R. Wojnar

Flow of electrolyte through porous piezoelectric medium: macroscopic equations

Abstract The aim of this contribution is to elaborate a general framework for modelling flows of two-ionic species electrolytes through porous piezoelectric media. By using the method of two-scale asymptotic expansions, the macroscopic phenomenological equations describing electrokinetics of such a structure are derived and the formulae for the effective mechanical and nonmechanical coefficients are given. Natural jump conditions are assumed on the interfaces between the piezoelectric skeleton and conductive fluid.

One-dimensional dynamic thermal stresses generated in an elastic half-space by laser pulses

An improved solution to the one-dimensional dynamic thermal stress problem for an elastic half-space analyzed previously by Danilowskaya [3] is given. In this problem the temperature and stress fields are produced by a particular heat supply generated by absorption of a laser pulse incident on the half-space. The betterment comprises: (i) eliminating some substantial and formal errors occurring in Danilowskaya [3], (ii) providing a qualitative and quantitative analysis of the solution that is missing in Danilowskaya [3],.and (iii) generalizing the solution to include an arbitrary step-like profile of the laser pulse. In particular, it is shown that for a rectangular pulse of duration t* > 0 and for a given cross section x0 > 0 of the half-space both the temperature and stress are continuous functions for every time t ≥ 0; while their time derivatives suffer jumps on the t-axis, the temperature rate jumps at the consecutive times t = 0 + 0 and t = t*, and the stress rate exhibits discontinuities at t = t* ...

UNIQUENESS OF DISPLACEMENT-HEAT FLUX AND STRESS-TEMPERATURE PROBLEMS IN THERMOELASTICITY WITH ONE RELAXATION TIME

Abstract Two uniqueness theorems of linear thermoelasticity with one relaxation time corresponding to natural initial boundary value problems described in terms of two different pairs of thermoelastic variables: displacement-heat flux and stress-temperature are proved.

Strain-induced energy gap variation in ZnTe/ZnMgTe core/shell nanowires

Strain-induced changes of ZnTe energy gap in ZnTe/ZnMgTe core/shell nanowires arising from lattice mismatch between the core and the shell semiconductor are studied by means of optical methods. It is shown that the increase of the Mg content in the shell, as well as the increase of the shell thickness result in an effective redshift of the near band edge photoluminescence from ZnTe nanowire cores, which reflects directly the decrease of energy gap under tensile strain conditions. The conclusions are supported by theoretical calculations in terms of the valence force field model. The observed change of ZnTe energy gap can be as large as 120 meV with respect to the unstrained conditions and can be tuned in a continuous manner by adjusting shell parameters, which open a path towards an effective band gap engineering in these structures.

Piezoelectric Phenomena in Biological Tissues

Biological structures, at different organization levels (macromolecules, tissues, etc.) present a typical spiral shape. Spirals do not have a center of symmetry and hence almost all biological matter possesses piezoelectricity properties. Thus, the possibility to convert mechanical signals into electric ones, and viceversa, is not only ascribed to minerals or ceramics. In this chapter, after reminding essential elements on piezoelectricity and its connection with material structure, the piezoelectric properties of two typical macromolecular components, cellulose (for plants) and collagen (for animals) are introduced, and their role in biological tissues is described.

On nonlinear heat equations and diffusion in porous media

The problem of diffusion of a Brownian particle in a liquid under the influence of an exterior field, taking into account thermal effects, as given by Streater [1–3], is reformulated for the case in which the thermal conductivity coefficient is nonhomogeneous. This modified formulation is applied to the description of diffusion in a liquid filling a porous medium. Macroscopic equations of Brownian diffusion for that case are obtained using the two-scale asymptotic method. As a result, in the macroscopic diffusion equation the friction term is absent, and the external force appears explicitly as a heat production term only; implicitly the drift force is found in the first correction f(1) in the asymptotic expansion of distribution function f.

UPPER AND LOWER BOUNDS ON HEAT FLUX

Some bounds on heat flow and entropy production analogous to those obtained in linear elasticity theory are discussed. The analogy is observed by introducing “mechanical” counterparts to a heat conduction process

Homogenization of piezoelectric solid and thermodynamics

Abstract The problem of homogenization of a piezoelectric periodic composite in which thermal effects are taken into account is treated by a method of 2-scale asymptotic expansions. Albeit a nonlinear entropy-temperature relation is used, the local problems are formulated in a way similar to that of a linear theory. Also, effective material coefficients are in majority the same as those obtained in a linearized theory. The difference appears in the homogenized thermoelastic, thermoelectric and specific heat coefficients only. A Francfort type result on shift of the initial conditions for a homogenized problem is also obtained.

Electrokinetics in Random Deformable Porous Media

The aim of this contribution is to derive macroscopic equations describing flow of two-ionic species electrolytes through porous piezoelectric media with random, not necessarily ergodic, distribution of pores. Under assumption of ergodicity the macroscopic equations simplify and are obtained by using the Birkhoff ergodic theorem.

Nonlinear heat equation and two-level diffusion

Abstract The interaction between the diffusion of a Brownian particle which can occupy two energy levels, and the heat flow described by the Streater nonlinear heat equation, cf. [1], is analysed. Particularly, the Streater effect in which the potential energy of a particle is converted to heat due to friction is taken into account. It is shown that for such a continuum, the first law of thermodynamics and the modified form of the second law hold true, while the Prigogine conjecture is not satisfied even in the approximation known from a one level diffusion. Also, the behaviour of a system in isothermal conditions beyond a detailed balance is considered.