Instability and bifurcation of a particle-encapsulating droplet in creeping shear flow*

In this study, we investigate a novel model system in order to understand the flow behavior of fluid particles such as nucleated cells and double-emulsions. The model consists of a finite-size particle encapsulated in a deforming droplet and we ask whether this composite system will stay concentric or not in a creeping shear flow. By performing numerical simulations based on a versatile boundary integral method, we find in addition to the concentric particle-droplet configuration, other eccentric and time-periodic equilibrium solutions emerge spontaneously via supercritical pitchfork and Hopf bifurcations. The loci of these solutions are presented around the codimenstion-two point. We adopt a dynamic system approach to model and characterize the two bifurcations and their interactions. By scrutinizing the flow fields and hydrodynamic forces, we identify the role of hydrodynamic particle-droplet interaction which gives rise to these bifurcations.