Progress In Modeling Of Fluid Flows In Crystal Growth Processes

Modeling of fluid flows in crystal growth processes has become an important research area in theoretical and applied mechanics. Most crystal growth processes involve fluid flows, such as flows in the melt, solution or vapor. Theoretical modeling has played an important role in developing technologies used for growing semiconductor crystals for high performance electronic and optoelectronic devices. The application of devices requires large diameter crystals with a high degree of crystallographic perfection, low defect density and uniform dopant distribution. In this article, the flow models developed in modeling of the crystal growth processes such as Czochralski, ammonothermal and physical vapor transport methods are reviewed. In the Czochralski growth modeling, the flow models for thermocapillary flow, turbulent flow and MHD flow have been developed. In the ammonothermal growth modeling, the buoyancy and porous media flow models have been developed based on a single-domain and continuum approach for the composite fluid-porous layer systems. In the physical vapor transport growth modeling, the Stefan flow model has been proposed based on the flow-kinetics theory for the vapor growth. In addition, perspectives for future studies on crystal growth modeling are proposed. (c) 2008 National Natural Science Foundation of China and Chinese Academy of Sciences. Published by Elsevier Limited and Science in China Press. All rights reserved.

Two-Dimensional Kinetics Of Beta(2)-Integrin And Icam-1 Bindings Between Neutrophils And Melanoma Cells In A Shear Flow

Cell adhesion, mediated by specific receptor-ligand interactions, plays an important role in biological processes such as tumor metastasis and inflammatory cascade. For example, interactions between beta(2)-integrin ( lymphocyte function-associated antigen-1 and/or Mac-1) on polymorphonuclear neutrophils (PMNs) and ICAM-1 on melanoma cells initiate the bindings of melanoma cells to PMNs within the tumor microenvironment in blood flow, which in turn activate PMN-melanoma cell aggregation in a near-wall region of the vascular endothelium, therefore enhancing subsequent extravasation of melanoma cells in the microcirculations. Kinetics of integrin-ligand bindings in a shear flow is the determinant of such a process, which has not been well understood. In the present study, interactions of PMNs with WM9 melanoma cells were investigated to quantify the kinetics of beta(2)-integrin and ICAM-1 bindings using a cone-plate viscometer that generates a linear shear flow combined with a two-color flow cytometry technique. Aggregation fractions exhibited a transition phase where it first increased before 60 s and then decreased with shear durations. Melanoma-PMN aggregation was also found to be inversely correlated with the shear rate. A previously developed probabilistic model was modified to predict the time dependence of aggregation fractions at different shear rates and medium viscosities. Kinetic parameters of beta(2)-integrin and ICAM-1 bindings were obtained by individual or global fittings, which were comparable to respectively published values. These findings provide new quantitative understanding of the biophysical basis of leukocyte-tumor cell interactions mediated by specific receptor-ligand interactions under shear flow conditions.

Mass transfer kinetics of neodymium(III) extraction by calix[4]arene carboxylic acid using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamics and kinetics data are both important to explain the extraction property. In order to develop a novel separation technology superior to current extraction systems, many promising extractants have been developed including calixarene carboxylic acids. The extraction thermodynamics behavior of calix[4]arene carboxylic acids has been reported extensively. In this study, the mass transfer kinetics of neodymium(III) and the interfacial behavior of calix[4]arene carboxylic acid were investigated.

Extraction kinetics of thorium(IV) with primary amine N1923 in sulfate media using a constant interfacial cell with laminar flow

Extraction kinetics of thorium(IV) with primary amine N1923 in sulfate media has been investigated by a constant interfacial cell with laminar flow. Studies of interfacial tension and effects of the stirring rate, temperature, and specific interfacial area on mass transfer rate show that the most probable reaction zone takes place at the liquid-liquid interface. According to the experimental data correlated as a function of the concentration of the relevant species involved in the extraction reaction, the rate equation of extracting thorium has been obtained as follows: -d[Th(IV)]((o))/dt = 10(-3.10)center dot[Th(IV)](0.89)center dot[(RNH3)(2)SO4](0.74).

Extraction kinetics of cerium(IV) from sulfuric acid medium by the primary amine N1923 using a constant interfacial area cell with laminar flow

BACKGROUND: Thermodynamic studies on Ce(IV) extraction with primary amine N1923 demonstrate that primary amine N1923 is an excellent extractant for separation of Ce(IV) from Re(III). In order to clarify the mechanism of extraction and to optimize the parameters in practical extraction systems used in the rare earth industry, the extraction kinetics was investigated using a constant interfacial area cell with laminar flow in the present work.RESULTS: The data indicate that the rate constant (k(ao).) becomes constant when stirring speed exceeds 250 rpm. The apparent forward extraction rate is calculated to be 10(-1.70). The activation energy (E.) was calculated to be 20.5 kJ/mol from the slope of log kao against 1000/T. The minimum bulk concentration of the extractant necessary to saturate the interface (C-min) is lower than 10(-5) mol L-1.CONCLUSION: Studies of interfacial tension and the effects of stirring rate and specific interfacial area on the extraction rate show that the extraction rate is kinetically controlled, and a mass transfer model has been proposed. The rate equation has been obtained as: -d[Ce(IV)]/dt = 10(-1.70)[Ce(IV)] [(RNH3)(2)SO4](1.376). The rate-controlling step has been evaluated from analysis of the experimental results.

