Effects of the orientation of microgravity on the concentration distribution in crystallization from solution

A quasi-steady state growth and dissolution in a 2-D rectangular enclosure is numerically investigated. This paper is an extension to indicate the effects of the orientation of gravity on the concentration field in crystallization from solution under microgravity, especially on the lateral non-uniformity of concentration distribution at the growth surface. The thermal and solute convection are included in this model.

Optical Diagnostic and Modeling Solution Growth Process of Sodium Chlorate Crystals

Both a real time optical interferometric experiment and a numerical simulation of two-dimension non-steady state model were employed to study the growth process of aqueous sodium chlorate crystals. The parameters such as solution concentration distribution, crystal dimensions, growth rate and velocity field were obtained by both experiment and numerical simulation. The influence of earth gravity during crystal growth process was analyzed. A reasonable theory model corresponding to the present experiment is advanced. The thickness of concentration boundary layer was investigated especially. The results from the experiment and numerical simulation match well.

The Flow Theory of Mechanism-Based Strain Gradient Plasticity

The flow theory of mechanism-based strain gradient (MSG) plasticity is established in this paper following the same multiscale, hierarchical framework for the deformation theory of MSG plasticity in order to connect with the Taylor model in dislocation mechanics. We have used the flow theory of MSG plasticity to study micro-indentation hardness experiments. The difference between deformation and flow theories is vanishingly small, and both agree well with experimental hardness data. We have also used the flow theory of MSG plasticity to investigate stress fields around a stationary mode-I crack tip as well as around a steady state, quasi-statically growing crack tip. At a distance to crack tip much larger than dislocation spacings such that continuum plasticity still applies, the stress level around a stationary crack tip in MSG plasticity is significantly higher than that in classical plasticity. The same conclusion is also established for a steady state, quasi-statically growing crack tip, though only the flow theory can be used because of unloading during crack propagation. This significant stress increase due to strain gradient effect provides a means to explain the experimentally observed cleavage fracture in ductile materials [J. Mater. Res. 9 (1994) 1734, Scripta Metall. Mater. 31 (1994) 1037; Interface Sci. 3(1996) 169].

Vibration of an Adhered Microbeam Under a Periodically Shaking Electrical Force

The vibration analysis of an adhered S-shaped microbeam under alternating sinusoidal voltage is presented. The shaking force is the electrical force due to the sinusoidal voltage. During vibration, both the microbeam deflection and the adhesion length keep changing. The microbeam deflection and adhesion length are numerically determined by the iteration method. As the adhesion length keeps changing, the domain of the equation of motion for the microbeam (unadhered part) changes correspondingly, which results in changes of the structure natural frequencies. For this reason, the system can never reach a steady state. The transient behaviors of the microbeam under different shaking frequencies are compared. We deliberately choose the initial conditions to compare our dynamic results with the existing static theory. The paper also analyzes the changing behavior of adhesion length during vibration and an asymmetric pattern of adhesion length change is revealed, which may be used to guide the dynamic de-adhering process. The abnormal behavior of the adhered microbeam vibrating at almost the same frequency under two quite different shaking frequencies is also shown. The Galerkin method is used to discretize the equation of motion and its convergence study is also presented. The model is only applicable in the case that the peel number is equal to 1. Some other model limitations are also discussed.

Peeling Experiments Of Ductile Thin Films Along Ceramic Substrates - Critical Assessment Of Analytical Models

Two types of peeling experiments are performed in the present research. One is for the Al film/Al2O3 substrate system with an adhesive layer between the film and the substrate. The other one is for the Cu film/Al2O3 substrate system without adhesive layer between the film and the substrate, and the Cu films are electroplated onto the Al2O3 substrates. For the case with adhesive layer, two kinds of adhesives are selected, which are all the mixtures of epoxy and polyimide with mass ratios 1:1.5 and 1:1, respectively. The relationships between energy release rate, the film thickness and the adhesive layer thickness are measured during the steady-state peeling process. The effects of the adhesive layer on the energy release rate are analyzed. Using the experimental results, several analytical criteria for the steady-state peeling based on the bending model and on the two-dimensional finite element analysis model are critically assessed. Through assessment of analytical models, we find that the cohesive zone criterion based on the beam bend model is suitable for a weak interface strength case and it describes a macroscale fracture process zone case, while the two-dimensional finite element model is effective to both the strong interface and weak interface, and it describes a small-scale fracture process zone case. (C) 2007 Elsevier Ltd. All rights reserved.

