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
