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In this paper a linear theory for dielectric relaxation phenomena in polarizable reacting fluid mixtures is developed, in the frame of thermodynamics of irreversible processes with internal variables. The microscopic irreversible phenomena giving rise to dielectric relaxation are described splitting the total specific polarization in two irreversible parts and introducing one of these partial specific polarizations as internal variable in the thermodynamic state vector. The phenomenological equations for these fluid mixtures are derived and, in the linear case, a generalized Debye equation for dielectric relaxation phenomena is derived. Special cases are also treated. Linear theories for polarizable continuous media with dielectric relaxation phenomena were derived in the same frame of non-equilibrium thermodynamics with internal variables in previous papers by one of the authors (LR). A phenomenological theory for these phenomena was developed by Maugin for complex materials, using microscopic considerations and introducing particular partial polarizations per unit mass. The obtained results in this paper have applications in several fields of applied sciences, as, for instance, in medicine and biology, where complex fluids presenting dielectric relaxation, are constitued by different types of molecules, with own dielectric susceptibility and relaxation time.

In a previous paper, in the framework of extended irreversible thermodynamics with internal variables, a model for nanostructures with thin porous channels filled by a fluid flow was developed. The porous defects of porous channels inside the structure, described by a permeability structure tensor, may have a strong influence on the effective thermal conductivity, and their own dynamics may couple in relevant way to the heat flux dynamics. Here, in the linear case a generalized telegraph heat equation for thermal perturbations with finite velocity is derived in the anisotropic and isotropic case for the nanosystems taken into account. The thermal disturbances are so fast that their frequency becomes of the order of reciprocal of the relaxation time, given, for instance, by the collision time of heat carriers. Furthermore, the complete system of equations describing the behaviour of the media under consideration is worked out and discussed. The obtained results have applications in "defect engineering" and an important technological interest.

In a previous paper of the second author the nonlinear Lyapunov stability of the thermodiffusive equilibrium of a viscoelastic rotating Walters fluid, in a horizontal rotating layer heated and salted from below was studied. If instability occurs as stationary convection a non linear stability bound coinciding with the linear one was derived. In this paper we reconsider the same problem recovering the same result without any restriction on the viscoelasticity parameter.

In this paper we study the nonlinear Lyapunov stability of the thermodiffusive equilibrium of a viscous electroconducting horizontal fluid layer heated from below. We reformulate the nonlinear stability problem, in terms of poloidal and toroidal fields, by projecting the initial perturbation evolution equations on some suitable orthogonal subspaces of the kinematically admissible functions. In such a way, if the principle of exchange of stabilities holds, we obtain, in the classical L^2-norm, the coincidence of linear and nonlinear stability bounds.

In this paper we study the nonlinear Lyapunov stability of the thermodiffusive equilibrium of a viscoelastic rotating Walters fluid, in a horizontal rotating layer heated and salted from below. We reformulate the nonlinear stability problem, projecting the initial perturbation evolution equations on some suitable subspaces of the space of kinematically admissible functions. In this way we preserve the contribution of the Coriolis term and, jointly, all nonlinear terms vanish. When the viscoelasticy parameter vanishes, that is for the classical rotating Bénard problem, if instability occurs as stationary convection, the linear and nonlinear stability bounds are equal.

In this paper we apply some variants of the classical energy method to study the nonlinear Lyapunov stability of the thermodiffusive equilibrium for a viscous thermoelectroconducting fully ionized fluid in a horizontal layer heated from below. The classical L^2 norm, too weak to highlight some stabilizing or unstabilizing effects, can be used to dominate the nonlinear terms. A more fine Lyapunov function is obtained by reformulating the initial perturbation evolution problem, in terms of some independent scalar fields. In such a way, if the principle of exchange of stabilities holds, we obtain the coincidence of linear and nonlinear stability bounds.

In this article we consider the stability of a chemical equilibrium of a thermally conducting two-component reactive viscous mixture, in a horizontal layer heated from below and experiencing a catalyzed chemical reaction at the bottom plate. After reformulating the perturbation evolution equations in a suitable equivalent form, we study the nonlinear Lyapunov stability and, assuming the validity of the principle of exchange of stabilities, we find a region of the parameter space in which the linear and nonlinear stability bounds coincide.