Particles confined in droplets are called compound particles. This work investigates the dynamics and stability of a concentric compound particle under external forces and imposed flows.

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Active particles encapsulated in a droplet are called active compound particles. In addition to the activity induced fluid flows, these multiphase structures may experience imposed flows in the process of generating and manipulating them in microfluidic devices or in their natural habitats. Therefore, we investigate the deformation dynamics and stability of a drop encapsulating a model microswimmer, a spherical squirmer (shaker) concentrically placed in a drop, when subjected to an imposed shear flow. Using Lamb’s general solution, Stokes equations are solved to determine the flow field and consequently the shape of the droplet interface. Shear flow always deforms the drop and the flow induced by the active particle may enhance or impede this deformation based on its orientation. The extent of deformation also depends on (i) the size of the active particle and the droplet, (ii) the viscosity of the droplet fluid and the fluid in which it is dispersed, (iii) the orientation of the active particle, and (iv) the relative strength of activity and imposed shear. Finally we find that the presence of an imposed vorticity field has a stabilizing effect on the active compound particle as it rotates the encapsulated swimmer and the drop undergoes a time periodic deformation.