A threshold for onset of natural convection in binary metallic alloys

Experiments were performed with a new radioscopic flow visualization technique on natural convection during melting of a binary metallic Ga-In alloy. This technique provides visualization of the density fields within opaque low Prandtl number fluids and their solids. Upon applying a horizontal temperature gradient to a gallium melt alloyed with 5 weight percent indium, the binary melt developed a vertical concentrational stratification and heat transfer was by conduction only. Convective flow developed at a higher temperature difference, which may be termed “critical”. After reducing the temperature difference the thermosolutal convection breaks down and a conductive state reappears at ΔT0 K. This threshold for onset of natural convection in binary Ga-In melts is in need of a theoretical explanation.     

A fixed domain model for microsegregation during solidification of binary alloys

A fixed-domain numerical model for microsegregation during alloy solidification is developed. The phenomena of solute partitioning at the moving solid/liquid interface and subsequent redistribution by diffusion in the solid and liquid phases have been formulated using volumetric terms. A solute balance equation valid for the whole domain comprising the solid and liquid phases has been obtained in terms of the liquid concentration. The effects of microstructure coarsening on microsegregation has been described and included in the present model. Numerical experiments and comparisons have been carried out between the present fixed-domain model, previous deforming-domain models, and the exact analytical solutions available in the literature. Good agreement has been observed between the predictions of the present fixed-domain model and the exact analytical solutions. Further extensions of the present model for the analysis of two-dimensional microsegregation have been also reported.     

Viscosity of moderately compeessed gases and their binary mixtures

The temperature dependence of the first correction in the density to the coefficient of viscosity of pure gases is obtained on the basis of an effective potential function of intramolecular interaction. The universality of this dependence and the possibility of its use to calculate the coefficient of viscosity of moderately compressed gases and their binary mixtures are shown.     

Petrov-Galerkin methods for natural convection in directional solidification of binary alloys

A Petrov-Galerkin finite element method is presented for calculation of the steady, axisymmetric thermosolutal convection and interface morphology in a model for vertical Bridgman crystal growth of nondilute binary alloys. The Petrov-Galerkin method is based on the formulation for biquadratic elements developed by Heinrich and Zienkiewicz and is introduced into the calculation of the velocity, temperature and concentration fields. The algebraic system is solved simultaneously for the field variables and interface shape by Newton's method. The results of the Petrov-Galerkin method are compared critically with those of Galerkin's method using the same finite element grids. Significant improvements in accuracy are found with the Petrov-Galerkin method only when the mesh is refined and when the formulation of the residual equations is modified to account for the mixed boundary conditions that arise at the solidification interface. Calculations for alloys with stable and unstable solute gradients show the occurrence of classical flow transitions and morphological instabilities in the solidification system.     

Solidification of hypereutectic and hypoeutectic binary alloys with buoyancy and surface tension driven natural convection

Convection patterns and evolution of macrosegregation during solidification of hypereutectic and hypoeutectic NH₄CL-H₂O binary systems in rectangular side chilled ingots have been numerically investigated. Under the conditions of pure thermal/solutal convection, without a free surface, solidification of NH₄CL 70%-H₂O hypereutectic alloy is characterized by the formation of channels and A-segregates, while solidification of NH₄CL 10%-H₂O hypoeutectic alloy is characterized by the formation of circulation cells in the narrow melt and V-segregates. Surface tension effects during solidification of NH₄CL 70%-H₂O results in establishing a counterclockwise rotating cell at the cavity top, changing the number and orientation of developed channels, and creating an area of negative segregation at the cavity top. During solidification of NH₄CL 10%-H₂O, surface tension effects increase the intensity of flow and results in a higher degree of macrosegregation. Received on 9 June 1998     

Numerical Approaches for microscopic modelling of solute redistribution during solidification of binary alloys

In the present study, two numerical approaches for single-domain modelling of microsegregation during solidification of binary alloys are presented. In the first approach, the concentration jump at the moving solid/liquid interface is formulated using a volumetric term and a Boolean function. The governing solute redistribution equation, valid for the whole domain comprising the solid and liquid regions, is derived in terms of the liquid phase composition. The effects of microstructure coarsening on microsegregation has been described and included in the model. In the second approach, the continuum mixture theory is utilized to derive a single domain solute redistribution equation in terms of the mixture composition. The solidification front motion and dendrite arm coarsening effects are accommodated by considering the representative elementary volume to consist of solid, interdendritic, and extradendritic liquid phases. Numerical solutions have been obtained using a control-volume based finite-difference method with a fixed grid. Good agreement has been observed between the predictions of the present fixed-domain models and the exact analytical and experimental results.     

