The transport of classical waves in strongly scattering media is investigated using ultrasonic techniques, allowing us to measure both the ballistic and scattered components of the wave field. We fmd that the ballistic propagation is dramatically slowed down by scattering resonances, although the group velocity remains well-defined. The propagation of the scattered waves is also strongly affected by resonant scattering, and is shown to be well described by using the diffusion approximation. A model based on the generalized coherent potential approximation gives a quantitative explanation of the experimental data.
We present a new use of dynamic light scattering that permits the determination of the viscoelastic behavior of a complex fluid. By describing the motion of a scattering particle in a viscoelastic medium in terms of a generalized Langevin equation with a memory function, we relate the time evolution of its mean-square displacement to the frequency-dependent storage and loss moduli of the medium. The utility of this technique is illustrated through the application of diffusing-wave spectroscopy to probe the viscoelastic behavior of two complex fluids. The properties of a concentrated suspension of colloidal particles interacting as hard spheres are shown to be strongly influenced by the incipient colloidal glass transition, which leads to an extended range of frequencies over which they behave like an elastic solid. Similar elasticity is observed in a compressed emulsion, resulting in this case from the additional interfacial energy of the deformed droplets. In both cases diffusing-wave spectroscopy is used to measure the frequency dependence of the storage and loss moduli, and these results are compared with those from mechanical measurements. Besides providing a purely optical method for measuring mechanical properties, this technique provides new insight into the origin of the viscoelastic behavior. (C) 1997 Optical Society of America.
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.
We use dynamic light scattering to measure the dynamic structure factor of density fluctuations occurring in colloidal suspensions that have attained a quiescent state long after aggregation. We find a stretched-exponential decay to a finite plateau. Our interpretation of the arrested decay is that these systems are gels, i.e., systems possessing a finite elastic modulus G. We develop a theory for the internal elastic modes of a fractal cluster and use it to derive G and the arrested, stretched-exponential behavior of colloidal gel dynamics. Good agreement between experiment and theory is obtained.
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).
We study the adsorption and desorption of hexane in porous Vycor, as the ambient vapor pressure is varied, through sorption isotherm, ultrasonic velocity and attenuation, and light scattering measurements. On adsorption, we show that the fluid fills the pore space uniformly until capillary condensation occurs; however, small, randomly distributed, vapor bubbles remain, as detected by a large increase in the attenuation of the ultrasound. On desorption, the mismatch in the index of refraction between the empty pores and the surrounding filled pores leads to intense scattering of light that reveals the presence of long-range correlations in the pore space. These correlations have a fractal dimension of 2.6, which is very near the value predicted for invasion percolation. Finally, we also investigate the time dependence of the changes in the adsorbed fluid mass and use these measurements to identify three distinct regimes with vastly differing mechanisms for mass transport. The results presented here provide information on the differences in pore-space correlations on filling and drainage, and highlight the critical role of the connectivity of the pores to the surface in determining the desorption behavior.
We have critically tested the application of the diffusion approximation to describe the propagation of ultrasonic waves through a random, strongly scattering medium. The transmission of short ultrasonic pulses has been measured through a concentrated suspension of glass beads immersed in water. The transmitted sound field is found to exhibit temporal fluctuations with a period determined by the width of the incident pulse. Provided that appropriate boundary conditions are used to account for the reflectivity of the interfaces, the time dependence of the ensemble-averaged transmitted intensity is shown to be well described by the diffusion equation. This enables us to determine both the diffusion coefficient for the sound waves as well as the inelastic absorption rate. The consistency of these results is established by varying the experimental geometry; while the transmitted pulse shape changes markedly, the values for the diffusion coefficient and absorption rate obtained through a description using the diffusion approximation remain unchanged. We have also measured the absolute transmitted intensity of the sound as the sample thickness is varied; this provides an accurate measure of the transport mean free path and thus also the energy transport velocity. These results convincingly demonstrate the validity of using the diffusion approximation to describe the propagation of sound waves through strongly scattering media.
The frequency-dependent viscoelastic shear modulus of concentrated suspensions of colloidal hard spheres is shown to be strongly modified as the volume fraction approaches the glass transition. The elastic or storage component, G', becomes larger than the viscous or loss component, G''. The frequency dependence of G' develops a plateau while that of G'' develops a minimum. We propose a physical model to account for these data, using a description of the glasslike behavior based on mode-coupling theory, and a description of the high-frequency behavior based on hydrodynamic flow calculations.
The elastic shear modulus of monodisperse emulsions is shown to exhibit a universal dependence on droplet volume fraction phi when scaled by the Laplace pressure of the droplets, increasing as phi(phi - phi(c)). where phi(c) approximate to 0.635, the value of random close packing of solid spheres. Surprisingly the osmotic pressure required to compress the emulsions to increase phi is nearly the same as the shear modulus over a large range of volume fraction, while the bulk osmotic modulus differs significantly. Models based on the structural disorder of the emulsions are discussed to account for these data.
Time-dependent hydrodynamic interactions in a colloidal suspension of hard spheres are studied, both experimentally and through computer simulation. The focus is on the behavior at small wave vectors, which directly probes the temporal evolution of hydrodynamic interactions between nearby particles. The computer simulations show that the time-dependent diffusion coefficient has the same functional form for all wave vectors, with a single characteristic scaling time for each length scale and for each volume fraction. Wave-vector-averaged effective diffusion coefficients, measured experimentally using diffusing wave spectroscopy, also scale to the same functional form. In this case, the scaling time is dependent on both volume fraction and particle size; it decreases sharply with decreasing particle radius, reflecting the greater contribution from smaller wave vectors that is contained in the scattering from the smaller particles. For a direct comparison of simulation and experiment, we simulate the experimentally observed correlation functions, by averaging the wavevector-dependent computer-simulation data with the weighting appropriate to the experimental technique. Although the overall scaling is similar, there are quantitative differences in the simulated and measured relaxation times. We suggest these differences are due to the compressibility of the suspension, and that the resultant pressure waves make an unexpectedly significant contribution to the hydrodynamic interactions.
We show that density measurements can provide an alternative method for determining the number and species of ions adsorbed onto colloidal particles. We cause charge-stabilized colloidal dispersions of polystyrene spheres to aggregate by adding various salts. The solvents are mixtures of H2O and D2O in which the colloids are neutrally buoyant after aggregation, which we verify by centrifugation of the samples, By this method we are able to determine the density of the aggregated colloids. We find that the density depends on the species of salt added to initiate the aggregation and can be calculated on the assumption that a cation of the added salt binds with each ionizable group on the surface of the colloidal particles. (C) 1995 Academic Press, Inc.