Shock wave reflection from a wedge in a dusty gas

The present paper contains a detailed study of shock wave reflection from a wedge placed in various suspensions. In past works, the incident shock propagated initially in pure gas and the suspension started only at the leading edge of the deflecting wedge. However, in the present case the entire flow field is filled with a gas-dust suspension and the initial shock wave has steady-state structure relative to the shock front. In former studies the transmitted shock wave starts its propagation into the suspension and is reflected from the wedge at the same time. It is therefore obvious that the two unrelated processes of (2D) reflection and (1D) "transitional" relaxation occur simultaneously. In the present case the suspension behind the incident shock wave has reached steady state (i.e., it is a traveling wave) before the shock reaches the wedge leading edge. The reflection process from the deflecting wedge is studied for different dust mass loadings and different dust-particle diameter. It is shown that when the dust loading is low and the dust particle diameter is small the wave reflection pattern is similar to that observed in a similar pure gas case. In addition, an equilibrium state is reached, behind the evolved waves, very quickly. On the other hand, when the dust loading is relatively high and/or the dust particle diameter is relatively large, the observed reflection wave pattern is very different from that seen in a similar pure gas case. In such cases it takes much longer time to reach an equilibrium state behind the reflecting waves. It is also shown that the dust presence significantly affects the (gas) pressure on the wedge surface. The higher the dust loading is, the higher the pressure on the wedge surface. Suspensions composed of solid particle of different size, but having the same dust mass loading, will approach the same equilibrium pressure. However, it will take longer time to reach an equilibrium state for suspensions having large diameter particles. (C) 2004 Elsevier Ltd. All rights reserved.

Concentration distribution in crystallization from solution under microgravity

Concentration distribution in crystallization from solution under microgravity is numerically studied. A quasi-steady state growth and dissolution in a 2D rectangular enclosure filled with sodium chlorate (NaClO3) aqueous solution, in which one wall is the growth surface of the crystal and the opposite one is the dissolution surface, is considered. The solute transport process at the growth surface is described by the diffusion-reaction theory with finite interface kinetics coefficient. The results show that the concentration at the growth surface is supersaturated and the supersaturation distribution is of non-uniformity, i.e. the supersaturation in a region facing an incoming flow is high. On the other hand, the non-uniformity of supersaturation at the growth surface is closely related to the gravity level even under microgravity, it exponentially increases as the thermal Rayleigh number on behalf of the gravity level rises.

Jet:progress in performance and understanding

In 1990 JET operated with a number of technical improvements which led to advances in performance and permitted the carrying out of experiments specifically aimed at improving physics understanding of selected topics relevant to the "NEXT STEP". The new facilities include beryllium antenna screens, a prototype lower hybrid current drive system, and modification of the NI system to enable the injection of He-3 and He-4. Continued investigation of the hot-ion H-mode produced a value of n(D)(0)tau-E(T)(i)(0) = 9 x 10(20)m-3s keV, which is near conditions required for Q(DT) = 1, while a new peaked density profile H-mode was developed with only slightly lower performance. Progress towards steady state operation has been made by achieving ELMy H-modes under certain operating conditions, while maintaining good tau-E values. Experimental simulation of He ash transport indicates effective removal of alpha-particles from the plasma core for both L and H mode plasmas. Detailed analyses of particle and energy transport have helped establish a firmer link between particle and energy transport, and have suggested a connection between reduced energy transport and reversed shear. Numerical and analytic studies of divertor physics carried out for the pumped divertor phase of JET have helped clarify the key parameters governing impurity retention, and an intensive model validation effort has begun. Experimental simulation of alpha-particle effects with beta-fast up to 8% have shown that the slowing down processes are classical, and have given no evidence of deleterious collective effects.

Kinetic theory for particle concentration distribution in two phase flow

The results of experiments in open channels and closed pipelines show two kinds of patterns for the vertical distribution of particle concentration (i.e., pattern I and pattern II). The former shows a pattern of maximum concentration at some location above the bottom and the downward decay of the concentration below the location. The latter always shows an increase of the particle concentration downward over the whole vertical, with the maximum value at the bottom. Many investigations were made on the pattern II, but few were made on pattern I. In this paper, a particle velocity distribution function is first obtained in the equilibrium state or in dilute steady state for the particle in two-phase flows, then a theoretical model for the particle concentration distribution is derived from the kinetic theory. More attention is paid to the predictions of the concentration distribution of pattern I and comparisons of the present model are made with the data measured by means of laser doppler anemometry (LDA). Very good agreements are obtained between the measured and calculated results.

Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

在激波波面中氧分子的非平衡离解

对强激波作用下双原子分子振动与离解耦合的非平衡离解过程进行了理论计算.本工作的特点是将计算起点建立在分子基本参数上,采用主方程理论处理振动与离解的耦合,振动跃迁几率用SSH理论计算,在离解限附近考虑多量子数跃迁并计及原子复合的影响.对O2-Ar体系,计算给出了在正激波后O2分子振动能级分布、振动弛豫时间、离解孕育时间、离解产物浓度、离解速率系数等物理量随时间的演化.计算结果分别与Camac和Wray的实验相符.计算显示,在激波作用的后期,有准稳态的振动能级布居分布.计算结果显示,Park模型低估了非平衡离解速率系数,Hansen模型则高估了非平衡离解速率系数.

