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.     

Criterion for establishing deviations from the local thermodynamic equilibrium in atmospheric pressure plasma jets

In this paper a dimensionless parameter is defined which allows the prediction of the thermodynamic state in the field-free plasma jet of D. C. operated plasma torches of various designs. This dimensionless parameterP is derived from the conservation equations applied to a two-step temperature and velocity model and contains only quantities which can be experimentally determined without using sophisticated equipment. Critical values ofP based on a critical electron density of 10¹⁶ cm^?3 have been calculated for argon, hydrogen, nitrogen, oxygen, and helium and corresponding values of P_crit have been determined experimentally for two different D. C. operated argon plasma torches using various diagnostic techniques. The experimental values corroborate the assumptions made for the calculation of P_crit. ForP < P_crit, substantial deviations from the local thermodynamic equilibrium (LTE) may occur.     

Generic aspects of convexification with applications to thermodynamic equilibrium

This work presents a mathematical analysis of the process of convexification of a smooth function based on singularity theory. The theory developed is applied to the problem of thermodynamic phase equilibrium. The central notion introduced here is that of phase simplex, which we use to discuss phase equilibrium and phase transition in an abstract framework. One of the by-products of the results of this paper is a rigorous proof of Gibbs' Phase Rule for multicomponent systems, in which a well-accepted mathematical notion of genericity is used to account for ostensible exceptions to the rule. Also, many other features known from theoretical or experimental thermodynamics can be rediscovered through purely mathematical arguments from the notions introduced here. Such features include, among other things, the existence of saturation pressures, the existence of multiple or critical points, and the existence of spontaneous or continuous changes in the composition of the phases at phase transitions.     

Deviations from thermodynamic equilibrium during recombination of a dispersing plasma

The relaxation of a dense low-temperature plasma during cooling of the electrons on heavy particles and during dispersion of a plasma cluster into a vacuum is examined. The population kinetics is analyzed in the limiting cases of free escape and radiation capture. The results are presented for a numerical solution of the self-consistent (with respect to temperature and concentration of free electrons) problem of the relaxation of an atomic hydrogen plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 3–10, September–October, 1973.     

Traveling wave with allowance for equilibrium radiation

Three modes of propagation of a traveling-wave front over a noncold gas with different propagation velocities are found using one thermodynamic model. When the indicated velocity is low, transition from constant values of the gas parameters on both sides of the traveling-wave front proceeds continuously. An increase in the traveling-wave velocity leads to an isothermal jump: the density and velocity of the gas undergo a strong discontinuity whereas the temperature varies continuously. With a further increase in the traveling-wave velocity, the isothermal jump disappears and the flow becomes continuous again. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 15–25, July–August, 2006.     

Shift of chemical equilibrium in a resonance infrared radiation field

The degree of displacement of chemical equilibrium in dissociation reactions, including three-particle recombination due to laser radiation at an isolated vibrational degree of freedom of the molecules, is determined. Dependences of the vibrational temperature and the chemical equilibrium constant on the vibrational excitation probability are obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 10–12, January–February, 1976.The authors wish to express their appreciation to R. V. Khokhlov for support and interest in the work.     

An investigation of thermodynamic states during high-pressure fuel injection using equilibrium thermodynamics

A numerical investigation of mixing processes between an injected fuel (an n-alkane) and a chamber inert gas (nitrogen) was carried out for high-pressure fuel injection. The objective is to determine conditions for the coexistence of both liquid and gas phases under the typical ambient conditions encountered in diesel engines. A phenomenological investigation was built by coupling phase stability analysis with the energy conservation equation. Phase changes (including separation and combination) are predicted to occur so as to yield the lowest Gibbs free energy. It is also shown that predicted states without considering phase transitions can be very different from the corresponding thermodynamically correct states. By comparing four n-alkane/nitrogen mixtures it is shown that the lower limit of the two-phase region occurs at similar temperatures. However, heavy n-alkane/nitrogen mixtures have a larger upper limit, and phase separation occurs at higher temperatures. The present model predicts the existence of multiple phases locally in the dense spray jet under high temperature and pressure ambient conditions due to the significant reduction of the mixture temperature caused by vaporization and cooling.     

Effects of vapor pressure on thermodynamic equilibrium in multiphase flow for thermochemical hydrogen production

This paper examines the effects of H₂O vapor pressure on the equilibrium conditions of a CuCl₂ hydrolysis reactor in the thermochemical Cu–Cl cycle of hydrogen production. A new predictive model is developed to determine the minimum steam requirement in the reactor based on the chemical equilibrium condition, reactor pressure and fraction of gaseous reactant. Experimental data, at three separate vapour pressures of steam, compared well with the new predictive formulation.     

