On the Maxwell-Stefan approach to multicomponent diffusion

We consider the system of Maxwell-Stefan equations which describe multicomponent diffusive fluxes in non-dilute solutions or gas mixtures. We apply the Perron-Frobenius theorem to the irreducible and quasi-positive matrix which governs the flux-force relations and are able to show normal ellipticity of the associated multicomponent diffusion operator. This provides local-in-time wellposedness of the Maxwell-Stefan multicomponent diffusion system in the isobaric, isothermal case.Comment: Based on a talk given at the Conference on Nonlinear Parabolic Problems in Bedlewo, Mai 200

Existence of radial stationary solutions for a system in combustion theory

In this paper, we construct radially symmetric solutions of a nonlinear noncooperative elliptic system derived from a model for flame balls with radiation losses. This model is based on a one step kinetic reaction and our system is obtained by approximating the standard Arrehnius law by an ignition nonlinearity, and by simplifying the term that models radiation. We prove the existence of 2 solutions using degree theory

On modified simple reacting spheres kinetic model for chemically reactive gases

Versão dos autores para esta publicação.We consider the modiffed simple reacting spheres (MSRS) kinetic model that, in addition to the conservation of energy and momentum, also preserves the angular momentum in the collisional processes. In contrast to the line-of-center models or chemical reactive models considered in [1], in the MSRS (SRS) kinetic models, the microscopic reversibility (detailed balance) can be easily shown to be satisfied, and thus all mathematical aspects of the model can be fully justi ed. In the MSRS model, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. Reactive and non-reactive collision events are considered to be hard spheres-like. We consider a four component mixture A, B, A*, B*, in which the chemical reactions are of the type A + B = A* + B*, with A* and B* being distinct species from A and B. We provide fundamental physical and mathematical properties of the MSRS model, concerning the consistency of the model, the entropy inequality for the reactive system, the characterization of the equilibrium solutions, the macroscopic setting of the model and the spatially homogeneous evolution. Moreover, we show that the MSRS kinetic model reduces to the previously considered SRS model (e.g., [2], [3]) if the reduced masses of the reacting pairs are the same before and after collisions, and state in the Appendix the more important properties of the SRS system.Fundação para a Ciência e a Tecnologi

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

Simple bimolecular reactions $A_1+A_2\rightleftharpoons A_3+A_4$ are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction $H_2+Cl\rightleftharpoons HCl+H$, and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.Comment: 11 pages, 5 figures, to appear in vol.42 of the Brazilian Journal of Physic

Direct Numerical Simulation Of Turbulent Multispecies Channel Flow With Wall Ablation

The design of solid rocket motors requires the prediction of changes induced by the ablation process occurring at the nozzle throat. The present study aims at understand-ing the effects of ablation on the turbulent boundary layer performing direct numerical simulations in a channel flow configuration. An ablation boundary condition for arbitrary chemical composition and pyrolysis scheme is developed and presented in this paper. Then, two DNS of a seven species reacting flow are performed: a) with inert walls; b) with ablated walls. Generated data are compared and analyzed looking at first order statistics. It is shown that the classical law of the wall for velocity and temperature are not appropriate to represent the numerical result. The chemical equilibrium assumption is shown to be valid in the inert case and a wall function consistent with this assumption is in fair agreement with the results. Nomenclature m ̇ wall mass flux, kg · m−2 · s−1 ṙc carbon surface recession rate, m/s ṡk surface production rate of k, kg · m−2 · s−

Kinetic Theory of Plasmas: Translational Energy

In the present contribution, we derive from kinetic theory a unified fluid model for multicomponent plasmas by accounting for the electromagnetic field influence. We deal with a possible thermal nonequilibrium of the translational energy of the particles, neglecting their internal energy and the reactive collisions. Given the strong disparity of mass between the electrons and heavy particles, such as molecules, atoms, and ions, we conduct a dimensional analysis of the Boltzmann equation. We then generalize the Chapman-Enskog method, emphasizing the role of a multiscale perturbation parameter on the collisional operator, the streaming operator, and the collisional invariants of the Boltzmann equation. The system is examined at successive orders of approximation, each of which corresponding to a physical time scale. The multicomponent Navier-Stokes regime is reached for the heavy particles, which follow a hyperbolic scaling, and is coupled to first order drift-diffusion equations for the electrons, which follow a parabolic scaling. The transport coefficients exhibit an anisotropic behavior when the magnetic field is strong enough. We also give a complete description of the Kolesnikov effect, i.e., the crossed contributions to the mass and energy transport fluxes coupling the electrons and heavy particles. Finally, the first and second principles of thermodynamics are proved to be satisfied by deriving a total energy equation and an entropy equation. Moreover, the system of equations is shown to be conservative and the purely convective system hyperbolic, thus leading to a well-defined structure

Weak and strong solutions of equations of compressible magnetohydrodynamics

International audienceThis article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions. Then, existence of strong solutions in the neighbourhood of equilibrium states is reviewed, in particular with the method of Kawashima and Shizuta. Finally, the special case of dimension one is highlighted : the use of Lagrangian coordinates gives a simpler system, which is solved by standard techniques