Breakup of concentric double emulsion droplets in linear flows

The behaviour of concentric double emulsion droplets in linear flows is examined analytically, for the case when both fluid-fluid interfaces remain nearly spherical, and numerically, for the effect of finite interface deformation. The theoretical analysis is used to calculate the velocity fields interior and exterior to the particle, the first effects of flow-induced deformation, and the effective viscosity of a dilute emulsion of compound droplets. The numerical simulations allow for a complete investigation of the finite deformation of both the outer drop and the encapsulated particle. For concentric multiphase particles, there appear to be two distinct mechanisms of globule breakup: (i) continuous extension of the globule corresponding to non-existence of a steady particle shape or (ii) contact of the two interfaces at the globule centre, owing to incompatibility of the steady inner and outer interface shapes, even though the globule is only modestly deformed. Finally, the effect of different flow-types, i.e, uniaxial or biaxial extensional flows, is shown, in one example, to suggest breakup of the inner droplet even though the outer droplet maintains a steady shape.