiltonian. The bound pairs of quasiparticles exist as a result of extremely large quasiparticle density of states. We also discuss the formation of a quartet of quasiparticles and the Bose condensation of the multiple pairs of quasiparticles.     

Superconductivity in a Two-Component Model with Local Electron Pairs

Superconductivity in the two-component model of coexisting local electron pairs (hard-core charged bosons) and itinerant fermions coupled via charge exchange mechanism is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s-wave and symmetries are analyzed for a 2D square lattice within the BCS-mean-field approximation (MFA) and the Kosterlitz–Thouless theory. The phase diagrams and superconducting characteristics of this induced pairing model as a function of the position of the local pair (LP) level and the total carrier concentration are reviewed. The model exhibits crossovers between the BCS-like behavior and that of LPs. In addition, the Uemura plots are obtained for extended s and pairing symmetries. Finally, we analyze the pairing fluctuation effects (in 3D) within a generalized T-matrix approach. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for high-temperature superconductors.     

Deposition of solid particles in laminar boundary layer on a flat plate

Results are given of experimental and theoretical investigation of deposition of small solid particles on the surface of a flat plate under conditions of vertical laminar boundary layer. The present investigation is aimed at qualitatively and quantitatively estimating the effect made by the parameters of two-phase flow of the “gas—solid particles” type and by the adhesive properties of particles and surface on the deposition of particles on the plate surface. The flow velocity is 1.5 and 3 m/s. In so doing, the value of Reynolds number along the plate does not exceed 10⁵. Synthetic corundum powders with average sizes of 12, 23, and 32 μm are used as the dispersed phase of two-phase flow. The mass concentration of particles in the flow is 0.01 kg/m³. A flat plate of stainless steel is used as the object of investigation. The distributions of gas velocity and concentration of particles within the boundary layer are measured using laser optical diagnostics. The number of particles deposited along the plate surface is measured by the gravimetric method. The adhesive properties of the “particle-surface” pair are studied using the centrifugal method of detachment of particles from the surface. Logarithmic-normal dependences of the number of adhesion of particles on the force of detachment are obtained. The hydrodynamic parameters of two-phase flow in the vicinity of the plate surface are calculated using the model of two-phase laminar boundary layer. The mathematical expression is suggested for the calculation of the magnitude of deposition of solid particles along the surface of a flat plate, which includes the special features of hydrodynamics of flow, the adhesive properties of the particles and surface, and the probabilistic pattern of the process of entrapment of particles by the surface.     

Dusty plasma of a dc glow discharge: methods of investigation and characteristic features of behavior

Results are given of experimental investigations of a dusty plasma in the strata of a dc glow discharge. Characteristic forms of plasma-dust structures formed by dust particles of spherical and highly asymmetric shapes are described. Results are given of observation of self-excited dust-acoustic waves, as well as of high-amplitude waves generated under pulsed gasdynamic stimulation. A method of measuring charges of dust particles levitating in strata is described, as well as a method of measuring the radial field of forces acting on dust particles in a plasma trap. Mention is made of methods for the investigation of plasma-dust structures under conditions of microgravity.Translated from Teplofizika Vysokikh Temperatur, Vol. 42, No. 6, 2004, pp. 821–834.Original Russian Text Copyright © 2004 by V. I. Molotkov, O. F. Petrov, M. Yu. Pustylnik, V. M. Torchinskii, V. E. Fortov, and A. G. Khrapak.     

Discrete element modelling and simulation of sand mould manufacture for the lost foam process

This paper presents a numerical model of mould manufacture for the lost foam casting process. The process of mould filling with sand and sand compaction by vibration are modelled using spherical (in 3D) or cylindrical (in 2D) discrete elements. The motion of discrete elements is described by means of equations of rigid body dynamics. Rigid particles interact among one another with contact forces, both in normal and tangential directions. Numerical simulation predicts defects of the mould due to insufficient sand compaction around the pattern. Combining the discrete element model of sand with the finite element model of the pattern allows us to detect possible distortion of the pattern during mould filling and compaction. Results of numerical simulation are validated by comparison with experimental data. Copyright © 2004 John Wiley & Sons, Ltd.     

Fracture characteristics of SiC particle reinforced oxynitride glass using chevron-notch three-point bend specimens

The fracture toughness K1c and the effective fracture surface energy γeff, of oxynitride glass (m)/SiC(p) brittle particulate composites were measured by means of stable fracture tests, using chevron-notch three-point bend specimens. In comparison to oxide glasses, the oxynitride glass matrix is noticeably tougher: K1cm = 1.2 MPa. and γeff = 5 J/m2. The addition of SiC particles, 6 μm in diameter, results in a significant toughening: K1c = 2.5 MPa. and γeff = 9.1 J/m2 for the composite with 40 vol\% SiC. In such systems, with strong particle-matrix interfacial bonding, and where (Ep, K1cp, σrp) > (Em, K1cm, σrm), the main toughening contribution is due to a discrete pinning of the crack by particles near the crack tip in conjunction to bowing of the crack front between particles, and to a small scale bridging mechanism. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electrostatic Potential of Charged Macroparticles in Plasma under Conditions of Thermal Equilibrium

