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Using confocal microscopy, we measure the packing geometry and interdropletforces as a function of the osmotic pressure in a 3D emulsion system. We findthat the nonlinear elastic response of the pressure with density is not aresult of the anharmonicity in the interaction potential, but of thecorrections to the scaling laws of the microstructure away from the criticalpoint. The bulk modulus depends on the excess contacts created undercompression, which leads to the correction exponent \alpha=1.5.Microscopically, the nonlinearities manifest themselves as a narrowing of thedistribution of the pressure per particle as a function of the global pressure.

A microscopic approach to the nonlinear elasticity of compressed emulsions