Toward a theory of evaporation processes in liquid-solid systems

A theoretical analysis is presented of isothermal evaporation of a volatile component from a solid covered by a liquid layer. Binary compounds are considered, with the covering liquid produced by thermal decomposition of the solid material. It is shown that the relaxation time of the volatile concentration profile is much shorter than the characteristic time of motion of the melting interface; i.e., the instantaneous profile of volatile concentration at any time is a linear function of the spatial coordinate. A new nonlinear Stefan-type problem of evaporation in a solid-liquid-vacuum system is formulated that involves two moving phase transition interfaces: an evaporating interface and a melting interface. Exact analytical solutions to the problem are found. It is shown that the melting interface moves faster than the evaporating interface; i.e., the thickness of the liquid layer increases with time, its growth rate increasing with evaporation rate coefficient. It is demonstrated that the concentration profile evolves self-similarly in the course of time. An increase in evaporation rate coefficient leads to a steepening of the concentration gradient across the liquid layer, changing the volatile concentration at the evaporating interface, and the evaporative flux changes accordingly.     

A stochastic model for solidification

A 3-dimensional (2-space, 1-time) model relating the diffusion of heat and mass to the kinetic processes at the solid-liquid interface, using a stochastic approach is presented in this paper. This paper is divided in two parts. In the first part the basic set of equations describing solidification alongwith their analysis and solution are given. The process of solidification has a stochastic character and depends on the net probability of transfer of atoms from liquid to the solid phase. This has been modeled by a Markov process in which knowledge of the parameters at the initial time only is needed to evaluate the time evolution of the system. Solidification process is expressed in terms of four coupled equations, namely, the diffusion equations for heat and mass, the equations for concentration of the solid phase and for rate of growth of the solid-liquid interface. The position of the solid-liquid interface is represented with the help of a delta function and it is defined as the surface at which latent heat is evolved. A numerical method is used to solve the equations appearing in the model. In the second part the results i.e. the time evolution of the solid-liquid interface shape and its concentration, rate of growth and temperature are given.     

定向结晶条件下聚乙二醇6000的强动力学效应

在单向温度场条件下, 采用不同抽拉速度实现了聚乙二醇6000的定向生长、界面形貌的实时观测及界面温度的测量, 进而揭示了其生长机制. 实验结果表明, 随着抽拉速度的增大, 界面的温度逐渐减小, 过冷度逐渐增大. 运用高聚物结晶的次级形核理论模型, 对实验数据进行了计算, 得到在界面过冷度为13.5 K左右时, 生长机制发生了由区域Ⅱ向区域Ⅲ的转变. 实验数据与等温结晶数据的比较发现等温结晶方法中获得过冷度相对较大, 是因为其包含了热过冷. 聚乙二醇6000定向结晶过程中需要的最大动力学过冷度为20 K, 说明由于高聚物的二维形核, 其生长主要由界面动力学控制, 具有较强的动力学效应.     

Boundary treatment effects on molecular dynamics simulations of interface thermal resistance

Molecular Dynamics simulations of heat conduction in liquid Argon confined in Silver nano-channels are performed subject to three different thermal conditions. Particularly, different surface temperatures are imposed on Silver domains using a thermostat in all and limited number of solid layers, resulting in heat flux in the liquid domain. Alternatively, energy is injected and extracted from solid layers to create a NVE liquid Argon system, which corresponds to heat flux specification. Imposition of a constant temperature region in the solid domain results in an unphysical temperature jump, indicating the presence of an artificial thermal resistance induced by the thermostat. Thermal resistance analyses for the components of each case are performed to distinguish the artificial and interface thermal resistance effects. Constant wall temperature simulations are shown to exhibit superposition of the artificial and interface thermal resistance values at the liquid/solid interface, while applying thermostat on wall layers sufficiently away from the liquid/solid interface results in consistent predictions of the interface thermal resistance. Injecting and extracting energy from each solid layer eliminates the artificial resistance. However, the method cannot directly specify a desired temperature difference between the two solid domains.     

Surface acoustic waves at the vacuum-thermoviscoelastic solid interface

The present investigation concerns the propagation of surface waves at the vacuum-solid interface of a solid which is isotropic and thermoviscoelastic, i.e., for which the effects of heat conductivity need to be taken into account. Calculations show that, in addition to the Rayleigh wave, a thermal surface wave propagates that couples both the thermal and the elasticity effects. This latter wave is interpreted in terms of evanescent plane waves. The displacement field associated with this wave is calculated and interpreted. Some experimental results are also presented.     