Enhancement of nucleate pool boiling heat transfer to dilute binary mixtures using endothermic chemical reactions around the smoothed horizontal cylinder

Experimental studies on enhancing the pool boiling heat transfer coefficient of binary dilute mixtures of water/glycerol, water/MEG (Mono-ethylene glycol) and water/DEG (di-ethylene glycol) have been carried out. Some particular endothermic chemical reactions related to ammonium salts were used to enhance the pool boiling heat transfer coefficient, simultaneously with occurrence of pool boiling heat transfer. Accordingly, 100?g of Ammonium nitrate, ammonium perborate and Ammonium sulfate were selected to dissolve into mixtures. High and extreme solution enthalpies of each of these ammonium salt powders are employed to reduce the surface temperature around the horizontal cylinder locally. Results demonstrated that presence of ammonium salts into the mixtures deteriorates the surface temperature of cylinder and as the result, higher pool boiling heat transfer coefficient is reported for tested solutions. Results are also reported and compared for different ammonium salts to find the influence of inducing different enthalpies of solution on pool boiling heat transfer coefficient. Obtained results also indicated that presence of endothermic reaction besides the pool boiling heat transfer enhances the heat transfer coefficients in comparison with nucleate pool boiling phenomenon solely.     

The Virk's criterion on the onset of dilute polymer solution phenomena

Summary The Virk's criterion on the onset of the Toms phenomenon in dilute polymer solution is shortly considered; a correlation parameter based on the time hypothesis is indicated, which is modified with respect to the usual similar parameter in that dependence of the intrinsic viscosity on the shear rate is taken into account. It is shown an energetic interpretation of such a parameter.

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Sommario Si considera brevemente il criterio di Virk relativo all'inizio del prodursi del fenomeno di Toms in soluzioni diluite di polimeri in moto turbolento, e si indica un parametro di correlazione dei dati sperimentali basato sul rapporto dei tempi di rilassamento del polimero e caratteristico delle fluttuazioni del moto turbolento, parametro modificato rispetto a quello già considerato da altri autori, in quanto si tiene conto delle variazioni della viscosità intrinseca colla velocità di scorrimento. Si dà di questo parametro una interpretazione energetica.

     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. I. Theory

Assuming the formation of doublets in the flow according to a mass action law, the shear rate and the concentration dependence of the extinction angle, of the birefringence, and of the average coil expansion are calculated for dilute solutions of flexible macromolecules. It is shown that this reversible association process has a strong influence on the measurable parameters in a flow birefringence experiment. c concentration (g/cm³) - h ² mean square end-to-end distance at shear rate - h ₀ ² mean-square end-to-end distance at zero-shear rate - n refractive index of the solution (not very different from the solvent for a very dilute solution) - E mean coil expansion - K ₀,K constant of the mass action law - M molecular weight - R _G gas constant - T absolute temperature - ₁ – ₂ optical anisotropy of the segment - ₀ Deborah number: - Deborah number: - shear rate - ₀, reduced concentration - _s viscosity of the solvent - [] ₀ intrinsic viscosity at zero-shear rate - [] intrinsic viscosity at shear rate - extinction angle - N _a Avodagro's number - _n magnitude of the birefringence     

The influence of finite extensibility on the eigenspectrum of dilute polymeric solutions

