Elasticity of Compressed Emulsions

The elastic shear modulus of monodisperse emulsions is shown to exhibit a universal dependence on droplet volume fraction $\phi$ when scaled by the Laplace pressure of the droplets, increasing as $\phi (\phi -{\phi }_c)$, where ${\phi }_c\approx 0.635$, the value of random close packing of solid spheres. Surprisingly the osmotic pressure required to compress the emulsions to increase $\phi$ is nearly the same as the shear modulus over a large range of volume fraction, while the bulk osmotic modulus differs significantly. Models based on the structural disorder of the emulsions are discussed to account for these data.