Demixing of Materials under Chemical Potential Gradients

A steady-state demixing of initially homogeneous solid solution which occurs in binary oxides under oxygen partial pressure gradient is treated by the path probability method of irreversible statistical mechanics from an atomistic point of view. The larger the difference between the diffusion coefficients of constituent species is, the larger is the degree of demixing. Essential features of demixing by diffusion, however, do not depend on whether the driving force is the chemical potential gradient, the electric field, or others.     

Time Evolution of Demixing in Oxides under an Oxygen Potential Gradient

Time evolution of concentration profiles leading to steady-state demixing in oxides under oxygen partial pressure gradient is treated based on a microscopic model by applying the path probability method of irreversible statistical mechanics. The redistribution of vacancies and cations toward the steady-state distribution has essentially been reduced to the diffusion of vacancies and the interdiffusion of cations along the specimen. Atomistic features of the problem, such as a vast difference in the relaxation times for the redistribution of vacancies and cations, are emphasized. Time required for the system to reach the steady state is then estimated in terms of fundamental material properties.     

Influence of Coherency Stress on Kinetic Demixing

The influence of coherency stress, arising from differences in the partial molar volumes of the cations or an imposed displacement boundary condition, on composition profiles during kinetic demixing in ternary oxides subjected to a gradient in oxygen chemical potential is investigated. Coherency stresses can either enhance or diminish the magnitude of the kinetic demixing and shifts in interfacial composition owing to coherency stress on the order of several atomic percent, measured with respect to the case where stress is neglected, can be expected. For (Co, Mg)O subjected to displacement boundary conditions, steady-state and time-dependent demixing profiles are calculated and compared with experimental measurements. Although the composition profiles in the demixed solids are modified because of coherency stress, the main features of kinetic demixing remain unchanged.     

非自然环境中制备PMMA梯度材料的研究

探讨了梯度材料的合成与制备方法的研究进展,提出在非自然环境中制备PMMA梯度折射率材料的制备方法和模型研究。研究表明,增加反应物中两相物质分子或颗粒的作用力差是制备具有应用前景的梯度高聚物材料的关键。并就非自然环境中制备高聚物梯度材料的实验方法、数学模型及利用该方法制备出的高聚物梯度材料的性能表征进行了研究。     

On the possibility of a significant temperature gradient in supported metal catalysts subjected to microwave heating

A simple model is presented which estimates the temperature gradients in microwave-irradiated 1 and 100 nm metallic particles which are typically found in a supported metal catalyst structure. The two particle sizes allow limiting case calculations of the temperature rise over the range of typical particle sizes. The model, based on a simple steady-state energy balance, uses the assumption that the particles only lose heat to the gas-phase, and not the support matrix. This represents a best-case scenario for a temperature gradient relative to the surroundings. The model indicates that the temperature gradient is insignificant and this conclusion is supported by an experiment in which the microwave-driven carbon monoxide reaction acts as an in situ temperature probe. This revised version was published online in July 2006 with corrections to the Cover Date.     

Diffusive and bulk flow transport in polymers

The transport properties of polymer membranes in various forms which have a wide variety of practical applications, such as ultrafiltration, dialysis and blood oxygenation, depend upon the structure (homogeneous or heterogeneous) and the transport characteristics of the membrane material. Among many possible driving forces of transport, the pressure gradient and the concentration gradient are considered to be the most general forces encountered in practical use of polymer membranes. The transport of various permeants (gas, dissolved gas, liquid solvent, and solute) through porous and homogeneous (nonporous) polymer membranes under these driving forces is discussed. In the absence of a pressure gradient, the transport of permeants can be described as diffusion, regardless of the permeant phase and the membrane structure. In the presence of a pressure gradient, the transport of permeants may occur by diffusion and/or bulk flow of the permeants, depending upon the membrane structure and the nature of the permeant. In homogeneous membranes, many noninteracting permeants such as gases and nonsolvent vapors permeate by diffusion under applied pressure gradient: however, solvent in homogeneously swollen membranes moves by bulk flow and the diffusion depending on the degree of swelling of the membrane. In heterogeneous membranes under applied pressure, most permeants move by bulk flow.     