Linear stability of plane Couette flow of dilute polymeric solutions modeled using the FENE-P constitutive equation has been examined. Specifically, the spurious, discrete and continuous spectra are identified as a function of the ratio of the solvent to the total viscosity β, maximum chain length L, disturbance wavenumber α and the Weissenberg number (We). It is observed that reducing L shifts the entire spectrum to the left (in the eigenspectrum plane) by a factor directly related to the steady-state value of the Peterlin function f. Additionally, decreasing the value of L causes the splitting of the regular continuous spectrum, initially located at −1/We, into two branches. Overall, the plane Couette flow of a FENE-P model is found to be unconditionally stable. Specifically, decreasing L increases the decay rate of the most dangerous disturbance while increasing the number of discrete and spurious modes. However, increasing both β and α decreases the number of discrete and spurious modes whereas increasing We has no influence on the number of spurious modes but results in an increase in the number of discrete modes.     

The effect of a solid wall for the flow of dilute macromolecular solutions

Summary In the vicinity of a wall the behavior of the molecules of a fluid is not only influenced by neighboring molecules but also by the wall. For a macromolecular solution this implies that the constitutive equations cannot be employed in any finite system except for the calculation of average quantities if, in addition, one accounts for a velocity slip at the solid wall. For planeCouette flow of a dilute solution of flexible macromolecules idealized asHookean dumbbells the slip velocity,u _s , is evaluated under the assumption that the interaction between the solute molecules and the wall is a hard core repulsion. This furnishes a slip velocity in the direction of the flow so that the apparent viscosity goes down by increasing the ratio of the length of the molecules to the distance between the plates. Increasing the intrinsic viscosity and/or the concentration will enhance that effect.

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Zusammenfassung In der Nähe einer Wand wird das Verhalten der Moleküle einer Flüssigkeit nicht nur von Nachbarmolekülen, sondern auch von der Wand beeinflußt. Für eine makromolekulare Lösung bedeutet das, daß die rheologischen Stoffgleichungen in einem endlichen System nicht anwendbar sind. Zur Berechnung gemittelter Größen kann sie jedoch noch verwendet werden, vorausgesetzt, man zieht eine Geschwindigkeitsgleitung mit in die Betrachtung ein. Für die ebeneCouette-Strömung einer verdünnten Lösung flexibler Makromoleküle, die man durchHookesche Hanteln idealisiert, läßt sich die Gleitungsgeschwindigkeitu _s berechnen unter der Annahme, daß die Wechselwirkung mit der Wand rein abstoßend ist. Es zeigt sich, daß dies eine Gleitungsgeschwindigkeit in Strömungsrichtung nach sich zieht, so daß sich die scheinbare Viskosität der Strömung bei größer werdendem Verhältnis von Länge der Moleküle zum Plattenabstand erniedrigt. Eine Vergrößerung desStaudinger-Index und/oder der Konzentration vergrößert den Effekt.

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Paper presented at the Annual Conference of German Rheologists in Berlin, April 28–30, 1975.

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With 2 figures     

The constitutive equation of a dilute suspension of spherical microcapsules

This paper studies the rheological behavior of a dilute suspension of spherical microcapsules, i.e. spherical thin elastic membranes filled with an incompressible liquid. Previous results obtained for the motion of such capsules freely suspended in a simple shear flow are first extended to general linear shear flows. Then the stresslet term in the external flow is computed to order ?², where ?, assumed to be small with respect to unity, is the ratio of viscous to elastic forces acting on the particle. The resulting constitutive equation is of the viscoelastic type and is similar to the one obtained for liquid droplets. It predicts that the microcapsule suspension exhibits a shear dependent viscosity and normal stress effects. The exact dependency of these phenomena on the microscopic parameters of the suspension is explicitly provided by the model.     

The application of numerical and analytical approaches for the determination of thermophysical properties of Al–Si–Cu–Mg alloys

Continuum Mechanics and Thermodynamics - Thermophysical properties are very important to simulate the behavior of materials. Computer simulations are low cost as compared to what is needed for...     

Filter paper-templated preparation of ZnO thin films and examination of their gas-sensing properties

ZnO thin films prepared by using quantitative filter paper as a template and Zn(CH3CO2) 2·2H2O ethanol precursor solution were characterized by scanning electron microscopy(SEM) and X-ray diffraction(XRD) . The effects of sample calcination temperature,precursor concentration and filter paper types were studied,and the growth process was investigated by infra-red(IR) spectroscopy and thermogravimetric analysis/differential thermal analysis(TGA/DTA) . The results show that samples soaked in a 1.5 mol/L Zn(CH...     

