Microscopic approach to the nonlinear elasticity of compressed emulsions.

Using confocal microscopy, we measure the packing geometry and interdroplet forces as a function of the osmotic pressure in a 3D emulsion system. We assume a harmonic interaction potential over a wide range of volume fractions and attribute the observed nonlinear elastic response of the pressure with density to the first corrections to the scaling laws of the microstructure away from the critical point. The bulk modulus depends on the excess contacts created under compression, which leads to the correction exponent α=1.5. Microscopically, the nonlinearities manifest themselves as a narrowing of the distribution of the pressure per particle as a function of the global pressure.