Analysis of moving boundary problem of growth of Bismuth germanate crystal by heat exchanger method

Transient two-dimensional model of the growth of BGO crystal by heat exchanger method has been developed. A finite element method with nonorthogonal mapping technique for the solution of the moving boundary problem is developed where the melt/solid interface shape changes from hemispherical to planar. The moving boundary problems for the melt/solid interface location and the temperature field were solved by two mapping rule method which enables the computation of interface shape changing from hemispherical to planar. The maximum deflection of interface is shown when the melt/solid interface meets the corner of crucible. As the excess heating temperature and the heat exchanger temperature were increased, more growth time for whole process is required but the quality of BGO crystal may be improved. The ratio of the height to the radius of crucible hardly affects the deflection of BGO melt/solid interface when it is greater than 1.5. As the cooling zone radius is decreased, maximum deflection is decreased. The heat transfer between the crucible and the heating element should be suppressed to maximize planarity of the interface shape.     

ANALYTICAL SOLUTIONS FOR THE MOVING INTERFACE PROBLEM IN FREEZE-DRYING WITH OR WITHOUT BACK HEATING

A mathematical model for freeze-drying without back surface heating is established first in this paper by a combination of URIF (uniformly retreating ice front) and Sheng/Peck's theories. Explicit analytical expressions are obtained for the rates of interface movement and drying. The predicted drying rate and temperature profile are in good agreement with the Sheng/Peck's model results. Furthermore, the model is extended to the process of freeze-drying with back heating in which the temperature at the interface is assumed to increase along the path of movement. It is shown that the average rates for drying and interface moving may be obtained by assuming a quadric distribution for the interface temperature.     

ANALYTICAL SOLUTIONS FOR THE MOVING INTERFACE PROBLEM IN FREEZE-DRYING WITH OR WITHOUT BACK HEATING

ABSTRACT

A mathematical model for freeze-drying without back surface heating is established first in this paper by a combination of URIF (uniformly retreating ice front) and Sheng/Peck's theories. Explicit analytical expressions are obtained for the rates of interface movement and drying. The predicted drying rate and temperature profile are in good agreement with the Sheng/Peck's model results. Furthermore, the model is extended to the process of freeze-drying with back heating in which the temperature at the interface is assumed to increase along the path of movement. It is shown that the average rates for drying and interface moving may be obtained by assuming a quadric distribution for the interface temperature.     

Surface grafting of carbon fibers with artificial silver‐nanoparticle‐decorated graphene oxide for high‐speed electrical actuation of shape‐memory polymers

Poor heat conduction in the interface between the carbon fiber and polymer matrix is a problem in the actuation of shape‐memory polymer (SMP) composites by Joule heating. In this study, we investigated the effectiveness of grafting silver‐nanoparticle‐decorated graphene oxide (GO) onto carbon fibers to improve the electrothermal properties and Joule‐heating‐activated shape recovery of SMP composites. Self‐assembled GO was grafted onto carbon fibers to enhance the bonding of the carbon fibers with the polymeric matrix via van der Waal's forces and covalent crosslinking, respectively. Silver nanoparticles were further self‐assembled and deposited to decorate the GO assembly, which was used to decrease the thermal dissimilarity and facilitate heat transfer from the carbon fiber to the polymer matrix. The carbon fiber was incorporated with SMP to achieve the shape recovery induced by Joule heating. We found that the silver‐nanoparticle‐decorated GO helped us achieve a more uniform temperature distribution in the SMP composites compared to those without decoration. Furthermore, the shape‐recovery behavior and temperature profile during the Joule heating of the SMP composites were characterized and compared. A unique synergistic effect of the carbon fibers and silver‐nanoparticle‐decorated GO was achieved to enhance the heat transfer and a higher speed of actuation. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41673.     

SIMPLIFIED MODELLING FOR THE DRYING OF A NON HYGROSCOPIC CAPILLARY POROUS BODY USING A COMBINATION OF DIELECTRIC AND CONVECTIVE HEATING

The drying of non-hygroscopic, capillary porous materials with dielectric and convective heating is considered. Simplified models are used to examine the effect of a partially wetted surface or receding evaporation front on the temperature of the wet material. Physical mechanisms which can enhance the internal moisture flow, as compared with convective heating alone, are examined ualitatively.     

SIMPLIFIED MODELLING FOR THE DRYING OF A NON HYGROSCOPIC CAPILLARY POROUS BODY USING A COMBINATION OF DIELECTRIC AND CONVECTIVE HEATING

The drying of non-hygroscopic, capillary porous materials with dielectric and convective heating is considered. Simplified models are used to examine the effect of a partially wetted surface or receding evaporation front on the temperature of the wet material. Physical mechanisms which can enhance the internal moisture flow, as compared with convective heating alone, are examined ualitatively.     

