Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality

We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on \emph{general reversible-irreversible couplings} and the associated mathematical attempts to formulate a \emph{non-equilibrium variational principle} in which these non-equilibrium couplings can be identified as minimizers. Based on this, we investigate two microscopic binary mixture formulations fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible fluid formulation without fluid flow; (b) a momentum-driven formulation for quasi-static and incompressible velocity fields. In both cases we state two novel, reliably upscaled equations for binary mixtures/multiphase fluids in strongly heterogeneous systems by systematically taking thermodynamic features such as free energies into account as well as the system's heterogeneity defined on the microscale such as geometry and materials (e.g. wetting properties). In the context of (a), we unravel a \emph{universality} with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known ${\cal O}(t^{1/3})$-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their \emph{thermodynamic foundation} relying on free energies, make the collected recent developments here highly promising for scientific, engineering and industrial applications for which we provide an example for lithium batteries

Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit

We study phase field equations based on the diffuse-interface approximation of general homogeneous free energy densities showing different local minima of possible equilibrium configurations in perforated/porous domains. The study of such free energies in homogeneous environments found a broad interest over the last decades and hence is now widely accepted and applied in both science and engineering. Here, we focus on strongly heterogeneous materials with perforations such as porous media. To the best of our knowledge, we present a general formal derivation of upscaled phase field equations for arbitrary free energy densities and give a rigorous justification by error estimates for a broad class of polynomial free energies. The error between the effective macroscopic solution of the new upscaled formulation and the solution of the microscopic phase field problem is of order $\epsilon^1/2$ for a material given characteristic heterogeneity $\epsilon$. Our new, effective, and reliable macroscopic porous media formulation of general phase field equations opens new modelling directions and computational perspectives for interfacial transport in strongly heterogeneous environments

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Near-critical point phenomena in fluids (19-IML-1)

Understanding the effects of gravity is essential if the behavior of fluids is to be predicted in spacecraft and orbital stations, and, more generally, to give a better understanding of the hydrodynamics in these systems. An understanding is sought of the behavior of fluids in space. What should emerge from the International Microgravity Lab (IML-1) mission is a better understanding of the kinetics of growth in off-critical conditions, in both liquid mixtures and pure fluids. This complex phenomenon is the object of intensive study in physics and materials sciences area. It is also expected that the IML-1 flight will procure key results to provide a better understanding of how a pure fluid can be homogenized without gravity induced convections, and to what extent the 'Piston Effect' is effective in thermalizing the compressible fluids

Prediction of the mechanical behaviour of TRIP steel

TRIP steel typically contains four different phases, ferrite, bainite, austenite and martensite. During deformation the metastable retained austenite tends to transform to stable martensite. The accompanying transformation strain has a beneficial effect on the ductility of the steel during forming. By changing the alloy composition, the rolling procedure and the thermal processing of the steel, a wide range of different morphologies and microstructures can be obtained. Interesting parameters are the amount of retained austenite, the carbon content of the austenite, the stability of the austenite as well as its hardness. A constitutive model is developed for TRIP steel which contains four different phases. The transformation of the metastable austenite to martensite is taken into account. The phase transformation depends on the stress in the austenite. Due to the differences in hardness of the phases the austenite stress is not equal to the overall stress. An estimate of the local stress in the austenite is obtained by homogenization of the response of the phases using a self-consistent mean-field homogenization method. Overall stress-strain results as well as stress-strain results for individual phases are compared to measurements found in literature for some TRIP steels. The model is then used to explore the influence of some possible variations in microstructural composition on the mechanical response of the steel

Multiscale Problems in Solidification Processes

Our objective is to describe solidification phenomena in alloy systems. In the classical approach, balance equations in the phases are coupled to conditions on the phase boundaries which are modelled as moving hypersurfaces. The Gibbs-Thomson condition ensures that the evolution is consistent with thermodynamics. We present a derivation of that condition by defining the motion via a localized gradient flow of the entropy. Another general framework for modelling solidification of alloys with multiple phases and components is based on the phase field approach. The phase boundary motion is then given by a system of Allen-Cahn type equations for order parameters. In the sharp interface limit, i.e., if the smallest length scale ± related to the thickness of the diffuse phase boundaries converges to zero, a model with moving boundaries is recovered. In the case of two phases it can even be shown that the approximation of the sharp interface model by the phase field model is of second order in ±. Nowadays it is not possible to simulate the microstructure evolution in a whole workpiece. We present a two-scale model derived by homogenization methods including a mathematical justification by an estimate of the model error

Multiscale thermo-mechanical analysis of multi-layered coatings in solar thermal applications

Solar selective coatings can be multi-layered materials that optimize the solar absorption while reducing thermal radiation losses, granting the material long-term stability. These layers are deposited on structural materials (e.g., stainless steel, Inconel) in order to enhance the optical and thermal properties of the heat transfer system. However, interesting questions regarding their mechanical stability arise when operating at high temperatures. In this work, a full thermo-mechanical multiscale methodology is presented, covering the nano-, micro-, and macroscopic scales. In such methodology, fundamental material properties are determined by means of molecular dynamics simulations that are consequently implemented at the microstructural level by means of finite element analyses. On the other hand, the macroscale problem is solved while taking into account the effect of the microstructure via thermo-mechanical homogenization on a representative volume element (RVE). The methodology presented herein has been successfully implemented in a reference problem in concentrating solar power plants, namely the characterization of a carbon-based nanocomposite and the obtained results are in agreement with the expected theoretical values, demonstrating that it is now possible to apply successfully the concepts behind Integrated Computational Materials Engineering to design new coatings for complex realistic thermo-mechanical applications.Peer ReviewedPostprint (author's final draft