Rigid Sphere Model Research Articles

Modeling of dense gas–solid reactive mixtures applied to biomass pyrolysis in a fluidized bed

A model is presented for mathematically describing the thermofluid dynamics of dense, reactive, gas–solid mixtures. The model distinguishes among multiple particle classes, either on the basis of their physical properties (diameter, density) or through their thermochemistry (reactive versus inert particles). A multifluid approach is followed where macroscopic equations are derived from the kinetic theory of granular flows using inelastic rigid-sphere models, thereby accounting for collisional transfer in high-density regions. Separate transport equations are constructed for each of the particle classes, allowing for the description of the independent acceleration of the particles in each class and the interaction between size classes, as well as for the equilibration processes whereby momentum and energy are exchanged between the respective classes and the carrier gas. Aimed at high-density suspensions, such as fluidized beds, the relations obtained for the stress tensor are augmented by a model for frictional transfer, suitably extended to multiple-class systems. This model, previously derived, is here enlarged to include heat and mass transfer, as well as chemical reactions and is therefore applicable to general gas–solid combustion systems. The noteworthy novelties of the model with respect to other derivations in the literature include: (i) a systematic and consistent derivation of the solids transport equations and transport properties within the multifluid concept, allowing for non-equilibrium effects between the respective particle classes, (ii) the ability to explicitly account for the possibility of porous solid fuel particles, and (iii) the modeling of multiple chemical reactions in both gas and solid phases and the associated effects of heat and mass transfer. The model, which includes a separately validated chemistry model, is applied to high-temperature biomass particle pyrolysis in a lab-scale fluidized bed reactor and is used to obtain yield of reaction products. The results indicate that, at fixed initial particle size, the fluidizing gas temperature is the foremost parameter influencing tar yield. The biomass feed temperature, the nature of the feedstock, and the fluidization velocity all have minor impact on the yield. It is also shown that the fluidizing gas temperature can be optimized for maximizing the tar yield.

Atomic structures and energetics ofLaNi5−Hsolid solution and hydrides

First-principles calculations on a primary solid solution of ${\mathrm{LaNi}}_{5}\ensuremath{-}\mathrm{H}$ and a hypothetically ordered full hydride, ${\mathrm{LaNi}}_{5}{\mathrm{H}}_{7}$ have been made employing ultrasoft pseudopotentials and plane-wave basis. Some intermediate hydrides were calculated as well. A full geometry optimization has been made to investigate their heat of formation in detail. Atomic positions of ${\mathrm{LaNi}}_{5}{\mathrm{H}}_{7}$ have been described in various ways through the Rietveld analyses of neutron-diffraction profile. The lowest energy structure by the present calculation is close to that of the model analyzed with the space group of ${P6}_{3}\mathrm{mc}$ by Lartigue et al. However, we found that the structure model with a single unit cell, i.e., $Z=1,$ cannot be ruled out for ${\mathrm{LaNi}}_{5}{\mathrm{H}}_{7}.$ Regarding the primary solid solution, the $12n$ site of ${\mathrm{LaNi}}_{5}$ is most stable among five possible interstices proposed in literature. The stability of the interstices can be explained by the number of near-neighbor Ni atoms, which is substantially different from the widely accepted view that the geometric radius by the rigid sphere model determines the stability. The theoretical heat of solution in the primary solid solution is $\ensuremath{-}33{\mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\ensuremath{-}\mathrm{H}}_{2},$ which roughly agrees with the experimental value. On the other hand, the heat of formation of ${\mathrm{LaNi}}_{5}{\mathrm{H}}_{7}$ is $\ensuremath{-}45{\mathrm{k}\mathrm{J}/\mathrm{m}\mathrm{o}\mathrm{l}\ensuremath{-}\mathrm{H}}_{2},$ which is 30--40 % more negative than the experimental value. This discrepancy may be ascribed to the fact that all hydride samples are generally highly defective. The theoretical heat of formation of intermediate phases indicates that the ${\mathrm{LaNi}}_{5}\ensuremath{-}\mathrm{H}$ system dissociates to the primary solid solution and the full hydride. Expansion of the cell volume associated with hydrogenation is well reproduced by the calculation.

Structure of Filled Liquid Crystals Studied by Acoustic Methods

The measurements of ultrasound velocity and absorption of the aerosil suspensions in nematic liquid crystal (LC) 5CB were carried out in the regime of linear acoustic for the aerosil concentrations of (0–6) volume % and sound frequencies of 1–120 MHz. The sound velocity decreases with the increase of aerosil fraction in the mixture. It shows structuring of aerosil as separated aggregates. Proceeding from the data of absorption in frame of the model of rigid spheres the aggregate parameters (size of aggregates, aggregation rate and volume fraction of aerosil in aggregate) were calculated.