An exact analytical solution of the Poisson-Boltzmann equation (PBE) is found in the case of spherical, axial, or plane geometry, which describes the potential distribution around a charged macroparticle (wire or plane) in plasma under conditions of thermal equilibrium with an arbitrary relationship between the charge densities of macroparticles and plasma. The solution is obtained as a logarithm of the power series in several different forms. A recurrent relation is found for coefficients of the power series. The exact solution of the PBE for the case of plane geometry is already known; its identity to that found in this study is shown in a particular case. In the case of not too high charges of macroparticles, the exact solution is approximated by the solution of linearized PBE; for a solitary particle, this solution corresponds to the DLVO and Debye-Huckel approximations. For high charges, the exact solution deviates from an approximate one (very appreciably too) only in the vicinity of the macroparticle. An approximate solution is used to renormalize the macroparticle charge and to construct a simple model of electrostatic interaction of like-charged particles, which demonstrates the possibility of their attraction. The equilibrium distance of attracting particles (the position of minimum of interaction energy) agrees well with the position of maximum of the experimentally obtained pair correlation function for dust particles in thermal plasma.__________Translated from Teplofizika Vysokikh Temperatur, Vol. 43, No. 3, 2005, pp. 331–342.Original Russian Text Copyright © 2005 by L. G. D’yachkov.     

Statistical packing of equal spheres

A computer model which allows us to describe the statistical packing of spherical particles is created. Based on a computer model of statistical packing of particles, research on the distribution of the distance between ‘contacting particles’ was carried out. Bimodality of distribution of the distance between particles is defined. Here the maximal value of a number of pair contacts corresponded to the coordination numbers 3 and 8-10.     

Polydispersity in fluids and composites: Some theoretical results

The effect of polydispersity in particle size on the structure of a solution or suspension of hard spheres in a continuum solvent is considered, with emphasis on the leading concentration corrections to ideal behavior on the pair distribution function and equation of state. Polydispersity in dispersions of randomly centered spherical particles and parallel cylindrical particles with randomly placed axes is also considered.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Low energy alphas in the drift detector

The Directional Recoil Identification From Tracks project is a US–UK endeavor to build and operate a low pressure negative ion TPC (NITPC) to search for weakly interacting massive particles (WIMPs) thought to make up the dark matter in our Galaxy. Low energy (∼10 keV) alpha events from U and Th decays within the walls and wires of the detector can enter the active volume of the detector and be confused for WIMP interactions. This paper presents data on and a model of low energy alphas in a NITPC operated at 40 Torr CS₂ with the aim of understanding and removing this potentially serious background. A comparison of the data to this model reveals good agreement with range predictions of SRIM2000 and allows us to calculate the energy dissipation per ion pair, W=19.0±0.5 eV for low energy alphas in CS₂.     

Effects of constituent particle clusters on fatigue behavior of 2024-T3 aluminum alloy

Fatigue tests of 2024-T3 aluminum sheet were run to determine the effects of constituent particles and particle clusters on fatigue life for all three metallurgical planes. In addition, a model to account for crack coalescence within particle clusters was developed to determine if particle clusters can be more damaging than single particles as crack nucleation sites. On the LS and ST planes, cracks formed primarily at single particles or holes, indicating that coalescence was not an issue. On the LT plane, coalescence was observed when the particle clusters were aligned with the crack growth direction, and the life was reduced about 30%. The crack coalescence and growth model showed that varying the initial separation between two particles (potential cracks) causes at most about a 15–20% change in fatigue life over a separation range of 5 μm to 1200 μm for a pair of 50 μm² particles.     

Convergence and energy bounding properties of the Nosanow cluster expansion

We consider a one-dimensional linear lattice of particles whose mass, pair potential, and nearest neighbor separation are those of a real rare gas crystal. Numerical solution of the Hartree equation shows that the model behaves as a quantum crystal in the low mass, weak attraction case. In the basic Nosanow cluster approximation the cohesive energy of this helium-like system drops from 6.903°K/N (Hartree) to 3.64°K/N. When all except nearest neighbor correlations in the Jastrow function are taken as unity, the result is 3.69°K/N. For the case of nearest neighbor correlations only, we introduce a positive integral operator with properties akin to those of a transfer matrix and thus form a rigorous upper bound on the cohesive energy of the model system. The convergence rate of the Nosanow expansion is shown to depend on the ratio of the two highest eigenvalues of this operator.Supported in part by the U.S. Air Force Office of Scientific Research under Grant No. AFOSR 918-67.     

Rheological behaviour and microstructure of stir-casting zinc-aluminium alloys

The influence of processing variables on the rheological and microstructural behaviour of stir-cast (rheocast) ZA-27 alloy (Zn-27 wt % Al-2wt % Cu) has been investigated experimentally. A concentric cylinder viscometer with shear rate range up to 650 sec^–1 was used to measure the apparent viscosity of the slurries. During continuous cooling and at high shear rates (300–640 sec^–1), non-dendritical materials obey the power-law fluid model, i.e. where _a is the apparent viscosity and the shear rate. At lower shear rates (125 sec^–1), the slurries display dendritical-liquid mixture with viscosity up to 50 poises. Microstructural studies of continuously cooled materials reveal a clear tendency of primary particles to cluster. This phenomenon could be explained by the reduction of the amount of entrapped liquid in the particles.