A mesoscopic approach to diffusion phenomena in mixtures

The mesosocpic concept is applied to the theory of mixtures. The aim is to investigate the diffusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the velocities of the components. Balance equations on this enlarged space are the equations of motion for the mesoscopic fields. Moreover, local distribution functions of the velocities are introduced as a statistical element, and an equation of motion for this distribution function is derived. From this equation of motion differential equations for the diffusion fluxes, and also for higher order fluxes are obtained. These equations are of balance type, as it is postulated in Extended Thermodynamics. The resulting evolution equation for the diffusion flux generalizes the Fick's law

The Role of the Second Law of Thermodynamics in Continuum Physics: A Muschik and Ehrentraut Theorem Revisited

In continuum physics, constitutive equations model the material properties of physical systems. In those equations, material symmetry is taken into account by applying suitable representation theorems for symmetric and/or isotropic functions. Such mathematical representations must be in accordance with the second law of thermodynamics, which imposes that, in any thermodynamic process, the entropy production must be nonnegative. This requirement is fulfilled by assigning the constitutive equations in a form that guaranties that second law of thermodynamics is satisfied along arbitrary processes. Such an approach, in practice regards the second law of thermodynamics as a restriction on the constitutive equations, which must guarantee that any solution of the balance laws also satisfy the entropy inequality. This is a useful operative assumption, but not a consequence of general physical laws. Indeed, a different point of view, which regards the second law of thermodynamics as a restriction on the thermodynamic processes, i.e., on the solutions of the system of balance laws, is possible. This is tantamount to assuming that there are solutions of the balance laws that satisfy the entropy inequality, and solutions that do not satisfy it. In order to decide what is the correct approach, Muschik and Ehrentraut in 1996, postulated an amendment to the second law, which makes explicit the evident (but rather hidden) assumption that, in any point of the body, the entropy production is zero if, and only if, this point is a thermodynamic equilibrium. Then they proved that, given the amendment, the second law of thermodynamics is necessarily a restriction on the constitutive equations and not on the thermodynamic processes. In the present paper, we revisit their proof, lighting up some geometric aspects that were hidden in therein. Moreover, we propose an alternative formulation of the second law of thermodynamics, which incorporates the amendment. In this way we make this important result more intuitive and easily accessible to a wider audience

Thermoelectric efficiency of silicon–germanium alloys in finite-time thermodynamics

We analyze the efficiency in terms of a thermoelectric system of a one-dimensional Silicon–Germanium alloy. The dependency of thermal conductivity on the stoichiometry is pointed out, and the best fit of the experimental data is determined by a nonlinear regression method (NLRM). The thermoelectric efficiency of that system as function of the composition and of the effective temperature gradient is calculated as well. For three different temperatures (T = 300K, T = 400K, T = 500K), we determine the values of composition and thermal conductivity corresponding to the optimal thermoelectric energy conversion. The relationship of our approach with Finite-Time Thermodynamics is pointed out

Application of the Mesoscopic Theory to Dipolar Media

Mesoscopic continuum theory is a way to deal with complex materials, i.e. materials with an internal structure, which can change under the action of external elds, within continuum theory. In the mesoscopic theory eld quantities are introduced, which depend not only on position and time, but also on an additional, so called mesoscopic variable. In our case this additional variable is the orientation of a dipole. The orientation distribution function (ODF) gives the fraction of dipoles of a particular orientation. The magnetization is proportional to the rst moment of the ODF. Balance equations for the mesoscopic elds, and an equation of motion for the distribution function have been derived in the general case. With some additional assumptions these equations are used here to derive a relaxation equation for the magnetization. The linear limit case of this relaxation equation is the well known DEBYE equation

Nonlinear thermal analysis of two-dimensional materials with memory

A nonlinear hyperbolic heat transport equation has been proposed based on the Cattaneo model without mechanical effects. We analyze the two-dimensional Maxwell-Cattaneo-Vernotte heat equation in a medium subjected to homogeneous and non-homogeneous boundary conditions and with thermal conductivity and relaxation time linearly dependent on temperature. Since these nonlinearities are essential from an experimental point of view, it is necessary to establish an effective and reliable way to solve the system of partial differential equations and study the behavior of temperature evolution. A numerical scheme of finite differences for the solution of the two-dimensional non-Fourier heat transfer equation is introduced and studied. We also investigate the attributes of the numerical method from the aspects of stability, dissipation and dispersive errors

A geometric model for magnetizable bodies with internal variables

In a geometrical framework for thermo-elasticity of continua with internal variables we consider a model of magnetizable media previously discussed and investigated by Maugin. We assume as state variables the magnetization together with its space gradient, subjected to evolution equations depending on both internal and external magnetic fields. We calculate the entropy function and necessary conditions for its existenc

Cardiovascular and thrombophilic risk factors for idiopathic sudden sensorineural hearing loss

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Exploiting the Reducing Properties of Lignin for the Development of an Effective Lignin@Cu2O Pesticide

Lignin is a natural polymer produced in huge amounts by the paper industry. Innovative applications of lignin, especially in agriculture, represent a valuable way to develop a more sustainable economy. Its antioxidant and antimicrobial properties, combined with its biodegradability, make it particularly attractive for the development of plant protection products. Copper is an element that has long been used as a pesticide in agriculture. Despite its recognized antimicrobial activity, the concerns derived from its negative environmental impact is forcing research to move toward the development of more effective and sustainable copper-based pesticides. Here a simple and sustainable way of synthesizing a new hybrid material composed of Cu2O nanocrystals embedded into lignin, named Lignin@Cu2O is presented. The formation of cuprite nanocrystals leaves the biopolymer intact, as evidenced by infrared spectroscopy, gel permeation chromatography, and Pyrolysis-GC analysis. The combined activity of lignin and cuprite make Lignin@Cu2O effective against Listeria monocytogenes and Rhizoctonia solani at low copper dosage, as evidenced by in vitro and in vivo tests conducted on tomato plants