### Uittreksel

The applicability of theories describing the kinetic evolution of fluid mixtures depends on the underlying physical assumptions. The Maxwell-Stefan equations, widely used for miscible fluids, express forces depending on coupled fluxes. They need to be inverted to recover a Fickian form which is generally impossible analytically. Moreover, the concentration dependence of the diffusivities has to be modeled, for example, by the multicomponent Darken equation. Cahn-Hilliard-type equations are preferred for immiscible mixtures, whereby different assumptions on the coupling of fluxes lead to the slow-mode and fast-mode theories. For two components, these were derived from the Maxwell-Stefan theory in the past. Here, we prove that the fast-mode theory and the generalized Maxwell-Stefan theory together with the multicomponent Darken equation are strictly equivalent even for multicomponent systems with very different molecular sizes. Our findings allow to reduce the choice of a suitable theory to the most efficient algorithm for solving the underlying equations.

Taal | Engels |
---|---|

Pagina's | 6035-6044 |

Aantal pagina's | 10 |

Tijdschrift | Macromolecules |

Volume | 52 |

Nummer van het tijdschrift | 15 |

DOI's | |

Status | Gepubliceerd - 2 aug 2019 |

### Vingerafdruk

### Citeer dit

*Macromolecules*,

*52*(15), 6035-6044. DOI: 10.1021/acs.macromol.9b01220

}

*Macromolecules*, vol. 52, nr. 15, blz. 6035-6044. DOI: 10.1021/acs.macromol.9b01220

**Strict equivalence between Maxwell-Stefan and fast-mode theory for multicomponent polymer mixtures.** / Ronsin, Olivier J.J.; Harting, Jens (Corresponding author).

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

TY - JOUR

T1 - Strict equivalence between Maxwell-Stefan and fast-mode theory for multicomponent polymer mixtures

AU - Ronsin,Olivier J.J.

AU - Harting,Jens

PY - 2019/8/2

Y1 - 2019/8/2

N2 - The applicability of theories describing the kinetic evolution of fluid mixtures depends on the underlying physical assumptions. The Maxwell-Stefan equations, widely used for miscible fluids, express forces depending on coupled fluxes. They need to be inverted to recover a Fickian form which is generally impossible analytically. Moreover, the concentration dependence of the diffusivities has to be modeled, for example, by the multicomponent Darken equation. Cahn-Hilliard-type equations are preferred for immiscible mixtures, whereby different assumptions on the coupling of fluxes lead to the slow-mode and fast-mode theories. For two components, these were derived from the Maxwell-Stefan theory in the past. Here, we prove that the fast-mode theory and the generalized Maxwell-Stefan theory together with the multicomponent Darken equation are strictly equivalent even for multicomponent systems with very different molecular sizes. Our findings allow to reduce the choice of a suitable theory to the most efficient algorithm for solving the underlying equations.

AB - The applicability of theories describing the kinetic evolution of fluid mixtures depends on the underlying physical assumptions. The Maxwell-Stefan equations, widely used for miscible fluids, express forces depending on coupled fluxes. They need to be inverted to recover a Fickian form which is generally impossible analytically. Moreover, the concentration dependence of the diffusivities has to be modeled, for example, by the multicomponent Darken equation. Cahn-Hilliard-type equations are preferred for immiscible mixtures, whereby different assumptions on the coupling of fluxes lead to the slow-mode and fast-mode theories. For two components, these were derived from the Maxwell-Stefan theory in the past. Here, we prove that the fast-mode theory and the generalized Maxwell-Stefan theory together with the multicomponent Darken equation are strictly equivalent even for multicomponent systems with very different molecular sizes. Our findings allow to reduce the choice of a suitable theory to the most efficient algorithm for solving the underlying equations.

U2 - 10.1021/acs.macromol.9b01220

DO - 10.1021/acs.macromol.9b01220

M3 - Article

VL - 52

SP - 6035

EP - 6044

JO - Macromolecules

T2 - Macromolecules

JF - Macromolecules

SN - 0024-9297

IS - 15

ER -