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

•We present a concise account of advanced variational and systematic non-equilibrium thermodynamic formulations for the evolution of binary fluid mixtures.•The hereby gained thermodynamic consistency enables us to reliably take the mixture’s specific free energy into account, which, following rigorous upscaling, provides a promising theoretical-computational tool for the reliable and systematic description of multiphase flow in porous media compared to the frequently used multiphase extension of Darcy’s law.•The upscaling under strong convective flows (i.e., large Péclet numbers) also allows us to obtain systematically and as simple byproducts of the thermodynamic frameworks we developed, the so-called diffusion-dispersion relations for interfacial transport, which have been studied in the context of classical diffusion-convection problems, often using phenomenological arguments.•Due to the increasingly growing interest in diffuse interface modelling and its wide range of applicability, we believe that the outlined formulations of effective macroscopic phase field equations provide a promising framework for future generations and applications, e.g. in lithium ion batteries.•For inhomogeneous porous media with porosity gradients, we have unravelled a “universal” behaviour of the coarsening rate O(t1/3), which turns out to be independent of the geometry of inhomogeneities/perforations in the domain.