Consistent multiphase-field theory for interface-driven multidomain dynamics
journal contributionposted on 06.11.2017 by Gyula Toth, Tamas Pusztai, Laszlo Granasy
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We present a new multiphase- eld theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical and physical consistency. We rst analyze previous multiphase- eld theories, and identify their advantageous and disadvantageous features. On the basis of this analysis, we introduce a new way of constructing the free energy surface, and derive a generalized multiphase description for arbitrary number of phases (or domains). The presented approach retains the variational formalism; reduces (or extends) naturally to lower (or higher) number of elds on the level of both the free energy functional and the dynamic equations; enables the use of arbitrary pairwise equilibrium interfacial properties; penalizes multiple junctions increasingly with the number of phases; ensures non-negative entropy production, and the convergence of the dynamic solutions to the equilibrium solutions; and avoids the appearance of spurious phases on binary interfaces. The new approach is tested for multi-component phase separation and grain coarsening.
This work has been supported by the VISTA basic research programme of the Norwegian Academy of Science and Letters and the Statoil, under Project No. 6359 “Surfactants for water/CO2/hydrocarbon emulsions for combined CO2 storage and utilization,” by ESA PECS Contracts No. 40000110756/11/NL/KML and No. 40000 110759/11/NL/KML, and by EU FP7 Project EXOMET (Contract No. NMP-LA-2012-280421, cofunded by ESA).
- Mathematical Sciences