Simulation of the extensional deformation of a drop with an elastoviscoplastic interface

A numerical implementation of two-phase flows of Newtonian fluids with a non-linear viscoelastic interface is validated and applied to the case of uniaxial extension of a drop in a matrix fluid. Second-order convergence in space and time is obtained with a Lagrangian-based interface tracking finite element method. The flow problem is analysed using dimensionless groups based on the relative magnitudes of the viscoelastic interfacial extra stress, the interfacial tension and the viscous stress of the bulk fluids. After fitting the intrinsic viscoelastic stress–strain behaviour of interfaces in shear to experimental results from the literature, the influence of interfacial rheology on the drop shape and interfacial stress is investigated. The drop shape is not significantly influenced by the viscoelastic properties of the interface if the interfacial viscoelastic stress, interfacial tension and bulk viscous stress are of the same order of magnitude. However, the interface develops distinct stress profiles for varying interfacial viscoelastic properties. For relatively large viscoelastic interface stress compared to interfacial tension and bulk viscous stress, simulations become unstable. Eventually, the interfacial viscoelastic stress exceeds the interfacial tension and bulk viscous stress, and possibly buckling of the interface occurs, caused by compressive stresses at the drop tip.