Karen E. Daniels

Defect turbulence and generalized statistical mechanics

We present experimental evidence that the motion of point defects in thermal convection patterns in an inclined fluid layer is well described by Tsallis statistics with an entropic index q ≈ 1.5. The dynamical properties of the defects (anomalous diffusion, shape of velocity distributions, power-law decay of correlations) are in good agreement with typical predictions of nonextensive models, over a range of driving parameters.

Shear-driven size segregation of granular materials: modeling and experiment.

Granular materials segregate by size under shear, and the ability to quantitatively predict the time required to achieve complete segregation is a key test of our understanding of the segregation process. In this paper, we apply the Gray-Thornton model of segregation (developed for linear shear profiles) to a granular flow with an exponential shear profile, and evaluate its ability to describe the observed segregation dynamics. Our experiment is conducted in an annular Couette cell with a moving lower boundary. The granular material is initially prepared in an unstable configuration with a layer of small particles above a layer of large particles. Under shear, the sample mixes and then resegregates so that the large particles are located in the top half of the system in the final state. During this segregation process, we measure the velocity profile and use the resulting exponential fit as input parameters to the model. To make a direct comparison between the continuum model and the observed segregation dynamics, we map the local concentration (from the model) to changes in packing fraction; this provides a way to make a semiquantitative comparison with the measured global dilation. We observe that the resulting model successfully captures the presence of a fast mixing process and relatively slower resegregation process, but the model predicts a finite resegregation time, while in the experiment resegregation occurs only exponentially in time.

Mixing and segregation rates in sheared granular materials

The vertical size segregation of granular materials, a process commonly associated with the Brazil-nut effect, has generally been thought to proceed faster the greater the size difference of the particles. We experimentally investigate sheared dense bidisperse granular materials as a function of the size ratio of the two species and find that the mixing rate at low confining pressure behaves as expected from percolation-based arguments. However, we also observe an anomalous effect for the resegregation rates, wherein the segregation rate is a nonmonotonic function of the particle size ratio with a maximum for intermediate particle size ratio. Combined with the fact that increasing the confining pressure significantly suppresses both mixing and segregation rates of particles of sufficiently dissimilar size, we propose that the anomalous behavior may be attributed to a species-dependent distribution of forces within the system.

Hysteresis and competition between disorder and crystallization in sheared and vibrated granular flow

Experiments on spherical particles in a 3D annular shear cell vibrated from below and sheared from above show a hysteretic freezing or melting transition. Under sufficient vibration a crystallized state is observed, which can be melted by sufficient shear. The critical line for this transition coincides with equal kinetic energies for vibration and shear. The force distribution is double peaked in the crystalline state and single peaked with an approximately exponential tail in the disordered state. Continuous relations between pressure and volume (with dP/dV>0) exist for a continuum of partially and/or intermittently melted states over a range of parameters.

Influence of network topology on sound propagation in granular materials.

Granular media, whose features range from the particle scale to the force-chain scale and the bulk scale, are usually modeled as either particulate or continuum materials. In contrast with each of these approaches, network representations are natural for the simultaneous examination of microscopic, mesoscopic, and macroscopic features. In this paper, we treat granular materials as spatially embedded networks in which the nodes (particles) are connected by weighted edges obtained from contact forces. We test a variety of network measures to determine their utility in helping to describe sound propagation in granular networks and find that network diagnostics can be used to probe particle-, curve-, domain-, and system-scale structures in granular media. In particular, diagnostics of mesoscale network structure are reproducible across experiments, are correlated with sound propagation in this medium, and can be used to identify potentially interesting size scales. We also demonstrate that the sensitivity of network diagnostics depends on the phase of sound propagation. In the injection phase, the signal propagates systemically, as indicated by correlations with the network diagnostic of global efficiency. In the scattering phase, however, the signal is better predicted by mesoscale community structure, suggesting that the acoustic signal scatters over local geographic neighborhoods. Collectively, our results demonstrate how the force network of a granular system is imprinted on transmitted waves.

Solid capillarity: when and how does surface tension deform soft solids?

