Solidification Of Binary Mixture Research Articles

An analytical procedure to determine constitutive coefficients of a mixture of two linear elastic solids

In this paper, we study the coefficients of constitutive equations of a binary mixture of elastic solids and give an analytical approach to determine them. Assuming a material of two-phase elastic composite with randomly distributed elastic spheres is equivalent to a mixture of two elastic solids, we find the values of unknown coefficients by making use of Boussinesq problem. Furthermore, a mean displacement vector definition is also given.

Spectroscopic study of rotation-crystalline modifications of mixtures of n-paraffins C 22–C 24

The binary solid mixtures of n-paraffins, C 22–C 24, with different molar ratios of 96:4, 3:1, 2:1, 1:4, 1:5, and 1:10 have been studied by FTIR spectroscopy, X-ray diffraction and differential scanning calorimetry (DSC). Temperature-dependent studies of Davydov splitting value, Δ ν 1,2, of in-phase CH 2 rocking vibrations have been shown to allow the determination of Δ T rot temperature intervals, where rotation-crystalline states, characterized by different types of molecular motion, exist. The comparison of the ΔT rot values obtained by FTIR and DSC methods with the corresponding temperature-dependent X-ray powder diffraction data has shown their good agreement.

Multicomponent nucleation: thermodynamically consistent description of the nucleation work.

A thermodynamically consistent formula is derived for the nucleation work in multicomponent homogeneous nucleation. The derivation relies on the conservative dividing surface which defines the nucleus as having specific surface energy equal to the specific surface energy sigma0 of the interface between the macroscopically large new and old phases at coexistence. Expressions are given for the radius of the nucleus defined by the conservative dividing surface and by the surface of tension. As a side result, the curvature dependence of the surface tension sigmaT of the nucleus defined by the surface of tension is also determined. The analysis is valid for nuclei of any size, i.e., for nucleation in the whole range of conditions between the binodal and the spinodal of the metastable old phase provided the inequality sigmaT < or = sigma0 is satisfied. It is found that under the conditions of validity of the analysis the nucleation rate is higher than the nucleation rate given by the classical nucleation theory. The general results are applied to nucleation of unary liquids or solids in binary gaseous, liquid or solid mixtures.

Shear deformation of binary mixtures of dry particulate solids

Abstract The shear deformation behavior of dry granular materials is of interest in the analysis of flowability, mixing, segregation and degradation. Quite often the particulate systems are mixtures of materials with a wide size distribution. In spite of a large amount of work reported in the literature, the shear behavior of poly-disperse systems has not been widely addressed. In this paper experimental work using an annular shear cell and numerical simulations by the distinct element method (DEM) have been carried out to quantify the normal and shear stress behavior of assemblies made of binary mixtures. The experimental results on mixtures of different sizes of glass beads show a linear relationship between the normal and shear stresses with a slope which depends on the shear rate and particle size ratio. This is an indication of flow in the intermediate regime between the quasi-static and rapid shear flows. The results also indicate a highly non-linear particle displacement distribution across the shear layer. Numerical simulations using the DEM agree qualitatively well with the experimental results for the normal-shear stress behavior.

Solubilities of two steroid drugs and their mixtures in supercritical carbon dioxide

The equilibrium solubilities of two steroid drugs, medroxyprogesterone acetate (med) and cyproterone acetate (cyp) in the binary (med+CO 2 and cyp+CO 2) and ternary (med+cyp+CO 2) systems were determined at temperatures ranging from 308 to 348 K and pressures from 122 to 355 bar. The experimental data for med were correlated using a semi-empirical model. Correlation of the results shows good self-consistency of the data obtained and reasonable agreement with the available published data. The crossover region, i.e. the pressure where solubility isotherms cross each other in that region, was observed for med at about 220 bar while for cyp this region was above 300 bar. In the ternary systems the solubility of med increased, but the solubility of cyp decreased (except for lower pressures and/or high temperatures) in comparison to their binary solubilities. Separations of binary solid mixtures of these drugs were investigated. The results showed that the med acetate could be separated from this mixture with a yield of 67%.