Extraction kinetics of Sc(III), Y(III), La(III) and Gd(III) from chloride medium by Cyanex 302 in heptane using the constant interfacial cell with laminar flow

The extraction kinetics of Sc, Y, La and Gd(III) from the hydrochloric acid medium using Cyanex 302 (hereafter HL) in heptane solution have been measured by the constant interfacial cell with laminar flow. Reaction regions are explored at liquid-liquid interface. Extraction regimes are deduced to be diffusion-controlled for Sc(Ill) and mixed controlled for Y, La and Gd(Ill). Extraction mechanisms are discussed according to the dimeric model of Cyanex 302 in non-polar solution. From the temperature dependence of rate measurement, the values of E-a, Delta H-+/-, Delta S-+/- and Delta G(300)(+/-) are calculated and it is found that the absolute values of these parameters keep crescent trend for Sc, Y, La and Gd(III). At the same time, it is found that it can easily achieve the mutual separation among the Sc, Y and La(III) with kinetics extraction methods.

Kinetics of extraction and stripping of y(III) by Cyanex 272 as an acidic extractant using a constant interfacial cell with laminar flow

The extraction and stripping kinetics of yttrium(III) with bis(2,4,4-trimethylpentyl) phosphinic acid (Cyanex 272, HA) dissolved in heptane as an acid extractant have been investigated by constant interfacial cell with laminar flow. The experimental hydrodynamic conditions have been chosen so that the contribution of diffusion to the measured rate of reaction is minimized. The plot of interfacial area on the rate has shown a linear relationship, which makes the interface the most probable local for the chemical reactions. At the same time, the extraction thermodynamic and kinetic methods are compared to determine the equilibrium extraction constant. A rate equation and the rate-determining step of the extraction and stripping of yttrium(III) have also been obtained, respectively.

Kinetics of ytterbium(III) extraction with Cyanex 272 using a constant interfacial cell with laminar flow

Studies have been made on the kinetics of ytterbium(III) with bis-(2,4,4-trimethylpentyl) phosphinic acid (Cyanex 272, HA) in n-heptane using a constant interfacial cell with laminar flow. The stiochiometry and the equilibrium constant of the extracted complex formation reaction between Yb3+ and Cyanex 272 are determined. The extraction rate is dependent of the stirring rate. This fact together with the Ea value suggests that the mass transfer process is a mixed chemical reaction-diffusion controlled at lower temperature, whereas it is entirely diffusion controlled at higher temperature. The rate equations for the ytterbium extraction with Cyanex 272 have been obtained. The rate-determining step is also made by predictions derived from interfacial reaction models, and through the approximate solutions of the flux equation, diffusion parameters and thickness of the diffusion film have been calculated.

Mass transfer kinetics of yttrium(III) using a constant interfacial cell with laminar flow. Part II. Extraction with Cyanex 272

The yttrium(III) extraction kinetics and mechanism with bis-(2,4,4-trimethyl-pentyl) phosphinic acid (Cyanex 272, HA) dissolved in heptane have been investigated by constant interfacial cell with laminar flow. The data has been analyzed in terms of pseudo-first order constants. Studies on the effects of stirring rate, temperature, acidity in aqueous phase, and extractant concentration on the extraction rate show that the extraction regime is dependent on the extraction conditions. The plot of interfacial area on the rate has shown a linear relationship. This fact together with the strong surface activity of Cyanex 272 at heptane-water interfaces has made the interface the most probable location for the chemical reactions. The forward, reverse rate equations and extraction rate constant for the yttrium extraction with Cyanex 272 have been obtained under the experimental conditions. The rate-determining step has been also predicted from interfacial reaction models. The predictions have been found to be in good agreement with the rate equations obtained from experimental data, confirming the basic assumption that the chemical reaction is located at the liquid-liquid interface.

Mass transfer kinetics of yttriium(III) using a constant interfacial cell with laminar flow. Part I. Extraction with Cyanex 302

The interfacial tension is measured for Cyanex 302 in heptane and adsorption parameters are calculated according to Gibbs equation and Szyskowski isotherm. The results indicate that Cyanex 302 has a high interfacial activity, allowing easy extraction reaction to take place at the liquid-liquid interface. The extraction kinetics of yttrium(III) with Cyanex 302 in heptane are investigated by a constant interfacial cell with laminar flow. The effects of stirring rate, temperature and specific interfacial area on the extraction rate are discussed. The results suggest that the extraction kinetics is a mixed regime with film diffusion and an aqueous one-step chemical reaction proposed to be the rate-controlling step. Assuming the mass transfer process can be formally treated as a pseudo-first-order reversible reaction with respect to the metal cation, the rate equation for the extraction reaction of yttrium(III) with Cyanex 302 at pH <5 is obtained as follows:R-f = 10(-7.85)[Y(OH)(2)(+)]((a))[H(2)A(2)]((o))(1.00)[H+]((a))(-1.00)Diffusion parameters and rate constants are calculated through approximate solutions of the flux equation.

