By focusing on entire bubbles rather than films or vertices, a simple model is proposed for the deformation and flow of foam in which dimensionality, polydispersity, and liquid content can easily be varied. Simulation results are presented for the linear elastic properties as a function of bubble volume fraction, showing a melting transition where the static shear modulus vanishes and the relaxation time scale peaks. Results are also presented for shear stress versus strain rate, showing intermittent flow via avalanchelike topological rearrangements and Bingham-plastic behavior. Disciplines Physical Sciences and Mathematics | Physics CommentsAt the time of publication, author Douglas J. Durian was affiliated with University of California, Los Angeles. Currently, he is a faculty member at the Physics Department at the University of Pennsylvania. pressure cannot be captured. Whereas previous attempts to incorporate finite liquid content start from the dry-foam limit, the model presented here is complementary in that it starts from the wet-foam limit.Simulations are performed for two-dimensional square systems of N X N bubbles. As depicted in Fig. 1

Supercooled liquids and dense colloids exhibit anomalous behaviour known as "spatially heterogeneous dynamics" (SHD), which becomes increasingly pronounced with approach to the glass transition [1][2][3]. Recently, SHD has been observed in confined granular packings under slow shear near the onset of jamming, bolstering speculation that the two transitions are related [4][5][6]. Here, we report measurements of SHD in a system of air-driven granular beads, as a function of both density and effective temperature. On approach to jamming, the dynamics become progressively slower and more spatially heterogeneous. The rapid growth of dynamical time and length scales characterizing the heterogeneities can be described both by mode-coupling theory [7] and the Vogel-Tammann-Fulcher (VTF) equation [8], in analogy with glass-forming liquids. The value of the control variable at the VTF transition coincides with point-J [9, 10] the random close-packed jamming density at which all motion ceases, indicating analogy with a zero temperature ideal glass transition. Our findings demonstrate further universality of the jamming concept and provide a significant step forward in the quest for a unified theory of "jamming" in disparate systems.

Experiments on the low-speed impact of solid objects into granular media have been used both to mimic geophysical events 1-5 and to probe the unusual nature of the granular state of matter [6][7][8][9][10] . Observations have been interpreted in terms of conflicting stopping forces: product of powers of projectile depth and speed 6 ; linear in speed 7 ; constant, proportional to the initial impact speed 8 ; and proportional to depth 9,10 . This is reminiscent of high-speed ballistics impact in the nineteenth and twentieth centuries, when a plethora of empirical rules were proposed 11,12 . To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 μs precision. For a 1-inch-diameter steel sphere dropped from a wide range of heights into noncohesive glass beads, we reproduce previous observations 6-10 either as reasonable approximations or as limiting behaviours. Furthermore, we demonstrate that the interaction between the projectile and the medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. Thus, we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, although fundamentally different from that of liquids and solids, can be simply understood.To measure dynamics, we use a line-scan digital CCD (chargecoupled device) camera to image a finely striped transparent rod attached vertically to the top of the projectile (see the Methods section). The instantaneous speed is the key quantity, deduced from the displacement of the striped pattern between successive frames. The temporal precision is 20 μs, set by the 50 kHz frame rate of the line-scan camera. The position resolution is 100 nm, set by the 3.8 μm per pixel magnification divided by the square root of the number of pixels. These combine to give a velocity resolution of 0.5 cm s −1 . Besides measurement fidelity, another advantage of our method is that it applies even to very deep impacts-as long as the striped rod does not submerge.Our complete dynamics data set is shown in Fig. 1, which shows position z, velocity v, and acceleration a, versus time t, for initial impact speeds, v 0 , ranging from 0 to −400 cm s −1 . Time is measured from initial impact; position is measured upwards from the granular surface, opposite to gravity. A striking feature is that, although the final position is approached smoothly, the velocity vanishes abruptly with a discontinuity in acceleration. Similar behaviour is evident in data from an embedded accelerometer (P. B. Umbanhowar, private communication, 2004; J. C. Amato, private communication, 2005). This is counter to the viscous approach to a stable equilibrium, where acceleration vanishes continuously, but it permits the stopping time, t stop , to be easily gauged from the velocity versus time data. Note that t stop actually decreases with increasing impact speed; surprisingly, deeper penetration requires less time. Evidently, granular matter is very different from ordinary ...

We use machine learning methods on local structure to identify flow defects -or regions susceptible to rearrangement -in jammed and glassy systems. We apply this method successfully to two disparate systems: a two dimensional experimental realization of a granular pillar under compression, and a Lennard-Jones glass in both two and three dimensions above and below its glass transition temperature. We also identify characteristics of flow defects that differentiate them from the rest of the sample. Our results show it is possible to discern subtle structural features responsible for heterogeneous dynamics observed across a broad range of disordered materials.

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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 camerafor 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 coarsening foam, where the dynamics can be treated as stationary and hence can be benchmarked by traditional methods. However, our speckle-visibility method is particularly appropriate for samples in which the dynamics vary with time, either slowly or rapidly, limited only by the exposure time fidelity of the camera. Potential applications range from soft-glassy materials, to granular avalanches, to flowmetry of living tissue. 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 coarsening foam, where the dynamics can be treated as stationary and hence can be benchmarked by traditional methods. However, our speckle-visibility method is particularly appropriate for samples in which the dynamics vary with time, either slowly or rapidly, limited only by the exposure time fidelity of the camera. Potential applications range from soft-glassy materials, to granular avalanches, to flowmetry of living tissue.

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.

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.