Non-equilibrium thermodynamics of interfacial systems: II. Boundary conditions for fluids with spin

The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids whose molecules possess internal angular momentum (spin) which are separated by an interface. The conservation laws and the Gibbs relation are used to derive the entropy production at the interface. The resulting linear laws relating the fluxes and forces represent boundary conditions on the hydrodynamic equations for the bulk phases. A limiting case is considered and boundary conditions derived by previous authors are obtained.     

液气相变界面间断关系浅议

对池沸腾传热现象局部传递过程的细致分析(例如微重力池沸腾传热研究文献中关于热毛细效应作用及其成因的各种相互冲突的观点),涉及汽液相变界面两侧的间断关系.相变(蒸发或凝结)过程的非平衡性导致相界面两侧物理量对经典平衡态热力学中的相界面关系的偏离,分子动理论比拟模型、统计率模型和非平衡热力学模型均给出了相关描述,本文对此进行了详细评述,指出了各模型的优缺点,并对进一步的研究方向进行了讨论.     

汽液界面动力学行为与热力学性质的分子动力学研究

本文采用分子动力学方法研究了热平衡条件下的汽液界面的动力学行为和热力学性质。统计获得了界面区的密度、压力张量及温度的分布,并且从分子层次观察分析了界面结构和动力学特性。研究表明汽液界面是一个随时间起伏涨落的曲面,界面层的分子并不是处于液相和蒸汽相之间的一种过渡状态,从汽相到液相密度的连续变化是长时间的统计结果,汽渡过渡区的厚度与汽液界面区的密度涨落的范围是一致的。对于平衡条件下的汽液界面,由于汽液相变的影响,在紧贴界面处存在一个分子平均动能非平衡分布的区域。此非平衡区域的存在与汽液两相的宏观热平衡并不矛盾,但可能对蒸发／凝结流率的估计有不可忽略的影响。     

Non-equilibrium thermodynamics of interfacial systems

The theory of non-equilibrium thermodynamics is applied to a multi-component system containing an interface using a method developed by Bedeaux, Albano, and Mazur. A singular mass density is allowed at the interface as well as singular densities of energy and entropy. All currents are also allowed to be singular at the interface. The conservation laws and the Gibbs relation for the entropy are used to derive the entropy production at the surface. Linear laws relating the fluxes and thermodynamic forces are presented. The theory is then applied to a two component system where one of the phases is a liquid and the other a low density gas and the boundary conditions at the free surface of the liquid derived. The boundary conditions include the conditions used by Levich in his theory of the damping of waves by surface-active substances, but include other effects as well.     

Non—equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method

In this paper, we propose a new approach to implementing boundary conditions in the lattice Boltzmann method (LBM). The basic idea is to decompose the distribution function at the boundary node into its equilibrium and non-equilibrium parts, and then to approximate the non-equilibrium part with a first-order extrapolation of the non-equilibrium part of the distribution at the neighbouring fluid node. Schemes for velocity and pressure boundary conditions are constructed based on this method. The resulting schemes are of second-order accuracy. Numerical tests show that the numerical solutions of the LBM together with the present boundary schemes are in excellent agreement with the analytical solutions. Second-order convergence is also verified from the results. It is also found that the numerical stability of the present schemes is much better than that of the original extrapolation schemes proposed by Chen et al. (1996 Phys. Fluids 8 2527).     

Hydrodynamic boundary conditions: An emergent behavior of fluid–solid interactions

By using the Onsager principle of minimum energy dissipation, the hydrodynamic boundary conditions at the fluid–solid interface are shown to be the natural emergent behavior of microscopic interactions that lead to the interfacial tension and the tangential friction at the fluid–solid interface [T. Qian, C. Qiu, P. Sheng, J. Fluid Mech. 611 (2008) 333]. This is satisfying because the equations of motion, e.g., the Stokes equation, and the hydrodynamic boundary conditions can now be derived from a unified framework. The resulting continuum hydrodynamic formulation yields predictions for immiscible two-phase flows that are in quantitative agreement with molecular dynamic simulations. In particular, the classical problem of the moving contact line is resolved. We also show results on the moving contact line over chemically patterned surfaces which exhibit striking nanoscale characteristics as well as sub-quadratic dependence of the moving contact line dissipation on its average velocity.     

Bose-Einstein condensation of S = 1 nickel spin degrees of freedom in NiCl2-4SC(NH2)2

It has recently been suggested that the organic compound NiCl2-4SC(NH2)2 (DTN) undergoes field-induced Bose-Einstein condensation (BEC) of the Ni spin degrees of freedom. The Ni S = 1 spins exhibit three-dimensional XY antiferromagnetism above a critical field H(c1) approximately 2 T. The spin fluid can be described as a gas of hard-core bosons where the field-induced antiferromagnetic transition corresponds to Bose-Einstein condensation. We have determined the spin Hamiltonian of DTN using inelastic neutron diffraction measurements, and we have studied the high-field phase diagram by means of specific heat and magnetocaloric effect measurements. Our results show that the field-temperature phase boundary approaches a power-law H - H(c1) proportional variant T(alpha)(c) near the quantum critical point, with an exponent that is consistent with the 3D BEC universal value of alpha = 1.5.     

