Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. IV. Flow rates in the presence of free and forced convections proceeding in the same direction

An experimental simulation study has been carried out on the convection flow rate under the crystal during its growth from a high-temperature solution by the TSSG method with prevailing heating of the crucible bottom and in the presence of simultaneous free and forced convections occurring in the same direction. It has been established that with increasing proportion of forced convection the rate of the resultant upflow passes through a minimum. Immediately before this minimum the flow is instable with respect to time. The minimum is observed at a definite ratio between the determining dimensionless numbers Gr and Re, which depends on the crystal diameter alone. A correlation allowing determination of the flow rate after the minimum has been found.     

Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. V. Shape of the crystal/liquid interface in the presence of simultaneous free and forced convections

The formation conditions of a concave, convex or flat crystal/liquid interface in the presence of simultaneous free and forced convections have been investigated using model liquids. Simultaneous free and forced convections with both the same and opposite flow directions have been considered. The interface shape was found to depend on the direction and rate of the resultant convection flow under the crystal. The formation conditions of a flat interface for liquids having kinematic viscosities of 0.001·10^?3 – 0.5·10^?3 m²/s and for crystal diameters of 10, 15 and 20 mm, respectively, have been established. These conditions have been compared with the optimum conditions found experimentally by other authors for the growth of several kinds of crystals from high-temperature solutions by the TSSG method and from melts by the Czochralski method. The comparison has shown that the model proposed describes well the real processes.     

Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. I. Forced convection

Investigations on forced convection have been carried out in model liquids (glycerol and glycerol-water containing 70, 80, 90 and 95 vol.% glycerol) with parameters corresponding to those of high-temperature solutions for crystal growth. Dependences between the rate of convection flow and the system parameters have been found for different interface shapes (flat, concave and convex). The explicit form of these functions has been established.     

Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. II. Free convection

Investigations have been carried out on the free convection in model liquids (glycerol, glycerol-water solutions, silicone oil and liquid paraffin). All possible heating conditions and temperature profiles for growing crystals from high-temperature solutions have been considered. Dependences between the rate of the up (down) convection flow and the parameters of the liquid have been established and the explicit form of these dependences has been found.     

Simulation studies of the hydrodynamics in high-temperature solutions for crystal growth. VI. Temperature fluctuations at the crystal/liquid interface

The temperature fluctuations at the crystal/liquid interface have been studied using model liquids. The character of the fluctuations varied depending on whether in the liquid there was only free convection or both free and forced convections were simultaneously present. It has been established that in the second case the amplitude of fluctuations is determined mainly by the rate of the resultant convection flow and the liquid viscosity. A maximum amplitude of fluctuations is observed at a resultant flow rate w_fl = O when the free and forced convections proceed in opposite directions, and at w_fl = min when both convection flows have the same direction. Larger amplitudes of temperature fluctuations are registered in low-viscosity liquids. The conditions under which a flat crystal/liquid interface showing no temperature fluctuations should be formed have been determined for crystal diameters of 10, 15 and 20 mm, respectively.     

A numerical study of similarity solutions for combined forced and free convection

Summary The similarity equations for combined forced and free convection flow over a horizontal plate when the wall temperature is inversely proportional to the square root of the distance from the leading edge are solved by introducing a scaling similar to that for the Blasius equation. The technique is also applied to the local similarity equations for the case of a constant wall temperature.With 7 Figures     

Dispersion of solutes in combined free and forced convective flow through a channel

Summary Dispersion of a solute in combined free and forced convective laminar flow through a parallel plate channel has been considered, when there is a uniform axial temperature variation along the channel walls. It is observed that the effective Taylor diffusion coefficient increases with increase in Grashof number and also the interesting fact that it is same for both heating and cooling of the plates.

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Dispersion von Lösungen bei freier und erzwungener Konvektion in einem Kanal

Zusammenfassung Es wird die Dispersion einer Lösung bei freier und erzwungener Konvektion in einem Kanal mit parallelen Wänden untersucht, falls ein konstanter horizontaler Temperaturgradient an den Kanalwänden auftritt. Es wird festgestellt, daß der effektive Taylor-Diffusionskoeffizient ansteigt mit wachsender Grashof-Zahl, und zwar gilt dies unverändert für Kühlung oder Heizung der Wände.