The Propagation Characteristics of Microwave in a Non-Equilibrium Plasma Layer

The influence of non-equilibrium plasma layer pressure and thickness on the transmission of microwave is considered when the incidence of wave is at an arbitrary angle. The plasma is cold, weakly ionized, and steady-state. It is assumed that it is a layered media with a kind of distribution of electron number density and the microwave is a plane wave. The results show that the pressure of plasma affects the absorption of microwave deeply, and the thickness relatively weakly in a non-equilibrium plasma slab.

3D Finite Volume Scheme for Czochralski Single Crystal Growth

Czochralski (Cz) technique, which is used for growing single crystals, has dominated the production of single crystals for electronic applications. The Cz growth process involves multiple phases, moving interface and three-dimensional behavior. Much has been done to study these phenomena by means of numerical methods as well as experimental observations. A three-dimensional curvilinear finite volume based algorithm has been developed to model the Cz process. A body-fitted transformation based approach is adopted in conjunction with a multizone adaptive grid generation (MAGG) technique to accurately handle the three-dimensional problems of phase-change in irregular geometries with free and moving surfaces. The multizone adaptive model is used to perform a three-dimensional simulation of the Cz growth of silicon single crystals.Since the phase change interface are irregular in shape and they move in response to the solution, accurate treatment of these interfaces is important from numerical accuracy point of view. The multizone adaptive grid generation (MAGG) is the appropriate scheme for this purpose. Another challenge encountered is the moving and periodic boundary conditions, which is essential to the numerical solution of the governing equations. Special treatments are implemented to impose the periodic boundary condition in a particular direction and to determine the internal boundary position and shape varying with the combination of ambient physicochemical transport process and interfacial dynamics. As indicated above that the applications and processes characterized by multi-phase, moving interfaces and irregular shape render the associated physical phenomena three-dimensional and unsteady. Therefore a generalized 3D model rather than a 2D simulation, in which the governing equations are solved in a general non-orthogonal coordinate system, is constructed to describe and capture the features of the growth process. All this has been implemented and validated by using it to model the low pressure Cz growth of silicon. Accuracy of this scheme is demonstrated by agreement of simulation data with available experimental data. Using the quasi-steady state approximation, it is shown that the flow and temperature fields in the melt under certain operating conditions become asymmetric and unsteady even in the absence of extrinsic sources of asymmetry. Asymmetry in the flow and temperature fields, caused by high shear initiated phenomena, affects the interface shape in the azimuthal direction thus results in the thermal stress distribution in the vicinity, which has serious implications from crystal quality point of view.

Information Preservation Modeling of Rayleigh-Benard Transition from Thermal Conduction to Convection

Onset and evolution of the Rayleigh-Benard (R-B) convection are investigated using the Information Preservation (IP) method. The information velocity and temperature are updated using the Octant Flux Splitting (OFS) model developed by Masters & Ye based on the Maxwell transport equation suggested by Sun & Boyd. Statistical noise inherent in particle approaches such as the direct simulation Monte Carlo (DSMC) method is effectively reduced by the IP method, and therefore the evolutions from an initial quiescent fluid to a final steady state are shown clearly. An interesting phenomenon is observed: when the Rayleigh number (Ra) exceeds its critical value, there exists an obvious incubation stage. During the incubation stage, the vortex structure clearly appears and evolves, whereas the Nusselt number (Nu) of the lower plate is close to unity. After the incubation stage, the vortex velocity and Nu rapidly increase, and the flow field quickly reaches a steady, convective state. A relation of Nu to Ra given by IP agrees with those given by DSMC, the classical theory and experimental data.

Subsonic interface crack with crack face contact

A steady-state subsonic interface crack propagating between an elastic solid and a rigid substrate with crack face contact is studied. Two cases with respective to the contact length are considered, i.e., semi-infinite and finite crack face contact. Different from a stationary or an open subsonic interface crack, stress singularity at the crack tip in the present paper is found to be non-oscillatory. Furthermore, in the semi-infinite contact case, the singularity of the stress field near the crack tip is less than 1/2. In the finite contact case, no singularity exists near the crack tip, but less than 1/2 singularity does at the end of the contact zone. In both cases, the singularity depends on the linear contact coefficient and the crack speed. Asymptotic solutions near the crack tip are given and analyzed. In order to satisfy the contact conditions, reasonable region of the linear contact coefficient is found. In addition, the solution predicts a non-zero-energy dissipation rate due to crack face contact.