Heat transfer in a fluidized bed. Part I. The effect of thermal driving force on the heat transfer coefficient

The influence of the thermal driving force on the coefficient for heat exchange between a fluidized bed (diam. 30 cm) and part of a submerged vertical cylinder (diam. 7 cm) is described. In the experiments both negative and positive driving forces have been applied (the heat flow being considered positive if directed towards the bed).

Beds of glass beads, quartz sand and silica-alumina catalyst powders have been used to cover a range of particle size and density. For powders exhibiting dense phase expansion, heat transfer coefficients are found which are significantly affected by the driving force. At driving forces of about − 70°C heat transfer coefficients in a 40 μm catalyst bed were only half of those at driving forces approaching zero.

The behaviour of a transparent ‘two-dimensional’ fluidized bed showed that this might be the result of a reduction of solids mobility in the vicinity of the relatively cold surface. In an attempt to explain this reduction three mechanisms were considered; of these the decrease of the dense phase expansion due to a temperature gradient proved to be the most important one.

Powders not exhibiting dense phase expansion show heat transfer coefficients which are only slightly affected by the driving force, the differences resulting entirely from changes in physical properties with temperature.     

Transient Thermal Gradients in Barium Titanate Positive Temperature Coefficient (PTC) Thermistors

Barium titanate positive temperature coefficient (PTC) ceramic disk thermistors can suffer major mechanical damage if inhomogeneous heating occurs under voltage. The steady-state and transient temperature distributions for thin disk samples (radius of 5 mm, thickness of 2 mm) have been studied with an infrared microscope, using a spatial resolution of 35 µm. The transient temperature distribution is observed to be particularly sensitive to the electrical boundary conditions during the initial heating period after application of a voltage. Small variations in electrode symmetry can lead to axial asymmetric thermal gradients up to 25 K/mm across the entire rim when an ac voltage of 100 V is applied. A finite-difference model in two dimensions, based on solution of the heat equation with a local-temperature-dependent Joule heating-source term, has been developed to describe the axial and radial transient temperature distributions in the cylindrical geometry. The predictions reveal current concentration at the edge of an electrode when the metal layer coverage is slightly smaller than that of the opposite face. This phenomenon results in stronger localized heating in a ring that initiates the thermal gradient.     

Theory for Sintering in Temperature Gradients: Role of Long-Range, Mass Transport

For a one-component crystalline solid, the driving force for diffusion in a temperature gradient by any path is the gradient in the equilibrium vapor pressure. A When transport is limited by a surface step, the driving force is the difference in vapor pressures at the extremes of the temperature gradients. Sample calculations suggest that temperature gradients are important in driving densification during fast firing and probably are important during conventional firing.     

Driving force evolution in solid-state sintering with coupling multiphysical fields

A phase field model based on coupled thermo–mechano–diffusional equations is presented to simulate the microstructure evolution of hot pressing sintering under nonisothermal conditions. Simulation results for different heating rates are basically consistent with the experimental densification curves. Further research shows that the temperature gradient driving force increases with the heating rates, whereas the driving force of concentration and strain gradients are the identical in the same shape (corresponding to a certain relative neck radius) with different heating rate. Moreover, Simulation results indicate the evolution trend of the concentration gradient driving force along with neck growth is consistent with that from the classical theory which derived using Fick's law in an ideal two-sphere equal-radius model. Finally, a dynamic equations of sintering driving force and neck growth rate are obtained under the assumption of constant temperature, and the dynamic equation of neck growth was proved to be valid in different phase field parameters and sintering temperatures.     

Thermal stability of Pd or Pt loaded Ce0.68Zr0.32O2 and Ce0.50Zr0.50O2 catalyst materials under oxidising conditions

The sintering behaviour of Pd or Pt loaded ceria–zirconia solid solutions of nominal composition Ce_0.50Zr_0.50O₂ and Ce_0.68Zr_0.32O₂ was studied under oxidising conditions. Calcination treatments were carried out under controlled oxidising atmosphere for periods of up to 96 h. Powder X-ray diffraction and BET nitrogen adsorption–desorption derived surface area data are reported for the bare materials and for those loaded with low (<1% w/w) amounts of the noble metals, palladium and platinum. Phase demixing was observed as sintering progressed for both of the compositions studied with some differences in behaviour observed between the noble metal free and noble metal loaded catalysts. The results are discussed from a thermodynamic viewpoint, which allows to distinguish the behaviour of the two compositions during the demixing process.     

