Wetting behaviour of a three-phase system in contact with a surface

We extend the Cahn-Landau-de Gennes mean field theory of binary mixtures to understand the wetting thermodynamics of a three phase system, that is in contact with an external surface which prefers one of the phases. We model the system using a phenomenological free energy having three minima corresponding to low, intermediate and high density phases. By systematically varying the \textit{(i)} depth of the central minimum, \textit{(ii)} the surface interaction parameters, we explore the phase behavior, and wetting characteristics of the system across the triple point corresponding to three phase coexistence. We observe a non-monotonic dependence of the surface tension across the triple point that is associated with a complete to partial wetting transition. The methodology is then applied to study the wetting behaviour of a polymer-liquid crystal mixture in contact with a surface using a renormalised free energy. Our work provides a way to interrogate phase behavior and wetting transitions of biopolymers in cellular environments.