Abstract:
We present an experimental study of the frequency omega dependence and volume fraction phi dependence of the complex shear modulus G*(omega,phi) of monodisperse emulsions which have been concentrated by an osmotic pressure Pi. At a given phi, the elastic storage modulus G'(omega)=Re[G*(omega)] exhibits a low-frequency plateau G'(p), dominating the dissipative loss modulus G''(omega)=Im[G*(omega)] which exhibits a minimum. Above a critical packing fraction phi(c), we find that both Pi(phi) and G'(p)(phi) increase quasilinearly, scaling as (phi-phi(c))(mu), where phi(c) approximate to phi(c)(rcp), the volume fraction of a random close packing of spheres, and mu 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 G and osmotic pressure Pi that are in excellent agreement with the experimental values of G'(p) and Pi.
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