Model-free real-time optimization of process systems using safe Bayesian optimization

Conventional real-time optimization (RTO) requires detailed process models, which may be challenging or expensive to obtain. Model-free RTO methods are an attractive alternative to circumvent the challenge of developing accurate models. Most model-free RTO methods are based on estimating the steady-state cost gradient with respect to the decision variables and driving the estimated gradient to zero using integral action. However, accurate gradient estimation requires clear time scale separation from the plant dynamics, such that the dynamic plant can be assumed to be a static map. For processes with long settling times, this can lead to prohibitively slow convergence to the optimum. To avoid the need to estimate the cost gradients from the measurement, this article uses Bayesian optimization, which is a zeroth order black-box optimization framework. In particular, this article uses a safe Bayesian optimization based on interior point methods to ensure that the setpoints computed by the model-free steady-state RTO layer are guaranteed to be feasible with high probability (i.e., the safety-critical constraints will not be violated at steady-state). The proposed method can thus be seen as a model-free variant of the conventional two-step steady-state RTO framework (with steady-state detection), which is demonstrated on a benchmark Williams-Otto reactor example.     

Natural convection in a heat generating fluid bounded by two horizontal concentric cylinders

Convective flow and heat transfer of a Boussinesq fluid contained between two horizontal concentric cylinders is investigated under the effects of two driving mechanisms – an externally-imposed temperature gradient across the annulus, and a uniform internal heat generation. Numerical results for flow field and temperature distribution are obtained in terms of four dimensionless parameters, namely the radius ratio, R, the Prandtl number, Pr, the Rayleigh number, Ra*, and the ratio, S, between the characteristic temperature induced by internal heating and the applied temperature difference between the boundaries. Depending on the value of S, the flow pattern is made up of either one or two vortices in each half cavity, and heat is transferred into or out of the cavity through the hot wall. In particular, for a certain value of the applied temperature difference, the hot wall apparently acts as a thermally-insulated boundary, the internal heat is completely lost through the cold wall, and the fluid undergoes a transition from a bicellular to a unicellular flow regime.     

Morphology formation during the nonisothermal thermally-induced phase separation (TIPS) process

In high-viscosity polymer solutions and blends, temperature variations during the quench process of the thermally-induced phase separation (TIPS) influence the dynamics and thermodynamics of phase separation. Hence, this study aims to investigate the impact of temperature variations on the morphology formation during the TIPS process. First, the influence of temporal temperature variations on phase separation is investigated by coupling a transient heat conduction model and the Cahn–Hilliard equation, and the results are compared with the isothermal phase separation process. Next, the morphology formation during phase separation is inspected by applying quench from two opposite sides of the sample to the same and different temperatures through coupling the Fourier heat transfer equation and the Cahn–Hilliard equation. The influence of the enthalpy of demixing on the morphology formation and the competition between the heat and mass transfer is also evaluated. It is confirmed that temporal variations of temperature alone have a significant impact on the morphology formation during the TIPS process. In addition, quenching the system to the same and different temperatures both leads to anisotropic morphology formation, which is affected by the quench rate, quench temperature, solution viscosity, and enthalpy of demixing. Upon applying different quench temperatures from opposite sides, two different types of morphologies and droplet sizes were formed as a result of the difference in the cooling rates between the two sides. Employing the enthalpy of demixing during phase separation induced a shallow quench effect on the deep quench side due to the fact that the heat moved toward the lowest temperature in the system, which led to the formation of a distinctive structure.     

Compositional Effect on the Liquid-Phase Formation in Lead Iron Tungstate Ferroelectric Ceramics

The iron content in Pb (Fe_2/3W_1/3) O₃ was demonstrated in this study to substantially affect the formation of a liquid phase during the heating process. This liquid phase was generated in iron-deficient specimens at a temperature around 870°C. However, no liquid phase could be formed in specimens with a stoichiometric or excess amount of iron. A slow cooling treament induced the liquid phase to migrate from the interior toward specimen surfaces and formulate a platelike phase. Formation of the liquid phase is attributed to the reaction of Pb₂WO₅ with residual iron species. The chemical gradient which occurred as a result of the temperature difference between the interior and the surface during slow cooling, as well as the capillary force in the narrowed pore channels between densified grains, are considered to be the driving forces for the migration of the liquid phase.     

