Modelling and analysis of time dependent processes in a chemically reactive mixture

In this paper, we study the propagation of sound waves and the dynamics of local wave disturbances induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in themodel in a proper way. For both time-dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen–Chlorine system as reference. Several numerical computations are included illustrating the behavior of the phase velocity and attenuation coefficient in a low-frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.The paper is partially supported by the Research Centre of Mathematics of the University of Minho, with the Portuguese Funds from the Foundation for Science and Technology (FCT) through the Project UID/MAT/00013/2013. We wish to thank the anonymous Referees for their valuable comments and suggestions that helped us to improve the paper.info:eu-repo/semantics/publishedVersio

Hydrodynamic analysis of sound wave propagation in a reactive mixture confined between two parallel plates

The aim of this work is to study the problem of sound wave propagation through a binary mixture undergoing a reversible chemical reaction of type A + A = B + B, when the mixture is con fined between two flat, info nite and parallel plates. One plate is stationary, whereas the other oscillates harmonically in time and constitutes an emanating source of sound waves that propagate in the mixture. The boundary conditions imposed in our problem correspond to assume that the plates are impenetrable and that the mixture chemically react at the surface plates, reaching the chemical equilibrium instantaneously. The reactive mixture is described by the Navier-Stokes equations derived from the Boltzmann equation in a chemical regime for which the chemical reaction is in its nal stage. Explicit expressions for transport coe fficients and chemically production rates are supplemented by the kinetic theory. Starting from this setting, we study the dynamics of the sound waves in the reactive mixture in the low frequency regime and investigate the influence of the chemical reaction on the properties of interest in the considered problem. We then compute the amplitude and phase pro les of the relevant macroscopic quantities, showing how they vary in the reactive flow between the plates in dependence on several factors, as the chemical activation energy, concentration of products and reactants, as well as oscillation speed parameter.Fundação para a Ciência e a Tecnologia (UID/MAT/00013/2013)info:eu-repo/semantics/acceptedVersio

Discrete velocity modelling of gaseous mixture flows in MEMS

The need of developing advanced micro-electro-mechanical systems (MEMS) has motivated the study of fluid-thermal flows in devices with micro-scale geometries. In many MEMS applications the Knudsen number varies in the range from 10(-2) to 10(2). This flow regime can be treated neither as a continuum nor as a free molecular flow. In order to describe these flows it is necessary to implement the Boltzmann equation (BE) or simplified kinetic model equations. The aim of the present work is to propose an efficient methodology for solving internal flows of binary gaseous mixtures in rectangular channels due to small pressure gradients over the whole range of the Knudsen number. The complicated collision integral term of the BE is substituted by the kinetic model proposed by McCormack for gaseous mixtures. The discrete velocity method is implemented to solve in an iterative manner the system of the kinetic equations. Even more the required computational effort is significantly reduced, by accelerating the convergence rate of the iteration scheme. This is achieved by formulating a set of moment equations, which are solved jointly with the transport equations. The velocity profiles and the flow rates of three different binary mixtures (He-Ar, Ne-Ar and He-Xe) in 2D micro-channels of various height to width ratios are calculated. The whole formulation becomes very efficient and can be implemented as an alternative methodology to the classical method of solving the Navier-Stokes equations with slip boundary conditions, which in any case is restricted by the hydrodynamic regime. (C) 2004 Elsevier Ltd. All rights reserved

Gaseous mixture flow between two parallel plates in the whole range of the gas rarefaction

The flow of binary gaseous mixtures between two parallel plates driven by gradients of pressure, temperature and concentration is studied, based on the McCormack model of the Boltzmann equation. The coupled kinetic equations are solved numerically by the discrete velocity method. The mass flow, the heat flux and the diffusion flux, which are the mixture quantities of practical importance, are expressed in terms of the so-called thermodynamic fluxes. The latter are written in a form that allows us to verify the Onsager-Casimir reciprocity relations. In addition, analytical expressions for these quantities are derived in the limit case of the hydrodynamic regime. Thus, the numerical solution together with these expressions provides the solution in the whole range of the gas rarefaction. The influence of the intermolecular interaction potential is also investigated by comparing the results for the rigid sphere model with those for a realistic potential. Numerical results are presented for two binary mixtures of noble gases (Ne-Ar and He-Xe) for various values of the molar concentrations. (C) 2003 Elsevier B.V. All rights reserved

Gas flow and heat transfer simulation in MEMS via a mesoscopic approach

The flow problem of binary gaseous mixtures in rectangular micro channels due to small pressure, temperature and molar concentration gradients over the whole range of the Kn number is solved. The solution is based on a meso scale approach, formally described by two coupled kinetic equations, subject to diffuse boundary conditions. The model proposed by McCormack substitutes the complicated collision term and the resulting kinetic equations are solved by an accelerated version of the discrete velocity method. Typical results are presented for the flow rates and the heat fluxes of two different binary mixtures (He-Ar and Ne-Ar) in 2-D micro-channels of various concentration and aspect (height to width) ratios, for the whole range of rare-faction. The formulation is very efficient and can be implemented as an alternative to the classical method of solving the Navier-Stokes equations with slip boundary conditions, which in any case is restricted by the hydrodynamic regime, as well as to particle-based simulations, which often become computationally inefficient

Flow of gaseous mixtures through rectangular microchannels driven by pressure, temperature, and concentration gradients

The flow of binary gaseous mixtures through rectangular microchannels due to small pressure, temperature, and molar concentration gradients over the whole range of the Knudsen number is studied. The solution is based on a mesoscale approach, formally described by two coupled kinetic equations, subject to diffuse scattering boundary conditions. The model proposed by McCormack substitutes the complicated collision term and the resulting kinetic equations are solved by an accelerated version of the discrete velocity method. Typical results are presented for the flow rates and the heat fluxes of two different binary mixtures (Ne-Ar and He-Xe) with various molar concentrations, in two-dimensional microchannels of different aspect (height to width) ratios. The formulation is very efficient and can be used instead of the classical method of solving the Navier-Stokes equations with slip boundary conditions, which is restricted by the hydrodynamic regime. Moreover, the present formulation is a good alternative to the direct simulation Monte Carlo method, which often becomes computationally inefficient. (c) 2005 American Institute of Physics