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

Olivier J.J. Ronsin, Jens Harting (Corresponding author)

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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.

TaalEngels
Pagina's6035-6044
Aantal pagina's10
TijdschriftMacromolecules
Volume52
Nummer van het tijdschrift15
DOI's
StatusGepubliceerd - 2 aug 2019

Vingerafdruk

Polymers
Fluxes
Fluids
Maxwell equations
Kinetics

Citeer dit

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

In: Macromolecules, Vol. 52, Nr. 15, 02.08.2019, blz. 6035-6044.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

TY - JOUR

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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.

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