Effect of the aspect ratio of the pre-existing rectangular adhesion failure on the structural integrity of the adhesively bonded single lap joint

Non-linear three dimensional (3-D) finite element analyses (FEA) of the single lap joints (SLJs) having pre-existing rectangular adhesion failure in the interface of the strap adherend and the adhesive have been carried out. The effect of the size, the shape and the aspect ratio of the pre-existing rectangular adhesion failure on (i) the strength, (ii) the interfacial stresses and (iii) the strain energy release rates (SERRs) in the vicinity of the adhesion failure front have been presented in this research work. The SLJ is subjected to uniformly applied tensile load. The adherends are made with very high strength steels and the adhesive is a commercially available AV119. The analyses of the adhesion failure propagation have been carried out by sequentially releasing the constraints of the nodes ahead of the pre-existing adhesion failure front in finite element model. The SERR values in the vicinity of the adhesion failure fronts are computed using the virtual crack closure technique (VCCT) for assessment of the structural integrity of the SLJ. The strength of the SLJ, the interfacial stresses, and the three modes of strain energy release rates (SERRs) have been found to be significantly affected by the shape and size of adhesion failures. The SERRs and interfacial stresses along the rectangular adhesion failure front are compared with the corresponding values around the circular adhesion failure front of same area, pre-existing in the SLJ. It is observed that the circular and rectangular adhesion failures of the same area will have dissimilar growth rate and the mode II is the dominant failure mode. The total strain energy release rate and the failure strength, computed from the 3-D FEA of the SLJ is in good agreement with the experimental fracture toughness of the AV119 adhesive and the experimentally obtained failure loads, respectively.     

Regime II–III transition in isotactic polybutene-1 tetragonal crystal growth

The lateral growth rate and growth shape morphology of isotactic polybutene-1 tetragonal crystals were investigated for crystallization from the melt at temperatures of 68–101 °C. The growth rate of tetragonal crystals shows supercooling dependence derived from the nucleation theory, and a regime II–III transition is observed at temperatures of 77–82.2 °C. The morphology of single crystals is rounded below temperatures of 77–85 °C, while the growth shape has a faceted morphology at a higher crystallization temperature of 100 °C. The kinetic roughening transition occurs between 77 and 85 °C. The regime II growth mode is observed above 82.2 °C and proceeds by multiple nucleation on the faceted growth front, while the regime III growth mode is observed below 77 °C and proceeds by rough surface growth on the kinetically roughened growth front. The observed regime II–III transition can therefore be explained by the morphology transition of crystal growth shape.     

Growth rate effect on colony formation in directional solidification of Al2O3/YAG/ZrO2

Mechanical properties of Al₂O₃/Y₃Al₅O₁₂/ZrO₂ ternary eutectic ceramics are strongly affected by structural defects as pores or colonies. Experimental investigation of the microstructure of this ternary composite indicates that the colonies are generally observed when the solidification occurs at high rates. In this work, the influence of the growth rate on the solid-liquid interface shape and formation of colonies in directional solidification of Al₂O₃/Y₃Al₅O₁₂/ZrO₂ by Bridgman, Edge-defined Film-fed Growth (EFG), and Czochralski (Cz) methods is numerically and experimentally investigated. Numerical modeling of the Bridgman growth process shows large curvatures of the solid-liquid interface when the pulling rate is increased up to 80 mm/h. The ingots solidified at rates between 5 and 80 mm/h exhibit colony type microstructure. The analysis of EFG growth of ceramic ribbons reveals less curved solid-liquid interfaces in this system. Numerical modeling shows significant increase in the interface curvature with increasing pulling rate. The microstructure of ribbons grown at pulling rates between 6 and 12 mm/h exhibits colonies only for the ingots solidified at higher rate. Simulations carried out for Czochralski growth process show that the solidification front is almost plane in this system. These results are in agreement with experimental observations showing good structural quality of Cz grown crystals with a flat solid-liquid interface. Finally it is concluded that formation of colonies in directional solidification of this ternary eutectic composite is linked to large curvatures of the growth interface.     

Evolution of thermoelastic strain and dislocation density during sublimation growth of silicon carbide

The evolution of crystallization front and growth conditions during sublimation growth of SiC bulk crystal is studied using a coupled heat and mass transport two-dimensional model. It is shown, in particular, that movement of the inductor coil used for heating of the growth crucible modifies the temperature profile at the growth surface but can have no remarkable effect on the growth rate.Anisotropic elasticity theory and a semi-empirical model of dislocation generation are applied for a detailed analysis of thermoelastic strain and dislocation density evolution during SiC bulk crystal growth. An important effect of a method of SiC seed attachment to the holder is revealed by modeling. It is shown that under optimal attachment, the maximum dislocation density is concentrated near the crystallization front at the periphery of the crystal. The region of high dislocation density expands with enlargement of the crystal.     

