Multiscale modelling analysis and computations of complex heterogeneous multiphase systems

In this thesis, we analytically and computationally investigate various aspects related to the multiphase-multicomponent interfacial processes and reactive transport in homogeneous domains and heterogeneous periodic perforated media. More precisely, we perform formal homogenization arguments to the microscopic Cahn-Hilliard type equations governed the dynamics in binary and ternary mixtures, in the presence of two or more phases. We additionally consider the coupling of the Cahn-Hilliard type species diffusion to fluid flow, a coupling which gives rise to more complex systems since a Navier-Stokes momentum balance is involved. Each particular model can be formally derived by an Energetic Variational Approach, that combines the classical idea of gradient flows for free energy minimization as a direct consequence of the second law of thermodynamics, together with the Least Action and Maximum Dissipation Principles. Moreover, as an extension of the already established two-scale convergence approach, we investigate further a reiterated homogenization procedure over three separated scales of periodic oscillations. Finally, we examine the General Equations for Non-Equilibrium Reversible-Irreversible Coupling commonly known by the abbreviation GENERIC, an extended two-generator variational framework, which was initially developed in order to model the rheological properties of complex fluids, far from thermodynamic equilibrium.Engineering and Physical Sciences Research Council (EPSRC

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

Chemical Reaction Monitoring Using Zero-Field Nuclear Magnetic Resonance Enables Study of Heterogeneous Samples in Metal Containers

We demonstrate that heterogeneous/biphasic chemical reactions can be monitored with high spectroscopic resolution using zero-field nuclear magnetic resonance. This is possible because magnetic susceptibility broadening is insignificant at ultralow magnetic fields. We show the two-step hydrogenation of dimethyl acetylenedicarboxylate with para-enriched hydrogen gas in conventional glass NMR tubes, as well as in a titanium tube. The low frequency zero-field NMR signals ensure that there is no significant signal attenuation due to shielding by the electrically conductive sample container. This method paves the way for in situ monitoring of reactions in complex heterogeneous multiphase systems and in reactors made from conductive materials without magnetic susceptibility induced line broadening.</div