Phase-field modeling of isothermal quasi-incompressible multicomponent liquids
journal contributionposted on 03.11.2017 by Gyula Toth
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In this paper general dynamic equations describing the time evolution of isothermal quasiincompressible multicomponent liquids are derived in the framework of the classical Ginzburg-Landau theory of first order phase transformations. Based on the fundamental equations of continuum mechanics, a general convection-diffusion dynamics is set up first for compressible liquids. The constitutive relations for the diffusion fluxes and the capillary stress are determined in the framework of gradient theories. Next the general definition of incompressibility is given, which is taken into account in the derivation by using the Lagrange multiplier method. To validate the theory, the dynamic equations are solved numerically for the quaternary quasi-incompressible Cahn-Hilliard system. It is demonstrated that variable density (i) has no effect on equilibrium (in case of a suitably constructed free energy functional), and (ii) can in uence non-equilibrium pattern formation significantly.
The work has been supported by the VISTA basic research programme Project No. 6359 Surfactants for water-CO2- hydrocarbon emulsions for combined CO2 storage and utilization of the Norwegian Academy of Science and Letters and the Statoil.
- Mathematical Sciences