Multicomponent lattice-Boltzmann model with interparticle interaction

A lattice Boltzmann model for simulating fluids with multiple components and interparticle forces proposed by Shan and Chen is described in detail. Macroscopic equations governing the motion of each component are derived by using the Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirment by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity, so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confiremoed numerically.     

Simple views on critical binary liquid mixtures in porous glass

A simple scenario, different from previous attempts, is proposed to resolve the problem of the slow phase separation dynamics of binary liquid mixtures confined in porous Vycor glass. We demonstrate that simply mutual diffusion, renormalized by critical composition fluctuations and geometrical hindrance of the porous glass, accounts for the slow phase separation kinetics. Capillary invasion studies of porous Vycor glass by the critical isobutyric acid-water mixture, close to the consolute solution temperature, corroborate our analysis.     

Nonlinear ultrasonic nature of organic liquid and organic liquid mixture

Based on Jacobson's molecular free length theory in liquids and the relationship between ultrasonic velocity and the molecular free length in organic liquids, this paper deduces the equations for pressure coefficient and temperature coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A in both of organic liquid and organic liquid binary mixtures. These nonlinear acoustic parameters are evaluated against the measured results and data from other sources. The equations reveal the connections between the nonlinear acoustic parameters and some internal structural of the medium or mixtures e.g. the sizes of molecule, several thermodynamic physical parameters and outside status e.g. condition of pressure and temperature of the liquid or liquid mixture. With the equations the nonlinear acoustic parameter B/A of organic liquid binary mixtures, which is impossible to know without the nonlinear acoustic parameter B/A of the tow components before, can be calculated based on the structural and physical parameters of organic liquid and organic liquid binary mixtures.     

A pseudobinary approach to study interdiffusion and the Kirkendall effect in multicomponent systems

Interdiffusion studies become increasingly difficult to perform with the increasing number of elements in a system. It is rather easy to calculate the interdiffusion coefficients for all the compositions in the interdiffusion zone in a binary system. The intrinsic diffusion coefficients can be calculated for the composition of Kirkendall marker plane in a binary system. In a ternary system, however, the interdiffusion coefficients can only be calculated for the composition where composition profiles from two different diffusion couples intersect. Intrinsic diffusion coefficients are possible to calculate when the Kirkendall markers are also present at that composition, which is a condition that is generally difficult to satisfy. In a quaternary system, the composition profiles for three different diffusion couples must intersect at one particular composition to calculate the diffusion parameters, which is a condition that is almost impossible to satisfy. To avoid these complications in a multicomponent system, the average interdiffusion coefficients are calculated. I propose a method of calculating the intrinsic diffusion coefficients and the variation in the interdiffusion coefficients for multicomponent systems. This method can be used for a single diffusion couple in a multicomponent pseudobinary system. The compositions of the end members of a diffusion couple should be selected such that only two elements diffuse into the interdiffusion zone. A few hypothetical diffusion couples are considered in order to validate and explain our method. Various sources of error in the calculations are also discussed.     

Ultrasonic study on organic liquid and binary organic liquid mixtures by using Schaaffs＇ collision factor theory

Based on Schaaff's collision factor theory (CFT) in liquids, the equations for nonlinear ultrasonic parameters in both organic liquid and binary organic liquid mixtures are deduced. The nonlinear ultrasonic parameters, including pressure coefficient, temperature coefficients of ultrasonic velocity, and nonlinear acoustic parameter B/A in both organic liquid and binary organic liquid mixtures, are evaluated for comparison with the measured results and data from other sources. The equations show that the coefficient of ultrasonic velocity and nonlinear acoustic parameter B/A are closely related to molecular interactions. These nonlinear ultrasonic parameters reflect some information of internal structure and outside status of the medium or mixtures. From the exponent of repulsive forces of the molecules, several thermodynamic parameters, pressure and temperature of the medium, the nonlinear ultrasonic parameters and ultrasonic nature of the medium can be evaluated. When evaluating and studying nonlinear acoustic parameter B/A of binary organic liquid mixtures, there is no need to know the nonlinear acoustic parameter B/A of the components. Obviously, the equation reveals the connection between the nonlinear ultrasonic nature and internal structure and outside status of the mixtures more directly and distinctly than traditional mixture law for B/A, e.g. Apfel's and Sehgal's laws for liquid binary mixtures.     

Phase-field simulation of the effect of interaction among ordered domains on interdiffusion in Ni--Al--Cr alloys

The effect of interaction among γ ' ordered domains on the interdiffusion process in γ +γ ' /γ and γ +γ ' /γ +γ ' diffusion couples is investigated by using the phase-field method, in which bulk free energy and mobility are linked with thermodynamic and kinetic databases. Simulated results show that the interaction among γ ' ordered domains has great influence on the microstructure, the interdiffusion velocity and the volume fraction of γ ' phase on both sides of the diffusion couples.     