Soft solids differ from stiff solids in an important way: their surface stresses can drive large deformations. Based on a topical workshop held in the Lorentz Center in Leiden, this Opinion highlights some recent advances in the growing field of solid capillarity and poses key questions for its advancement.

Equilibrating Temperaturelike Variables in Jammed Granular Subsystems

Although jammed granular systems are athermal, several thermodynamiclike descriptions have been proposed which make quantitative predictions about the distribution of volume and stress within a system and provide a corresponding temperaturelike variable. We perform experiments with an apparatus designed to generate a large number of independent, jammed, two-dimensional configurations. Each configuration consists of a single layer of photoelastic disks supported by a gentle layer of air. New configurations are generated by cyclically dilating, mixing, and then recompacting the system through a series of boundary displacements. Within each configuration, a bath of particles surrounds a smaller subsystem of particles with a different interparticle friction coefficient than the bath. The use of photoelastic particles permits us to find all particle positions as well as the vector forces at each interparticle contact. By comparing the temperaturelike quantities in both systems, we find compactivity (conjugate to the volume) does not equilibrate between the systems, while the angoricity (conjugate to the stress) does. Both independent components of the angoricity are linearly dependent on the hydrostatic pressure, in agreement with predictions of the stress ensemble.

Sound propagation and force chains in granular materials

Granular materials are inherently heterogeneous, leading to challenges in formulating accurate models of sound propagation. In order to quantify acoustic responses in space and time, we perform experiments in a photoelastic granular material in which the internal stress pattern (in the form of force chains) is visible. We utilize two complementary methods, high-speed imaging and piezoelectric transduction, to provide particle-scale measurements of both the amplitude and speed of an acoustic wave in the near-field regime. We observe that the wave amplitude is on average largest within particles experiencing the largest forces, particularly in those chains radiating away from the source, with the force-dependence of this amplitude in qualitative agreement with a simple Hertzian-like model of particle contact area. In addition, we are able to directly observe rare transiently strong force chains formed by the opening and closing of contacts during propagation. The speed of the leading edge of the pulse is in agreement with the speed of a one-dimensional chain, while the slower speed of the peak response suggests that it contains waves which have travelled over multiple paths even within just this near-field region. These effects highlight the importance of particle-scale behaviors in determining the acoustical properties of granular materials.

Fluctuations, correlations and transitions in granular materials: statistical mechanics for a non-conventional system

In this work, we first review some general properties of dense granular materials. We are particularly concerned with a statistical description of these materials, and it is in this light that we briefly describe results from four representative studies. These are: experiment 1: determining local force statistics, vector forces, force distributions and correlations for static granular systems; experiment 2: characterizing the jamming transition, for a static two-dimensional system; experiment 3: characterizing plastic failure in dense granular materials; and experiment 4: a dynamical transition where the material ‘freezes’ in the presence of apparent heating for a sheared and shaken system.

Fluorescent visualization of a spreading surfactant

The spreading of surfactants on thin films is an industrially and medically important phenomenon, but the dynamics are highly nonlinear and visualization of the surfactant dynamics has been a long-standing experimental challenge. We perform the first quantitative, spatiotemporally resolved measurements of the spreading of an insoluble surfactant on a thin fluid layer. During the spreading process, we directly observe both the radial height profile of the spreading droplet and the spatial distribution of the fluorescently tagged surfactant. We find that the leading edge of a spreading circular layer of surfactant forms a Marangoni ridge in the underlying fluid, with a trough trailing the ridge as expected. However, several novel features are observed using the fluorescence technique, including a peak in the surfactant concentration that trails the leading edge, and a flat, monolayer-scale spreading film that differs from concentration profiles predicted by current models. Both the Marangoni ridge and the surfactant leading edge can be described to spread as R∝tδ. We find spreading exponents δH≈0.30 and δΓ≈0.22 for the ridge peak and surfactant leading edge, respectively, which are in good agreement with theoretical predictions of δ=1/4. In addition, we observe that the surfactant leading edge initially leads the peak of the Marangoni ridge, with the peak later catching up to the leading edge.