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With 1 Figure     

Turbulent forced flow and heat exchange in vertical channels in conditions of free convection

Based on a unified approach, data are analyzed and generalized concerning the distributions of velocity and temperature, frictional resistance and heat transfer in the case of turbulent free-convective flow, and forced flow in conditions of the significant effect of the gravitational field.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 801–811, November, 1978.     

Quartz crystal microbalance studies of polymer gels and solutions in liquid environments

Spreading of liquids and soft solids on a rigid surface in a surrounding liquid medium is investigated by utilizing the lateral sensitivity of the quartz crystal microbalance (QCM). While the QCM has been used extensively to study systems with spatial variations in the direction normal to the crystal's electrodes, few studies have exploited the QCM's ability to sense changes in loading in the plane of the electrodes. We propose equations to describe the predicted response of the QCM to a generalized viscoelastic material spreading at the QCM surface at the expense of the surrounding liquid medium. Several experimental examples are given in order to support the validity of the proposed equations, including situations where the spreading material is a Newtonian liquid, a viscoelastic liquid, or one of two viscoelastic solids. The first viscoelastic solid is a physically cross-linked gel based on a styrene/ethylene-butene/styrene triblock copolymer in mineral oil, and the second is a cross-linked poly(ethylene glycol) hydrogel.     

Simulation of bead-and-spring chain models for semidilute polymer solutions in shear flow

We report preliminary results of simulations of the steady-state rheological behavior for semidilute polymer solutions of head-and-spring chain models in planar Couette now. The simulations include examination of the effects of excluded volume. hydrodynamic interactions and density. Hydrodynamic interactions are modeled by the Rotne -Prager Yamakawa tensor. The simulations are based on the nonequilibrium Brownian dynamics algorithm of Ermak and McCammon. In addition to the spring potential between neighboring beads in the chain. the interaction between any two beads in the solution is modeled using a shifted, repulsive Leonard-Jones potential. Lees Edward sliding brick boundary conditions are used for consistency with the Couette flow field.Paper presented at the Twelfth Symposium on Thermophysical Properties. June 19–24. 1994, Boulder. Colorado. U.S.A.     

A generalized method for determining the crystal nucleation and growth rates in glasses by differential thermal analysis

A generalized experimental method that uses differential thermal analysis (DTA) has been developed for determining the nucleation rate (I), the crystal growth rate (U), and the concentration of quenched-in nuclei (N _q) in glasses. The method is applicable even for glasses, whose I and U curves (as a function of temperature) overlap to a considerable degree. Measuring I by the conventional method may yield an overestimated value for I if the chosen crystal growth temperature is within the region of overlap between I and U. When applied to a Na₂O · 2CaO · 3SiO₂ glass, whose I and U curves are known to overlap considerably, the present DTA method yields values for I, U, and N _q that are in excellent agreement with the same values determined by the conventional methods.     

Analytical solutions for free and forced vibrations of a multiple cracked Timoshenko beam subject to a concentrated moving load

An analytical approach for evaluating the forced vibration response of uniform beams with an arbitrary number of open edge cracks excited by a concentrated moving load is developed in this research. For this purpose, the cracked beam is modeled using beam segments connected by rotational massless linear elastic springs with sectional flexibility, and each segment of the continuous beam is assumed to satisfy Timoshenko beam theory. In this method, the equivalent spring stiffness does not depend on the frequency of vibration and is obtained from fracture mechanics. Considering suitable compatibility requirements at cracked sections and corresponding boundary conditions, characteristic equations of free vibration response are derived. Then, forced vibration response is treated under a moving load with a constant velocity. Using the determined eigenfunctions, the forced vibration response may be obtained by the modal superposition method. Finally, some parametric studies are presented to show the effects of crack parameters and moving load velocity.     

Finite element solutions of free convective Casson fluid flow past a vertically inclined plate submitted in magnetic field in presence of heat and mass transfer

The aim of this research work is to study the influence of thermal radiation on steady magnetohydrodynamic-free convective Casson fluid flow of an optically thick fluid over an inclined vertical plate with heat and mass transfer. Combined phenomenon of heat and mass transfer is considered. Numerical solutions in general form are obtained by using the finite element method. The sum of thermal and mechanical parts is expressed as velocity of fluid. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained numerical solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Numerical results for the controlling flow parameters are drawn graphically and discussed in detail. In some special cases, the obtained numerical results are compared and found to be in good agreement with the previously published results which are available in literature. Applications of this study includes laminar magneto-aerodynamics, materials processing and magnetohydrodynamic propulsion thermo-fluid dynamics, etc.     