DOUBLE HIGH ORDER S－BREAKING BIFURCATION POINTS AND THEIR NUMERICAL DETERMINATION

ＤＯＵＢＬＥＨＩＧＨＯＲＤＥＲＳ－ＢＲＥＡＫＩＮＧＢＩＦＵＲＣＡＴＩＯＮＰＯＩＮＴＳＡＮＤＴＨＥＩＲＮＵＭＥＲＩＣＡＬＤＥＴＥＲＭＩＮＡＴＩＯＮ￥(杨忠华，叶瑞松)ＹａｎｇＺｈｏｎｇｈｕａ；（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｓｈａｎｇｈ...     

Influence of the formation of associations of macromolecules on the rheo-optical properties of their dilute solutions. II. Comparison with experimental results

The results of the theory presented in part I are compared to already published flow birefringence data obtained with dilute up to semi-dilute solutions of polyethylene oxide which have also shown shear thickening effects. The agreement with the theory is quite good so that the reversible formation of associations in flow seems to be a process which has to be taken in account for high molecular weight flexible macromolecules solutions in relatively poor solvents.     

The velocity field of dilute cationic surfactant solutions in a Couette-viscometer

With the aid of particle image velocimetry (PIV) momentary two-dimensional velocity fields of dilute cationic surfactant solutions are measured in an annular gap between coaxial cylinders. In the shear-induced state the velocity profiles of the surfactant solutions differ from a Couette profile drastically: Time dependent flows with high shear rates near the walls are observed. The flow is almost one-dimensional, velocity components in radial or axial direction cannot be detected. The velocity profile can exhibit a local maximum. A macroscopic heterogeneous structure is observed, domains with high viscosity alternate with low viscosity regions. Elastic phenomena are observed in a relaxation experiment. Existing rheometric data of cationic surfactant solutions in the shear-induced state give only apparent viscosities.     

Moderate time scale finite amplitude analysis of large stefan number convection in a gravity modulated mushy layer during the solidification of binary alloys

We investigate the convection amplitude in a binary alloy mushy layer subjected to a vibration body force that is collinear with the gravitational acceleration. The analysis shows that the convection amplitude decreases over time for all vibration frequencies tested. The analysis further reveals that as the vibration frequency increases, the convection amplitude subsequently decreases until a critical vibration frequency; at which the amplitude reaches the lowest value. Further increases in the vibration frequency increase the convection amplitude but gradually.     

应力作用下NiTi形状记忆合金微结构演化的相场模拟及其本征应变率敏感性

基于Ginzburg-Landau动力学控制方程建立了NiTi形状记忆合金非等温相场模型,实现了对NiTi合金内应力诱导马氏体相变的数值模拟。同时将晶界能密度引入系统局部自由能密度,从而考虑多晶系统中晶界的重要作用。数值计算了单晶和多晶NiTi形状记忆合金在单轴机械载荷作用下微结构的动态演化过程和宏观力学行为,并重点研究了晶粒尺寸为60 nm的NiTi纳米多晶在低应变率下（0.000 5～15 s-1）力学行为的本征应变率敏感性。研究结果表明,单晶NiTi合金系统高温拉伸-卸载过程中马氏体相变均匀发生,未形成奥氏体-马氏体界面。而纳米多晶系统在加载阶段出现了马氏体带的形成-扩展现象,在卸载阶段出现了马氏体带的收缩-消失现象。相同外载作用过程中,NiTi单晶系统的宏观应力-应变曲线具有更大的滞回环面积,拥有更优的超弹性变形能力。计算结果显示,在中低应变率下纳米晶NiTi形状记忆合金应力-应变关系表现出较明显的应变率相关性,应变率升高导致材料相变应力提升。这一应变率相关性主要源于相场模型中外加载荷速率与马氏体空间演化速度的相互竞争关系。