Film condensation of multicomponent mixtures

The classic Nusselt model is generalized for the condensation process of a multicomponent vapor mixture. The condensed vapors may be miscible in their liquid state or contain noncondensable gases.The reduction in the condensation rate owing to the accumulation of a noncondensable gas or the more volatile components near the condensate interface is demonstrated for three component systems of methanol—water—air and acetone—methanol—water. Also the effects of interfacial suction and forced convection are included.The analytical solution incorporates Diffusion Law for a multicomponent system and both exact and approximate integral method solutions are applied. The accuracy of the integral method turns out to be remarkably good.     

Effective diffusion of multicomponent mixtures in multidimensional flows

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 113–120, July–August, 1991.     

Viscosity of multicomponent gas mixtures of polar gases

Summary The rigorous binary viscosity expression _mix as transformed to the form originally suggested by Sutherland is studied for mixtures involving polar gases. Any attempt to simplify the _ij of the Sutherland viscosity expression turns out to be only approximately successful. A relation for _ij / _ji is however derived, and the procedure suggested for computing _mix on this basis appears to be very successful. The _ij to a large extent are temperature and composition independent and it has been shown that this fact can be utilised with success for predicting _mix values at high temperatures.     

Numerical simulation of flow of multicomponent mixtures in porous media

A study is made of the isothermal flow of multicomponent mixtures in a porous medium, accompanied by phase transitions, interphase mass exchange, and change in the physicochemical properties of the phases [1–3], It is assumed that at each point of the flow region, phase equilibrium is established instantaneously and the flow velocities of the separate phases conform to Darcy's law. Approximate solutions of problems of displacing oil by high-pressure gas were obtained in [1]. By generalizing the theory developed in [4], a study is made in [5] of the structure of the exact solutions of the problems of the flow of three-component systems which describe the displacement of oil by different reactants (gases, solvents, micellar solutions). The numerical solutions of the problems of multicomponent system flow are considered in [2, 3, 6, 7]. This paper presents a numerical method which is distinguished from the well-known ones [2, 3, 6, 7] by the following characteristics. The flow equations are approximated by a completely conservative finite-difference scheme of the implicit pressure-explicit saturation type, the calculation being carried out using Newton's method of iteraction with spect to both the pressure and the composition of the mixture. The minimum derivative principle [8] is used in the approximation of the divergence terms of the equations. The phase equilibrium is calculated using the equation of state.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 101–110, July–August, 1985.     

Diffusion in multicomponent gaseous mixtures in a model of local thermodynamic equilibrium

Diffusion of chemical elements into an ionized multicomponent gaseous mixture is considered in a model of local thermodynamic equilibrium. A linear dependence of the mass flows of chemical elements and the heat flow on the temperature gradient, mass fractions of the chemical elements, and the electric field is obtained. An example is given of a calculation of the effective diffusion coefficients for a hydrogen-helium mixture.     

Field fluctuations and macroscopic properties for nonlinear composites

A recently introduced nonlinear homogenization method [J. Mech. Phys. Solids 50 ( 2002) 737–757] is used to estimate the effective behavior and the associated strain and stress fluctuations in two-phase, power-law composites with aligned-fiber microstructures, subjected to anti-plane strain, or in-plane strain loading. Using the Hashin–Shtrikman estimates for the relevant “linear comparison composite,” results are generated for two-phase systems, including fiber-reinforced and fiber-weakened composites. These results, which are known to be exact to second-order in the heterogeneity contrast, are found to satisfy all known bounds. Explicit analytical expressions are obtained for the special case of rigid-ideally plastic composites, including results for arbitrary contrast and fiber concentration. The effective properties, as well as the phase averages and fluctuations predicted for these strongly nonlinear composites appear to be consistent with deformation mechanisms involving shear bands. More specifically, for the case where the fibers are stronger than the matrix, the predictions appear to be consistent with the shear bands tending to avoid the fibers, while the opposite would be true for the case where the fibers are weaker.     

The higher order Chapman-Cowling bracket integrals for the viscosity coefficient of multicomponent gas mixtures

Summary The rigorous kinetic theory bracket integrals for the Chapman-Cowling third order approximation to the viscosity coefficient of multicomponent gas mixtures are reported. These expressions will be found useful in interpreting the highly accurate viscosity data on multicomponent gas mixtures now possible. Specially for mixtures involving molecules quite different in nature the contribution is comparable with experimental accuracy.     