Mutual Diffusion in Liquid Rubidium–Bismuth Alloys

The mutual diffusion in rubidium–bismuth melts was investigated using a gammaray attenuation technique. The concentration dependence of the interdiffusion coefficient has two maxima in the vicinity of 25 and 50 at.% Bi. The analysis based on Darken’s relation shows that this feature is connected to a tendency for the formation of associated complexes in the liquid alloys.     

NpT-ensemble Monte Carlo calculations for binary liquid mixtures

A Monte Carlo method for the calculation of thermodynamic properties in the isothermal-isobaric ensemble is described. Application is made to the calculation of excess thermodynamic properties (enthalpy, volume and Gibbs free energy) of binary mixtures of Lennard-Jones 12-6 liquids. Comparison is made with the predictions of a number of theories of liquid mixtures; the so-called van der Waals one-fluid model and the variational theory of Mansoori and Leland are both found to give excellent results. The accuracy attainable in estimates of the excess properties is discussed in terms of statistical fluctuations in various calculated quantities and the advantages and disadvantages of the method are examined in relation to calculations by the more familiar constant-volume method.     

Interdiffusion and thermotransport in Ni–Al liquid alloys

In this paper, we present extensive self-consistent results of molecular dynamics (MD) simulations of diffusion and thermotransport properties of Ni–Al liquid alloys. We develop a new formalism that allows easy connection between results of the MD simulations and the real experiments. In addition, this formalism can be extended to the case of ternary and higher component liquid alloys. We focus on the temperature and composition dependence of the self-diffusion coefficients, interdiffusion coefficients, thermodynamic factor, Manning factor and the reduced heat of transport. The two latter quantities both represent measures of the off-diagonal Onsager phenomenological coefficients. The Manning factor and the reduced heat of transport can be related to experimentally obtainable quantities provided the thermodynamic factor is available. The simulation results for the reduced heat of transport show that for all compositions, in the presence of a temperature gradient, Ni tends to migrate to the cold end. This is in agreement with an available experimental study for a Ni_21.5Al_78.5 melt (only qualitative result is available so far).     

Analysis of vacancies produced at non-equilibrium concentrations by interdiffusion

In this paper, we address the fundamental problem of chemical interdiffusion in binary alloys for the case where vacancies at non-equilibrium concentrations may be generated during the interdiffusion process. We take a very general phenomenological approach to interdiffusion but develop it in a new way. Both high vacancy and low vacancy concentrations are dealt with. For the commonly encountered small vacancy concentration case our strategy centres on directing the information about the driving force associated with the non-equilibrium vacancies (which is effectively not measurable) onto the velocity of inert marker(s) in the diffusion zone. Assuming access to independent knowledge of the two tracer diffusivities we derive expressions for the transport coefficient (for the case of non-equilibrium vacancies) using an analysis along Boltzmann–Matano lines. Using the random alloy model we show that in principle it is possible to measure the relative concentration of non-equilibrium vacancies produced during interdiffusion.     

The Manning factor for direct exchange and ring diffusion mechanisms

Abstract

In this paper, we consider lattice-based diffusion kinetics for the direct exchange and ring mechanisms as possible proxy diffusion mechanisms for diffusion in liquid alloys. For these mechanisms, we assessed the Manning factor that arises from the Darken–Manning relation relating the interdiffusion coefficient and tracer diffusion coefficients and which can be obtained experimentally. The maximum values of the Manning factor for these two mechanisms occur when the exchange only takes place between the atoms of different type but not between the atoms of the same type. These values have strong composition dependence and reach a value of 2 (ignoring tracer correlation factors) for the direct exchange mechanism at equal compositions of the two components in binary alloys. But for the three atom ring mechanism, these values as a function of composition have a much more complicated form that sits below the direct exchange mechanism for compositions between 10 and 90%. When all exchanges (allowed by a mechanism) occur with approximately the same probability, then the Manning factor is about unity for all compositions.     

The effect of the evaporation coefficient on the thermophoresis of a volatile single-component drop in a binary gas mixture

A theory of the uniform thermophoretic motion of a liquid volatile spherical drop in a binary gas mixture is developed based on hydrodynamic analysis. One of the components undergoes the phase transition on the surface. The solution of the problem makes it possible to estimate the effect of the evaporation rate on the rate and direction of thermophoresis, as well as on the distributions of the velocity, temperature, and concentration of the volatile component. The thermal diffusion of the gas mixture, together with Stefan and capillary phenomena, is taken into account. The velocity of thermophoretic transport is expressed through the evaporation coefficient of the drop by the formula that generalizes the known results of the conventional theories for the cases of weak and moderately intense diffusive evaporation of a liquid drop.     