卧式三重套管高温余热回收装置

通过对近年来合成氨系统高温余热回收装置的分析,采用直连式卧式三重套管废热锅炉,使高温部件不承受高压、高压部件不承受高温,保证了生产的安全经济运行,并降低了设备的投资成本。     

Studies on thermally stimulated shape memory effect of segmented polyurethanes

The shape memory behavior of a series of polycaprolactone/methane diisocyanate/butanediol (PCL/MDI/BDO) segmented polyurethanes of different composition was studied. The molecular weight of PCL diols was in the range of 1600–7000, and the hard segment content varied from 7.8 to 27% by weight. Film specimens for shape memory measurements were prepared by drawing at temperatures above the melting temperature of the soft segment crystals and subsequent quick cooling to room temperature under constrained conditions. The shape memory process was observed and recorded in a heating process. Parameters describing the recovery temperature, ability, and speed were used to study the influence of structure and processing conditions on the shape memory behavior of the sample. It was found that the high crystallinity of the soft segment regions at room temperature and the formation of stable hard segment domains acting as physical crosslinks in the temperature range above the melting temperature of the soft segment crystals are the two necessary conditions for a segmented copolymer with shape memory behavior. The response temperature of shape memory is dependent on the melting temperature of the soft segment crystals. The final recovery rate and the recovery speed are mainly related to the stability of the hard segment domains under stretching and are dependent on the hard segment content of the copolymers. © 1997 John Wiley & Sons, Inc. J Appl Polym Sci 64: 1511–1516, 1997     

聚丙烯低速拉伸时的形变特征

本文利用扫描电镜拉伸工作台观察了聚丙烯样条(带单边切口和不带切口两种样条)在低速拉伸时的形变特征。聚丙烯样条在低速拉伸时,先产生银纹和微裂纹,裂纹方向垂直于作用力方向,继续拉伸,可见到剪切屈服变形,剪切区的微裂纹方向与作用力方向平行。聚丙烯样条剪切区的取向强化效应和微裂纹转向与作用力方向一致是聚丙烯低速拉伸时表现出韧性的两个主要因素。具有单边切口的聚丙烯样条在低速拉伸时,尖端裂缝发展可分为3个阶段,即首先在切口尖端前方产生微裂纹,形成一个椭圆形区域,接着在切口尖端前方产生微孔,并进一步形成空洞,最后尖端裂缝与空洞并合,使裂缝向前发展,最终导致样条断裂。     

Numerical Simulation of Semiconductor Crystal Growth by Directional Melt Solidification

A new method is suggested for solving the Stefan problem for crystal growth by directional solidification. The problem is treated as an essentially unsteady one. The conditions ensuring a constant growth rate and the controllability of the shape of the crystallization front are found. The observed and calculated data are in satisfactory agreement. The effect of an oscillating external force on the melt that initiates macrosegregation is analyzed. It is demonstrated that fluctuations of the crystal growth rate cause the formation of transverse growth striations. The radial inhomogeneity of the crystal is investigated.     

Direct Numerical Simulations of Three‐Layer Viscosity‐Stratified Flow

Two‐dimensional simulations of flow instability at the interface of a three‐layer, density‐matched, viscosity‐stratified Poiseuille flow are performed using a front‐tracking/finite difference method. This is an extension of the study for the stability of two‐layer viscosity‐stratified flow of Cao et al., Int. J. Multiphase Flow, 30 , 1485‐1508 (2004). We present results for large‐amplitude non‐linear evolution of the interface for varying viscosity ratio m, Weber number We, and phase difference between the perturbations of the two interfaces. Strong non‐linear behaviour is observed for relatively large initial perturbation amplitude. The higher viscosity fluid is drawn out as a finger that penetrates into the lower viscosity layer. The finger originates at the crest of the perturbation at the interface. The simulated interface shape compares well with previously reported experiments. Increasing interfacial tension retards the growth rate of the interface as expected, whereas increasing the viscosity ratio enhances it. The sinuous instability appears to evolve faster than the varicose one. For certain flow parameters the high‐viscosity finger displays a bulbous tip, which is also seen in our previously conducted experiments and two‐layer results, although it is less pronounced. The low‐viscosity intruding finger does not display this curious bulbous tip. Drop formation is precluded by the two‐dimensional nature of the calculations.     

