Phase‐field modeling of chemically reactive multi‐component and multi‐phase systems. Issue 1 (24th March 2023)

• Record Type: Journal Article
• Authors: Seupel, Andreas; Roth, Stephan; Kiefer, Bjoern
• Other Names: Böhm Ch. guestEditor.; Mang K. guestEditor.; Markert B. guestEditor.; Reese S. guestEditor.; Schmidtchen M. guestEditor.; Waimann J. guestEditor.; Kaliske M. editorInChief.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 22:Issue 1(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2023-03-24
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202200154
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The present phase‐field approach is based on a mixture theory for multiple components and phases within the framework of non‐equilibrium thermodynamics of internal state variables. More specifically, diffuse interfaces are included in the state potential by terms depending on spatial gradients of the component mass fractions as well as order parameters representing different phases. Coupled field equations of generalized Cahn‐Hilliard and Allen‐Cahn type are derived directly from a local entropy balance, under the assumption of a localized Gibbs fundamental equation. Additionally, thermodynamically consistent kinetics for equilibrium reactions are formulated. The field equations are recast into a mixed variational formulation, which allows a discretization by finite elements with low‐order ansatz functions. The numerical implementation is discussed by means of a benchmark problem for reactive binary systems, of which the thermodynamic equilibrium solution is known.