Temperature and pressure equilibrium distribution in a steady-state discharge with radiation

Results of a numerical solution of the equations of energy and momentum balance are given for a steady-state discharge in a dense plasma.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 4, pp. 133–135, July–August, 1971.     

The problem of radiation transport in the channels of a polysectional thermodynamic system

The problem of radiation energy transfer in ballistic radiative-gas compression facilities is considered. For constructing mathematical models of these facilities, an algorithm for splitting the thermodynamic system into sections (with consideration of the interconnections of the polysectional system) is used. The conditions of applicability of the thermodynamic approach to describing the processes in a ballistic plasmotron are established. It is shown that, in most practical problems, the losses in the intersectional channels are insignificant as compared with the losses in the sections and can be neglected.     

Versatile code DLAYZ for investigating population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium

A versatile code DLAYZ based on collisional-radiative model is developed for investigating the population kinetics and radiative properties of plasmas in non-local thermodynamic equilibrium. DLAYZ is implemented on the detailed level accounting (DLA) approach and can be extended to detailed configuration accounting (DCA) and hybrid DLA/DCA approaches. The code can treat both steady state and time-dependent problems. The implementation of the main modules of DLAYZ is discussed in detail including atomic data, rates, population distributions and radiative properties modules. The complete set of basic atomic data is obtained using relativistic quantum mechanics. For dense plasmas, the basic atomic data with plasma screening effects can be obtained. The populations are obtained by solving the coupled rate equations, which are used to calculate the radiative properties. A parallelized version is implemented in the code to treat the large-scale rate equations. Two illustrative examples of a steady state case for carbon plasmas and a time-dependent case for the relaxation of a K-shell excited argon are employed to show the main features of the present code.     

On the Gibbs conditions of stable equilibrium,convexity and the second-order variations of thermodynamic potentials in nonlinear thermoelasticity

The Gibbs conditions of stable thermodynamic equilibrium are formulated for nonlinear thermoelastic materials, based on the constrained minimization of four fundamental thermodynamic potentials. Sufficient conditions for incremental stability are stated in each case. The previously unexplored connections between the second-order variations of thermodynamic potentials are used to establish the convexity or concavity properties of all thermodynamic potentials in relation to each other, and to derive the relationships between the specific heats at constant stress and deformation, and between the isentropic and isothermal elastic moduli and compliances. The comparison with the derivation based on the classical thermodynamic approach is also given.     

On the instability of equilibrium when the potential has a non-strict local minimum

Instability is studied for a mechanical system with two degrees of freedom whose potential has a non-strict local minimum at the origin. Under suitable conditions of smoothness it is shown that the corresponding equilibrium is unstable when the potential has a local minimum along a curve passing through the origin. As a particular case, we get instability if the potential is analytic and has a non-isolated minimum at the origin. These results improve those of G. Hamel [1] and Silla [5] on the same subject.

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Résumé On étudie l'instabilité d'un système mécanique à deux degrés de liberté quand le potentiel a un minimum non isolé a l'origine. On montre que l'équilibre correspondant est instable si le potentiel est assez régulier et a un minimum local en chaque point d'une courbe passant par l'origine. Comme cas particulier, on prouve l'instabilité de l'origine si le potentiel est analytique et y présente un minimum non isolé. Ces résultats améliorent ceux de G. Hamel [1] et L. Silla [5] sur le même sujet.

     

Instability of the liquid equilibrium state in an ice-water system with account for radiation heating

The problem of the stability of the equilibrium state of a weakly compressible fluid bounded from below by a stationary rigid wall and from above by a heat-conducting finite-thickness wall is studied. The thermal state of the system is investigated with account for volume heat sources due to radiation. It is shown that the mechanical equilibrium of the system is unstable. The neutral curves are plotted and the critical Rayleigh numbers are found.     

Temperature determination in a transient free fuel jet with equilibrium temperature of the local molar mixture fraction

This paper presents the space-resolved temperature determination in the mixing zone of a transient free dimethyl ether jet flowing into a non-moving atmosphere via the time-resolved local molar mixture fraction, obtained with tracer added Laser-induced Fluorescence. The temperature of the mixture is calculated with an approach of an adiabatic mixing temperature. To validate the obtained temperatures a high-speed thermocouple measures the local temperature with high temporal resolution. The thermocouple data is corrected using a detailed model that includes all relevant effects of radiation, convection and conduction. The corrected thermocouple temperature is compared with the temperature data obtained via the local molar mixture fraction. Comparison of the corrected thermocouple data with the mixture-derived data shows excellent agreement for pressure and temperature conditions sufficiently far from the critical point of dimethyl ether.