纳米尺度下气泡核化生长的分子动力学研究

采用分子动力学方法模拟纳米尺度下液体在固体壁面上发生核化沸腾的过程,主要研究壁面浸润性对气泡初始核化过程和气泡生长速率的影响以及固-液界面效应在液体核化沸腾的能量传递过程中所起到的作用.研究结果发现：壁面浸润性越强,气泡在固壁处越容易核化.该结果与经典核化理论中“疏水壁面易于产生气泡”的现象产生了明显的区别.其根本原因是在纳米尺度下,固-液界面热阻效应不能被忽略.一方面,在相同的壁温下,通过增强固-液相互作用,可以显著降低界面热阻,使得热量传递效率提高,导致靠近壁面处的流体温度升高,气泡核化等待时间缩短,有利于液体沸腾核化.另一方面,气泡的生长速率随着壁面浸润性的增强而明显升高.当气泡体积生长到一定程度时,会在壁面处形成气膜,从而导致壁面传热性能恶化.因此,通过壁面的热流密度呈现出先增大后减小的规律.     

Heat treatment-induced bond layer diffusion and re-crystallization in copper carbon interface systems measured by modulated IR radiometry

Copper-carbon interface systems with additional Mo bond layers in the range of 25 nm to 200 nm have been analyzed with respect to their effective thermal depth profiles before and after heat treatment using modulated IR radiometry. Comparing the inverse calibrated modulated IR phase lags before and after heat treatment, several effects can be identified: – (1) The effusivity of the interface layer, which – due the contact resistance between the two elements copper and carbon – is rather low before heat treatment, increases considerably with heat treatment. – (2) This effect is accompanied by an increase of the thermal diffusion time of the interface layer, relying on the diffusion of Mo and Cu particles. – (3) The sputter-deposited copper films, which before heat treatment can be characterized as effective multi-layer structures, re-crystallize with heat treatment and show modulated IR phases, which are characteristic for thermally homogeneous thin films. – (4) The thermal diffusion times of the Cu films decrease considerably with heat treatment due to increased thermal diffusivities, and – (5) the thermal effusivities of the Cu films increase with heat treatment.     

A three-dimensional model of steady flame spread over a thin solid in low-speed concurrent flows

Athree-dimensional model of a steady concurrent flame spread over a thin solid in a low-speed flowtunnel in microgravity has been formulated and numerically solved. The gas-phase combustion model includes the full Navier-Stokes equations for the conservation of mass, momentum, energy and species. The solid is assumed to be a thermally thin, non-charring cellulosic sheet and the solid model consists of continuity and energy equations whose solution provides boundary conditions for the gas phase. The gas-phase reaction is represented by a one-step, second-order, finite-rate Arrhenius kinetics and the solid pyrolysis is approximated by a one-step, zeroth-order decomposition obeying an Arrhenius law. Gas-phase radiation is neglected but solid radiative loss is included in the model. Selected results are presented showing detailed three-dimensional flame structures and flame spread characteristics.

In a parametric study, varying the tunnel (solid) widths and the flow velocity, two important three-dimensional effects have been investigated, namely wall heat loss and oxygen side diffusion. The lateral heat loss shortens the flame and retards flame spread. On the other hand, oxygen side diffusion enhances the combustion reaction at the base region and pushes the flame base closer to the solid surface. This closer flame base increases the solid burnout rate and enhances the steady flame spread rate. In higher speed flows, three-dimensional effects are dominated by heat loss to the side-walls in the downstream portion of the flame and the flame spread rate increases with fuel width. In low-speed flows, the flames are short and close to the quenching limit. Oxygen side diffusion then becomes a dominant mechanism in the narrow three-dimensional flames. The flame spreads faster as the solid width is made narrower in this regime. Additional parametric studies include the effect of tunnelwall thermal condition and the effect of adding solid fuel sample holders.     

A simplified approximate analytical model for Rayleigh–Taylor instability in elastic–plastic solid and viscous fluid with thicknesses

A simplified theoretical model for the linear Rayleigh-Taylor instability of finite thickness elastic-plastic solid constantly accelerated by finite thickness viscous fluid is performed.With the irrotational assumption,it is possible to consider viscosity,surface tension,elasticity or plasticity effects simultaneously.The model considers thicknesses at rigid wall boundary conditions with the velocity potentials,and deals with solid elastic-plastic transition and fluid viscosity based on the velocity continuity and force equilibrium at contact interface.The complete analytical expressions of the amplitude motion equation,the growth rate,and the instability boundary are obtained for arbitrary Atwood number,viscosity,thicknesses of solid and fluid.The thicknesses effects of two materials on the growth rate and the instability boundary are discussed.     

