R.M. Velasco

Maximum entropy formalism for a dense gas

The maximum entropy formalism is developed to implement a complete description of a dense gas in non-equilibrium situations. Two variational schemes are discussed in this context. The kinetic equations describing the system are consistently closed with the N-particle distribution function obtained via this formalism. The equilibrium state obtained on this basis is consistent with the description of the theory of liquids in the equilibrium state.

Entropy balance equation for a dense gas

This work is concerned with the description of the time evolution for the entropy functional in a dense fluid out of equilibrium. We consider the fluid as a collection of N particles interacting via the superposition of pairwise additive short range intermolecular potentials. Such an interaction is assumed to be central and the particles do not have internal structure. To reach this goal we use the maximum entropy formalism in which the Gibbs entropy is maximized under the restrictions imposed by the normalization of the N-particle distribution function and the knowledge of the one and two-particle distribution functions. This procedure leads to an expression for the entropy functional in terms of such distribution functions. On the other hand, the evolution equations allow for the construction of a balance equation for the entropy functional in the system. An analysis of the entropy flux and entropy source is given for a particular expression in the Lagrange multipliers coming from the maximization procedure. Such an analysis shows the connection of the entropy production with the conversion rate of kinetic and potential energy between particles. Interesting conclusions about the temperature are reached in this case.

Entropy production bound in a dense gas

This paper concerns the behavior of the entropy production in a dense gas. A bound for this quantity is found in terms of the energy conversion rate between particles and Fishers information integrals describing the system.

THE CLOSURE HYPOTHESIS IN THE MAXIMUM ENTROPY FORMALISM

Abstract Closure hypotheses in kinetic theory constitute a point of comparison between different approaches to describe the behavior of a macroscopic system. The maximum entropy formalism (MEF-I) gives us a way to close the BBGKY hierarchy equations and its discussion is the main objective of this paper.

Kinetic model of thermotransport in semiconductors

In this work we develop a semiclassical kinetic model to construct hydrodynamic equations to study the nonequilibrium behavior of an electron gas in a semiconductor. To describe the system we assume that the Boltzmann transport equation is valid and we solve it in terms of the first 13 moments, which become the basic fields to describe thermotransport in this system. The closure of the transport equations is achieved through an expansion around the nonequilibrium Fermi–Dirac distribution function. The nonconserved variables satisfy relaxation equations and their characteristic times are expressed in kinetic terms. The electric current density and the heat flux can be written as generalized constitutive equations, allowing us to obtain thermotransport coefficients as functions of the frequency, where the relaxation times play a very important role.

Transport coefficients for polyatomic gases

We use Grads method to solve the Wang-Chang-Uhlenbeck-de Boer equation for dilute polyatomic gases, and we study the non-equilibrium mean energy associated with the internal degrees of freedom in order to calculate the thermal conductivity and the Eucken factor.

Light scattering in the kinetic regime

The dynamic structure factor as well as the generalized Landau–Placzek relation are calculated from a set of equations describing a monatomic gas in the moderately dense region. These studies start from the 13-moment Grads approximation to solve the Enskog equation giving us a description of the system which is valid out of the hydrodynamic regime. The hydrodynamic matrix is written in terms of the generalized transport coefficients up to second order in the density, where the bulk viscosity is taken into account.

Onsager's symmetry in the Burnett regime

The Onsager Symmetry Relations (OSR), which are of fundamental importance in Linear Irreversible Thermodynamics (LIT), are not obeyed by the linearized Burnett equations for a dilute gas. In this paper we present a solution to this problem, which consists of an enlargement of the space of relevant variables to include the heat flux and the viscous tensor as state variables besides the usual conserved ones, an ansatz which has a kinetic foundation in the Grads method of solution to the Boltzmann equation. After showing that the evolution equations for the non-conserved moments reduce to the usual constitutive relations for the Burnett approximation, we prove that the resultant set of hydrodynamical equations indeed satisfy the OSR.

Slip boundary conditions in Couette flow

The influence of a boundary layer in the Couette flow of a rarefied gas is studied by means of the Grads solution for the Boltzmann equation. The boundary conditions satisfied by the relevant Grads moments are calculated through the simplest wall model which is characterized by some accommodation coefficients in the surface. Accordingly, temperature and velocity profiles in the gas are calculated.

Generalized hydrodynamics in Enskog gases

The generalized hydrodynamic behavior of an Enskog moderately dense gas has been studied mainly through the correlation functions approach. However, the kinetic model based on the Grads method to solve the Enskog equation seems to be a good alternative to such studies. In this work, we explore the behavior of the generalized transport coefficients and obtain several relationships between Grads method and the usual Chapman–Enskog scheme. The calculation is developed up to a second order in the density expansion, so we can obtain the complete hydrodynamic limit, also involving the volumetric–thermal effects.