Kramers' problem for a variable collision frequency model

The often-studied problem known as Kramers' problem, in the general area of rarefied-gas dynamics, is investigated in terms of a linearized, variable collision frequency model of the Boltzmann equation. A convenient change of variables is used to reduce the general case considered to a canonical form that is well suited for analysis by analytical and/or numerical methods. While the general formulation developed is valid for an unspecified collision frequency, a recently developed version of the discrete-ordinates method is used to compute the viscous-slip coefficient and the velocity defect in the Knudsen layer for three specific cases: the classical BGK model, the Williams model (the collision frequency is proportional to the magnitude of the velocity) and the rigid-sphere model.

BIFLOW DISTRIBUTION WITH SCREW MODES

A bimodal distribution is constructed for the rigid-sphere model in the form of a linear combination of stationary nonhomogeneous Maxwellians. It describes the interaction between two gas flows that are in rotational motion about fixed axes and in translational motion along them. Limiting cases are found in which this distribution minimizes the uniform integrated discrepancy between the parts of the Boltzmann equation.

Collision-dominated to collisionless electron-free space-charge sheath in a plasma with variable ion temperature

A theory of the near-cathode space-charge sheath in the case when the near-cathode voltage is high enough and the presence of electrons in the sheath is unessential is developed on the basis of a fluid description of the ion motion with account of ion-atom collisions and of variable ion temperature. The model spans the range of conditions from a collision-free to collision-dominated space-charge sheath. Detailed analytical and numerical results are presented for two models of ion-atom interaction, the model of rigid spheres (constant mean free path) and the model of Maxwell molecules (constant frequency of momentum transfer). It is found, in particular, that the assumption of cold ions provides a good accuracy in the problem considered. An analytical solution has been obtained under this assumption for the model of Maxwell molecules.

Auditory localization of nearby sources. Head-related transfer functions.

Although researchers have long recognized the unique properties of the head-related transfer function (HRTF) for nearby sources (within 1 m of the listener's head), virtually all of the HRTF measurements described in the literature have focused on source locations 1 m or farther from the listener. In this study, HRTFs for sources at distances from 0.12 to 1 m were calculated using a rigid-sphere model of the head and measured using a Knowles Electronic Manikin for Acoustic Research (KEMAR) and an acoustic point source. Both the calculations and the measurements indicate that the interaural level difference (ILD) increases substantially for lateral sources as distance decreases below 1 m, even at low frequencies where the ILD is small for distant sources. In contrast, the interaural time delay (ITD) is roughly independent of distance even when the source is close. The KEMAR measurements indicate that the direction of the source relative to the outer ear plays an important role in determining the high-frequency response of the HRTF in the horizontal plane. However, the elevation-dependent characteristics of the HRTFs are not strongly dependent on distance, and the contribution of the pinna to the HRTF is independent of distance beyond a few centimeters from the ear. Overall, the results suggest that binaural cues play an important role in auditory distance perception for nearby sources.

Analysis of the Spinning Mechanism of a Golfball Using the "s parameter" and Its Experimental Certification.

Understanding the spinning mechanism of an impacted golfball is an important factor in golf science and engineering. The rigid sphere model which considers the Coulomb-type slip friction presented independently by Daish and Kawamura (referred to here as the Daish-Kawamura model) seems to well explain the experimental results of golfball spinning. For a more general interpretation of the spin phenomenon, we attempted to modify this model by introducing a physical quantity called the s parameter, which is defined as the ratio of the circumferential velocity of the ball to its centroid velocity. An experiment performed to verify the appropriateness of the new parameter introduction led to the following conclusions: The spin phenomenon in golf impact can be divided into two phases, in both of which the Daish-Kawamura model is effective. A method is described to evaluate the coefficient of slip friction under high sliding velocities, and the value is estimated as 0.07 for a slippery surface condition.

Prediction of the viscosity of supercritical fluid mixtures

A method for predicting the viscosity of supercritical, multicomponent fluid mixtures, at any density, from the zero-density viscosity of pure components is presented. The method is based upon the results for a rigid-sphere model, suitably interpreted to apply to real fluids, and on the finding that the excess viscosity of pure supercritical fluids can be adequately described by a density function independent of temperature. The density range of the method extends to twice the critical density of the pure component with the smallest critical density. The only exception is for the methane-rich mixtures where the mixture density should not exceed 12000 mol·m−3. The uncertainty ascribed to the predictions made by this method is of the order of ±5%.