On the accuracy of oxygen pressure measurements

Zirconia-based oxygen sensors are used in many applications and in research. However, the measurement of oxygen partial pressures with these devices is not necessarily correct. Reasons for deviation between sensor reading and nominal composition of the gas mixture are reviewed in this work. The sensor electrochemical permeability is introduced as a starting point. The impact of this oxygen leak on the composition of the surrounding atmosphere is evaluated from mass balances to all species in the system. This procedure shows that even the use of mixtures like CO+CO₂ to establish a given oxygen partial pressure has a limited range of applicability. This is due to the small buffer behavior of some of these mixtures. The gas phase transport of oxygen away from the sensor electrode is also studied. High concentration overpotentials are expected to develop under the circumstances where the buffer behavior of the gas mixture is small. In fact, high concentrations of the CO/CO₂ couple are required both to optimize the gas-mixture buffer effect and the oxygen transport in the gas phase. The latter instead of consisting exclusively of simple diffusion of free oxygen molecules might also involve combined diffusion and counter diffusion of both carbon oxides as oxygen carriers.     

Investigation of the Soret effect in binary liquid mixtures by thermal-diffusion-forced Rayleigh scattering (contribution to the benchmark test)

Within the framework of an international benchmark test we have performed measurements of the transport coefficients S T (Soret coefficient), D (mutual diffusion coefficient) and D T (thermal diffusion coefficient) on the three binary organic liquid mixtures 1,2,3,4-tetrahydronaphthalene- n -dodecane, 1,2,3,4-tetra- hydronaphthalene-isobutylbenzene and isobutylbenzene- n -dodecane with the weight fraction c = 0.5 at T = 298.15 K by means of thermal-diffusion-forced Rayleigh scattering (TDFRS) for benchmarking purposes. Our results for the coefficients are in good agreement with those obtained by annular and parallelepipedic thermogravitational columns and by other benchmark tests which also apply TDFRS measurements.     

Determination of binary diffusion coefficients of gases using photothermal deflection technique

A photothermal deflection (PD) technique was applied to measure the binary diffusion coefficients of various gases (CO₂–N₂, CO₂–O₂, N₂–He, O₂–He, and CO₂–He). With an in-house-made Loschmidt diffusion cell, a transverse PD system was employed to measure the time-resolved PD signal associated with the variation of the thermal diffusivity and the temperature coefficient of the refractive index of the gas mixture during the diffusion. The concentration evolution of the gas mixture was deduced from the PD amplitude and phase signals based on our diffraction PD model and was processed using two mass-diffusion models explored in this work for both short- and long-time diffusions to find the diffusion coefficient. An optical fiber oxygen sensor was also used to measure the concentration changes of the mixtures with oxygen. Experimental results demonstrated that the binary diffusion coefficients precisely measured with the PD technique were in agreement with the literature values. Moreover, the PD technique can measure the diffusion coefficients of various gas mixtures with both short- and long-time diffusions. In contrast, the oxygen sensor is only suitable for the long-time diffusion measurements of the gas mixtures with oxygen. PACS 78.20.Nv; 51.20.+d     

Mechano-chemistry; diffusion in multicomponent compressible mixtures

In the present work we derive the volume continuity equation and demonstrate its use to define the volume frame of reference in the multicomponent, compressible systems. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass diffusion, heat flow, etc. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the translation of the Newton’s discrete mass-point molecular mechanics into continuum mechanics and the use of the Cauchy linear momentum equation of fluid mechanics and Navier-Lamé equation of mechanics of solids.Our proposed modifications of Navier-Lamé and energy conservation equations are self-consistent with the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport. We do show that the local diffusion processes do not change the centre of mass of the system and that the stress and viscosity depend only on the local volume velocity.     

Influence of a magnetic field on diffusion and thermal diffusion in gaseous mixtures

The influence of a magnetic field on the transport properties of binary mixtures of a polyatomic and a noble gas is studied theoretically. Using an inverse operator technique, first thermal conductivity and viscosity are treated. Then diffusion and thermal diffusion are discussed in detail, with special emphasis on the composition dependence. A relation connecting the magnitudes of the field effects on thermal conductivity, diffusion, and thermal diffusion is derived. This relation is used to estimate the field effect on diffusion.     

A brief study on the mixture rules of the acoustic non-linearity parameter B/A in binary biological mixtures

Using the improved thermodynamic method, the acoustic non-linearity parameter B/A of binary biological mixtures — such as pig blood, sheep blood and bovine blood — is measured in order to test the mixture rules proposed by Apfel and Sehgal. The results show that the B/A values of the above-mentioned blood decrease with an increasing volume fraction of water. The B/A value varies linearly with the volume fraction of protein. It is also shown that, treated as a binary mixture, the blood obeys the trend that the B/A value varies with the volume of water. This is in agreement with the rules proposed by Apfel and Sehgal. However, the measured B/A value is not exactly equal to that of the mixture rules.