Numerical Solution Strategies in Permeation Processes

In this work, the strategy for numerical solutions in transport processes is investigated. Permeation problems can be solved analytically or numerically by means of the Finite Difference Method (FDM), while choosing the Euler forward explicit or Euler backwards implicit formalism. The first method is the easiest and most commonly used, while the Euler backwards implicit is not yet well established and needs further development. Hereafter, a possible solution of the Crank-Nicolson algorithm is presented, which makes use of matrix multiplication and inversion, instead of the step-by-step FDM formalism. If one considers the one-dimensional diffusion case, the concentration of the elements can be expressed as a time dependent vector, which also contains the boundary conditions. The numerically stable matrix inversion is performed by the Branch and Bound (B&B) algorithm [2]. Furthermore, the paper will investigate, whether a larger time step can be used for speeding up the simulations. The stability range is investigated by eigenvalue estimation of the Euler forward and Euler backward. In addition, a third solver is considered, referred to as Combined Solver, that is made up of the last two ones. Finally, the Crank-Nicolson solver [9] is investigated. All these results are compared with the analytical solution. The solver stability is analyzed by means of the Steady State Eigenvector (SSEV), a mathematical entity which was developed ad hoc in the present work. In addition, the obtained results will be compared with the analytical solution by Daynes [6,7].

Membrane Covered Probes for O2 and H2 Determination - Diffusion through Liquid Films and Solid Membrane in Practice

In the era of the expansion of hydrogen use, its concentration measurement becomes more important. We further focus on one of the H2 concentration measurement purposes, where the hydrogen diffusion in a solid membrane and in a liquid electrolyte play the key role. To keep optimal process conditions in the primary cooling circuit of nuclear power plants, various chemical species are dosed in. Among the species the concentration of which is monitored in primary coolant, belong oxygen and hydrogen. While plenty of companies offer oxygen sensors suitable for the measurement in the primary coolant, the hydrogen sensor, really selective to H2 concentration, is offered by only one company. It is worth, therefore, accomplishing the development of a hydrogen sensor, which began at UCT Prague in the 1990's and, after several successful measurements in nuclear power plant, interrupted due to fateful events in the research team. We introduce here the results of the first part of contemporary work of the Mass Transfer Laboratory based on new technologies but using the experience from 1990's. Having at disposal modern functional samples to measure both oxygen and hydrogen concentrations, we verified a fair long-term stability of the sensors and, further, we would like to cooperate with an industrial partner to finalize the development of prototypes and start the production of monitoring units.

On the Analytical Inversion of Solver Matrices Used in Numerical Approximations for the Diffusion Equation

The goal of this paper is to introduce an analytical approach for the inversion of nxn solver matrices, which are typically used in Finite Difference Method approximations. In the present case, they are used to solve the Diffusion Equation numerically, since in many physics and engineering fields, partial differential equations cannot be solved analytically. The method presented in this work is primarily formulated for cylindrical coordinates, which are often used in Gas Release Experiments as those described in [8]. However, it is possible to introduce a generalized method, which also allows solutions for Cartesian solvers. The advantage of having the explicit inverse is considerable, since the computational effort is reduced. In this paper we also carry out an investigation on the eigenvalues of the backward and forward solver matrix in order to determine an optimal range for the discretization parameters.

Microwave Absorption Properties of Fe40Co60 Based Nanocomposites

Microwave absorbing materials are applied in stealth, communications and information processing technologies. This kind of material dissipates an electromagnetic wave by converting it into thermal energy. The nanostructuration of materials became a reliable route over the years to enhance the dielectric and magnetic properties, which induce the required interaction. Nanostructured Fe-Co alloys are soft magnetic materials that make them promising candidates for microwave absorption when combined with other materials. The aim of our study was therefore to investigate the microwave absorption properties of based nanocomposites. The nanocomposites were obtained by the solution dispersion method. Nanocrystalline alloys elaborated by mechanical alloying (MA) in a high-energy planetary ball mill (RETSCH PM400) were dispersed into commercial epoxy resin matrix to form thin polymer nanocomposites. The grain size refinement and structural properties changes during milling process were characterized using powder’s X-ray Diffraction (XPERT PRO MPD diffractometer) at different milling durations. XRD spectra analysis show that a grain size refinement of 4.54 nm was reached after 60h milling accompanied with 1.2 % microdeformations. Obtained powders were shaped in small discs for which resonant cavity measurements were undertaken. The based nanocomposites have been subject to an experiment of two-port S parameters measurement in a rectangular waveguide (R120). The microwave experiments involved a Network Analyzer (VNA). Obtained results in terms of reflection losses show a good absorbing characteristic over the [8-15] GHz microwaves band.