Size segregation of binary mixture of solids in bubbling fluidized beds

The fluidization behavior of binary mixture differing in size in the gas bubbling fluidized bed is experimentally and theoretically studied. The segregation phenomena are analyzed, and the relevancy of the pressure drop profile of binary mixture to the definition of its minimum fluidization velocity is discussed. The distributions of mass fraction of particles along the bed height are measured, and the profiles of the mean particle diameters of binary mixture are determined. A multi-fluid gas–solid flow model is presented where equations are derived from the kinetic theory of granular flows. Separate transport equations are constructed for each of the particle class, allowing for the interaction between size classes, as well as the momentum and energy are exchanged between the respective classes and the carrier gas. The segregations of the mean diameter are predicted. The numerical results are analyzed and compared with experimental data.

Estimation of properties of ternary mixtures of solids using the mixing rule

In this work, a model ternary system of zeolite NaY, kaolin (both from Aldrich®) and alumina (from Vetec®), was studied. True and bulk densities, powder and particle porosities, specific surface area, and sorption isotherms were determined for single solids and mixtures. Physical properties and sorption isotherms of mixtures were calculated from the mixing rule using mass and volume fractions of each solid in the mixture. Calculated and experimental values presented very good agreement for true density, specific surface area, and sorption isotherms. For bulk density and porosity, the mixing rule does not work well, since the mixtures do not follow the mass proportion due to the particle–particle interactions. Zeolite NaY presents isotherm type I, while kaolin and alumina present isotherm type II, all mixtures present the curves between those of the single solids. The results show that it is possible to use the mixing rule to evaluate some physical properties as well as the sorption isotherms of binary and ternary mixtures of solids.

Oxide potentials from ab initio molecular dynamics: An assessment of their transferability

An aspherical ion model (AIM) description of interatomic interactions in alkaline earth oxides MgO, CaO, SrO, and BaO has been obtained. The parameters were determined by matching the forces predicted by the models to those calculated from an ab initio dynamics calculation in finite temperature simulations. The models were shown to be transferable in the sense that they offered equally accurate descriptions of the pure materials over very wide ranges of temperature and pressure and in phases with different coordination number. In the present paper, more wide-ranging transferability considerations are pursued. First, we check transferability between chemically related substances: we transform the model for CaO into a potential for BeO by scaling parameters according to the changes in ion sizes and polarizabilities. Second, we test transferability upon compound formation, by combining the MgO and CaO potentials in order to describe the interatomic interactions in MgO–CaO solid binary mixtures. The results show that the proposed models are able to provide a good description of interatomic interactions in both cases. The calculations demonstrate that the AIM represents the different contributions to the interionic forces faithfully and that the force-matching procedure finds physically meaningful values for the parameters therein.

Three-dimensional double-diffusive convection and macrosegregation during non-equilibrium solidification of binary mixtures

A three-dimensional transient mathematical model (following a fixed-grid enthalpy-based continuum formulation) is used to study the interaction of double-diffusive natural convection and non-equilibrium solidification of a binary mixture in a cubic enclosure cooled from a side. Investigations are carried out for two separate test systems, one corresponding to a typical model “metal–alloy analogue” system and other corresponding to a real metal–alloy system. Due to stronger effects of solutal buoyancy in actual metal–alloy systems than in corresponding analogues, the convective transport mechanisms for the two cases are quite different. However, in both cases, similar elements of three-dimensionality are observed in the curvature and spacing of the projected streamlines. As a result of three-dimensional convective flow patterns, a significant solute macrosegregation is observed across the transverse sections of the cavity, which cannot be captured by two-dimensional simulations.

Residence Time Distribution of Solids in a Fluidized Bed

AbstractExperimental investigation on RTD of solids is carried out in a single‐stage fluidized bed provided with an internal, using uniformly sized particles and a binary solid mixture, varying gas flow rate, solids rate, bed height, dilution and the bed geometry. The effect of these variables on first and second moments as well as on F‐curves has been determined. Using a binary solid mixture or an internal inside the bed is found to reduce backmixing of solids. The data is fitted to FTEM and the values of N obtained were compared for different variables.

