Papers by Author: Robert Filipek

Abstract: Motivation for this work comes from the application of the inverse method to electrochemical systems. The basic process operating in these systems is electrodiffusion, which can be described by the full form of the Nernst-Planck and Poisson equations. No simplification like electroneutrality assumption is used. Numerical procedure based on the method of lines (MLs) for time dependent electrodiffusion transport is presented with any number of ionic species. The resulting system of ODEs is effectively solved by employing different integrators (Radau IIA, Rosenbrock, SEULEX). Selected electrochemical systems (liquid junction, bi-ionic case, ion selective electrodes (ISE)) are treated. Performance of the integrators is compared.

Abstract: Ionic concentrations and electric field space profiles in one dimensional membrane are described using Nernst-Planck-Poisson (NPP) equations. The usual assumptions for the steady state NPP problem requires knowledge of the boundary values of the concentrations and electrical potential difference. In analytical chemistry the potential difference may not be known and its theoretical prediction from the model is desirable. The effective methods of the solution to the NPP equations are presented. The Poisson equation is solved without widely used simplifications such as the constant field or the electroneutrality assumptions. The first method uses a steady state formulation of NPP problem. The original system of ODEs is turned into the system of non-linear algebraic equations with unknowns fluxes of the components and electrical potential difference. The second method uses the time-dependent form of the Nernst-Planck-Poisson equations. Steady-state solution has been obtained by starting from an initial profiles, and letting the numerical system evolve until a stationary solution is reached. The methods have been tested for different electrochemical systems: liquid junction and ion selective electrodes (ISEs). The results for the liquid junction case have been also verified with the approximate solutions leading to a good agreement. Comparison with the experimental results for ISEs has been carried out.

Abstract: The application of the Danielewski-Holly model of interdiffusion for modelling of selective and concurrent oxidation of multi-component alloys is presented. This model enables prediction of the evolution of components distributions taking into account interdiffusion and the reactions at the boundary, e.g, due to the oxidation/sulphidation processes. The model is subsequently reformulated to the form suitable for numerical calculation. For illustrating its capabilities modelling of the selective oxidation of Ni-Pt alloys is presented. The results are compared with those obtained from Wagner model. Both models give exactly the same results for the longer reaction times. In Wagner model the equilibrium concentration of the elements at the boundary is reached instantly while in this model it changes with time. Consequently the model allows modelling of initial stages of oxidation.

Abstract: Aluminide diffusion coatings act as a remedy against the aggressive environments in which modern aero-gas turbines operate. Platinum addition to basic aluminide coatings significantly improves the oxidation resistance of these coatings. The increase in operating temperatures of industrial energy systems and gas turbines, has led to the extensive use of coatings capable of providing improved service life. Interdiffusion plays a critical role in understanding the integrity of such coatings. The Danielewski-Holly model of interdiffusion which allows for the description of a wide range of processes (including processes stimulated by reactions at interfaces) is employed for studying of interdiffusion in the Pt-modified β-NiAl coatings. Using the inverse method the intrinsic diffusivities of Ni, Al and Pt were calculated. Such obtained diffusivities were subsequently used for modelling of thermal stability of Pt-modified aluminide coatings in air and in argon atmosphere.

Abstract: Experimental measurements do not allow for a unique determination of the concentration profiles, e.g., in case of multi-layer systems. The measured concentration of the elements at the alloy/scale interface is an average concentration in an alloy and in a scale near the spot of the beam [1]. The knowledge of the concentration of the elements at the boundary is necessary for the understanding corrosion of alloys. This essential obstacle of experimental techniques can be overcome by computer modelling. Namely, by combining the different methods (non-unique measurement with unique modelling). The Danielewski-Holly model of interdiffusion has a unique solution. This model enables to predict the evolution of component distributions in the reacting alloy. The model is valid for time dependent boundary conditions and consequently can be used for modelling the more complex reactions, eg., the formation of complex oxides. To avoid the nonphysical values of fluxes in reacting alloy the kinetic constraint on all fluxes was introduced, i.e., the flux limitation method. The results of the selective oxidation of the P91 steel (0,1 wt.% C, 8,6 wt.% Cr, 0,25 wt.% Ni) are presented. Calculated concentration profiles are compared with the experimental data. We show the evolution of chromium distribution in oxidizing steel up to 3 000 hours. The computations demonstrate that chromium depletion is the key factor determining the scale composition.

Abstract: Mathematical model of selective and competitive oxidation of multi-component non ideal alloys is used for modelling oxidation of Fe-Cr-Ni alloys. The model is based on: a) the Danielewski-Holly model of interdiffusion, b) the Wagner model of the Ni-Pt alloy oxidation, c) the postulate that the values of fluxes in reacting alloy are limited (the kinetic constraint) and d) the thermodynamics of the Fe-Ni-Cr system. In this paper for the first time modelling of oxidation of a ternary non-ideal alloy based on Danielewski-Holly model is presented. The model is used to predict the evolution of component distributions in the reacting ternary Fe-Cr-Ni alloy. The results of the modelling of oxidation of the 316L stainless steel at 1173 K are presented. We compute the chromium depletion during the long term oxidation. The results allows to conclude that the oxidation reaction is limited by interdiffusion in reacting alloy. The computations demonstrate that the chromium depletion is the key factor affecting the scale stability during the long time exposition.

Abstract: Interdiffusion in Co-Fe-Ni alloys was studied in 1373-1588 K temperature range. The Danielewski-Holly model was used for the description of the interdiffusion process in ternary Co- Fe-Ni diffusion couples both for the finite and infinite geometry. Using the inverse method the average intrinsic diffusivities of components in the Co-Fe-Ni system were calculated and compared with the results of the other authors. The activation energies of cobalt, iron and nickel intrinsic diffusion have been found in 1373-1588 K temperature range.