Solidification Of Binary Mixture Research Articles

Nonlocal diffusion models: Application to rapid solidification of binary mixtures

Various theoretical treatments and models for nonlocal diffusion are briefly reviewed and discussed. The nonlocal effects arise in far from equilibrium processes, which involve extremely fast heat and mass transfer at very small time and length scales. With only diffusive dynamics, the nonlocal models result in a set of transfer equations of parabolic type with an infinite velocity of diffusive disturbances. With the wavelike dynamics, the models lead to a set of transfer equations of hyperbolic type with a finite velocity of diffusive disturbances. Rapid solidification of binary alloys has been used to illustrate the influence of the nonlocal diffusion effects on solute partitioning at the phase interface.

Diffusion-stress coupling in liquid phase during rapid solidification of binary mixtures

Abstract An analytical model has been developed to describe the diffusion-viscous stress coupling in the liquid phase during rapid solidification of binary mixtures. The model starts with a set of evolution equations for diffusion flux and viscous pressure tensor, based on extended irreversible thermodynamics. It has been demonstrated that the diffusion-stress coupling leads to non-Fickian diffusion effects in the liquid phase. With only diffusive dynamics, the model results in the nonlocal diffusion equations of parabolic type, which imply the transition to complete solute trapping only asymptotically at an infinite interface velocity. With the wavelike dynamics, the model leads to the nonlocal diffusion equations of hyperbolic type and describes the transition to complete solute trapping and diffusionless solidification at a finite interface velocity in accordance with experimental data and molecular dynamic simulation.

CFD simulation of bubbling fluidized bidisperse mixtures: Effect of integration methods and restitution coefficient

In this work we simulated the dynamics of a fluidized bed of a binary solid mixture using the isothermal multi-fluid model of the commercial CFD code Fluent 12. We focused the attention on the role of both restitution coefficient and integration methods on the dynamics of the bed, adopting a mixture of solids assorted in size (with constant density) as case study. We employed two methods of spatial discretization: first-order upwind scheme (FUS) and second-order upwind scheme (SUS). We investigated implicit versus explicit time integration methods as well. The numerical diffusion introduced by the FUS resulted in a low bubble fraction in the bed, in turn reducing solid mixing rates. Simulations carried out adopting the SUS were characterized by a reasonable bubble fraction and associated solid mixing rate. The latter method successfully predicted the transition to fully mixed, uniform fluidization conditions. The value of the restitution coefficient did not significantly affect the results of the simulations, as bubble volume fraction and jetsam concentration profiles did not show any significant change within the interval of restitution coefficient values investigated, with the exception of the nearly ideal value of 0.99.

Mathematical Modelling and Numerical Simulation of Dendrite Growth Using Phase-Field Method with a Magnetic Field Effect

AbstractIn this paper, we present a new model developed in order to analyze phenomena which arise in the solidification of binary mixtures using phase-field method, which incorporates the convection effects and the action of magnetic field. The model consists of flow, concentration, phase field and energy systems which are nonlinear evolutive and coupled systems. It represents the non-isothermal anisotropic solidification process of a binary mixture together with the motion in a melt with the applied magnetic field. To illustrate our model, numerical simulations of the influence of magnetic-field on the evolution of dendrites during the solidification of the binary mixture of Nickel-Copper (Ni-Cu) are developed. The results demonstrate that the dendritic growth under the action of magnetic-field can be simulated by using our model.

Hydrodynamic behavior of binary mixture of solids in a triple-bed combined circulating fluidized bed with high mass flux

Flow behaviors of binary mixture of silica sand and nylonshot (coal char substitute) were investigated in a triple-bed circulating fluidized bed (TBCFB) as a cold model of coal gasifier. The TBCFB consisted of a downer (ϕ 0.1m×6.5m), a bubbling fluidized bed (0.75m×0.27m×1.9m), a riser (ϕ 0.1m×16.6m) and a gas-sealing bed (GSB, ϕ 0.158m×5m). The initial fraction of the nylonshot in the solid mixture (Xnylon,i) was 15.4 and 30% on mass and volume bases, respectively, or otherwise, 30.7 and 50%. The maximum solids mass flux (Gs) at Xnylon,i of 15.4 and 30.7wt% were 394 and 349kg/m2s, respectively, when the gas velocity in the riser (Ugr) was 10m/s. Apparent solids holdups of silica sand and nylonshot were calculated separately from the static pressure gradient across the riser and the downer. The results showed possibility of large-mass-flux circulation of char in the gasifier, which plays a significant role in decomposition of tar from pyrolysis as the primary step of gasification. A newly developed pressure balance model successfully predicted Gs of the binary mixtures in TBCFB.

