Douglas J. Durian

Speckle-Visibility Spectroscopy: A Tool to Study Time-Varying Dynamics

We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern formed by the scattered light as detected by a single exposure of a digital camera. Whereas previous multispeckle methods rely on correlations between images, here the connection with scattering site dynamics is made more simply in terms of the variance of intensity among the pixels of the camera for the specified exposure duration. The essence is that the speckle pattern is more visible, i.e., the variance of detected intensity levels is greater, when the dynamics of the scattering site motion is slow compared to the exposure time of the camera. The theory for analyzing the moments of the spatial intensity distribution in terms of the electric-field autocorrelation is presented. It is tested for two well-understood samples, a colloidal suspension of Brownian particles and a...

Multiple Light-Scattering Probes of Foam Structure and Dynamics

The structure and dynamics of three-dimensional foams are probed quantitatively by exploiting the strong multiple scattering of light that gives foams their familiar white color. Approximating the propagation of light as a diffusion process, transmission measurements provide a direct probe of the average bubble size. A model for dynamic light scattering is developed that can be used to interpret temporal fluctuations in the intensity of multiply scattered light. The results identify previously unrecognized internal dynamics of the foam bubbles. These light-scattering techniques are direct, noninvasive probes of bulk foams and therefore should find wide use in the study of their properties.

Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions

Dynamic light-scattering techniques provide noninvasive probes of diverse media, such as colloidal suspensions, granular materials, or foams. In homodyne photon correlation spectroscopy, the dynamical properties of the medium are extracted from the intensity autocorrelation g(2)(τ) of the scattered light by means of the Siegert relation g(2)(τ)=1+|〈E(0)E*(τ)〉|2/〈EE*〉2. This approach is unfortunately limited to systems where the electric field is a Gaussian random variable and thus breaks down when the scattering sites are few or correlated. We propose to extend the traditional analysis by introducing intensity correlation functions g(n) of higher order, which allow us both to detect non-Gaussian scattering processes and to extract information not available in g(2) alone. The g(n) are experimentally measured by a combination of a commercial correlator and a custom digital delay line. Experimental results for g(3) and g(4) are presented for both Gaussian and non-Gaussian light-scattering processes and compared with theoretical predictions.

Scattering optics of foam

The multiple scattering of light by aqueous foams is systematically studied as a function of wavelength, bubble size, and liquid fraction. Results are analyzed in terms of the transport mean free path of the photons and an extrapolation length ratio for the diffuse photon concentration field. The wavelength dependence is minimal and may be attributed entirely to the wavelength dependence of the refractive index of water rather than thin-film interference effects. The transport mean free path is found to be proportional to the bubble diameter and the reciprocal of the square root of liquid fraction. The extrapolation length ratio varies almost linearly with liquid fraction between the values for water-glass-air and air-glass-air interfaces.

Effective Temperatures of a Driven System Near Jamming

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.

Low-speed impact craters in loose granular media.

We report on craters formed by balls dropped into dry, noncohesive, granular media. By explicit variation of ball density rho(b), diameter D(b), and drop height H, the crater diameter is confirmed to scale as the 1/4 power of the energy of the ball at impact: D(c) approximately equal (rho(b)D(3)(b)H)(1/4). Against expectation, a different scaling law is discovered for the crater depth: d approximately equal (rho(3/2)(b)D(2)(b)H)(1/3). The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.

Vanishing Elasticity for Wet Foams: Equivalence With Emulsions and Role of Polydispersity

We present an experimental study of the rheology of polydisperse aqueous foams of different gas volume fractions φ. With oscillatory deformation at fixed frequency, we determine the behavior of the maximum stress as a function of the strain amplitude. At low strain, the maximum stress increases linearly, defining a shear modulus G. At progressively higher strains, the response eventually becomes nonlinear, defining the yield strain and the yield stress. While φ decreases toward φc=0.635±0.01, G goes to zero, and the yield stress decreases by many orders of magnitude with a quadratic behavior. The yield strain, which can be extrapolated to 0.18±0.02 at φ=1, has a minimum value of 0.045±0.010 at φc. This behavior shows the occurrence of a melting transition located at φc, which can be correlated to the random close packing of spheres. We compare these results to similar ones obtained previously for monodisperse and polydisperse emulsions. Our new experiments clarify the rheological similarities between emul...

Diffusing-Wave Spectroscopy: The Technique and Some Applications

We discuss the entension of dynamic light scattering to very strongly scattering media, where the propagation of light is described by the diffusion approximation, allowing the distribution of the light paths to be determined. The temporal evolution of the length of each of these paths, due to the dynamics of the scattering medium, is calculated, and an expression for the temporal autocorrelation function of the intensity fluctuations of the scattered light is obtained. This relates the measured decay of the autocor-relation function to the dynamics of the medium. This technique is called diffusing wave spectroscopy (DWS). To extend its utility, we consider the consequences of interactions between the scattering particles on the light scattering. To illustrate its applications, we consider several examples of new physics that can be investigated using DWS. We study the transient nature of hydrodynamic interactions between a particle and the surrounding fluid. We are able to probe the decay of the velocity correlation function of the particles, and we demonstrate its algebraic decay, with a t−3/2 time dependence. We also show that the time-dependent self diffusion coefficient exhibits an unexpected scaling behavior, whereby all the data, from samples of different volume fractions, can be scaled onto a single curve. Finally, we discuss the applications of DWS to the study of the dynamics of foams, and show how it can be used to probe the rearrangement of the bubbles within the foam as they coarsen.

Microfluidic Rheology of Soft Colloids above and below Jamming

The rheology near jamming of a suspension of soft colloidal spheres is studied using a custom microfluidic rheometer that provides the stress versus strain rate over many decades. We find non-Newtonian behavior below the jamming concentration and yield-stress behavior above it. The data may be collapsed onto two branches with critical scaling exponents that agree with expectations based on Hertzian contacts and viscous drag. These results support the conclusion that jamming is similar to a critical phase transition, but with interaction-dependent exponents.

Electrical conductivity of dispersions: from dry foams to dilute suspensions

We present new data for the electrical conductivity of foams in which the liquid fraction ranges from two to seventy per cent. We compare with a comprehensive collection of prior data, and we model all results with simple empirical formulae. We achieve a unified description that applies equally to dry foams and emulsions, where the droplets are highly compressed, as well as to dilute suspensions of spherical particles, where the particle separation is large. In the former limit, Lemlichs result is recovered; in the latter limit, Maxwells result is recovered.