Experimental Determination of the Longitudinal Dispersivity During the Injection of a Micro-Cement Grout in a One-Dimensional Soil Column

In order to describe the basic phenomenon of miscible grout propagation during the injection in a saturated and deformable porous medium, a general mathematical model was proposed, which accounts for the existing coupling between the fluid flow analysis, the miscible grout transport, and the solid skeleton deformation, leading to a realistic prediction of the injected zone. The development of the model was made concurrently with laboratory experiments to determine the model parameters. This paper describes the determination of the longitudinal dispersivity during the transport of a micro-cement grout injected in a one-dimensional soil column, by relying on image processing analysis. The application concerned here is the injection of soils for improving their properties, that is, to reduce permeability, increase mechanical strength or reduce the deformability. The longitudinal dispersion coefficient is an essential parameter governing the mixing process and the evolution of the transition zone, and thus the injection efficiency. Finally, the comparison between simulated results from the developed model and experimental data, essential to validate the model from a phenomenological standpoint, is made.     

On minimal non-M_rC-groups

A group $G$ is said to be a minimax group if it has a finite series whose factors satisfy either the minimal or the maximal condition. Let $D(G)$ denotes the subgroup of $G$ generated by all the Chernikov divisible normal subgroups of $G$ . If $G$ is a soluble-by-finite minimax group and if $D(G)=1$ , then $G$ is said to be a reduced minimax group. Also $G$ is said to be an $ M_{r}C$ -group (respectively, $PC$ -group), if $G/C_{G} \left(x^{G}\right)$ is a reduced minimax (respectively, polycyclic-by-finite) group for all $x\in G$ . These are generalisations of the familiar property of being an $FC$ -group. Finally, if $\mathfrak X $ is a class of groups, then $G$ is said to be a minimal non- $\mathfrak X $ -group if it is not an $\mathfrak X $ -group but all of whose proper subgroups are $\mathfrak X $ -groups. Belyaev and Sesekin characterized minimal non- $FC$ -groups when they have a non-trivial finite or abelian factor group. Here we prove that if $G$ is a group that has a proper subgroup of finite index, then $G$ is a minimal non- $M_{r}C$ -group (respectively, non- $PC$ -group) if, and only if, $G$ is a minimal non- $FC$ -group.     

Analytical Determination of Flow Patterns in a Double Porosity Medium Containing Ellipsoidal Occluded Macro-Voids

This article presents the analytical study of fluid flow in a porous medium presenting pores of two different length scales: at the smallest or microscopic scale, the presence of connected voids confers a porous medium structure to the material investigated, while at the upper or mesoscopic scale, occluded macro-pores are present. This microstructure is employed to represent the progressive opening of inter-aggregate pore spaces observed in natural compacted montmorillonites polluted by heavy metal ions. Three-dimensional analytical expressions are rigorously derived for the pore fluid velocity and excess pore fluid pressure within the porous matrix, around an occluded ellipsoidal inter-aggregate void. The eccentricity ratio is employed to characterize the geometrical shape of the ellipsoidal void, while its size is characterized by the macro-porosity. Confrontations are made with numerical solutions in order to investigate the applicability of the analytical pressure and velocity solutions to microstructures of finite size.     

Existence of positive solutions of delay dynamic equations

In this article we study the existence of positive solutions for a dynamic equations on time scales. The main tool employed here is the Schauder’s fixed point theorem. The asymptotic properties of solutions are also treated. The results obtained here extend the work of Dorociakova and Olach (Tatra Mt Math Publ 43:63–70, 2009). Three examples are also given to illustrate this work.     

Crystallization kinetics study of melt-spun Zr66.7Ni33.3 amorphous alloy by electrical resistivity measurements

In this paper, the electronic transport properties of as-spun Zr_66.7Ni_33.3 alloys were studied in detail by a combination of electrical resistivity and absolute thermoelectric power measurements over a temperature range from 25 up to 400 °C. Moreover, the isochronal and isothermal crystallization kinetics of Zr_66.7Ni_33.3 glassy alloy has been investigated based on the electrical resistivity measurements. The comparative study of the crystallization kinetics of these binary amorphous alloys was carried out, for the first time to our knowledge, using an accurate method for electrical resistivity measurements. In the isochronal heating process, the apparent activation energy for crystallization was determined to be, respectively, 371.4 kJ mol⁻¹ and 382.2 kJ mol⁻¹, by means of Kissinger and Ozawa methods. The Johnson–Mehl–Avrami model was used to describe the isothermal transformation kinetics, and the local Avrami exponent has been determined in the range from 2.97 to 3.23 with an average value of 3.1, implying a mainly diffusion-controlled three-dimensional growth with an increasing nucleation rate. Based on an Arrhenius relationship, the local activation energy was analyzed, which yields an average value E_x = 376.2 kJ mol⁻¹.

     

A numerical and analytical study on calcite dissolution and gypsum precipitation

This paper presents a simple model for the study of the dissolution of calcite and precipitation of gypsum in acidic solutions. The numerical predictions of calcium and hydroxyl ion concentration have been used to develop approximate analytical expressions for the growth rate of calcium in solution, and the hydroxyl ions concentration. These expressions have been used in turn to determine the evolution of the kinetic rate constants, and to make predictions that show good agreement with experimental data.