Drying behavior of uniform and binary mixture of solids in a batch fluidized bed dryer

The drying behavior of solids has been studied in a batch fluidized bed dryer using different uniformly sized solids and various binary mixtures of solids at different dilutions in falling rate periods one and two. To predict the drying behavior in falling rate periods one and two, correlations were developed for uniformly sized particles and for binary mixture of solids. The mixing index has been incorporated to develop the correlations for two types of falling rate periods. The average moisture content has been taken to predict the effect of various parameters on drying behavior. The correlations for average moisture content have been developed by considering the effect of various parameters such as air velocity, initial moisture content of solids, temperature, initial bed height and particle diameter for uniformly sized particles. The effect of various parameters on drying behavior has been investigated for different binary mixture of solids. To predict the drying behavior of binary solid mixtures, mixing index has been incorporated with other parameters in correlation development. The mixing index has been found to decrease with increase in the dilution of fine particles with coarse particles. The drying behavior of binary mixture of solids has been found to be similar to the uniformly sized particles. Effect of dilution on drying has been investigated, where in it is noticed that 10% diluted binary mixture gave highest drying rate and no improvement in drying behavior is found for dilution beyond 30%. The work finds importance in practice, as it involves the use of solid mixtures. The experimental results were compared with the predicted values and are found to be in good agreement.

Just‐suspended agitation of solid mixtures

AbstractFor binary solid mixtures, the mixture just‐suspended speed is predicted with reasonable accuracy from the sum of powers to suspend the solids individually. Exceptions to this behaviour occur for mixtures of low‐density solids and for mixtures involving a small, high‐density solid. For these systems, summing the powers required to individually suspend the solids over‐predicts the mixture just‐suspended speed. Limited testing of ternary solid mixtures indicates that summing the powers required to individually suspend the solids also predicts the just‐suspended speed in these more complex systems.

Temperature and composition dependence of kinetics of phase separation in solid binary mixtures

We present results on the effects of temperature variation and composition in the kinetics of phase separation in solid binary mixtures (A1 + A2) from Monte Carlo simulations of the Ising model in two dimensions. The simulation results are understood via an appropriate application of the finite-size scaling theory. At moderately high temperatures, for symmetric (50 : 50) compositions of A1 and A2 particles the average size of the domains exhibits power-law growth with the exponent having a Lifshitz-Slyozov value of 1/3 from very early time. However, our analysis shows that for low enough temperatures, the growth exponent at an early time is smaller than the Lifshitz-Slyozov value. For composition dependence, we find that at moderate temperature, even for extreme off-critical composition, the curvature dependent correction to the growth law is weak which is counter-intuitive in case of droplet morphology. This is, however, consistent with the recent understanding on the curvature dependence of surface tension. Results from rather general studies on the finite-size effects with the variations of temperature and composition have also been presented.

Solid Suspension by an Upflow Mixture of Fluid and Larger Particles

In this paper new experimental observation is reported in order to shed light on the fluid dynamic interactions between the solid and the fluid phases in binary solid mixture suspensions. More specifically the case where a solid particle species is suspended by a slurry made up of fluid and larger particles has been investigated as there appear to be no previous studies on this type of systems. The effect of the presence of the larger solids in the fluidising media is quite evident from the experimental observation, and this effect can be quantified in first approximation by a very simple model based on the assumption that the larger solid restricts the available area for the fluid flow.

