Imperial College London

Professor Grigorios A. Pavliotis

Faculty of Natural SciencesDepartment of Mathematics

Professor of Applied Mathematics



+44 (0)20 7594 8564g.pavliotis Website




736aHuxley BuildingSouth Kensington Campus






BibTex format

author = {Schmuck, M and Pavliotis, GA and Kalliadasis, S},
doi = {10.1016/j.commatsci.2018.08.026},
journal = {Computational Materials Science},
pages = {441--451},
title = {Recent advances in the evolution of interfaces: Thermodynamics, upscaling, and universality},
url = {},
volume = {156},
year = {2019}

RIS format (EndNote, RefMan)

AB - 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 general reversible-irreversible couplings and the associated mathematical attempts to formulate a 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 universality with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known O(t1/3)-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their 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.
AU - Schmuck,M
AU - Pavliotis,GA
AU - Kalliadasis,S
DO - 10.1016/j.commatsci.2018.08.026
EP - 451
PY - 2019///
SN - 0927-0256
SP - 441
TI - Recent advances in the evolution of interfaces: Thermodynamics, upscaling, and universality
T2 - Computational Materials Science
UR -
UR -
VL - 156
ER -