Investigation of the ballistic propagation of acoustic waves through a resonantly scattering, Inhomogeneous medium indicates that although the ballistic signal remains coherent with the incident pulse, it is nevertheless strongly affected by scattering resonances. These resonances cause considerable frequency dispersion and substantially reduce the phase and group velocities. The experimental data are quantitatively described by a theoretical model that correctly accounts for the coupling between the resonant scatterers, leading to an effective renormalization of the scattering within the medium. This approach; resolves a long-standing problem in the definition of the group velocity in strongly scattering materials.
We introduce a method for using dynamic light scattering to measure the frequency-dependent linear viscoelastic moduli of complex fluids. The technique exploits the fluctuation dissipation theorem, which relates the relaxation of thermal excitations of a probe particle to the viscoelastic properties of the surrounding medium. The relaxation of the thermal excitations of probe particles are determined by measuring the time evolution of the mean square displacement using dynamic light scattering. A Langevin equation with a time-dependent damping term is used to relate this mean square displacement to the dynamic shear modulus of the medium. This method probes the linear viscoelastic moduli over a much larger frequency range than traditional mechanical means, and in particular, easily extends their measurement to much higher frequencies.
We have measured the yield transition of monodisperse emulsions as the volume fraction, phi, and droplet radius, alpha, are varied. We study the crossover from the perturbative shear regime, which reflects the linear viscoelastic properties, to the steady shear regime, which reflects nonlinear, plastic flow. For small oscillatory strains of peak amplitude gamma, the peak stress, tau, is linearly proportional to gamma. As the strain is increased, the stress becomes nonlinear in gamma at the yield strain, gamma(y). The phi dependence of gamma(y) is independent of alpha and exhibits a minimum near the critical volume fraction, phi(c) approximate to 0.635, associated with the random close packing of monodisperse spheres. We show that the yield stress, tau(y), increases dramatically as the volume fraction increases above phi(c); tau(y) also scales with the Laplace pressure, sigma/alpha, where sigma is the interfacial tension. For comparison, we also determine the steady shear stress over a wide range of strain rates, gamma. Below phi approximate to 0.70, the flow is homogeneous throughout the sample, while for higher phi, the emulsion fractures resulting in highly inhomogeneous flow along the fracture plane. Above phi approximate to 0.58, the steady shear stress exhibits a low strain rate plateau which corresponds with the yield stress measured with the oscillatory technique. Moreover, tau(y) exhibits a robust power law dependence on gamma with exponents decreasing with phi, varying from 2/3 to 1/2. Below phi approximate to 0.58, associated with the colloidal glass transition, the plateau stress disappears entirely, suggesting that the equilibrium glassy dynamics are important in identifying the onset of the yield behavior. (C) 1996 Academic Press, Inc.
We propose a model for concentrated emulsions based on the speculation that a macroscopic shear strain does not produce an affine deformation in the randomly close-packed droplet structure. The model yields an anomalous contribution to the complex dynamic shear modulus that varies as the square root of frequency. We test this prediction using a novel light scattering technique to measure the dynamic shear modulus, and directly observe the predicted behavior over six decades of frequency and a wide range of volume fractions.
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 phi(c).