The Effective Convectivity Model for Simulation of Molten Metal Layer Heat Transfer in a Boiling Water Reactor Lower Head

This paper is concerned with the development of approaches for assessment of core debris heat transfer and Control Rod Guide Tube (CRGT) cooling effectiveness in case of a Boiling Water Reactor (BWR) severe accident. We consider a hypothetical scenario with stratified (metal layer atop) melt pool in the lower plenum. Effective Convectivity Model (ECM) and Phase-Change ECM (PECM) are developed for the modeling of molten metal layer heat transfer. The PECM model takes into account reduced convection heat transfer in mushy zone and compositional convection that enables simulations of noneutectic binary mixture solidification and melting. The ECM and PECM are (i) validated against relevant experiments for both eutectic and noneutectic mixtures and (ii) benchmarked against CFD-generated data including the local heat transfer characteristics. The PECM is then applied to the analysis of heat transfer in a stratified heterogeneous debris pool taking into account CRGT cooling. The PECM simulation results show apparent efficacy of the CRGT cooling which can be utilized as Severe Accident Management (SAM) measure to protect the vessel wall from focusing effect caused by metallic layer.

Experimental determination and activity coefficient based models for mixture solubilities of nitrophenol isomers in supercritical carbon dioxide

The experimental solubilities of the mixture of nitrophenol (m- and p-) isomers were determined at 308, 318 and 328K over a pressure range of 10–17.55MPa. Compared to the binary solubilities, the ternary solubilities of m-nitrophenol increased at 308, 318 and 328K. The ternary solubilities of p-nitrophenol increased at 308K, while the ternary solubilities decreased at lower pressures and increased at higher pressure at 318 and 328K. The solubilities of the solid mixtures in supercritical carbon dioxide (SCCO2) were correlated with solution models by incorporating the non-idealities using activity coefficient based models. The Wilson and NRTL activity coefficient models were applied to determine the nature of the interactions between the molecules. The equation developed by using the NRTL model has three parameters and correlates mixture solubilities of solid solutes in terms of temperature and cosolute composition. The equation derived from the Wilson model contains five parameters and correlates solubilities in terms of temperature, density and cosolute composition. These two new equations developed in this work were used to correlate the solubilities of 25 binary solid mixtures including the current data. The average AARDs of the model equations derived using the NRTL and Wilson models for the solid mixtures were found to be 7% and 4%, respectively.

Eulerian-Eulerian Simulations of Segregating Binary Gas-Solid Fluidized Beds

Abstract This work is aimed at investigating a bidisperse gas-solid fluidized bed by Computational Fluid Dynamics simulations. The selected simulation approach is based on the Eulerian unsteady equations of motion for each phase coupled with a model based on the granular kinetic theory. The effect of grid size and time step on axial segregation of two different binary solid mixtures is investigated. The analysis of the simulation results, which strengthen previous findings with new data, confirms that firm conclusions on the capacity of the CFD model to predict the segregation dynamics in fluidized beds can be drawn only after careful verification of numerical uncertainties at the operating conditions under investigation. The relationship between the average absolute error, which is evaluated by comparison of the simulation results with literature experimental data, and a global parameter, which takes into account both the operating conditions and the spatial and temporal resolutions, is shown.

Fixed-bed adsorption of Malachite Green onto binary solid mixture of adsorbents: seashells and eggshells

In this work, continuous removal of Malachite Green from aqueous solution by adsorption was investigated using a laboratory scale fixed-bed column packed with binary solid mixture of seashell powder (SSP) and eggshell powder (ESP). The effects of initial dye concentration, feed flow rate, bed height, and the SSP : ESP ratio in the binary solid mixture on the breakthrough characteristics were studied. The breakthrough time decreased with increase in the flow rate and the initial dye concentration. The breakthrough time also varied greatly with change in bed height. The breakthrough time increased from 17.2 h to 34.5 h with increase in bed height from 6 cm to 12 cm. The breakthrough time was significantly affected by the change in the SSP : ESP ratio in the binary mixture. The breakthrough time decreased with increase in the SSP ratio in the binary mixture. In order to determine the column kinetic parameters, three different column kinetic models, namely Adams–Bohart, Bed Depth Service Time (BDST), and Yoon–Nelson models were fitted to the dynamic flow experimental data. The BDST model showed good agreement with the experimental results at all the process parameters studied. Results suggest that this novel approach of simultaneous utilization of adsorbents can be adopted for the treatment of dye-bearing effluents.

