Vita Triani

A generalized Coleman–Noll procedure for the exploitation of the entropy principle

A generalization of the classical Coleman–Noll procedure for the exploitation of second law of thermodynamics in the presence of first-order non-local constitutive functions is proposed. The local balance of entropy is regarded as a differential inequality constrained by the governing equations for the set of the unknown fields as well as by their gradient extensions. The thermodynamic compatibility of such a class of materials is achieved without any modification of the basic thermodynamic laws. The results so obtained are applied to model nonlinear heat conduction in solids, in the presence of a dynamical semi-empirical temperature scale.

Exploitation of the Second Law: Coleman–Noll and Liu Procedure in Comparison

Abstract A comparison is made between two classical methods for the exploitation of the second law of thermodynamics: the Coleman–Noll and the Liu procedure. On the example of a rigid heat conductor with general entropy flux, it is shown that the two procedures are equivalent. This equivalence is demonstrated in the case of a state space including the wanted fields, only, as well as in the case of gradients being relevant for constitutive equations, too. Also, the possible importance of an internal variable or an internal degree of freedom is considered.

A new thermodynamic framework for second-grade Korteweg-type viscous fluids

A model of viscous fluid of Korteweg type, with first-order nonlocal constitutive equations, is developed. The restrictions placed by the dissipation principle are investigated by applying a generalized Liu procedure. Some remarkable nonlocal properties of the entropy function are carried out.

Exploitation of the entropy principle: Proof of Liu theorem if the gradients of the governing equations are considered as constraints

The exploitation of the entropy principle in thermodynamics with Lagrange multipliers (the so called Liu procedure) is based on the celebrated Liu theorem. In some recent papers, where either rigid heat conductors or Korteweg fluids have been considered, the Liu procedure has been generalized by using the gradients of the governing equations as additional constraints. Here, a rigorous proof of the validity of the extended procedure to arbitrary first-order nonlocal continua is provided, thus explicitly generalizing the Liu theorem. As an application, heat conducting first-order Korteweg-type fluids with a scalar internal variable are analyzed. The thermodynamic restrictions are determined by the extended Liu procedure. Moreover, a comparison with the thermodynamic analysis obtained by the application of an extended Coleman–Noll procedure is performed.

A new perspective on the form of the first and second laws in rational thermodynamics: Korteweg fluids as an example

Abstract A generalized Coleman–Noll procedure for the exploitation of the entropy principle is presented. It is shown that it is able to dismantle some physical properties of nonlocal materials, which do not emerge if one uses the classical procedure. As an application, Korteweg fluids with a scalar internal variable are studied.

Entropy principle, non-regular processes, and generalized exploitation procedures

The classical Coleman-Noll approach to the exploitation of the entropy principle regards the classical balances of mass, linear and angular momentum and energy as differential constraints for the entropy inequality, and presupposes that the second law of thermodynamics is a restriction on the constitutive equations describing the material properties [B. D. Coleman and W. Noll, “The thermodynamics of elastic materials with heat conduction and viscosity,” Arch. Rational Mech. Anal. 13, 167–178 (1963)10.1007/BF01262690]. In 1996, Muschik and Ehrentraut proved that this presupposition may be confirmed by a rigorous proof, provided that an amendment to the classical second law of thermodynamics, which asserts that, except in equilibria, reversible process directions in state space do not exist, is postulated [“An amendment to the second law,” J. Non-Equilib. Thermodyn. 21, 175–192 (1996)10.1515/jnet.1996.21.2.175]. In their paper, the authors considered regular processes only. In a recent article [V. Triani an...

Non-equilibrium thermodynamics with higher order fluxes: Balance laws and exploitation of the entropy inequality

Weakly non-local extended thermodynamics of rigid heat conductors is presented. The two celebrated procedures by Coleman-Noll and Liu for the exploitation of second law of thermodynamics are compared. It is proved that the two procedures are equivalent, if in the Coleman-Noll procedure all relevant equations are taken into account as constraints.

Modelling of capillary forces in viscous fluids of grade two

We apply a generalized Liu procedure for the exploitation of second law to investigate the thermodynamic compatibility of the constitutive functions modelling capillarity forces in viscous fluids of grade two. We prove that these constitutive equations are fully compatible with the restrictions placed by the requirement of nonnegative entropy production.