Kinetics of Y(III) stripping for the system Y/HCl/Cyanex 272-P507/heptane with constant interfacial area cell with laminar flow

Kinetics and mechanism of stripping of yttrium(III) previously extracted by mixtures of bis(2,4,4-trimethylpentyl)phosphinic acid (Cyanex 272, HA), and 2-ethylhexyl phosphonic acid mono-2-ethylhexl ester (P507, HB) dissolved in heptane have been investigated by constant interfacial-area cell by laminar flow. The corresponding equilibrium stripping equation and equilibrium constant were obtained. The studies of effects of the stirring rate and temperature on the stripping rate show that the stripping regime is dependent on the stripping conditions. The plot of interfacial area on the rate has shown a linear relationship. This fact together with the strong surface activity of mixtures of Cyanex 272 and P507 at heptane-water interfaces makes the interface the most probable locale for the chemical reactions. The stripping rate constant is obtained, and the value is compared with that of the system with Cyanex 272 and P507 alone. It is concluded that the stripping ability with the mixtures is easier than that of P507 due to lower the activation energy of the mixtures. The stripping rate equation has also been obtained, and the rate-determining steps are the two-step interfacial chemical reactions as predicted from interfacial reaction models.

Kinetics of cerium(IV) extraction with DEHEHP from HNO3-HF medium using a constant interfacial cell with laminar flow

Studies of the extraction kinetics of cerium(IV) into n-heptane solutions of di(2-ethylhexyl)-2-ethylhexyl phosphonate DEHEHP from HNO3-HF solutions have been carried out using a constant interfacial cell with laminar flow. The experimental hydrodynamic conditions were chosen so that the contribution of diffusion to the measured rate of reaction was minimized. The data were analyzed in terms of pseudo-first order constants. The effects of the stirring rate, specific interfacial area, and temperature on the extraction rate showed that the most probable reaction zone is in the aqueous homogeneous phase. The results were compared with those of the system without HF. It was concluded that the presence of HF decreases the extraction rate of cerium. The addition of HF increases the activation energy for the forward reaction from 21.2 to 55.3 kJ/mol and for the reverse process from 57.9 to 79.0 kJ/mol. According to the experimental data correlated as a function of the concentration of the relevant species involved in the extraction reaction, the corresponding rate equation was deduced as follows:-d[Ce]/dt = k[Ce] center dot B-0.62 center dot HF-0.58 center dot [NO3-](0.57)

Kinetics and mechanism of Y(III) extraction with CA-100 using a constant interfacial cell with laminar flow

The Yttrium(III) extraction kinetics and mechanism with secnonylphonoxy acetic acid (CA-100) were investigated by a constant interfacial cell with laminar flow. The studies of interfacial tension and solubility of extractant and effects of the stirring rate, temperature, specific interfacial area and species concentration on the extraction rate showed that the extraction regime was dependent on the extraction conditions and the most probable reaction zone was at the liquid-liquid interface. The rate equation of extracting yttrium by CA-100 in heptane was Rf = k[Y3+]((a))[H(2)A(2)]((o))(0.88)[H+]((a))(-1.08).

The kinetics study in liquid-liquid systems with constant interfacial area cell with Laminar flow

A novel constant interfacial cell with laminar flow is proposed as an approach to obtain extraction kinetics data in liquid-liquid systems. Applications and theoretical fundamentals of the apparatus have been elaborated.. The equation which can express the mass transfer of liquid-liquid system run in the constant interfacial cell with laminar flow is deduced. Simulations from the equations indicate that diffusivity is a suitable factor to represent the characteristics of extraction kinetics rather than the extraction rate in the diffusion controlling step. The dependence of the aqueous phase concentration on time is recommended to determine the extraction regime. The diffusivities of the EuCl3-HDEHP extraction system obtained by different methods are compared to certify the hydrodynamic theory of the cell. The diffusivities of the ErCl3-HEH/EHP extraction system are determined, which show that this technique is a convenient method to obtain the diffusivities in the liquid-liquid system and to determine the extraction regime. (C) 1998 Elsevier Science Ltd. All rights reserved.

A Numerical Model of Rapid Solidification Processing of Ni-Al Alloy in Planar Flow Casting

A numerical model has been developed for simulating the rapid solidification processing (RSP) of Ni-Al alloy in order to predict the resultant phase composition semi-quantitatively during RSP. The present model couples the initial nucleation temperature evaluating method based on the time dependent nucleation theory, and solidified volume fraction calculation model based on the kinetics model of dendrite growth in undercooled melt. This model has been applied to predict the cooling curve and the volume fraction of solidified phases of Ni-Al alloy in planar flow casting. The numerical results agree with the experimental results semi-quantitatively.