  We study the elastic properties of soft solids containing air bubbles.
Contrary to standard porous materials, the softness of the matrix allows for a
coupling of the matrix elasticity to surface tension forces brought in by the
bubbles. Thanks to appropriate experiments on model systems, we show how the
elastic response of the dispersions is governed by two dimensionless
parameters: the gas volume fraction and a capillary number comparing the
elasticity of the matrix to the stiffness of the bubbles. We also show that our
experimental results are in good agreement with computations of the shear
modulus through a micro-mechanical approach.
