title: Phase-field modeling of isothermal quasi-incompressible multicomponent liquids.
abstract: In this paper general dynamic equations describing the time evolution of isothermal quasi-incompressible 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 influence nonequilibrium pattern formation significantly.
authors.affiliation: Department of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway and Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary.
authors.forename: Gyula I
authors.initials: GI
authors.lastname: Tóth