Multiscale modelling analysis and computations of complex heterogeneous multiphase systems
Abstract
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.