Defect and Diffusion Forum Vol. 413

Abstract: 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.

Abstract: 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.

Abstract: 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].

Abstract: Our investigations show that electrochemical corrosion of copper is faster than electrochemical corrosion of aluminium at temperatures below 100°C. Literature data analysis shows that the Al atoms diffuse faster than the Cu atoms at temperatures higher than 475°C, Al rich intermetallic compounds (IMCs) are formed faster in the Cu-Al system, and the Kirkendall plane shifts toward the Al side. Electrochemical corrosion occurs due to electric current and due to diffusion. An electronic devise working time, for example, depends on initial copper cover thickness on aluminium wire, connected to the electronic devise, temperature, and volume and dislocation pipe diffusion coefficients, so copper, iron, and aluminium electrochemical corrosion rates are investigated experimentally at room temperature and at temperature 100°C. Intrinsic diffusivities ratios of copper and aluminium at different temperatures and diffusion activation energies in the Cu-Al system are calculated by proposed here methods using literature experimental data. Dislocation pipe and volume diffusion activation energies of pure iron are calculated separately by earlier proposed method using literature experimental data. Aluminium dissolved into NaCl solution as the Al³⁺ ions at room temperature and at temperature 100°C, iron dissolved into NaCl solution as the Fe²⁺ (not Fe³⁺) ions at room temperature and at temperature 100°C, copper dissolved into NaCl solution as the Cu⁺ ions at room temperature and as the Cu⁺ and the Cu²⁺ ions at temperature 100°C. It is found experimentally that copper corrosion is higher than aluminium corrosion, and ratio of electrochemical corrosion rates, k_Cu/k_Al>1, decreases with temperature increasing, although iron electrochemical corrosion rate does not depend on temperature below 100°C. It is obvious, because the melting point of iron is more higher than the melting point of copper or aluminium. It is calculated that the copper electrochemical corrosion rate is approximately equal to aluminium electrochemical corrosion at temperature about 300°C, so copper can dissolve into NaCl solution mostly as the Cu²⁺ ions at temperature about 300°C. The ratio of intrinsic diffusivities, D_Cu/D_Al<1, increases with temperature increasing, and the intrinsic diffusivity of aluminium could be approximately equal to the intrinsic diffusivity of copper at temperature about 460oC. Intrinsic diffusivities ratios in the Cu-Zn system at temperature 400°C and in the Cu-Sn system at temperatures from 190°C to 250°C are analyzed theoretically using literature experimental data. Diffusion activation energies and pre-exponential coefficients for the Cu-Sn system are calculated combining literature experimental results.

Abstract: In this paper, a theoretical model based on multi-gene genetic programming (MGGP) approach has been applied to predict the structural and magnetic properties in nanocrystalline Fe–Ni powders prepared by mechanical alloying (MA) using a planetary ball mill. The MGGP model was used to correlate the input parameters (milling speed, chemical composition, and milling time), to output parameters (crystallite size and coercivity) of nanocrystalline Fe–Ni powders. The model obtained was tested with additional data to demonstrate its performance and prediction ability. The MGGP model is a robust and efficient method to find an accurate mathematical relationship between input and output data. A sensitivity analysis study was applied to determine the most influential milling parameters on the crystallite size and coercivity.

Abstract: The continuing depletion of light oil supplies and the rapidly growing demand for energy are forcing oil and gas companies to explore unconventional oil extraction techniques. The structure and flow rate implies an impact on the trapping and mobilization of oil in the reservoir. This article studies the effect of pore geometry and dynamics on water-oil displacement as a two-phase flow system. The pore geometries of sandstone were extracted using the non-destructive 3D micro computational tomography (micro-CT) technique. Two-phase flow simulations were performed using COMSOL Multiphysics on the micro-CT images to show the effect of the capillary number and the flow pattern. Velocity and relative permeability of the non-wetting phase at different points of the porous structure was computed. The effect of viscosity of wetting fluid on the pore structure was also studied to evaluate the parameters affecting enhanced oil recovery (EOR).

Abstract: 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.

Abstract: The influence of water-filled nanoscale defects on the total movement of helium atoms through a quartz crystal is considered. The approximation of local chains is used, the interaction constant of which characterizes the interaction of the helium atom with the environment. The appearance of water molecules in defects (pores) leads to the renormalization of this interaction. The D'Alembert principle is used to evaluate this renormalization. The effect of such a renormalization of the interaction on the diffusion coefficient of helium through a crystal with defects filled with water is considered.

Abstract: 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.