Influence of isothermal approximation on the phase-field simulation of directional growth in undercooled melt

By using the phase-field approach,we have simulated the directional growth of alloys in undercooled moten states under the isothermal and nonisothermal conditions.The influences of the isothermal approximation on simulation results are discussed.We found that for undercooling greater than 25K,the isothermal approximation overestimates the interface growth velocity and reduces a critical velocity for an absolute stable planar interface,thus in this simulation,the uinterface morphology shows the plane-cell-plane transition with increasing initial undercooling of the mele,and the planar interface obtained under a large undercooling is absolutely stable.Whereas in the nonisothermal simulation,only plane-cell transition occures in the same range of the initial undercoolings of the melt,and the planar interface tends to be destabilized and evolve into cells.     

Analysis of ignition of a porous energetic material

A theory of ignition is presented to analyse the effect of porosity on the time to ignition of a semi-infinite porous energetic solid subjected to a constant energy flux. An asymptotic perturbation analysis, based on the smallness of the gas-to-solid density ratio and the largeness of the activation energy, is utilized to describe the inert and transition stages leading to thermal runaway. As in the classical study of a nonporous solid, the transition stage consists of three spatial regions in the limit of large activation energy: a thin reactive–diffusive layer adjacent to the exposed surface of the material where chemical effects are first felt, a somewhat thicker transient–diffusive zone and, finally, an inert region where the temperature field is still governed solely by conductive heat transfer. Solutions in each region are constructed at each order with respect to the density-ratio parameter and matched to one another using asymptotic matching principles. It is found that the effects of porosity provide a leading-order reduction in the time to ignition relative to that for the nonporous problem, arising from the reduced amount of solid material that must be heated and the difference in thermal conductivities of the solid and gaseous phases. A positive correction to the leading-order ignition-delay time, however, is provided by the convective flow of gas out of the solid, which stems from the effects of thermal expansion and removes energy from the system. The latter phenomenon is absent from the corresponding calculation for the nonporous problem and produces a number of modifications at the next order in the analysis arising from the relative transport effects associated with the gas flow.     

The effect of two-dimensional shear flow on the stability of a crystal interface in a supercooled melt

A model is developed based on the time-related thermal diffusion equations to investigate the effects of twodimensional shear flow on the stability of a crystal interface in the supercooled melt of a pure substance.Similar to the three-dimensional shear flow as described in our previous paper,the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude.However,compared with the case of the Laplace equation for a steady-state thermal diffusion field,due to the existence of time partial derivatives of the temperature fields in the diffusion equation the absolute value of the gradients of the temperature fields increases,therefore destabilizing the interface.The circular interface is more unstable than in the case of Laplace equation without time partial derivatives.The critical stability radius of the crystal interface increases with shearing rate increasing.The stability effect of shear flow decreases remarkably with the increase of melt undercooling.     

The effect of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt

A model is developed based on the time-related thermal diffusion equations to investigate the effects of two-dimensional shear flow on the stability of a crystal interface in the supercooled melt of pure substance. Similar to the three-dimensional shear flow as described in our previous paper, the two-dimensional shear flow can also be found to reduce the growth rate of perturbation amplitude. However, compared with the case of Laplace equation for steady state thermal diffusion field, due to the existence of time partial derivatives of the temperature fields in diffusion equation the absolute value of the gradients of the temperature fields increases, therefore destabilizing the interface. The circular interface is more unstable than in the case of Laplace equation without time partial derivatives. The critical stability radius of the crystal interface increases with shearing rate increasing. The stability effect of shear flow decreases remarkably with the increase of melt undercooling.     

Crystallization and grain growth characteristics of yttria-stabilized zirconia thin films grown by pulsed laser deposition

Knowledge about the crystallization and grain growth characteristics of metal oxide thin films is essential for effective microstructural engineering by thermal post-annealing and the integration to Si-based miniaturized electroceramic devices. Finite size and interface effects may cause fundamentally different behavior compared to three dimensional macroscopic systems. This work presents a comprehensive investigation of the crystallization kinetics and microstructural evolution upon thermal post-annealing of amorphous 200 nm and 1.2 μm thin films of 8 mol% yttria-stabilized zirconia grown by pulsed laser deposition (PLD) using ex- and in-situ X-ray diffraction, Raman spectroscopy, and electron microscopy techniques. The layers exhibit a remarkably low crystallization temperature of 200-250 °C while exposure to energetic electrons induces the formation of randomly dispersed ~ 20 nm sized crystallites already at ambient temperature. The isothermal amorphous to crystalline phase transformation kinetics can be described quantitatively by the Johnson-Mehl-Avrami-Kolmogorov model. They reveal characteristics of a three dimensional growth under cation bulk diffusion control with heterogeneous nucleation that changes from continuous to instantaneous initial seeding at temperatures above 300 °C. Large (> 100 nm) equiaxed grains are formed rapidly without a stabilization of transient nanocrystals during the thermally induced phase transformation. A stagnation of normal grain growth resulting in a logarithmic normal size distribution is observed once the average grain dimensions approach the film thickness. The results on the crystallization and grain growth of the PLD-grown YSZ films are evaluated with regards to the fabrication of YSZ solid electrolyte membranes for Si-supported micro solid oxide fuel cells and gas sensors.     

