  The rheological properties of suspensions of bubbles in yield stress fluids
are investigated through experiments on model systems made of monodisperse
bubbles dispersed in concentrated emulsions. Thanks to this highly tunable
system, the bubble size and the rheological properties of the suspending yield
stress fluid are varied over a wide range. We show that the macroscopic
response under shear of the suspensions depends on the gas volume fraction and
the bubble stiffness in the suspending fluid. This relative stiffness can be
quantified through capillary numbers comparing the capillary pressure to stress
scales associated with the rheological properties of the suspending fluid. We
demonstrate that those capillary numbers govern the decrease of the elastic and
loss moduli, the absence of variation of the yield stress and the increase of
the consistency with the gas volume fraction, for the investigated range of
capillary numbers. Micro-mechanical estimates are consistent with the
experimental data and provide insight on the experimental results.
