Herein, a diffusion model for the dissolution of oxide particles in multicomponent slag systems is developed. It is assumed in this model that a sharp-interface separates the solid particle from the liquid slag. Minimization of the Gibbs energy provides the conditions at the interface. The differential equations for multicomponent diffusion in the liquid slag are solved numerically via a finite-difference scheme. It is indicated via parameter studies that the diffusion controlled dissolution kinetics may result in strongly different dissolution profiles depending on the initial conditions. It is demonstrated that the rate-controlling dissipative process is the diffusion of components for cases where earlier investigations claimed that a coupled diffusion-reaction process is in charge of the dissolution kinetics. Eventually, the numerical results are compared to data obtained from high-temperature laser scanning confocal microscopy (HT-LSCM) experiments.

The kinetics of a triple junction of grain boundaries with distinct specific energies and mobilities and a finite mobility of the triple junction is investigated. The microstructure is approximated by different 2D settings consisting of typical structural elements. First, the migration of the triple point together with the adjacent grain boundaries, is simulated, assuming that the grains are infinitely large. Secondly, growth or shrinkage of finite n-sided grains is simulated by altering the boundary conditions and the results are compared to the already published analytical solution. The numerical results coincide with the corrected analytical solution. This solution can be derived either by applying the principle of maximum dissipation, or by applying the force balance at the triple junction within the framework of linear irreversible thermodynamics. The change of the area of infinite and finite grains is investigated analytically and numerically. By comparing the results of both approaches, the influence of the initial topology of the structural elements on the kinetics of grain growth can be estimated. Furthermore, the kinetics of grain growth of different idealized grain boundary networks is investigated. It is shown that square shaped grains surrounded by hexagons and dodecagons result in a more realistic grain growth scenarios than squares surrounded by octagons. A deviation from idealized grain boundary arrangements is e.g., observed, due to different triple junction mobilities, and the initially n-sided regular grain deforms in a complex manner.

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The cyclic growth and shrinkage of solid oxides (i.e. wollastonite) in $$\text {CaO}$$ CaO –$$\text {SiO}_2$$ SiO 2 -based slags is investigated in-situ by means of High-Temperature Confocal Scanning Laser Microscopy (HT-CSLM). The compositions of the slags are carefully selected to induce different phase transformation conditions, i.e. congruent and incongruent melting/solidification. To complement the experimental results, the kinetics of growth and shrinkage of oxide crystals is investigated by means of a sharp interface model where the interfacial reaction and diffusion in the liquid bulk are considered as possible rate-controlling processes. The modelling approach combined with data analysis from key experiments reveals the underlying dissipative processes of solidification and melting phenomena, here, diffusion in the liquid bulk material and/or the interfacial reactions. The modelling approach is likely to be applicable for future materials design and processing problems from this perspective.