  Elasticity of soft materials can be greatly influenced by the presence of air
bubbles. Such a capillary effect is expected for a wide range of materials,
from polymer gels to concentrated emulsions and colloidal suspensions. Whereas
experimental results and theory exist for describing the elasto-capillary
behavior of bubbly materials (i.e. with moderate gas volume fractions), foamy
systems still require a dedicated study in order to increase our understanding
of elasticity in aerated materials over the full range of gas volume fractions.
Here we elaborate well-controlled foams with concentrated emulsion and we
measure their shear elastic modulus as a function of gas fraction, bubble size
and elastic modulus of the emulsion. Such complex foams possess the elastic
features of both the bubble assembly and the interstitial matrix. Moreover,
their elastic modulus is shown to be governed by two parameters, namely the gas
volume fraction and the elasto-capillary number, defined as the ratio of the
emulsion modulus with the bubble capillary pressure. We connect our results for
foams with existing data for bubbly systems and we provide a general view for
the effect of gas bubbles in soft elastic media. Finally, we suggest that our
results could be useful for estimating the shear modulus of aqueous foams and
emulsions with multimodal size distributions.
