### 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(t^{1/3})-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.

Language | English |
---|---|

Pages | 441-451 |

Number of pages | 11 |

Journal | Computational Materials Science |

Volume | 156 |

Early online date | 24 Oct 2018 |

DOIs | |

State | Published - Jan 2019 |

### Fingerprint

### Keywords

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

### Cite this

*Computational Materials Science*,

*156*, 441-451. DOI: 10.1016/j.commatsci.2018.08.026

}

*Computational Materials Science*, vol. 156, pp. 441-451. DOI: 10.1016/j.commatsci.2018.08.026

**Recent advances in the evolution of interfaces : thermodynamics, upscaling, and universality.** / Schmuck, Markus; Pavliotis, Grigorios A.; Kalliadasis, Serafim.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Recent advances in the evolution of interfaces

T2 - Computational Materials Science

AU - Schmuck,Markus

AU - Pavliotis,Grigorios A.

AU - Kalliadasis,Serafim

PY - 2019/1

Y1 - 2019/1

N2 - 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.

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.

KW - Coarsening rates

KW - Complex heterogeneous multiphase systems

KW - Energy

KW - Entropy

KW - GENERIC

KW - Homogenization

KW - Porous media

KW - Universality

KW - Variational theories

UR - http://www.scopus.com/inward/record.url?scp=85055285780&partnerID=8YFLogxK

U2 - 10.1016/j.commatsci.2018.08.026

DO - 10.1016/j.commatsci.2018.08.026

M3 - Article

VL - 156

SP - 441

EP - 451

JO - Computational Materials Science

JF - Computational Materials Science

SN - 0927-0256

ER -