Causes of liquid phase migration in powdered metal materials during consolidation by self-propagating high-temperature synthesis

The phenomena of liquid phase migration in the combustion of powdered metal pressings are investigated. The onset of a temperature gradient induced by a combustion wave is established as one of the causes of migration. The resulting capillary potential difference in the pores is directed toward the cooler side of the pressing. It is hypothesized that part of the melt (layers adjacent to the walls of the capillary pores) can move toward the hot side. Techniques are proposed for eliminating the negative consequences of liquation of the molten phase under the influence of the temperature gradient in the sintering of manufactured parts by self-propagating high-temperature synthesis.Institute of Very Hard Materials, Russian Academy of Sciences, Chernogolovka. Translated from Fizika Goreniya i Vzryva, No. 1, pp. 60–65, January–February, 1995.     

A DEM study on the effective thermal conductivity of granular assemblies

A discrete element method (DEM) is developed to simulate the heat transfer in granular assemblies in vacuum with consideration of the thermal resistance of rough contact surfaces. Average heat flux is formulated by the positions and heat flow rates of particles on the boundaries of the granular assemblies. Average temperature gradient is given as a best-fit formulation, which is computed from the relative position and temperature of particles. With the thermal boundary condition imposed on the border region, the effective thermal conductivity (ETC) of granular assemblies can be calculated from the average heat flux and temperature gradient obtained from DEM simulations. Moreover, the effects of particle size, solid volume fraction and coordination number on the ETC are also investigated. Simulation results show that granular assemblies with coarse particles and under large external compression forces exhibit a better heat conduction behavior. The effects of particle size and external compression forces on the ETC are in good agreement with experiment observations.     

不同铁基合金助剂熔渗法制备PDC及其烧结形貌

在高温高压条件下(5.6GPa,1400℃),以不同铁基合金(Fe55Ni26Mn14Co5、Fe55Ni26Co19、FeNi36)为烧结助剂(熔渗质),采用高压熔渗技术制备了金刚石复合片(PDC)。采用扫描电子显微镜(SEM)观察了PDC的烧结组织形貌,对铁基合金的熔渗机制进行了探讨。实验结果表明,三种合金能够均匀渗透金刚石层,与金刚石颗粒形成了致密交错的网状结构,PDC结合界面复合牢固。腔体的压力差(δP)和温度梯度即为合金熔渗的驱动力。     

Non-equilibrium phase transitions in suspensions of oppositely driven inertial particles

The structural evolution of a two-specie suspension of inertial particles under opposite driving forces is investigated by molecular dynamics simulations. The effects of the driving force (F) and the total number density of the particles (ρ) on the final structure are explored. When F is increased under a high ρ, the system starts with a frozen phase, passes through an ordered phase characterized by two demixed lanes moving in opposite directions, and finally returns to a disorder phase. When ρ is increased under a low F, a novel re-entrant phase transition is found: more than two lanes parallel to the driving forces are observed first, followed by a disordered phase with different kinds of particles blocking each other, and then an ordered state with all particles separating into two demixed lanes. We comment on the possible mechanisms underlying these phase transitions in terms of the compromise between the directional driven motion and random thermal fluctuation.     

Experimental investigation of the influence of a temperature gradient on the intensity of light scattering in borate melts

The influence of a temperature gradient on the intensity of light scattering in the boron oxide melt and the lithium borate melts containing 1.2 and 1.6 mol % Li₂O has been investigated over a wide range of temperatures. It has been revealed that, for the temperature gradient used, the reached steady-state intensity of light scattering in the boron oxide melt remains almost unchanged and the intensity of light scattering in the lithium borate melts increases. The specific feature of variations in the light scattering intensity during the attainment of steady-state values in the melts is a nonmonotonic time dependence of the intensity with a minimum. It has been established that additional scattering arising in the lithium borate melts depends on the temperature. The spatial distribution of the light scattering intensity in the objects under study is changed under the action of the temperature gradient.