Osmotic pressure and viscoelastic shear moduli of concentrated emulsions

We present an experimental study of the frequency ω dependence and volume fraction φ dependence of the complex shear modulus [Formula Presented] of monodisperse emulsions which have been concentrated by an osmotic pressure Π. At a given φ, the elastic storage modulus [Formula Presented] exhibits a low-frequency plateau [Formula Presented] dominating the dissipative loss modulus [Formula Presented] which exhibits a minimum. Above a critical packing fraction [Formula Presented] we find that both Π(φ) and [Formula Presented] increase quasilinearly, scaling as [Formula Presented] where [Formula Presented] the volume fraction of a random close packing of spheres, and μ is an exponent close to unity. To explain this result, we develop a model of disordered droplets which interact through an effective repulsive anharmonic potential, based on results obtained for a compressed droplet. A simulation based on this model yields a calculated static shear modulus [Formula Presented] and osmotic pressure Π that are in excellent agreement with the experimental values of [Formula Presented] and Π. © 1997 The American Physical Society.