STRUCTURE ANALYSIS OF ${\rm Si}(111)(\sqrt{3}\times\sqrt{3}$)–Al BY ENERGY-FILTERED RHEED

Rocking curves of energy-filtered reflection high-energy electron diffraction (EF-RHEED) intensities from the Si(111)([Formula: see text])–Al surface have been measured. The EF-RHEED apparatus is a recently developed one, equipped with a retarding field analyzer to exclude inelastic scattering component from an entire RHEED pattern. The energy-filtered rocking curves measured at E loss =90 eV and 0 eV are compared. It is found that when the E loss value comes close to 0 eV the relative intensities of reflection beams become remarkably weak at the lower angle side. Three structure models, which have already been presented as the T4 model, and additionally two simple rigid sphere models, are examined by dynamical calculations of RHEED. It is found that Hanada et al.'s structure model is the most favorable one among them. In the analysis of zero-loss rocking curves, especially, an extended imaginary potential distribution into the vacuum is tentatively used to express the absorption due to surface plasmon loss and fairly good agreements between the calculated and experimental rocking curves are obtained.

Attenuation in suspensions of irregularly shaped sediment particles: A two-parameter equivalent spherical scatterer model

Results are presented from an acoustic attenuation spectroscopy study of suspensions of irregularly shaped sediment particles and of nominally spherical lead-glass beads. The measured spectra cover a wide frequency band of 1–100 MHz. It is shown that the spectra can be brought into close agreement with the rigid movable sphere model using two equivalent sphere size parameters. One parameter is the diameter dG of an equal cross-sectional area sphere, and is used to scale the frequency to obtain the nondimensional size/frequency parameter ka. The other parameter is the diameter dp of an equal volume sphere, and is used to scale the particle volume to obtain the particle number density N. It was observed that for the irregular particles the attenuation for ka>1 is enhanced with respect to the sphere case. The observed enhancement factors are considerable: up to 1.6 for natural sand particles and 1.8 for the most irregular particles studied (ground quartz). In terms of the two-parameter model the enhancement factor is equal to a shape parameter b0=(dG/dp)3 and can indeed be explained as a shape effect. The implications of this result for the acoustic detection of suspended sediments in aqueous environments are discussed.

Pressure and temperature electron paramagnetic resonance studies of crystal

The effect of temperature and hydrostatic pressure on the spin-Hamiltonian parameter for in elpasolite is studied up to a pressure of 700 MPa over the temperature range 180 - 360 K. It is found that 56% of the temperature change in is caused by the spin - phonon interaction, and the remaining 44% is related to the thermal expansion of the crystal. The temperature at which the phase transition from the cubic to the tetragonal phase occurs is a linear function of pressure, with the pressure coefficient . The dependence of on the lattice constant and hydrostatic pressure is interpreted within the rigid-sphere model. No precursive behaviour above is observed.

Geometrical consideration of the crystallography of the transformation from α-Fe2O3 to Fe3O4

A mechanism is proposed for the transformation from α-Fe 2 O 3 to Fe 3 O 4 using the rigid-sphere model. By the shear slipping in every other {0001} hem plane, the h.c.p.-type stacking sequence of oxygen layers in α-Fe 2 O 3 changes to the f.c.c.-type stacking sequence of Fe 3 O 4 . Since the octahedral sites in the α-Fe 2 O 3 lattice change to tetrahedral sites after the restacking, the lattice is expanded by the restacking. Then the Coulomb force between the iron ion and the oxygen ion in restacked α-Fe 2 O 3 becomes weaker. By the reduction, the iron/oxygen ratio in the restacked α-Fe 2 O 3 increases, and during the reduction, Fe 3+ ions in the kagome lattice turn into Fe 2+ ions to maintain electroneutrality. Then the excess iron ions migrate in the restacked α-Fe 2 O 3 in the state of Fe 3+ , resulting in an increase in the iron/oxygen ratio of the oxide. Then iron ions are rearranged and the Fe 3 O 4 lattice is formed. This proposed mechanism can explain the experimental observation that the orientation relationship between α-Fe 2 O 3 and Fe 3 O 4 lattices satisfies the Shoji-Nishiyama relationship.

