Influence of the feeding mechanism on deposits of square particles

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

Figure 1

Scheme of the experimental setup. A, hopper; B, top reservoir; C, slot where a metal piece is introduced to keep the particles accumulated at the reservoir; D, proper silo. The shadowed region in the middle of the proper silo is the region where pictures are taken and measurements performed. The black region corresponds to the closeup of the deposit of squares presented in the figure at the right. At the top right corner a sketch of the model is presented.

Figure 2

Pictures of the deposits of square particles obtained when pouring the grains at different initial volume fractions (${\varphi }_0$), as indicated by the labels.

Figure 3

Probability that the particles align vertically (with the direction of the lateral wall of the silo) at different distances to the wall ($x$) for different values of the initial volume fraction, as indicated in the legend. This probability is calculated as the number of particles aligned with $\theta =\pi /2\pm 0.035$ (or what is the same $\theta =0\pm 0.035$) with respect to the total number of particles found at the different positions of the silo.

Figure 4

Volume fraction of deposits of squares (${\varphi }_f$) obtained from different initial volume fractions (${\varphi }_0$). For the simulation we illustrate, as indicated by the legend, the results obtained from a system of particles deposited with an initial random orientation distribution (protocol I) and from an ordered system of particles with ${\theta }_0=\pi /4$ (protocol II).

Figure 5

Orientation distributions of squares in the final deposits obtained in experiments and simulations following protocol I, for different initial volume fractions, as indicated in the legend.

Figure 6

Maximum value of the particle orientation distribution function $f(\theta =\pi /4)$, for different initial volume fractions. As indicated in the legend, results are reported for experimental deposits as well as for numerical ones obtained from the two different protocols.

Figure 7

Orientation distributions of squares in the final deposits obtained in experiments (a) and simulations following protocol I (b) and protocol II (c) for different initial volume fractions, as indicated in the legends.

Figure 8

Spatial correlation function obtained for packing of squares in experiments (a) and simulations following protocol I (b) and protocol II (c) for different initial volume fractions, as indicated in the legends.

Figure 9

Relative number of face-to-face contacts, in packing of squares obtained from simulations following protocols I and II. Results for several volume fractions are shown.

Figure 10

Polar distribution of the principal direction (larger eigenvalue of the stress tensor) for deposits of squares obtained with protocol I: Squares are thrown with completely random orientations. Results are presented for different initial volume fractions, as indicated in the graphs.

Figure 11

Polar distribution of the principal direction (larger eigenvalue of the stress tensor) for deposits of squares obtained with protocol II: Squares are thrown with their diagonal aligned with the gravity ${\theta }_0=\pi /4$. Results are presented for different volume fractions, as indicated in the graphs.