Wall jumps in temperature,partial pressures and populations of multicomponent mixtures of nonequilibrium polyatomic gases

The Maxwell-Loyalka method is used to derive formulas for the jumps in the macroparameters of a multicomponent nonequilibrium gas mixture. It is assumed that within the kinetic (Knudsen) wall layer one group of internal states of the molecules is close to equilibrium at the translational temperature, while another group and homogeneous chemical reactions are excited fairly slowly, so that they may be considered to be frozen and the corresponding inelastic collision integrals in the kinetic equations can be neglected. However, at the wall different groups of internal states of the molecules may be excited and chemical reactions may take place. The final calculation formulas are obtained under a series of simplifying assumptions in accordance with the recommendations made in [1, 2].Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 133–141, March–April, 1993.The author is grateful to N. K. Makashev for important comments.     

Field fluctuations in a heterogeneous elastic material—an information theory approach

Internal stress and strain fields in disordered elastic solids such as multiphase materials or polycrystals are considered. In order to derive a probability distribution for those random internal fields, the information theory entropy is maximized subject to constraints representing the basic equations of elasticity and certain experimental data. Thus one can find the probability distribution which agrees with all known facts but makes no assertions about the internal fields which cannot be supported by the available information. This approach is in accordance with the formal exact solution of the statistical problem if one has complete microstructural information. In case of incomplete microstructural data, useful approximate solutions can easily be obtained. In particular, the following set of data is sufficiently detailed for the prediction of internal field fluctuations: the average strain, the one-point probability density of the random elastic constants, and the effective (overall) elastic constants. Especially the information supplied by the effective elastic constants plays a major role since it reflects the microstructural topology of the heterogeneous material. One obtains Gaussian probability distributions for stress and strain, which are applied to calculate mean values and fluctuations of stresses in a cemented metal carbide and a zinc polycrystal.     

Modeling viscosity and diffusion of plasma for pure elements and multicomponent mixtures from weakly to strongly coupled regimes

An analytic model is presented that predicts viscosity and diffusion of plasma for pure elements and multicomponent mixtures, from the high-temperature low-density weakly coupled regime to the low-temperature high-density strongly coupled regime. It relies on a pseudo-ion in jellium modeling that incorporates the effect of electron screening on the ion–ion interaction in the pseudo-ionization. Mixtures are treated using approximate kinetic expressions and mixing laws applied to the excess viscosity and self-diffusion of pure elements. Comparisons are made with classical and quantum molecular dynamics results to assess its accuracy. The mean deviations are in the range 20–40% with almost no predictions further than a factor of 2 over many decades of variation. Applications of this model in the inertial confinement fusion context could help in predicting the appearance and the growth of hydrodynamic instabilities.     

多主元合金中的化学短程有序

大量的研究表明多主元合金中广泛地存在对其性能提升有重要影响的化学短程序. 利用先进的透射电子显微成像技术可以在原子分辨率水平分析多主元合金中化学短程序的尺度、成分和构型.      

Spherical blast waves in multicomponent media

The solution of the problem of propagation of a wave in soils is presented for the case when the wave is produced by the detonation of a spherical charge of some explosive material (EM). The solution is obtained on a computer by the method of characteristics. The soils are regarded as multicomponent media consisting of solid particles, water, and air in conformity with the model proposed in [1, 2]. The dependence of the pressure, velocity of the particles, and the density in the wave front on the distance is determined; the variation of these parameters with time at fixed points of the medium is also determined. The results are compared with the results of tests [1, 2]. Their close agreement for different contents of the components indicates the applicability of the multicomponent model to soils. The limits of applicability of the model are determined. The propagation of a plane wave under the same conditions was investigated in [3].     

Stress concentration in incompressible multicomponent materials

A method for determining the effective elastic constants and the factors of stress concentration in microstructural elements is proposed for nonlinear incompressible multicomponent composite materials randomly reinforced with spheroidal inclusions with an arbitrary ratio of the longitudinal and lateral dimensions. Use is made of the Mori-Tanaka scheme that has, as a first approximation, the result of calculation of the elastic characteristics based on a model taking account of two-point statistical moment functions of arbitrarily high order. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 108–114, March, 2000.