Model for the Elasticity of Compressed Emulsions

We present a new model to describe the unusual elastic properties of compressed emulsions. The response of a single droplet under compression is investigated numerically for different Wigner-Seitz cells. The response is softer than harmonic, and depends on the coordination number of the droplet. Using these results, we propose a new effective interdroplet potential which is used to determine the elastic response of a monodisperse collection of disordered droplets as a function of volume fraction. Our results are in excellent agreement with recent experiments. This suggests that anharmonicity together with disorder are responsible for the quasilinear increase of $G$ and $\Pi$ observed at ${\varphi }_c$.