  Yield stress fluids are widely used in industrial application to arrest dense
solid particles, which can be studied by using a concentrated emulsion as a
model fluid. We show in experiments that particle sedimentation in emulsions
cannot be predicted by the classical criterion for spheres embedded in a yield
stress fluid. Phase separation processes take place, where a liquid layer forms
and particle sedimentation is enhanced by the emulsion drainage. In addition,
emulsion drainage can be arrested or enhanced by the amount of particles
embedded in the emulsion. A minimal mathematical model is developed and solved
in numerical simulations to describe the emulsion drainage in the presence of
particles, which favorably compares with the experimental stability diagram and
the sedimentation dynamics.
