Sliding Friction on Wet and Dry Sand

We show experimentally that the sliding friction on sand is greatly reduced by the addition of some—but not too much—water. The formation of capillary water bridges increases the shear modulus of the sand, which facilitates the sliding. Too much water, on the other hand, makes the capillary bridges coalesce, resulting in a decrease of the modulus; in this case, we observe that the friction coefficient increases again. Our results, therefore, show that the friction coefficient is directly related to the shear modulus; this has important repercussions for the transport of granular materials. In addition, the polydispersity of the sand is shown to also have a large effect on the friction coefficient.

Figure 1

Wall painting from 1880 B.C. on the tomb of Djehutihotep [1]. The figure standing at the front of the sled is pouring water onto the sand.

Figure 2

Force-displacement curves for wet and dry Iranian sand. Inset: Picture of the setup. The picture on the left was taken while sliding over dry normalized sand. The picture on the right was taken while sliding over normalized sand wetted with 5% water. In the dry sand, a heap clearly builds up in front of the sled. The $11\times 7.5\mathrm{cm}$ sled is made out of PVC with rounded edges (as the Egyptian sled) and a roughness of $35\mu \mathrm{m}$ with sandpaper on its bottom; the results were qualitatively similar but less reproducible with a smooth bottom.

Figure 3

Sections through 3D x-ray microtomograms of $500\mu \mathrm{m}$ polystyrene beads mixed with different amounts of liquid.

Figure 4

(a) Macroscopic dynamic friction coefficient for different water contents (Iranian sand). (b) Friction coefficient and shear elastic modulus (right axis) as a function of the water content in Iranian sand. The blue horizontal line indicates the optimum shear modulus according to the model in [15] using a grain radius of $100\mu \mathrm{m}$, a Young’s modulus of the grains of 60 GPa, and a water surface tension of $70\mathrm{mN}/\mathrm{m}$. The latter measurements were done on a commercial rheometer using a plate-in-cup geometry where the bottom of the cup, as well as the plate, was covered with sandpaper and the sand was compacted as for the sled experiments.

Figure 5

Dynamic friction coefficient as a function of water-volume fraction for different types of sand.

Figure 6

Grain size distribution for four sand types. The probability distribution function gives the relative occurrence of different grain sizes. The data for the Egyptian desert sand were taken from Ref. [17]. Nemours sand and Iranian sand are similar, both containing mainly grains in the $150–300\mu \mathrm{m}$ range, while ISO 679 standard sand is much more polydisperse.

Figure 7

Dynamic friction coefficient as a function of shear modulus for the three sand types. Sand was mixed with varying amounts of water. The friction coefficient follows from Fig. 5, and the shear modulus was measured on a commercial rheometer as described in the caption of Fig. 4.