Influence of water content on the rates of crystal nucleation and growth in lithia-silica and soda-lime-silica glasses

Two sets of glasses were studied with compositions close to Li₂O·2SiO₂ and Na₂O·2CaO·3SiO₂, and with water contents ranging from 0.019 to 0.136 wt% and 0.007 to 0.040 wt%, respectively. The crystal nucleation and growth rates increased markedly with increase in water content, whereas the viscosities of the glasses decreased. For the lithia glasses, increases in nucleation rates at various temperatures closely corresponded to reductions in viscosity, indicating that the main effect of water was to lower the kinetic barrier to nucleation (G _D), rather than to alter the thermodynamic barrier to nucleation (W*). For the soda-lime glasses, G _D was also lowered by water content but additional effects due to differences in base compositions were observed. The kinetic barriers to growth were lowered by water content for both sets of glasses, increases in growth rates corresponding closely to reductions in the viscosities. It is suggested that the large effects of water on nucleation and growth may be due to an increase in the oxygen ion diffusion coefficient. In the soda-lime glasses addition of sodium fluoride produced similar effects to the addition of water. Liquidus temperature measurements, and the results of DTA, optical microscopy and electron microscopy are also reported.     

Electrophoretic separation of small DNA fragments in the presence of electroosmotic flow using poly(ethylene oxide) solutions.

A new and simple method was demonstrated for separating phi X-174/Hae III DNA restriction fragments and DNA markers V and VI, respectively, without filling capillaries with polymer solutions prior to analysis. Using this novel method, poly(ethylene oxide) (PEO) solutions containing ethidium bromide migrated into capillaries by electroosmotic flow (EOF) during the separation. Two DNA fragments (123 and 124 bp) in markers V and VI were well-resolved. RSD values for the separation of phi X-174/Hae III DNA restriction fragments were less than 0.52% for 3 runs using a single 75-micron capillary and less than 3.96% using three different 75-micron capillaries. A highly viscous polymer solution prepared from 3% PEO was also used for separation of DNA markers V and VI. Theoretical plates up to 11.91 million/m and separation times of less than 7 min were achieved in the separation of phi X-174/Hae III DNA restriction fragments using a 10-micron capillary and a 2% PEO solution. Advantages of this method include simplicity, short separation times, the ability to use highly viscous polymer solutions for separating small DNA fragments, and the possibility of introducing several different polymer solutions into capillaries to extend the DNA separation range.     

硅单晶Czochralski法生长全局数值模拟I．传热与流动特性

利用有限元方法对炉内的动量和热量传递过程进行了全局数值模拟，研究了硅单晶Czochral—ski(Cz)法生长时的总体传热和流动特性假定熔体和气相中的流动都为准稳态轴对称层流，熔体为不可压缩流体，Cz炉外壁温度维持恒定，模拟结果表明：熔体流型及炉内传热特性与Marangoni效应密切相关，设置在晶体和坩埚间的气体导板能降低加热器的功率并改变熔体流型．     

水平HVPE反应器中气流动力学模拟与GaN生长

建立了GaN HVPE系统的流体动力学模型，研究了反应气体在反应室内的浓度场，讨论了反应室内GaCl和NH3管道空间配置对气体在衬底表面浓度分布的影响，并对HVPE系统反应室的设计进行了优化。材料生长结果表明，厚度均匀性良好，直接在蓝宝石衬底上生长的GaN外延层摇摆曲线半宽为660aresee。     

Simulation of dendritic growth in the platform region of single crystal superalloy turbine blades

A cellular automaton model of the solid-liquid interface, combined with a finite difference computation of solute diffusion has been developed to simulate single crystal solidification in molds with step changes in geometry. Simulations were carried out for columnar dendrites passing from the narrow airfoil region of a blade into the platform region, which has an increased cross-sectional area. Different shapes of isotherms moving at a constant velocity were considered in the simulations. The change in mold geometry leads to a significant increase in the undercooling in front of the dendrite tips as they spread around the mold corner. The model was applied to geometries investigated by prior authors, correctly predicting the formation of a <001> to <010> boundary observed experimentally.