Turbulent-like velocity fluctuations in two-dimensional granular materials subject to cyclic shear.

We perform a systematic experimental study to investigate the velocity fluctuations in the two-dimensional granular matter of low and high friction coefficients subjected to cyclic shear of a range of shear amplitudes, whose velocity fields are strikingly turbulent-like with vortices of different scales. The scaling behaviors of both the transverse velocity power spectra ET(k) ∝ k-αT and, more severely, the longitudinal velocity power spectra EL(k) ∝ k-αL are affected by the prominent peak centered around k ≈ 2π of the inter-particle distance due to the static structure factor of the hard-particle nature in contrast to the real turbulence. To reduce the strong peak effect to the actual values of αν (the subscript 'ν' refers to either T or L), we subsequently analyze the second-order velocity structure functions of S(2)ν(r) in real space, which show the power-law scalings of S(2)ν(r) ∝ rßν for both modes. From the values of ßν, we deduce the corresponding αν from the scaling relations of αν = ßν + 2. The deduced values of αν increase continuously with the shear amplitude γm, showing no signature of yielding transition, and are slightly larger than αν = 2.0 at the limit of γm → 0, which corresponds to the elastic limit of the system, for all γm. The inter-particle friction coefficients show no significant effect on the turbulent-like velocity fluctuations. Our findings suggest that the turbulent-like collective particle motions are governed by both the elasticity and plasticity in cyclically sheared granular materials.

The Edwards volume ensemble in cyclically sheared granular experiments.

We experimentally investigate the Edwards volume ensemble in cyclically sheared bidisperse disks of two friction coefficients (µ ≈ 0.3 and µ → ∞) subjected to a range of shear amplitudes γm. Despite the local and global anisotropy, hysteresis, and the potential long-range correlation of the free volume, the Edwards volume ensemble surprisingly provides an excellent statistical description of disk packings in cyclically sheared systems. Our finding can be better understood from the comprehensive analysis of the geometric and statistical properties of Voronoi cells of individual particles. First, the average degrees of anisotropy of Voronoi cells are weak at both the microscopic and macroscopic scales within a range of shear amplitudes γm of up to γm = 12% regardless of the inter-particle friction coefficients µ even though the azimuthal distributions of the Voronoi cell depend on µ. Second, there is only negligible hysteresis of global compactivity and volume fluctuations. Finally, the spatial correlations of the free volume and the orientation are weakly anisotropic and short ranged for practical purposes. Both results are independent of µ. Interestingly, our free-volume statistical results are consistent with the simple physical picture that the free volume is directly proportional to the compactivity.

Friction-Controlled Entropy-Stability Competition in Granular Systems.

Using cyclic shear to drive a two-dimensional granular system, we determine the structural characteristics for different interparticle friction coefficients. These characteristics are the result of a competition between mechanical stability and entropy, with the latter's effect increasing with friction. We show that a parameter-free maximum-entropy argument alone predicts an exponential cell order distribution, with excellent agreement with the experimental observation. We show that friction only tunes the mean cell order and, consequently, the exponential decay rate and the packing fraction. We further show that cells, which can be very large in such systems, are short-lived, implying that our systems are liquidlike rather than glassy.