We extend the Cahn-Landau-de
Gennes mean field theory of wetting
in binary mixtures to understand the wetting thermodynamics of a three
phase system (e.g., polymer dispersed liquid crystals or polymer-colloid
mixtures) that is in contact with an external surface, which prefers
one of the phases. Using a model free-energy, which has three minima
in its landscape, we show that as the central minimum becomes more
stable compared to the remaining ones, the bulk phase diagram encounters
a triple point and then bifurcates and we observe a novel non-monotonic
dependence of the surface tension as a function of the stability of
the central minimum. We show that this non-monotonicity in surface
tension is associated with a complete to partial wetting transition.
We obtain the complete wetting phase behavior as a function of phase
stability and the surface interaction parameters when the system is
close to the bulk triple point. The model free-energy that we use
is qualitatively similar to that of a renormalized free energy, which
arises in the context of polymer-liquid crystal mixtures. Finally,
we study the thermodynamics of wetting for an explicit polymer-liquid
crystal mixture and show that its thermodynamics is similar to that
of our model free-energy.