On the singular limit of three-phase contact lines in a ternary Cahn-Hilliard model

We investigate the physically relevant singular limit of a thermodynamically-consistent model of ternary liquid-liquid phase separation. The emergence of three-phase contact lines significantly complicates the analysis. We combine three techniques to purse this analysis to arbitrary asymptotic order: 1. Physically meaningful and geometrically elegant coordinate systems adapted to each subproblem. 2. A comprehensive symbolic algebra system for performing and validating the analysis. 3. Little-known identities for complete analytic solutions to the codimension-1 spectral subproblem. We also discuss the algorithms needed for accurate numerical validation of these models, and explore the applications of these simplified models to microfluidic manufacture of Janus droplets.