Ellipsoidal particles encapsulated in droplets†
Using hydrodynamic focusing, we encapsulated polystyrene ellipsoidal particles in water droplets dispersed in an immiscible, continuous phase of light mineral oil. The axisymmetric shape of the drop partially encapsulating an elongated particle was computed as a function of the particle aspect ratio, droplet volume, and contact angle. When the droplet volume is within a certain range, pinned (partially engulfed) and fully engulfed equilibrium configurations coexist. Partial encapsulation may be preferred (has a lower free energy) even when the droplet's volume is sufficient to fully engulf the particle. The co-existence of multiple equilibrium states suggests possible hysteretic encapsulation behavior. We also estimate the axial capillary force exerted by the droplet on the particle as a function of volume and contact angle. The theoretical predictions are critically compared with experimental observations.