Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session J14: Jammed Particles |
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Sponsoring Units: DFD Chair: Corey O'Hern, Yale University Room: 315 |
Tuesday, March 17, 2009 11:15AM - 11:27AM |
J14.00001: Porosity of mixed granular media of hard and soft grains Emilie Verneuil, Douglas J. Durian The addition of soft particles to granular materials modifies the packing properties such as the volume fraction and the interconnection of pores as a consequence of the particles squishiness. A macroscopic property that depends on the local arrangement of the grains is the hydraulic conductivity. Hence, hydrogel particles are developed as additives to sandy soils to improve the irrigation efficiency by decreasing the rate of far depth infiltration. However the parameters that control the mixed material porosity have not been explored. Our experimental study of the flow properties of mixtures of glass beads and swollen hydrogels aims at deriving simple arguments to connect the macro-scale measurement of the hydraulic conductivity to the arrangement of the grains around the soft particles, which determines the fraction of blocked pores. Our results show that the porosity decreases with the number of swollen gel per unit volume of the mixture. The conductivity also decreases as the size ratio of gel to glass bead decreases down to 1. A simple description accounting for the elastic contacts between glass beads and gel surface qualitatively accounts for the data. [Preview Abstract] |
Tuesday, March 17, 2009 11:27AM - 11:39AM |
J14.00002: Experimental characterization of microstate probabilities in mechanically stable packing of frictionless disks. M.D. Shattuck, G.-J. Gao, J. Blawzdziewicz, C.S. O'hern We report on a new experimental technique to produce mechanically stable packings of frictionless disks. The system consists of a quasi-2D vertical cell filled with bi-disperse disks. The disks are vigorously shaken and then allowed to settle under gravity in the presence of high-frequency low-amplitude vibrations to eliminate frictional effects. For a system of 7 particles we find approximately 1000 mechanically stable states. The most probable states occur at least $10^6$ times more often than those that are least probable. This is in direct contradiction to the fundamental postulate in statistical mechanics, that all possible microstates are equally probable and calls into question granular theories based on this assumption. We have measured the frequency distribution of the states in the experiments and in corresponding discrete element simulations, and find excellent agreement. We have also examined how the microstate distribution scales with system size and will connect the microstates to macroscopic quantities such as the density to predict the statistics of macroscopic properties. [Preview Abstract] |
Tuesday, March 17, 2009 11:39AM - 11:51AM |
J14.00003: Spectral responses in granular compaction Ling-Nan Zou I study the compaction of a granular pack under periodic tapping. The magnitude of acceleration $\Gamma$ at each tap is modulated with frequency $\omega$ and amplitude $\delta\Gamma$: $\Gamma(t) = \Gamma_{\mathrm{DC}} + \delta \Gamma \sin(\omega t)$, where $t$ is time measured by the number of taps. From the temporal modulation $\delta v$ in packing volume $v$, frequency- locked to the modulated tapping input, we can define the real and imaginary volume susceptibilities $\chi_{v}' = (\delta v/\delta \Gamma) \cos \theta$ and $\chi_{v}'' = (\delta v/\delta \Gamma) \sin \theta$; here $\theta$ is the phase lag between $\Gamma(t)$ and $v(t)$. As a function of $\Gamma_{\mathrm{DC}}$, $\chi_{v}'$, $\chi_{v}''$ are peaked at low $\Gamma_{\mathrm{DC}}$, a behavior reminiscent of the temperature-dependent susceptibilities in dielectric and spin glasses. For the packing of small particles ($d = 0.5$ mm) in ambient pressure, $\chi_{v}'$ exhibits memory and rejuvenation effects under $\Gamma_{\mathrm{DC}}$ cycling, similar to that seen in the magnetic susceptibility of spin glasses when subjected to thermal cycling [1]. However this memory effect is suppressed for the packing of larger particles and in vacuum. The measurement of volume susceptibilities shows promise as a new way to study the packing of granular materials, and as an avenue to explore analogies between jammed grains and molecular and spin glasses. \\[3pt] [1] K. Jonason \textit{et al.}, Phys. Rev. Lett. \textbf{81}, 3243 (1998). [Preview Abstract] |
Tuesday, March 17, 2009 11:51AM - 12:03PM |