Modelling transient heat conduction in solids at multiple length and time scales: A coupled non-equilibrium molecular dynamics/continuum approach

A method for controlling the thermal boundary conditions of non-equilibrium molecular dynamics simulations is presented. The method is simple to implement into a conventional molecular dynamics code and independent of the atomistic model employed. It works by regulating the temperature in a thermostatted boundary region by feedback control to achieve the desired temperature at the edge of an inner region where the true atomistic dynamics are retained. This is necessary to avoid intrinsic boundary effects in non-equilibrium molecular dynamics simulations. Three thermostats are investigated: the global deterministic Nosé–Hoover thermostat and two local stochastic thermostats, Langevin and stadium damping. The latter thermostat is introduced to avoid the adverse reflection of phonons that occurs at an abrupt interface. The method is then extended to allow atomistic/continuum models to be thermally coupled concurrently for the analysis of large steady state and transient heat conduction problems. The effectiveness of the algorithm is demonstrated for the example of heat flow down a three-dimensional atomistic rod of uniform cross-section subjected to a variety of boundary conditions.     

Quasi-steady-state modeling of dendritic growth

A new method of the moving-boundary problem analysis is developed. After proposed coordinate transformation, the quasi-steady-state differential equation was reduced to equivalent Laplace equation. Transformed boundary conditions of a rescaled field distribution reflect the presence of rate-dependent sources on interface. Taking into account the local rate-dependence of the Neumann's boundary conditions, non-equilibrium pattern formation was considered. The problem of dendrite fractal growth was reduced to one of interaction of conformal to tips charged particles. Conditions of the quasi-steady growth and the recurrence formula for k-order dendrite spacing were derived. Theoretically obtained scaling laws for interface shape, dendrite spacing, critical sidebranch distance are confirmed by available experimental data.     

Spin thermopower and thermoconductance in a ferromagnetic graphene nanoribbon

The spin thermoelectric properties of a zigzag edged ferromagnetic (FM) graphene nanoribbon are studied theoretically by using the non-equilibrium Green's function method combined with the Landauer-Büttiker formula. By applying a temperature gradient along the ribbon, under closed boundary conditions, there is a spin voltage ΔV(s) inside the terminal as the response to the temperature difference ΔT between two terminals. Meanwhile, the heat current ΔQ is accompanied from the 'hot' terminal to the 'cold' terminal. The spin thermopower S?=?ΔV(s)/ΔT and thermoconductance κ?=?ΔQ/ΔT are obtained. When there is no magnetic field, S versus E(R) curves show peaks and valleys as a result of band selective transmission and Klein tunneling with E(R) being the on-site energy of the right terminal. The results are in agreement with the semi-classical Mott relation. When |E(R)|??M, the quantized value of [Formula: see text] appears. In the quantum Hall regime, because Klein tunneling is suppressed, S peaks are eliminated and the quantized value of κ is much clearer. We also investigate how the thermoelectric properties are affected by temperature, FM exchange split energy and Anderson disorder. The results indicate that S and κ are sensitive to disorder. S is suppressed for even small disorder strengths. For small disorder strengths, κ is enhanced and for moderate disorder strengths, κ shows quantized values.     

Non-equilibrium thermodynamics of interfaces including electromagnetic effects

The application of non-equilibrium thermodynamics to a system consisting of two bulk phases and their interface is extended to include electromagnetic effects. The interface is assumed to carry singular mass, energy, and entropy densities as well as singular electric charge, electric current, polarization and magnetization. Electric and magnetic fields are allowed to be discontinuous across the interface, but not singular.Maxwell's equations are used to derive relationships among electromagnetic quantities on the surface and boundary conditions for the bulk phases. An expression for the surface entropy production including electromagnetic effects is obtained, and the resulting linear laws relating thermodynamic forces and fluxes are investigated.     

Heat Transfer Characteristics for Condensation of R134a in a Vertical Smooth Tube

In this study, condensation of pure refrigerant R134a vapor inside a smooth vertical tube was experimentally investigated. The test section was made of a copper tube with inside diameter of 7.52 mm and length of 1 m. Experimental tests were conducted for mass fluxes in the range of 20–175 kg/m²s with saturation pressure ranging between 5.8 and 7 bar. The effects of mass flux, saturation pressure, and temperature difference between the refrigerant and tube inner wall (ΔT) on the heat transfer performance were analyzed through experimental data. Obtained results showed that average condensation heat transfer coefficient decreases with increasing saturation pressure or temperature difference (ΔT). In addition, for the same temperature difference (ΔT), heat can be removed from the refrigerant at a higher rate at relatively low pressure values. Under the same operating conditions, it was shown that average condensation heat transfer coefficient increases as mass flux increases. Finally, the most widely used heat transfer coefficient correlations for condensation inside smooth tubes were analyzed through the experimental data. The best fit was obtained with Akers et al.'s (1959) correlation with an absolute mean deviation of 22.6%.     

