Giselle M. Alves

Effect of chemical reactions on the transport coefficients of binary mixtures

The effects caused by the chemical reactions on the transport coefficients of a mixture of ideal gases which undergo a simple reversible symmetric reaction of the type A+A⇌B+B are analyzed within the framework of a kinetic theory based on the Boltzmann equation. The analyzed system is closed to the final stage of a chemical reaction where the affinity is considered to be a small quantity and the system tends to the chemical equilibrium. This kind of reaction is known as “fast” reactions, because the reactive processes are of the same order as the elastic ones. The internal degrees of freedom of the molecules of the gas are not taken into account. This enables to represent the gas molecules as rigid spheres and therefore to determine the coefficients of thermal conductivity, diffusion, thermal-diffusion ratio, shear viscosity, and the forward reaction rate analytically. It was verified that some factors—among others, the concentration of the reagents (or products of the reaction), the activation energy, th...

Light scattering and sound propagation in a chemically reacting binary gas mixture

The aim of this paper is to study time-dependent problems like sound propagation and light scattering in binary mixtures undergoing a simple reversible symmetric reaction—of the type A+A⇌B+B—close to the final stage of the chemical reaction where the system tends to chemical equilibrium. The molecules of the gas are modeled as rigid spheres and—apart from the binding (or formation) energy of the molecules—the internal degrees of freedom were not taken into account. The hydrodynamic description is based on the conservation laws of mass, momentum and energy closed by the constitutive equations for the pressure tensor, heat flux vector, diffusion velocity and rate of reaction which correspond to the Navier–Stokes law and generalized laws of Fourier, Fick and Arrhenius, respectively. For the problem of sound propagation it is shown how endothermic and exothermic reactions have influence on the phase speed and on the attenuation coefficient, whereas for the problem of light scattering, their influences on the width of the Rayleigh and Brillouin lines and the position of the Brillouin peak are analyzed.

A kinetic model for chemical reactions without barriers: transport coefficients and eigenmodes

The kinetic model of the Boltzmann equation proposed in the work of Kremer and Soares 2009 for a binary mixture undergoing chemical reactions of symmetric type which occur without activation energy is revisited here, with the aim of investigating in detail the transport properties of the reactive mixture and the influence of the reaction process on the transport coefficients. Accordingly, the non-equilibrium solutions of the Boltzmann equations are determined through an expansion in Sonine polynomials up to the first order, using the Chapman–Enskog method, in a chemical regime for which the reaction process is close to its final equilibrium state. The non-equilibrium deviations are explicitly calculated for what concerns the thermal–diffusion ratio and coefficients of shear viscosity, diffusion and thermal conductivity. The theoretical and formal analysis developed in the present paper is complemented with some numerical simulations performed for different concentrations of reactants and products of the reaction as well as for both exothermic and endothermic chemical processes. The results reveal that chemical reactions without energy barrier can induce an appreciable influence on the transport properties of the mixture. Oppositely to the case of reactions with activation energy, the coefficients of shear viscosity and thermal conductivity become larger than those of an inert mixture when the reactions are exothermic. An application of the non-barrier model and its detailed transport picture are included in this paper, in order to investigate the dynamics of the local perturbations on the constituent number densities, and velocity and temperature of the whole mixture, induced by spontaneous internal fluctuations. It is shown that for the longitudinal disturbances there exist two hydrodynamic sound modes, one purely diffusive hydrodynamic mode and one kinetic mode.

Kinetic theory for binary mixtures of monatomic and polyatomic gases

A kinetic theory is developed for binary mixtures of a monotomic gas (consisting of perfectly smooth, elastic, and rigid spherical particles) and a polyatomic gas (consisting of perfectly rough, elastic, and rigid spherical molecules). A macroscopic state of the mixture is characterized by 29 scalar fields of partial mass densities, partial velocities, partial pressure tensors, partial translational heat fluxes, and partial rotational heat flux. By using the field equations of the 29-field theory and an iterative scheme akin to the Maxwellian procedure, the generalized laws of Fick, Fourier, and Navier-Stokes are obtained. The results of this theory are applied to specific binary mixtures of monatomic gases (He, Ne, Ar, Kr, and Xe) and polyatomic gases (CH4, and CF4, and compared with experimental data.

Transport Coefficients of a Single Reactive Gas

The influence of chemical reactions upon the transport coefficients of the simple chemical reaction A + A → products — where the concentrations of the products are negligible in comparison with those of the reagents — are determined from the Boltzmann equation. Two models for the reactive collision integral are used: (a) in one model the “loss term” of the Boltzmann equation takes into account the elastic and reactive collisions, whereas the “gain term” considers only the elastic collisions, and (b) in the other model the “loss term” considers only the elastic collisions, whereas the “gain term” takes into account the difference between the elastic and the reactive collisions. Explicit expressions for the coefficients of shear viscosity, thermal conductivity and reaction rate as functions of the activation energy are given. It is also shown how the reactant fields of particle number density, pressure and temperature, and the coefficients of shear viscosity, thermal conductivity and reaction rate evolve wi...

Transport Properties of a Kinetic Model for Chemical Reactions without Barriers

A kinetic model of the Boltzmann equation for chemical reactions without energy barrier is considered here with the aim of evaluating the reaction rate and characterizing the transport coefficient of shear viscosity for the reactive system. The Chapman‐Enskog solution of the Boltzmann equation is used to compute the chemical reaction effects, in a flow regime for which the reaction process is close to the final equilibrium state. Some numerical results are provided illustrating that the considered chemical reaction without energy barrier can induce an appreciable influence on the reaction rate and on the transport coefficient of shear viscosity.

Ondas superficiais de gravidade

In this article we discuss the propagation of small amplitude waves in a liquid of constant depth based on a wave equation. The general solution shows that propagation speed depends on the wavelength and consequently there is waves dispersion. Solutions for shallow and the deep water are shown.