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

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Title: Recent advances in the evolution of interfaces: Thermodynamics, upscaling, and universality
Author(s): Schmuck, M
Pavliotis, GA
Kalliadasis, S
Item Type: Journal Article
Abstract: 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.
Publication Date: 1-Jan-2019
Date of Acceptance: 13-Aug-2018
URI: http://hdl.handle.net/10044/1/65637
DOI: https://dx.doi.org/10.1016/j.commatsci.2018.08.026
ISSN: 0927-0256
Start Page: 441
End Page: 451
Journal / Book Title: Computational Materials Science
Volume: 156
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/H034587/1
EP/K008595/1
EP/L025159/1
EP/L027186/1
Copyright Statement: © 2018 Elsevier B.V. All rights reserved. This manuscript is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords: Science & Technology
Technology
Materials Science, Multidisciplinary
Materials Science
Complex heterogeneous multiphase systems
GENERIC
Coarsening rates
Homogenization
Porous media
Universality
Entropy
Energy
Variational theories
FOURIER-SPECTRAL METHOD
CAHN-HILLIARD EQUATION
PHASE-FIELD MODELS
GENERAL FORMALISM
COMPLEX FLUIDS
POROUS-MEDIA
DYNAMICS
KINETICS
HOMOGENIZATION
CONVERGENCE
0912 Materials Engineering
0204 Condensed Matter Physics
Materials
Publication Status: Published
Embargo Date: 2019-10-24
Online Publication Date: 2018-10-24
Appears in Collections:Faculty of Engineering
Mathematics
Chemical Engineering
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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