Computer simulations of electrodiffusion problems based on Nernst-Planck and Poisson equations

A numerical procedure based on the method of lines for time-dependent electrodiffusion transport has been developed. Two types of boundary conditions (Neumann and Dirichlet) are considered. Finite difference space discretization with suitably selected weights based on a non-uniform grid is applied. Consistency of this method and the method put forward by Brumleve and Buck are analysed and compared. The resulting stiff system of ordinary differential equations is effectively solved using the RADAU5, RODAS and SEULEX integrators. The applications to selected electrochemical systems: liquid junction, bi-ionic case, ion selective electrodes and electrochemical impedance spectroscopy have been demonstrated. In the paper we promote the use of the full form of the Nernst-Planck and Poisson (NPP) equations, that is including explicitly the electric field as an unknown variable with no simplifications like electroneutrality or constant field assumptions. An effective method of the numerical solution of the NPP problem for arbitrary number of ionic species and valence numbers either for a steady state or a transient state is shown. The presented formulae - numerical solutions to the NPP problem - are ready to be implemented by anyone. Moreover, we make the resulting software freely available to anybody interested in using it. (C) 2012 Elsevier B.V. All rights reserved

Breakthrough in Modeling of Electrodiffusion Processes; Continuation and Extensions of the Classical Work of Richard Buck

In 1978 Brumleve and Buck published an important paper [1] pertaining to numerical modeling of electrodiffusion. At the time their approach was not immediately recognized and followed. However, it has changed since the beginning of 21st century. The approach of Brumleve and Buck based on Nernst-Planck-Poisson (NPP) equations is utilized to model transient behavior of various electrochemical processes. Multi-layers and reactions allow extending applications to selectivity and low detection limit with time variability, influence of parameters (ion diffusivities, membrane thickness, permittivity, rate constants), and ion interference on ion-sensor responses. Solution of NPP inverse problem allows for optimizing sensor properties and measurement environment. Conditions under which experimentally measured selectivity coefficients are true (unbiased) and detection limit is optimized are demonstrated. Impedance spectra obtained directly from NPPs are presented. Modeling durability and diagnosis of reinforced concrete is presented. Chlorides transport in concrete is modeled using NPPs and compared to other solutions

Transport ciepła i zagadnienia odwrotne; wybrane przykłady w geometrii jedno- i trójwymiarowej

Heat transport phenomena in the framework of continuum media mechanics is presented. Equations for conservation laws and finite volume numerical method based on these equations are discussed. This method is the foundation of the FLUENT computational fluid dynamics (CFD) package which was used for calculations of the temperature distribution in several examples: steady and evolutional states for single and multiphase systems. Comparison with analytical solutions was carried out. This allows verification of the FLUENT results for various boundary conditions. Independent procedure based on the method of lines was applied for 1D cases and compared with FLUENT and/or analytical results. Formulation of a special type inverse problem for heat equation was given. Analytical solution of the steady-state inverse problem in 1D geometry was developed. Analogues case for 3D geometry was tested using FLUENT. This led to the optimization problem with clear and well defined optimum. This result suggests that in similar but more general inverse problems global optimum may exist which justifies the inverse problem methodology.Zaprezentowano zjawiska transportu ciepła w kontekście mechaniki ośrodków ciągłych. Omówiono równania wyrażające prawa zachowania oraz metodę numeryczną objętości skończonych bazującą na tych prawach. Metoda ta będaca podstawa pakietu FLUENT, który służy do obliczeń w dynamice płynów (CFD, compuational fluid dynamics) została użyta do symulacji rozkładu temperatury w kilku przykładach ilustrujących stany ewolucyjne i stacjonarne dla jedno- i wielo-fazowych układów. Przeprowadzono porównanie z wybranymi rozwiązaniami analitycznymi. Pozwoliło to na weryfikacje wyników z FLUENT-a dla różnych warunków brzegowych. Niezależna procedura oparta o metodę linii dla przypadku jednowymiarowego została wykorzystana do porównania z wynikami z FLUENT-a oraz wynikami analitycznymi. Sformułowano pewien specjalny przypadek zagadnienia odwrotnego dla równania ciepła i przedstawiono jego analityczne rozwiązanie. Analogiczny przypadek w geometrii trójwymiarowej przetestowano numerycznie z użyciem FLUENT-a. Prowadzi to do problemu optymalizacji z dobrze określonym minimum globalnym. Wynik ten sugeruje, że w podobnych, ale bardziej ogólnych zagadnieniach odwrotnych może istnieć optimum, co usprawiedliwia metodologie zagadnienia odwrotnego w takich sytuacjach

Corrosion of Steel in Concrete - Modeling of Electrochemical Potential Measurement in 3D Geometry

The paper presents a 3D model and simulations of corroding reinforcement bars in a concrete element. Electric potential distributions are calculated in the concrete matrix and on its surface for two rebars arrangements with one or three active (anodic) sites to assess the reliability and identify possible problems when standard test measurements for corrosion assessment in concrete structures are used and conclusion on the corrosion state is inferred. The values of the potential strongly depend on a concrete layer thickness and beyond the threshold of 5-7 cm it is hardly possible to detect the number of active sites on the rebar. Also conductiv-ity – which is not constant in real world constructions – is an important factor. Thus without estimation of the state of concrete it is difficult to draw reliable conclusions on the corroding activity from shear potential measurements on the surface

Growth kinetics of the intermetallic phase in diffusion-soldered (Cu-5 at.%Ni)/Sn/(Cu-5 at.%Ni) interconnections

A stereological analysis was carried out in order to obtain the kinetics parameters of the (Cu1-xNix)6Sn5 growth in the diffusion soldered (Cu–5 at.%Ni)/Sn/(Cu–5 at.%Ni) interconnections where previously anomalous fast growth of this phase was described. The n-parameter in the equation x = ktn was found to be 0.27–0.15 in the temperature range 240–260 °C, respectively. This is far away from the volume control process (n = 1 if total surface of forming phase is the reference). The TEM/EDX microanalysis made across the (Cu1-xNix)6Sn5/Sn – solder showed sudden change of Sn and Cu content typical for the grain boundary diffusion as the rate controlling mechanism