Experimental Analysis of the Fluidization Process of Binary Mixtures of Solids

The simultaneous treatment of dissimilar solids is encountered in a number of processes that exploit fluidization technology (granulation, combustion, pyrolysis, etc.), but a satisfactory description of multicomponent fluidization dynamics is far from being achieved even for the relatively simple case of binary fluidization.This paper discusses the fluidization properties of two-component beds of solids differing either in particle density or diameter. It is shown that although the minimum fluidization velocity of the mixture can be calculated by fully theoretical equations, it has very little meaning if referred to a two-component particle system. Experiments on both kinds of mixtures demonstrate that the binary fluidization process occurs within a characteristic velocity range whose boundaries coincide with the “initial” and the “final fluidization velocity” of the particle mixture. Substitution of the conventional concept of umf by these parameters allows us to recognize that the fluidization dynamics of any binary mixture is determined by the initial arrangement of the fixed bed, as well as by the system composition and size or density ratio of its components.

Density segregation of a binary solids mixture during batch operation in a two-dimensional hopper

Abstract Segregation patterns of binary particle mixtures of different densities during emptying after filling of a two-dimensional hopper were theoretically analyzed on the basis of a proposed mathematical model. It includes the segregation process over an inclined heap surface and a velocity profile in the radial direction toward the hopper apex. As a result, it was found that the segregation time zone during emptying as mixing ratio versus discharge time expands and the value of the maximum points in the segregation profile decreases with the increase in the volumetric initial mixing ratio of the denser component and the volumetric feed rate, and that the zone shrinks with the increase in the apex angle and the discharge rate. The steeper radial velocity profile inside the hopper results in a slightly non-uniform time-segregation profile. The initial mixing ratio changes the segregation time zone more than the discharge rate.

Numerical Simulation Of Heat And Mass Transfer During Solidification Of Binary Mixtures On N-alkanes

Numerical Simulation Of Heat And Mass Transfer During Solidification Of Binary Mixtures On N-alkanes

An analytical solution for conduction-dominated unidirectional solidification of binary mixtures

In this paper, a fully analytical solution technique is established for the solution of unidirectional, conduction-dominated, alloy solidification problems. By devising appropriate averaging techniques for temperature and phase-fraction gradients, governing equations inside the mushy region are made inherently homogeneous. The above formulation enables one to obtain complete analytical solutions for solid, liquid and mushy regions, without resorting to any numerical iterative procedure. Due considerations are given to account for variable properties and different microscopic models of alloy solidification (namely, equilibrium and non-equilibrium models) in the two-phase domain. The results are tested for the problem of solidification of a NH 4Cl–H 2O solution, and compared with those from existing analytical models as well as with the corresponding results from a fully numerical simulation. The effects of different microscopic models on solidification behaviour are illustrated, and transients in temperature and heat flux distribution are also analysed. A good agreement between the present solutions and results from computational simulation is observed.

A fundamental approach to the phenomenology of fluidization of size segregating binary mixtures of solids

The paper reports an experimental study of the fluidization behaviour of mixtures of two solids differing in size at various average compositions. The segregation phenomena accompanying the onset of the fluidized state are analysed and the relevance of the composition profile of the binary bed to the definition of its minimum fluidization velocity is discussed. It is demonstrated that the recognition of the dependence of bed voidage and particle average diameter on mixture composition is the essential condition for getting over current empirical approaches to segregating fluidization and for restoring the predictive ability of theoretical equations. To this purpose, Carman–Kozeny equation is rewritten in a differential form suitable for the peculiar characteristics of two-component systems. The good agreement with experimental data indicates that the extension of the fundamental approach from monodisperse to binary beds greatly reduces the number of independent variables to be dealt with in the study of segregating fluidization of dissimilar solids. The evolution of bed composition profiles from the fixed to the fully fluidized state, where the gas drag force first balances the particulate bed weight, makes clear that full fluidization is constantly associated to the achievement of practically thorough mixing. It can therefore be assumed that component segregation is not a distinctive property of binary fluidization, rather it is the sign of its incompleteness.

