Strict equivalence between maxwell-stefan and fast-mode theory for multicomponent polymer mixtures
Ronsin OJJ, Harting J (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 52
Pages Range: 6035-6044
Journal Issue: 15
DOI: 10.1021/acs.macromol.9b01220
Abstract
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.
Involved external institutions
Germany (DE)How to cite
APA:
Ronsin, O.J.J., & Harting, J. (2019). Strict equivalence between maxwell-stefan and fast-mode theory for multicomponent polymer mixtures. Macromolecules, 52(15), 6035-6044. https://doi.org/10.1021/acs.macromol.9b01220
MLA:
Ronsin, Olivier J. J., and Jens Harting. "Strict equivalence between maxwell-stefan and fast-mode theory for multicomponent polymer mixtures." Macromolecules 52.15 (2019): 6035-6044.
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