Effect of hydrostatic pressure on phase transitions in perovskite-like ferroelastics

Abstract The analysis of hydrostatic pressure influence on ferroelastic phase transitions in three- and two-dimensional perovskite-like crystals is carried out. The nonlinear effects and the change of the dT 0/dp sign are discussed on the ground of the thermodynamic theory. Simple model of rigid spheres is used to connect the T 0 shift under pressure with the bonds stresses.

Theory for Radii and Second Virial Coefficients. 1. Highly Charged Polyelectrolytes

We develop a theory for the dependence of the radii of gyration and second virial coefficients of highly charged polyelectrolytes on molecular weight and ionic strength. The theory is based on using (i) the Flory-Fisk 1 distribution of chain conformations to describe the elastic entropy and (ii) a charged rod model of local intrachain repulsions based on the full Poisson-Boltzmann equation. To describe the overlap between two approaching chains, we go beyond the rigid sphere model of Orofino and Flory 2 and assume the chains can change coil size and can deform as elastic ellipsoids to avoid unfavorable interchain repulsions. Added salt weakens electrostatic repulsions, leading to reduced radius of gyration and second virial coefficients. Without adjustable parameters this approach gives reasonable agreement with data on T7 DNA, Col El DNA, and poly(styrenesulfonate)s over two decades of ionic strength.

Influence of hydrostatic pressure on the phase transition in Ni(NH3)6I2: EPR studies

Electron paramagnetic resonance techniques are used to determine the phase transition temperature Tc of Ni(NH3)6I2 as a function of hydrostatic pressure. The hydrostatic pressure causes Tc to increase and the value of the pressure coefficient dTc/dp is (10 ± 2) K/GPa. Tc and dTc/dp for hexammine halides is calculated on the basis of the “rigid-sphere model” and good agreement with the experimental data is obtained.

Hydrostatic pressure electron paramagnetic resonance studies of the phase transition discontinuity in RbCaF3 up to 800 MPa

The influence of hydrostatic pressure on the cubic-to-tetragonal phase transition in RbCaF3 is studied by monitoring the EPR spectra of the Gd3+-O2- pairs and Gd3+ centres. The phase transition remains of first order up to 800 MPa and the discontinuity of the order parameter phi at Tc slightly increases with increasing pressure. Similarly, the nonlinearity of the cubic parameter b40(T), caused by the rotational fluctuations, near Tc becomes larger under pressure. The pressure shift of the phase transition temperature is determined: dTc/dp=(36.5+or-0.3) K GPa-1. The values of Tc as well as dTc/dp are interpreted within the rigid-sphere model.

Broadband measurements of the acoustic backscatter cross section of sand particles in suspension

A method using a broadband transducer to measure the acoustic backscatter cross section of suspended sand particles is investigated. The frequencies used range from 1.3 to 2.8 MHz, and the sand sizes from 100- to 350-μm diameter. The measurements are made in the transducer near field. The measured form factor is compared with the theoretical result for the movable rigid sphere model, and with previous narrow-band measurements.

Effects of ordering type and degree on monoclinic distortion of 18R-type martensite in Cu-Zn-Al alloys

In order to clarify the relationship between the extent of the distortion from the ideal structure and the nature of ordering (type, degree), a rigid hard sphere model for the M18R structure is developed by introducing the modified Bragg-Williams-Gorski-type order parameters. The ide- ally close-packed 9R or 18R structures are produced from the disordered or D03 ordered parent phases, while the modified 9R and 18R structures are produced from the B2 ordered and L21 ordered parent phases, respectively. The extent of the distortion in the close-packed plane in- creases with increasing degree of B2 order or with decreasing degree of L21 order. Related experiments based on the variation of X-ray diffraction pattern for the stabilization of Cu- Zn-Al shape memory alloy have confirmed the validity of the theoretical development.

Viscosity of high-temperature iodine.

The viscosity coefficient of iodine in the temperature range 500\ensuremath{\le}T\ensuremath{\le}3000 K is calculated. Because of the low dissociation energy of the ${\mathrm{I}}_{2}$ molecules, the dissociation degree of the gas increases quickly with temperature, and I+${\mathrm{I}}_{2}$ and I+I collisions must be taken into account in calculations of viscosity at temperatures greater than 1000\ifmmode^\circ\else\textdegree\fi{}. Several possible channels for atom-atom interaction are considered, and the resulting collision integrals are averaged over all the important channels. It is also shown that the rigid-sphere model is inaccurate in predictions of the viscosity. The approach of the present work is general and can be used for other diatomic gases with arbitrary dissociation degree.