Delay Model for a Cycling Transport Through Porous Medium

A solute transport through a porous medium is examined provided that the fluid leaving the porous sample returns back in a continuous way. The porous medium is thus included into a closed hydrodynamic circuit. This cycling process is suggested as an experimental tool to determine porous medium parameters describing transport. In the present paper the mathematical theory of this method is developed. For the advective type of transport with solute retention and degradation in porous medium, the system of transport equations in a closed circuit is transformed to a delay differential equation. The exact analytical solution to this equation is obtained. The solute concentration manifests both the oscillatory and monotonous behaviors depending on system parameters. The number of oscillation splashes is shown to be always finite. The maximum/minimum points are determined as solutions of a polynomial equation whose degree depends on the unknown solution itself. The cyclic methods to determine porous medium parameters as porosity and retention rate are developed.     

Dispersion de Taylor généralisée à un fluide à propriétés physiques variablesGeneralized Taylor dispersion for heterogeneous fluid

The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004).     

Singular nature of nonlinear macroscale effects in high-rate flow through porous mediaNature singulière des effets macroscopiques non linéaires dans un écoulement à hautes vitesses en milieux poreux

The quadratic law of laminar flow through porous media at high Reynolds numbers, which is well confirmed by the multiple experimental data, is shown to give rise to three fundamental paradoxes. All them can be resolved by assuming the singular structure of flow. The singularity is produced by the formation of jet brunches which invade the stagnant zones and sharply loss their kinetic energy. The numerical simulation confirms this effect. To cite this article: M. Panfilov et al., C. R. Mecanique 331 (2003).     

Effect of metakaolin structure on its binding properties in alkaline hydration

Aluminum ion coordination to oxygen in metakaolin of different origin was studied by a solid-state ²⁷Al NMR spectroscopy, as well as changes in aluminum ion coordination in an interaction of metakaolins with sodium silicate solution. At the same time a durability of structures resulting from this interaction was examined. Based on the findings the relationship between the structure of metakaolin and its astringent properties in alkaline environment was considered.     

Resistive properties of La2 ? x Sr x CuO4 low-dopped cuprates in the antiferromagnetic state at low temperatures

The nonlinear dependence of conductivity and negative differential resistance of ceramic samples of La_{2 ? x} Sr _x CuO₄ in the antiferromagnetic state is revealed. The possible influence of a spatially inhomoge-neous distribution of strontium impurities on the low-temperature behavior of conductivity is discussed.     

Transport with a Very Low Density Contrast in Hele–Shaw Cell and Porous Medium: Evolution of the Mixing Zone

The optimal concentration of a blue dye solution with 'tracer' properties, enabling a pollutant to be marked was determined by the use of numerical, theoretical and experimental approaches. Experimental investigations were performed on a transparent Hele–Shaw cell and the concentration distribution was analyzed using an optical technique based on dye light absorption properties. The injected optimal concentration was established thanks to a theoretical and experimental study carried out on the output signal dynamics. Using the same experimental conditions, numerical simulations were performed. The very good agreement between the data (experimental and numerical) clarified that: (i) the choice of the blue dye optimal concentration was valid and (ii) the concentration-dependent density should not be neglected in flow and transport equations even if it concerns a so-called 'tracer'. Following this remark, a theoretical aspect was developed in order to determine the analogous conditions between a Hele–Shaw cell and a porous medium for the variable density transport phenomenon. The structure of the concentration-dependent dispersion tensor used in the numerical code was obtained by homogenizing the Stokes flow of a bi-component mixture. The numerical results show that, as long as the tracer density does not exceed a certain value, it is not necessary to take into account a density contrast in terms of the dispersion tensor. The classical form of the Taylor dispersion tensor can be used successfully.     

Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

Effect of magnetic (phase) inhomogeneities on the conductivity of an antiferromagnetic La2CuO4 + δ single crystal at low temperatures

It has been established that, at a strongly nonuniform distribution of oxygen in a La₂CuO_{4 + δ} single crystal, isolated superconducting inclusions can be formed at an average hole concentration not higher than 0.0024 per copper atom. The behavior of the conductivity in a magnetic field below 20 K is consistent with possible existence of a insulating low-temperature magnetic phase (spin density waves), which is typical of cuprates with excess oxygen.     

Electrocyclic reaction of crown-containing 2-styrylbenzothiazoles

The photoinduced electrocyclic transformation of 15-crown-5-containing 2-styrylbenzothiazoles into condensed benzothiazoloquinoline derivatives was discovered. The process is accompanied by the formation of a C-N bond and elimination of a hydrogen atom. __________ Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 1290–1292, May, 2005.