R.F. Rodríguez

On the foundations of extended irreversible thermodynamics

A theory of macroscopic systems which takes as independent variables the slow (conserved) ones plus the fast dissipative fluxes is carefully analyzed at three levels of description: macroscopic (thermodynamic), microscopic (projection operators) and mesoscopic (fluctuation theory). Such a description is compared with the memory function approach based only on the conserved variables. We find that the first theory is richer and wider than the second one, and some misunderstandings in this connection are clarified and discussed.

A thermodynamic approach to non-linear viscoelasticity

We show that Extended Irreversible Thermodynamics (EIT) may be regarded as a unifying thermodynamic scheme which generates a variety of non-linear viscoelastic equations of state. In particular, we show how the so-called eight-constants Oldroyd model, with all its invariant properties, may be derived from the postulates of EIT. It is also shown that the structure of the thermodynamic based rheological equations of state is in complete agreement with that of the representation theorems formulation of constitutive relationships originally proposed by Rivlin and Ericksen. We discuss how more complex rheological models can be derived from higher order approximations of the theory. Finally, the connections between our approach and other related works are briefly discussed.

Fluids with internal degrees of freedom. I. Extended thermodynamics approach

Extended irreversible thermodynamics (EIT) is used to derive a complete set of time evolution equations for the state variables describing a general polyatomic fluid. The internal degrees of freedom of the fluid are represented by suitable nonconserved variables. In particular, these time evolution equations are shown to resemble relaxation‐type equations. The sign of the unknown coefficients included in such equations is undetermined. However, when a comparison is made with the results obtained from the moment solution method of a kinetic equation for a dilute polyatomic fluid, several of the general features of the phenomenological results are clarified. Indeed, the predictions of kinetic theory fully agree with the basic equations of EIT. This provides a mesoscopic foundation for the theory. The sign of the unknown coefficients appearing in the relaxation‐type equations for the nonconserved variables is such that the corresponding relaxation times are positive definite. Therefore, such equations are in...

Linear viscoelasticity and irreversible thermodynamics

The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.

Superstatistics of Brownian motion: A comparative study

The dynamics of temperature fluctuations of a gas of Brownian particles in local equilibrium with a nonequilibrium heat bath are described using an approach consistent with Boltzmann–Gibbs (BG) statistics. We use mesoscopic nonequilibrium thermodynamics (MNET) to derive a Fokker–Planck equation for the probability distribution in phase space including the local intensive variables fluctuations. We contract the description to obtain an effective probability distribution (EPD) from which the mass density, van Hoves function and the dynamic structure factor of the system are obtained. The main result is to show that in the long time limit the EPD exhibits a similar behavior as the superstatistics distribution of nonextensive statistical mechanics (NESM), therefore implying that the coarse-graining procedure is responsible for the so-called nonextensive effects.

Extended thermodynamic description of diffusion in an inert binary mixture

The equilibrium concentration autocorrelation function for an inert binary mixture is calculated by means of extended irreversible thermodynamics. The ensuing generalized transport coefficient is explicitly evaluated and the corresponding k‐dependent relaxation time is also obtained. The connection with neutron scattering experiments is suggested and expressions for the dynamic structure factor and the half‐width dispersion relation are given.

Fluids with internal degrees of freedom. II. Rayleigh–Brillouin scattering

The extended thermodynamic treatment developed in part I for a fluid with internal degrees of freedom, is used to calculate its Rayleigh–Brillouin spectrum. A hydrodynamic model is first constructed which involves unspecified phenomenological coefficients. When these coefficients are identified in terms of experimental parameters, reasonably good agreement is obtained between the calculated and measured dynamic structure factor of CS2 at 20 °C with a density 1.262 g/cm3 and for k=8.608×10 cm−1. It is also shown that when the relaxation times of the trace and the nondeviatoric part of the stress tensor of the fluid tend to zero, the results previously derived by Mountain are recovered. The possible connections between this extended thermodynamic approach and Rytov’s hydrodynamic theory are also hinted at.

Model for the electrorheological effect in flowing polymeric nematics

An analytical model to study the response of a polymeric nematic confined in a rectangular cell, to a dc electric field is presented. The effect of a pressure-driven plane Poiseuille flow and its competition with the electric field is explicitly considered. For the final stationary state where the induced reorientation of the director has already occurred, an aligned structure with a greatly enhanced viscosity (electrorheological effect) is produced. For this same state the first normal stress difference is calculated as a function of position and of the applied field. For this quantity, regions of negative and positive values develop along the direction of the velocity gradient and an increase in the electric field or the flow causes an augmented effect in its profiles. The net force between the plates is also calculated. As the Reynolds number increases, it is found that it also changes sign from positive to negative, and the effect is more pronounced as the strength of the electric field increases. Fin...

Coupling-constant description of coupled flow and diffusion

Abstract We show how the effects of a complicated membrane structure on the transport of solute through the membrane can be represented rather accurately by a single new constant. This constant, which lies between 0 and 1, represents the coupling between the transport of solute by diffusion and by convective flow, as caused by the membrane structure. For a structural model of independent parallel pores, the coupling constant can be interpreted as representing a certain bound on the pore size distribution. By means of theorems on lower and upper bounds, we show that the errors resulting from this coupling-constant approximation are at most a few percent. The same theorems are also used to establish error bounds for a coupling-constant description of the rejection curves ( R vs. Q v ) for sieving membranes.

Long-range order and dynamic structure factor of a nematic under a thermal gradient

Abstract.We use a fluctuating hydrodynamic approach to calculate the orientation fluctuations correlation functions of a thermotropic nematic liquid crystal in a nonequilibrium state induced by a stationary heat flux. Since in this nonequilibrium stationary state the hydrodynamic fluctuations evolve on three widely separated times scales, we use a time-scale perturbation procedure in order to partially diagonalize the hydrodynamic matrix. The wave number and frequency dependence of these orientation correlation functions is evaluated and their explicit functional form on position is also calculated analytically in and out of equilibrium. We show that for both states these correlations are long-ranged. This result shows that indeed, even in equilibrium there is long-range orientational order in the nematic, consistently with the well known properties of these systems.We also calculate the dynamic structure of the fluid in both states for a geometry consistent with light scattering experiments. We find that as with isotropic simple fluids, the external temperature gradient introduces an asymmetry in the spectrum shifting its maximum by an amount proportional to the magnitude of the gradient. This effect may be of the order of 7 per cent. Also, the width at half height may decrease by a factor of about 10 per cent. Since to our knowledge there are no experimental results available in the literature to compare with, the predictions of our model calculation remains to be assessed.