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

Markus Schmuck, Grigorios A. Pavliotis, Serafim Kalliadasis

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages441-451
Number of pages11
JournalComputational Materials Science
Volume156
Early online date24 Oct 2018
DOIs
Publication statusPublished - Jan 2019

Fingerprint

Upscaling
Binary Mixtures
Binary mixtures
binary mixtures
Universality
Thermodynamics
Perforated Domains
formulations
thermodynamics
Formulation
Heterogeneous Systems
Free energy
Non-equilibrium
Free Energy
free energy
Phase-field Equations
permeating
Immiscible Fluids
Fluids
Lithium batteries

Keywords

  • Coarsening rates
  • Complex heterogeneous multiphase systems
  • Energy
  • Entropy
  • GENERIC
  • Homogenization
  • Porous media
  • Universality
  • Variational theories

ASJC Scopus subject areas

  • Computer Science(all)
  • Chemistry(all)
  • Materials Science(all)
  • Mechanics of Materials
  • Physics and Astronomy(all)
  • Computational Mathematics

Cite this

Schmuck, Markus ; Pavliotis, Grigorios A. ; Kalliadasis, Serafim. / Recent advances in the evolution of interfaces : thermodynamics, upscaling, and universality. In: Computational Materials Science. 2019 ; Vol. 156. pp. 441-451.
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Recent advances in the evolution of interfaces : thermodynamics, upscaling, and universality. / Schmuck, Markus; Pavliotis, Grigorios A.; Kalliadasis, Serafim.

In: Computational Materials Science, Vol. 156, 01.2019, p. 441-451.

Research output: Contribution to journalArticle

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