Hydrodynamic simulation of viscoelastic phase separation via coupled Model-H and Oldroyd-B equations

Viscoelastic phase separation governs the nonequilibrium demixing dynamics of soft-matter systems. Here, we introduce an efficient continuum framework that couples the Cahn-Hilliard phase-field model with the Oldroyd-B constitutive equation. By treating the mixture as a single incompressible fluid, our model captures macromolecular deformation through a continuous conformation tensor and reveals distinct kinetic pathways across different thermodynamic regimes. In the spinodal regime, the minority polymer-rich phase undergoes morphological inversion into a persistent interconnected network, sustained by intense velocity gradients that stretch polymer chains and generate elastic stresses that suppress coarsening. In the nucleated-droplet regime, the model reveals strain-induced coarsening acceleration, in which highly elongated domains enhance the initial coalescence rate before elastic arrest sets in as the relaxation time increases. Tuning the rheological parameters recovers the classical Newtonian regime, demonstrating that this framework provides a simple, efficient, and robust platform for modeling phase separation in complex fluids.