J14.00004: Deformed Droplets in Static Two-Dimensional Emulsions Pearl J. Young, Dandan Chen, Eric R. Weeks We confine oil-in-water emulsions between two parallel plates, so that the droplets are essentially squeezed into quasi two-dimensional disks, somewhat analogous to granular photoelastic disks. By varying droplet area fraction, we seek to quantify the jamming transition of this static system. At a critical area fraction, the composition of the system should no longer be characterized primarily by circular disks but by disks deformed to varying degrees. We study a system of toluene droplets in water. As expected, we find that an increase in area fraction corresponds with an increase in average droplet deformation. Further, an increase in average droplet deformity corresponds with an increase in the heterogeneity of deformity within a given sample. [Preview Abstract] |
Tuesday, March 17, 2009 12:03PM - 12:15PM |
J14.00005: Jamming of Rod-like Granular Materials in Hoppers Summer Saraf, Scott Franklin Long thin rods form solid plugs that are far more rigid than piles of ordinary sand, greatly affecting their ability to flow through small openings. We have built a hopper whose aperture, angle, and width can be independently varied and are studying the frequency with which rods of different length, width, and aspect ratio jam. As the opening aperture becomes larger, the mean number of particles that exit the hopper before a jam occurs naturally increases, but the probability distribution of fluctuations about this mean is unchanged. Unexpectedly, whereas the event distribution function $P(s)$ for spheres decays exponentially, we find the distribution for rods falls off as a power law with exponent $\alpha $=-1.41$\pm $0.08. We are also investigating the growth of the mean event size <$s$> as the aperture increases for possible divergence, which would imply a critical aperture size above which particles would never jam. [Preview Abstract] |
Tuesday, March 17, 2009 12:15PM - 12:27PM |
J14.00006: Forces and displacements near the granular jamming threshold Mahesh Bandi, Andras Libal, Michael Rivera, Robert Ecke We experimentally study the dynamics of jamming by dragging a probe disk in a two-dimensional bi-dispersed system of randomly packed photo-elastic disks. All measurements are made at packing fractions relative to the critical fraction at which jamming occurs. We measure the local force felt by the probe disk and compare it with the system's global response with sensors placed along the system boundaries. We also visually monitor the disk displacements in the system, which are expected to become increasingly constrained as a function of increasing packing fraction. [Preview Abstract] |
Tuesday, March 17, 2009 12:27PM - 12:39PM |
J14.00007: The angoricity describes the approach to the jamming Kun Wang, Chaoming Song, Ping Wang, Hernan Makse The application of concepts from equilibrium statistical mechanics to out of equilibrium systems has a long history offering the fascinating possibility to describe a diverse range of systems from glasses to grains. For jammed systems, the key idea was to replace the energy ensemble describing conservative systems by the volume ensemble for dissipative jammed systems. However, this approach is not able to describe the jamming critical point for deformable particles such as emulsions where the volume fraction, coordination number and elastic moduli behaves as power-law of the external stress as the system approaches jamming. The geometrical considerations have to be augmented by the ensemble of stresses described by the angoricity which replaces the role played by the temperature in thermal systems. Here we perform a basic test of the stress ensemble of jammed matter by following two independent approaches: we exhaustively enumerate the available jammed states and numerically follow the dynamics of the system near the jamming point. A direct comparison between both methods supports the idea of thermalization at a given angoricity which is shown to determine the systems state as it approaches the jamming transition. This result opens the possibility to calculate important quantities near J-point. [Preview Abstract] |
Tuesday, March 17, 2009 12:39PM - 12:51PM |
