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

Isocline curves and variational scalar field

The equations of isocline curves can be obtained from a variational principle with the exceptional scalar field Lagrangian. Shocks are shown to propagate on characteristic curves. Monge-Ampere equation, von Karman fluid, and Born-Infeld theory appear as examples

Second sound and multiple shocks in superfluid helium

A temperature pulse propagating in superfluid helium is studied through the simple waves theory. Our aim is to determine the shape change of this pulse, initially represented by a gaussian profile, using a generalized non-linear Cattaneo model proposed, in the framework of Extended Thermodynamics, by Ruggeri and co-workers in the case of a rigid conductor. The theoretical basis of our arguments is given in a previous paper where the differential system of a binary mixture of Euler's fluids is written as a system for a single heat conducting fluid. We prove that there exist three characteristic temperatures playing an essential role in the shape change of the propagating second sound wave; in particular, several families of multiple shocks (i.e. usual double shocks, double shocks only ahead or behind the wave profile, and very strange quadri-shocks) can appear, depending on the relation among the unperturbed temperature of Helium II and the characteristic temperatures and, in some cases, on the wave's amplitude. Both the cases of a hot wave and a cold wave are discussed, proving that this last process is not symmetric with respect to the previous one. Finally, suitable choices of some parameters are suggested in order to better point out the changes of the wave profile and, in particular, the formation of multiple shocks

An approximated model of multi-temperature mixtures for the description of second sound propagation

In this paper, we analyze a multi-temperature model for the description of second sound propagation with an application to superfluid helium. To this aim, we consider a binary inert mixture of Euler\u2019s fluids and we investigate the case in which the temperatures of the two components are sufficiently close to each other so that a linearization in the neighborhood of an equilibrium state is possible. We also compare the results with those obtained under the single-temperature assumption