Formation and dissociation of gas hydrate inclusions during migration in water

The paper studies the process of floating a gas hydrate particle in liquid. The typical depths when gas bubble floating is accompanied by gas hydrate formation (or with zero gain of hydrate) were calculated. The low depths were identified when floating occurs with hydrate dissociation. The model assumes that the gas hydrate formation is limited by heat transfer from interface to the surrounding liquid. The model for gas hydrate dissociation assumes the rate governed by thermal conductivity of hydrate particle and by convective heat transfer to surrounding water. The temperature of the gas hydrate surface equals the phase transition temperature at the given water pressure. Comparative analysis of thermal conductivity and convective heat transfer effects on hydrate dissociation rate was performed for different initial radius of the particle.     

Influence of initial solid–liquid interface morphology on further microstructure evolution during directional solidification

Preparation of the initial solid–liquid interface on which growth is started is a very critical step in directional solidification experiments. Dedicated experiments concerning preparation of the initial solid–liquid interface morphology and its influence on further directionally solidified microstructure were performed on Cu-20 wt% Sn peritectic alloy in a Bridgman-type furnace. To verify the morphology of the initial solid–liquid interface, steady-state directional dendritic growth was interrupted by thermal stabilization ranging from 0 to 1 h prior to quenching. With thermal stabilization duration increase, the solid–liquid interface morphology degenerated from dendritic to cellular and finally to planar. To verify the influence of the initial state on further solidification microstructure, directional solidification experiments were performed at a low pulling rate of 1 μm/s with different initial solid–liquid interface morphologies. The initial state affects solute redistribution and formation of peritectic coupled growth structure in the subsequent directional solidification process.     

振荡流共轭换热格子-Boltzmann模拟

振荡流共轭换热现象广泛存在于热声热机等工程应用中.基于双分布格子-Boltzmann模型,对平行平板间振荡流共轭换热进行了数值模拟.通过假定共轭界面处流体和固体的未知内能分布函数均为对应的平衡态滑移修正格式,提出了一种处理共轭换热边界的新方法.模拟结果表明,该方法可以保证共轭界面上温度连续和热流连续.分析了不同流体与固体导热系数比情况下振荡流共轭换热的速度场、温度场以及热流分布的特点.     

Thermal focusing effect in solid-state microchip lasers connected directly with vertical-cavity surface-emitting laser diodes

In this paper, we model and analyze thermal focusing effect in the microchip lasers pumped by vertical-cavity surface-emitting lasers (VCSELs) for a special pump scheme, in which the microchip is axially connected with the VCSEL pump source without a gap between them to form a sort of ultra-compact monolithic micro-lasers. Thus, the thermal effects are related to twofold heating processes in the microchip. One is the common pump beam heating. The other is the heat flux diffusion from VCSEL to microchip through the contact interface between both, the latter leads to different thermo-optic characteristics from that generated only by the pump beam heating in the microchip. The temperature-, the stress- and the expansion-related phase variations and thus the thermal focusing properties of the microchip regarding the twofold heating processes are calculated and discussed for various pump power densities and temperatures of the VCSEL using analytical models. The results show that both heating processes in such a pump configuration can produce comparable thermal effects to each other. The influence of the heat transfer from the VCSEL to the microchip laser performance is discussed as well.     

Computation of solidification problems with hydrodynamic convection resolving energetic anisotropies at the microscale quantitatively

In this work we propose a new numerical approach to solve the solidification of microstructures from a pure melt including hydrodynamic effects in the molten phase. The model is based on the classical sharp-interface model, i.e the solid–liquid interface is tracked and latent heat is released. An enhanced scheme is employed to solve fluid flow in the melt. The no-slip condition is applied on the interface by enforcing the velocities in the solid phase to be zero. The morphology evolution of the solidifying crystal microstructure under the influence of convection is compared with an existing morphology diagram for pure diffusion controlled growth (see Brener et al. [1]). The peculiarity of our approach is that it models the physical anisotropies along the solid–liquid interface with high accuracy. This allows us to report changes in the morphology diagram given by Brener et al. [1] due to the influence of forced flow. Moreover, we present some results on the scaling of the dendritic tip in such cases.