Transient natural convective heat transfer in porous medium with solidification of binary mixture

In this paper an enthalpy porosity method associated with finite control volume scheme and SIMPLE iteration was employed to solve Navier–Stokes equation coupled with energy equation through Ergun equation and Boussinesq approximation for studying the effect of two-dimensional transient natural convective heat transfer from a closed region of porous medium with the different porosity on solidification in carbon–iron system. As shown in the results, it is fund that the thickness of solidification layer is increased with time due to thermal coupled flow induced by natural convection; and the wall temperature is faster changed in porous medium with larger porosity, which corresponds to slow the growth of the solidification layer in binary system.

Crossover in growth laws for phase-separating binary fluids: Molecular dynamics simulations

Pattern and dynamics during phase separation in a symmetrical binary (A+B) Lennard-Jones fluid are studied via molecular dynamics simulations after quenching homogeneously mixed critical (50:50) systems to temperatures below the critical one. The morphology of the domains, rich in A or B particles, is observed to be bicontinuous. The early-time growth of the average domain size is found to be consistent with the Lifshitz-Slyozov law for diffusive domain coarsening. After a characteristic time, dependent on the temperature, we find a clear crossover to an extended viscous hydrodynamic regime where the domains grow linearly with time. Pattern formation in the present system is compared with that in solid binary mixtures, as a function of temperature. Important results for the finite-size and temperature effects on the small-wave-vector behavior of the scattering function are also presented.

An analysis of a phase-field model for isothermal binary alloy solidification with convection under the influence of magnetic field

This paper is devoted to the study of a new phase-field model with convection under the influence of magnetic field for the isothermal solidification of binary mixtures in two-dimensional geometry. A brief description of the system governing the model is given. The existence of weak solutions as well as the regularity and uniqueness results are established under certain conditions on the nonlinearities. A maximum principle under additional assumptions are also derived. A numerical calculation is performed.

WITHDRAWN: Quantitative analysis of solid binary mixtures—Vibrational spectroscopy of β-lactam antibiotics within THz-region

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Volume-change of mixing at incipient fluidization of binary-solid mixtures: Experimental data and predictive models

The component additive rule for the prediction of the volume of fluidized mixtures of binary-solids does not hold owing to the phenomenon of the volume-change of mixing. A significant contraction in the volume of the mixed bed is often observed. This phenomenon has an important bearing on the hydrodynamics of the binary-solid fluidization. In the present, the volume-change of mixing is experimentally investigated for several liquid-fluidized binary-solid mixtures for a wide range of compositions at the incipient fluidization. Seven different binaries are composed from eight different solid species that differ in their sizes as well as densities, and therefore exhibit a wide range of stratification pattern. The use of packing models reported in the literature results in rather poor predictions of the observed volume-change of mixing. Incorporating the hydrodynamic aspects of the fluidization however helps to substantially improve predictions. A two-level integration of the hydrodynamic information is implemented here. The level one involves using the hydrodynamic drag diameter evaluated from the expansion of individual solid species instead of the commonly used volume-equivalent or the packing-equivalent diameter. The level two in addition involves accounting for the expansion of either of the solid species should it occur at the incipient fluidization of the mixture.

Global theory of steady deep-cellular growth in directional solidification

The present paper is concerned with the global asymptotic theory of steady deep-cellular growth in directional solidification of binary mixtures. We consider the two-dimensional model with nonzero isotropic surface tension and obtain the global uniformly valid asymptotic solutions for the steady state of the system in the limit of the Péclet number ε→0; ε is defined as the ratio of the radius of the cell's tip and mass diffussion length. The whole physical space is divided into the outer region and root region; the solutions in each subregion are solved, respectively, and matched with each other in the intermediate region. The results show that given growth conditions and material properties, the global solutions for steady state of the system contain two free parameters: the Péclet number and asymptotic width parameter λ(0), which are related to the geometry of cellular structure: the cell tip radius and primary spacing. One of the most important conclusions drawn from this analysis is that the steady-state solutions of cellular growth have a complicated structure with three internal layers in the root region; for given (ε,λ(0)), there exists a discrete set of the global steady-state solutions subject to the quantization condition that are profoundly affected by the surface tension. Each eigenvalue calculated from this quantization condition determines the total length of the finger described by the corresponding global steady-state solution.

Influence of Feed Entry on the Segregation of a Binary Mixture of Solids in a Continuous Fast Fluidized Bed

Influence of Feed Entry on the Segregation of a Binary Mixture of Solids in a Continuous Fast Fluidized Bed