Phase-feld theory of multi-component incompressible Cahn-Hilliard liquids

TL;DR

This paper extends the Cahn-Hilliard theory to multi-component incompressible liquids, providing a thermodynamically consistent framework, generalized free energy functional, and validation through equilibrium and dynamic simulations.

Contribution

It introduces a generalized Cahn-Hilliard model for multi-component liquids with independent interfacial properties and validates it through equilibrium and flow simulations.

Findings

Equilibrium interfaces minimize the generalized free energy functional.

Energy penalization increases with the number of components.

Model accurately predicts contact angles and spinodal decomposition behaviors.

Abstract

In this paper a generalization of the Cahn-Hilliard theory of binary liquids is presented for multi-component 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 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 demonstrate, that the energy penalization for multi-component 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 (4-component) systems. Simulations addressing liquid flow assisted spinodal decomposition in these systems are also presented.