Motion and deformation of viscoplastic double emulsion drops in stokes flow

•Sedimentation of a deformable compound drop of viscoplastic fluid shell and viscous core in an unbounded Newtonian medium is simulated making use of a boundary integral approach.•Computations are performed for the gravity-induced sedimentation of compound drops with various shell thickness and various physical parameters of the system.•The focus of the study is on the dynamics of interface deformation and un-yielded zones inside the shell. Sedimentation of a deformable compound drop of viscoplastic fluid shell and viscous core in an unbounded Newtonian medium is simulated making use of a boundary integral approach. The flow is considered under quasi-stationary creeping flow approximation. The Green function for the Stokes equation is used and the non-Newtonian stress is treated as a source term. Computations are performed for the gravity-induced sedimentation of compound drops with various shell thickness and various physical parameters of the system. The focus of the study is on the dynamics of interface deformation and un-yielded zones inside the shell.