Phase-field theory of multicomponent incompressible Cahn-Hilliard liquids

Gyula I. Tóth, Mojdeh Zarifi, and Bjørn Kvamme
Phys. Rev. E 93, 013126 – Published 25 January 2016

Abstract

In this paper, a generalization of the Cahn-Hilliard theory of binary liquids is presented for multicomponent incompressible liquid mixtures. First, a thermodynamically consistent convection-diffusion-type dynamics is derived on the basis of the Lagrange multiplier formalism. Next, a generalization of the binary Cahn-Hilliard free-energy functional is presented for an arbitrary number of components, offering the utilization of independent pairwise equilibrium interfacial properties. We show that the equilibrium two-component interfaces minimize the functional, and we demonstrate that the energy penalization for multicomponent states increases strictly monotonously as a function of the number of components being present. We validate the model via equilibrium contact angle calculations in ternary and quaternary (four-component) systems. Simulations addressing liquid-flow-assisted spinodal decomposition in these systems are also presented.

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  • Received 28 September 2015
  • Revised 8 December 2015

DOI:https://doi.org/10.1103/PhysRevE.93.013126

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

Gyula I. Tóth*

  • 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

Mojdeh Zarifi and Bjørn Kvamme

  • Department of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway

  • *Gyula.Toth@ift.uib.no

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Vol. 93, Iss. 1 — January 2016

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