The Diffusion Isotope Effect and Diffusion Mechanism in Liquid Cu-Ag and Cu-Ni Alloys

In this paper, the diffusion isotope effect and diffusion mechanism are investigated by means of molecular dynamics simulations in two liquid alloys, Ni-Ag and Ni-Cu. The values for the diffusion isotope effect parameter allow for the estimate of the number of atoms which are moving cooperatively in a basic diffusion event as experienced by a given atomic species. It is shown that the composition dependence of ND is typically very small. However, the temperature dependence of this parameter is much more pronounced. In addition, it is shown that, on average, in these alloys and temperatures considered, ND is limited to the range: 5<ND<17. This is consistent with results of molecular dynamics simulations on the average coordination number calculations. This would suggest that, together with a given atom, depending on temperature, the neighbouring atoms are all involved in the basic diffusion event.

Analysis of the Influence of the Degree of Reduction of Iron Ore Materials on the Shape and Location of the Cohesion Zone in a Blast Furnace

The paper considers the theoretical foundations of softening of iron ore materials in a blast furnace (the so-called ‘cohesion zone’). The dependences of the temperature range of softening of iron ore materials (the temperatures of the beginning and ending of softening) on the degree of reduction are calculated and experimentally obtained. Physical modelling of the softening process of reduced iron ore materials was carried out using the Russian State Standard No 26517-85. The results of calculations of the location and shape of the cohesion zone in the blast furnace for iron ore materials with different metallurgical characteristics are presented.

Influence of Diffusion through a Porous Film under Electrode Surface in Chronoamperometry Problems

In the presented work on chronoamperometry, the Cottrell model has been generalized by taking into account a thin porosity layer covering the surface of the electrode and Tafel kinetics of an electrode reaction. The effective diffusion coefficient inside a porosity layer is calculated by Bruggeman’s law. It is shown that in the quasi-stationary approximation of diffusion inside a thin porous layer, the chronoamperometry problem can be solved analytically. The obtained solution has been compared with the results of direct numerical simulations and a good agreement is shown. Limiting cases of the solution related to low and high porosity are considered.

Study on the Wear of Cutting-Tools Used in Dry Machining of Cu-10wt%Al-5wt%Ni-5wt%Fe Alloy

Aluminium bronze alloys are special copper alloys that have a machinability rate from 20 to 40% compared to free cutting brasses, so the cutting parameters and type of tools suitable for machining of these materials may be very different for other copper alloys. Also, due to the relative high costs of the raw material, the absence of contamination of the chips by cutting fluids improve its intrinsic resales value and encourage the use of machining process without coolant. The aim of this work is to evaluate the tool wear mechanisms in the finishing machining of the Cu-10wt%Al-5wt%Ni-5wt%Fe aluminium-bronze alloy with carbide and cermet inserts at different cutting speeds under dry machining condition. The turning of material showed lower surface roughness in higher speed conditions and better dimensional stability at lower speeds. It was observed the formation of continuous chips, but of little volume occupied. The scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS) analyses of tool wear show the adhesion as the main tool wear mechanism, followed by abrasion. At the lower cutting speed, the adhesion wears affected significantly the surface finish, reducing the tool life in comparison to the higher speeds.

The Effect of Flux Dysconnectivity Functions on Concentration Gradients Changes in a Multicomponent Model of Convectional Reaction-Diffusion by the Example of a Neurovascular Unit

A convectional diffusion of nutrients around the blood vessels in brain occurs in well-structured neurovascular units (NVU) including neurons, glia and micro vessels. A common feature of the process is a combination of a relatively high-speed delivery solution stream inside the blood vessel and a low-speed convectional flow in parenchyma. The specific trait of NVU is the existence of a tight cover layer around the vessels which is formed by shoots (end-feet) of astrocytes. This layer forms so called blood-brain barrier (BBB). Under different pathological states the permeability of BBB is changed. The concentration gradient of a chemical compound in NVU has been modelled using a combination of mathematical description of a cerebral blood flow (CBF) and further 3D diffusion away from the blood vessels borders. The governing equation for the blood flow is the non-steady-state Navier–Stokes equation for an incompressible non-Newtonian fluid flow without buoyancy effects. BBB is modeled by the flux dysconnectivity functions. The velocity of fluid flow in the paravascular space was estimated using Darcy's law. Finally, the diffusion of the nutrient is considered as a convectional reaction-diffusion in a porous media. By the example of glucose, it was shown that increased permeability of BBB yields an increased level of the nutrient even under essential (on 70%) decrease of CBF. Contrarily, a low BBB permeability breeds a decreased concentration level under increased (on 50%) CBF. Such a phenomenon is explained by a smooth enlarge of the direct diffusion area for a blood-to-brain border glucose transport having three-level organization.

Diffusion in Metallic Glasses and in Oxide Glasses - An Overview

We remind the reader to some common features of metallic and oxide glasses. We then introduce the radiotracer method for diffusion studies, which can be applied for both types of glasses. We provide an overview on diffusion in metallic glasses in which we consider both types of metallic glasses – conventional and bulk metallic glasses. In the last part we discuss diffusion and ionic conduction in oxide glasses. For ionic glasses, conductivity measurements are an important complement to tracer diffusion studies. We remind the reader to the method of impedance spectroscopy. We discuss results for soda-lime silicate glasses, single alkali borate glasses and mixed alkali borate glasses and present evidence for collective jump processes in glasses.