Kinetic boundary condition at a vapor-liquid interface

By molecular dynamics simulations, the boundary condition for the Boltzmann equation at a vapor-liquid interface is found to be the product of three one-dimensional Maxwellian distributions for the three velocity components of vapor molecules and a factor including a well-defined condensation coefficient. The Maxwellian distribution for the velocity component normal to the interface is characterized by the liquid temperature, as in a conventional model boundary condition, while those for the tangential components are prescribed by a different temperature, which is a linear function of energy flux across the interface. The condensation coefficient is found to be constant and equal to the evaporation coefficient determined by the liquid temperature only.     

Conserved dynamics and interface roughening in spontaneous imbibition: A phase field model

The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field . The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent , indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horv'ath and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface. Received 24 November 1999     

Surface plasmon damping due to rough boundary scattering

The surface plasmon damping due to carriers scattering at the statistically rough (semiconductor-dialectric) interface is considered. The specular parameter and the integral relation are used as the boundary condition for a non-equilibrium part of the distribution function. There exist certain cases when the rough surface scattering of carriers is shown to play an important role in the surface plasmon damping.     

Boundary conditions and non-equilibrium thermodynamics

The theory of non-equilibrium thermodynamics is applied to a system of two immiscible fluids and their interface. A singular energy density at the interface, which is related to the phenomenon of surface tension, is taken into account. Furthermore the momentum and the heat currents are allowed to be singular at the interface. Using the conservation laws and the Gibbs' relation for the surface, an expression for the singular entropy production density at the interface is obtained. The linear phenomenological laws between fluxes and thermodynamic forces occurring in this singular entropy production density are given. Some of these linear laws are boundary conditions for the solution of the differential equations governing the evolution of the state variables in the bulk.     

Discussions on the non-equilibrium effects in the quantitative phase field model of binary alloys

All the quantitative phase field models try to get rid of the artificial factors of solutal drag,interface diffusion and interface stretch in the diffuse interface.These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys.Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface.The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process.The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.     

多孔介质对流干燥外部传热传质的非平衡热力学理论

从非平衡热力学理论出发,以广义热力学力作为传质过程驱动势,建立了描述多孔介质恒速干燥阶段外部对流传热传质过程的热力学理论模型,并进行了数值计算,计算值与已有的实验数据吻合较好;同时,还将计算结果与传统的理论进行了比较,结果表明,非平衡热力学理论更能反映过程的物理本质。     

Unified phase-field model for epitaxial growth of multi-scale three-dimensional islands on insulating surfaces

In this paper we present a unified phase-field model for non-equilibrium growths of various three-dimensional metal islands on insulating surfaces. We introduce a phase-field variable to distinguish the island from the non-island regions and substrate and a density variable to describe local density of deposited adatoms. Two partial differential equations with appropriate boundary conditions, as the governing equations, are used to describe the evolution of the three-dimensional metal islands and the diffusion of adatoms. We solve the equations by using an adaptive mesh refinement method so that we can simulate the non-equilibrium growth of three-dimensional metal islands from tens of nanometers to several micrometers. We investigate the dependence of simulated results on the model parameters and experimental conditions. Equilibrium shape of such islands can be obtained through sufficient post-deposition relaxation. Experimental trends of island size and shape on various scales are obtained with reasonable parameters. This method should be a good approach to non-equilibrium growths of multi-scale three-dimensional metal islands.     

Magnetic anisotropy of the antiferroquadrupole phase in Ce0.50La0.50B6

Magnetic phase diagrams for antiferroquadrupole (AFQ) phase II and antiferromagnetic (AFM) phase III in Ce0.50La0.50B6 with a Gamma(8) ground state have been investigated by ultrasonic measurements. The hybrid magnet (Gama) in the National Institute for Materials Science was employed for high-field measurements up to 30 T and a 3He-4He dilution refrigerator was used for low-temperature experiments down to 20 mK. The phase boundary from paramagnetic phase I to AFQ phase II under [001] magnetic fields closes at H(I-II) approximately 29 T, while the boundary is still open under fields along the [110] and [111] directions even up to 30 T. This anisotropic character of phase II in fields is consistent with the theoretical calculation based on the O(xy)-type AFQ ordering. We also found that AFM phase III reduces considerably in fields turning from the [001] to [110] and [111] directions.