Dilatancy in Slow Granular Flows

When walking on wet sand, each footstep leaves behind a temporarily dry impression. This counterintuitive observation is the most common illustration of the Reynolds principle of dilatancy: that is, a granular packing tends to expand as it is deformed, therefore increasing the amount of porous space. Although widely called upon in areas such as soil mechanics and geotechnics, a deeper understanding of this principle is constrained by the lack of analytical tools to study this behavior. Using x-ray radiography, we track a broad variety of granular flow profiles and quantify their intrinsic dilatancy behavior. These measurements frame Reynolds dilatancy as a kinematic process. Closer inspection demonstrates, however, the practical importance of flow induced compaction which competes with dilatancy, leading more complex flow properties than expected.

Figure 1

(a) Shear flow cell. (b) Gravity flow cell. Moving parts, shown with darker sides, move over 3 cm (20–50 grains) for (a) and 8 cm (50–100 grains) for (b). The beam enters the chambers from the front side. (c) X-ray images acquisition setup. Source settings: 80 kV and $150\mu \mathrm{A}$. A 2 mm Al filter reduces beam hardening. The cell is 2.3 m away from the source, ensuring a quasiparallel beam. (d) Illustration of the path of an x-ray and (e) resulting material length image $L_g(x,y)$. Circle indicates the grain size.

Figure 2

Series of radiographs describing the flow and density profiles for a shear flow (top) and gravity driven flow (bottom). Material: monodisperse acrylic spheres, 1 mm in diameter. Numbers on the top right corner of each image indicate the upward displacement of the moving wall. See EPAPS [24] movies Nos. 1 and 2 for the complete sequence of images. Letters designate specific regions discussed in the text and Fig. 4b.

Figure 3

Evolution of the local density as a function of the local shear for both flow chambers and various bead sizes; all domains and all times are shown. Piles have been compacted before the experiment starts. The scale for the density (i.e., the value of the absorption length) is measured with $\pm 0.5\%$ accuracy. The inset and dashed line highlight a typical single domain evolution for the gravity flows. Note that these data are unfiltered and show the characteristic noise in the system and measurement.

Figure 4

Local density as a function of the local shear for various materials and initial densities in the shear cell. (a) with monodisperse pasta cylinders, 2 mm in height and diameter. (b) with polydisperse semolina grains, diameters ranging from 0.5 to 1 mm. The dashed lines represent the typical behaviors of the regions $A$, $B$, and $C$ defined on Fig. 2. Because of the nature of these materials, absorption coefficients are poorly defined, and the density scale is largely arbitrary. Relative variations are however precise up to 0.1%. (c) Experiment with 1 mm acrylic beads, starting with a loose pile.