A viscoelastic two-phase solver using a phase-field approach

In this work we discuss the implementation and the performance of an in-house viscoelastic two-phase solver, based on a diffuse interface approach. The Phase-Field method is considered and the Cahn-Hilliard equation is employed for describing the transport of a binary fluid system. The interface between the two fluids utilises a continuum approach, which is responsible for smoothing the inherent discontinuities of sharp interface models, facilitating studies that are related to morphological changes of the interface, such as droplet breakup and coalescence. The two-phase solver manages to predict the expected dynamics for all the cases investigated, and exhibits an overall good performance. The numerical implementation is able to predict the expected physical response of the oscillating drop case, while the performance is also validated by examining the droplet deformation case. The corresponding history of the deformation is predicted for several systems considering Newtonian fluids, viscoelastic fluids and combinations of both. Finally, we demonstrate the ability of the solver to capture the complex interfacial patterns of the Rayleigh-Taylor instability for different Atwood numbers when Newtonian fluids are considered. In the two regimes identified, the system is modified to consider viscoelastic fluids and the influence of elasticity is investigated.