Elasticity of Compressed Emulsions

Abstract

The elastic shear modulus of monodisperse emulsions is shown to exhibit a universal dependence on droplet volume fraction $\ensuremath{\varphi}$ when scaled by the Laplace pressure of the droplets, increasing as $\ensuremath{\varphi}(\ensuremath{\varphi}\ensuremath{-}{\ensuremath{\varphi}}_{c})$, where ${\ensuremath{\varphi}}_{c}\ensuremath{\approx}0.635$, the value of random close packing of solid spheres. Surprisingly the osmotic pressure required to compress the emulsions to increase $\ensuremath{\varphi}$ 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.