Filling thin cavities of variable gap thickness: A numerical and experimental investigation

A theoretical and experimental investigation is presented for filling thin cavities of variable gap thickness. The modeling is based upon a finite-element/finite-difference formulation for an inelastic power-law fluid and includes the effects of viscous heating and conduction upon the flow dynamics. Extensive results are presented for polypropylene and polystyrene melts injected into two variable-gap-thickness cavities, of which one has an insert. Good agreement is found between the predictions and measurements concerning the shape of the advancing melt front, the location of weld lines, and the temporal pressure trace at various positions in the cavity.     

Thermal-solutal flows and segregation and their control by angular vibration in vertical Bridgman crystal growth

Thermal-solutal flows and their induced segregation and supercooling are important in the growth of an alloy crystal. For the vertical Bridgman crystal growth having a stabilized thermal profile, in addition to the thermal convection induced by radial thermal gradients, solute gradients can either induce or suppress the flow depending on the solute density. Such thermal-solutal flows significantly affect the segregation behavior, constitutional supercooling, and thus the morphological instability of the solidification front. A transparent Bridgman growth of succinonitrile containing a lighter (acetone) or heavier (salol) solute was investigated. The evolution of the interface shape as well as morphological instability was visualized and was interpreted through computer simulation. To further control the flow and segregation, angular vibration was applied and its effects on the thermal-solutal flows and morphological instability were investigated.     

A model of advancing flow front in RIM

A two-dimensional model is developed for mold filling in Reaction Injection Molding using a Petrov-Galerkin finite-element method with free surface parameterization. Dependence of viscosity on the conversion and temperature is represented by the Castro-Macosko function. The model predicts the velocity, pressure, temperature, and conversion distributions with time during the filling stage of a rectangular mold. No a priori assumptions are made regarding the shape of the advancing flow front, or regarding any variables in the flow front region. The accuracy is further improved by using the Petrov-Galerkin formulation, rather than the Galerkin formulation. The results are presented for well-characterized polyurethane systems, for which reliable experimental data is available. The predictions of the model for the pressure rise are in excellent agreement with the experimental data (1) even close to the gel point. These refined predictions are expected to assist in estimating fiber orientation and bubble growth in the final RIM parts, in which the flow front region plays the most important role. Characterization of polyurethane/polyurea and polyurea materials is underway, and will be subsequently incorporated in the model.     

CREEPING MOTION OF A BUBBLE WITH FIXED SURFACE CHARGE IN A UNIFORM ELECTRIC FIELD

Approximate solutions of the shape function and the electrophoretic movement of a bubble in an aqueous medium with ionized detergent and a small number of electrolytes under the influence of uniform electric field are derived. Specifically, a bubble that has the interface saturated and densely packed with detergent molecules is considered, and the charges were deemed to be fixed provided the position change among the detergent molecules is hindered relative to the free molecule. The surface tension at the interface is weakened with the addition of the detergent, and the deformation can be significant. The variation of the shape of the bubble was represented by the Legendre polynomial and the perturbed velocity profile was used to derive the drag force for the deformed bubble. The speed and size of the bubble was assumed to be very small so that the flow around it is in the creeping flow regime. The shape of the bubble with fixed surface charge undergoes a prolate deformation with axial symmetry around the axis parallel to the direction of the electric field and exhibits asymmetry with respect to the plane that goes through the center of the bubble and is perpendicular to the axis. But this asymmetry is not significant unless the surface charge density and the electric field are very large. Only symmetric deformation governs the movement, and, consequently, the drag force is not dependent on the sign of surface charge. As the bubble becomes more slender with deformation, the movement is enhanced.     

Dynamics of the phase inversion process

An analysis of the dynamics of phase inversion based on mathematical modeling and in situ experimental observations is presented. Calculations based on ternary diffusion models illustrate the effects of casting film composition, evaporation time, and film thickness on the precipitation time and resulting polymer film profiles, which correlate with observed final morphologies. An experimental method based on the use of dark ground optics, interface visualization, and reflected light illumination is used for in situ monitoring of the mass transfer and phase separation dynamics during the quench step. Observations on the systems water—dimethylsulfoxide cellulose acetate and water—dioxane—cellulose acetate show regions in the films corresponding to gel formation and growth, instabilities associated with finger formation, and homogeneous ternary diffusion. Data for the kinetics of the diffusion and gel front motions show that both propagate as the square root of time with rates dependent on the bath—film compositions. Examples of interface structures characteristic of deep quenching and nucleated droplet growth are also shown. Semiquantitative analyses in terms of the ternary models developed earlier and a phenomenological model for diffusion in the growing gel are used to explain the trends seen. © 1992 John Wiley & Sons, Inc.