  We study the rheological behavior of mixtures of foams and pastes, which can
be described as suspensions of bubbles in yield stress fluids. Model systems
are designed by mixing monodisperse aqueous foams and concentrated emulsions.
The elastic modulus of the suspensions decreases with the bubble volume
fraction. This decrease is all the sharper as the elastic capillary number
(defined as the ratio of the paste elastic modulus to the bubble capillary
pressure) is high, which accounts for the softening of the bubbles as compared
to the paste. By contrast, the yield stress of most studied materials is not
modified by the presence of bubbles. Their plastic behavior is governed by the
plastic capillary number, defined as the ratio of the paste yield stress to the
bubble capillary pressure. At low plastic capillary number values, bubbles
behave as nondeformable inclusions, and we predict that the suspension
dimensionless yield stress should remain close to unity. At large plastic
capillary number values, we observe bubble breakup during mixing: bubbles are
deformed by shear. Finally, at the highest bubble volume fractions, the yield
stress increases abruptly: this is interpreted as a 'foamy yield stress fluid'
regime, which takes place when the paste mesoscopic constitutive elements are
strongly confined in the films between the bubbles.

Soft Condensed Matter