J14.00008: Equilibration in model granular subsystems: An experimental test for Edwards' compactivity Frederic Lechenault, James Puckett, Karen Daniels We experimentally investigate the statistical features of the stationary states reached by two idealized granular liquids able to exchange volume. The system consists in two binary mixtures of the same number (and area) of soft disks, but with different surface properties. The disks sit on a horizontal air table and are separated by a mobile wall. Energy is injected in the system by means of an array of randomly activated coil bumpers standing as the edges of the cell. Due to the energy injection, the system acts like a slow liquid and eventually jams at high packing fraction. We characterize the macroscopic states by studying the motion of the piston. We find that its average position is different from one half, and is a non monotonic function of the overall packing fraction, which reveals the crucial role played by the surface properties in the corresponding density of states. We then study the bulk statistics of the packing fraction and find confirmation of the macroscopic behavior. However, the local fluctuations of the packing fraction are uniquely determined by its average, and hence independent of the interaction between disks. This result, together with the existence of a point at which the two sub-systems have the same volume, enables us to show that Edwards' compactivity does not have the same value in the two equilibrated subsystems. [Preview Abstract] |
Tuesday, March 17, 2009 12:51PM - 1:03PM |
J14.00009: Stability of Packings of Soft Elliptical Grains in 2D Mitchell Mailman, Bulbul Chakraborty, Carl Schreck, Corey O'Hern Simulations of hard ellipse packings show that these ellipse packings are generally hypostatic. By using a dynamical matrix approach to analyzing the stability of two-dimensional ellipse packings, we show that the degree of hypostaticity is related to the fraction of zero-frequency modes. The packings are generated using a compression protocol previously employed in disk packings and an energy function based on the overlap model developed by Perram and Wertheim. The density of states exhibits a low frequency peak that approaches zero as the compression is reduced. There is a gap separating this peak from the higher frequency modes. In this talk, we will demonstrate the existence of a scaling relation between the vibrational spectra at different aspect ratios. We will also discuss the origin of the low frequency modes and the origin of the scaling. Analysis of the relationship between contact numbers and vibrational modes will be used to compare and contrast the jamming transition in disks and ellipses. [Preview Abstract] |
Tuesday, March 17, 2009 1:03PM - 1:15PM |
J14.00010: Shearing dynamics and jamming density Peter Olsson, Daniel V{\aa}gberg, Stephen Teitel We study the effect of a shearing dynamics on the properties of a granular system, by examining how the jamming density depends on the preparation of the starting configurations. Whereas the jamming density at point J was obtained by relaxing \emph{random} configurations [O'Hern et al, Phys.\ Rev.\ E 68, 011306 (2003)], we apply this method to configurations obtained after shearing the system at a certain shear rate. We find that the jamming density increases somewhat and that this effect is more pronounced for configurations produced at smaller shear rates. Different measures of the order of the jammed configurations are also discussed. [Preview Abstract] |
Tuesday, March 17, 2009 1:15PM - 1:27PM |
J14.00011: Theory of Elasticity and Glassy Dynamics of Suspensions of Soft Particles Jian Yang, Kenneth Schweizer A microscopic theory for the shear modulus and slow dynamics of soft colloidal systems composed of many arm star-polymers and intra-molecularly crosslinked microgels is described. The role of particle volume fraction and softness (arm number for stars and contact modulus for microgel particles) on the ideal mode coupling kinetic arrest transition, elastic modulus, relaxation time in the activated hopping regime, diffusion constant, dynamic fragility, and absolute yield stress and strain have been systematically explored. The low-frequency shear modulus is characterized by two volume fraction regimes: power law scaling at intermediate volume fractions and a linear law beyond the nominal jamming point. Connections between single particle softeness, interparticle packing correlations, and viscoelastic properties have been established. For both microgels and many arm stars, the effective dynamical fragility varies over a wide range as a function of particle softness. Comparisons of the theoretical results with experiments on many arm star and microgel paste systems have been carried out. [Preview Abstract] |
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