Maximum stability of a single spherical particle attached to an emulsion drop

The stability of a single, solid, spherical particle attached to a liquid drop in an emulsion is discussed. Ignoring effects due to gravity and line tension, we calculate the energies required to either detach the particle from the drop or to engulf the particle within the drop. The stability of the attached particle is here defined as the smaller of these two energies. A simple formula is derived for the value of Young's angle which gives maximum stability for a given radius ratio of particle to detached drop. For maximum stability the particle should be preferentially wetted by the liquid forming the drop.