Solubilities of Mixed Acenaphthene, Fluoranthene, and Triphenylene in Supercritical Carbon Dioxide and the Separation of Binary Solid Mixtures of Polycyclic Aromatic Hydrocarbons

The equilibrium solubilities of mixtures of acenaphthene, fluoranthene, and triphenylene in supercritical CO2 were determined at temperatures ranging from 308 K to 338 K and pressures ranging from (121.6 to 354.6) bar. It was observed that in a quaternary system (acenaphthene + fluoranthene + triphenylene + CO2) the solubility of each substance increased in comparison to each binary system (pure substance + CO2). Finally the separation of binary solid mixtures of acenaphthene + triphenylene, acenaphthene + fluoranthene, and fluoranthene + triphenylene at 328 K and 121.6 bar was investigated. The results showed that the acenaphthene can be separated from triphenylene and fluoranthene with yields of 99% and 90%, respectively, and fluoranthene was separated from triphenylene with a yield of 89%.

Modified Retrograde Crystallization Process for Separation of Binary Solid Mixtures Exploiting the Crossover Region of Supercritical Carbon Dioxide

A modified retrograde crystallization process with the circulation of supercritical carbon dioxide has been designed and tested for the separation of a mixture containing two solids. The apparatus consists of an extractor and a crystallizer, which are kept at different temperatures but at a fixed pressure within the crossover region. The metastable zone within the crossover region of the ternary system is first determined. Separation experiments are then conducted under various conditions with the crystallizer temperatures within or slightly above the metastable zone. The benzoic acid/1,10-decanediol/CO2 system with a wide crossover region represents an ideal example of the modified process, and the results show that it is possible to obtain essentially pure products of both components (>97 wt %) from a 50/50 wt % mixture of benzoic acid and 1,10-decanediol. The average recovery is 49.3% for benzoic acid and 85.8% for 1,10-decanediol. The other system of 2,3-/2,6-dimethylnaphthalene/CO2 with a narrow crossover region is then analyzed to demonstrate the possibility for the separation of organic isomers, and the results show that the modified process can produce the 2,6-dimethylnaphthalene of almost 100 wt % purity with a recovery of 37.1% starting from a mixture of 50/50 wt % isomers.

POTENTIAL METHOD IN THE LINEAR THEORY OF BINARY MIXTURES OF THERMOELASTIC SOLIDS

This article deals with the diffusion model of the linear theory of binary mixtures of the thermoelastic solids. A wide class of external (with respect to an unbounded domain) boundary value problems of steady oscillations is investigated using the potential method. Sommerfeld-Kupradze-type radiation conditions are established. The uniqueness and existence theorems of classical solutions of the aforementioned problems are proved.

Thin film mixtures synthesized by cross-beam PLD

Fabrication of metastable binary solid state film mixtures with continuously variable composition by asymmetric cross-beam PLD is demonstrated. In this technique, the materials are mixed directly in the intersection region of colliding plasmas of individual target materials. This technique can be advantageous for synthesis of solid state quasi-solutions of partially miscible materials, where one can expect interesting mechanic properties and magnetic transformations.

Liquid fluidisation of binary particle mixtures—III Stratification by size and related topics

This final paper in a series of three on continuous steady-state liquid fluidisation of an unchanging batch of bottom-restrained binary solid mixtures deals primarily with the problem of stratification by size, which is shown to depend on the bulk density difference of the two particle components when each is fluidised separately by the same liquid at the same velocity, normalised with respect to the buoyed density of the particles. This simple composition-independent approach to particle segregation by size is formulated in the context of the more sophisticated composition-dependent approach to the bed inversion problem developed by Gibilaro et al. (1986, Chem. Engng Sci., 41, 379–387), which involves complete or partial segregation by density (‘sorting’) at low velocity and partial or complete segregation by size (‘sizing’) at high velocity.