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MM: Fachverband Metall- und Materialphysik
MM 5: Interfaces I
MM 5.4: Vortrag
Montag, 26. März 2007, 11:00–11:15, H6
Modelling grains and bubbles: phase boundary evolution with volume constraints — Harald Garcke2, Britta Nestler1, Björn Stinner3, and •Frank Wendler1 — 1University of Applied Sciences Karlsruhe, Moltkestr. 30, D-76133 Karlsruhe — 2Department of Mathematics, University Regensburg, D-93040 Regensburg — 3Department of Mathematics, University of Sussex, BN1 9RF, United Kingdom
In our talk we present a new phase-field model for the evolution of grain or bubble systems, where the motion of the interfaces is determined by the mean curvature and the volume of some or all of the phases is preserved. Based on previously published results [1] a multi-phase-field model of Allen-Cahn type is introduced wich includes nonlocal forcing terms. The phase boundary dynamics results from a gradient flow of a Ginzburg-Landau type energy and incorporates anisotropic surface energies and kinetics. The algorithms for the volume constraints and the numerical realization for a high number of phases are briefly presented. Simulation results are shown for 2D and 3D problems dominated by surface energy minimization like the formation of Wulff shapes, double crystals and bubble clusters. Wetting phenomena with a constant fraction of liquid phase are treated for cases where the bubble phase volume either is preserved (foams) or may change in time (solid/melt grain coarsening). Additional forcing terms due to a solid/liquid phase transition allow to simulate the inclusion of inert particles into a growing front.
[1] B. Nestler, H. Garcke and B. Stinner, Phys. Rev. E 71 (2005), 041609-1