Sculpting sandcastles grain by grain: Self-assembled sand towers

F. Pacheco-Vázquez, F. Moreau, N. Vandewalle, and S. Dorbolo

Phys. Rev. E 86, 051303 – Published 9 November 2012

Abstract

We study the spontaneous formation of granular towers produced when dry sand is poured on a wet sand bed. When the liquid content of the bed exceeds a threshold value $W^{☆}$ , the impacting grains have a nonzero probability to stick on the wet grains due to instantaneous liquid bridges created during the impact. The trapped grains become wet by the capillary ascension of water and the process continues, giving rise to stable narrow towers. The growth velocity is determined by the surface liquid content which decreases exponentially as the tower height augments. This self-assembly mechanism (only observed in the funicular and capillary regimes) could theoretically last while the capillary rise of water is possible; however, the structure collapses before reaching this limit. The collapse occurs when the weight of the tower surpasses the cohesive stress at its base. The cohesive stress increases as the liquid content of the bed is reduced. Consequently, the highest towers are found just above $W^{☆}$ .

Received 30 May 2012

DOI:https://doi.org/10.1103/PhysRevE.86.051303

Authors & Affiliations

F. Pacheco-Vázquez, F. Moreau, N. Vandewalle, and S. Dorbolo

GRASP, Physics Department B5, Université de Liège, B4000-Liège, Belgium

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Issue

Vol. 86, Iss. 5 — November 2012

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Images

Figure 1
(a) Sand pile formed by pouring dry grains on a flat surface. (b) A similar pile is obtained when the grains are poured into water. (c) When the pile reaches the air-water interface a vertical structure starts to show up, see movie 1 [17]. (d) A stable sand tower growth onto a wet sand bed (movie 2 [17]). (e) Experimental setup used in our experiments. (f) Stable tower obtained using our experimental setup (movie 3 [17]). The scale bars correspond to 10 mm.Reuse & Permissions
Figure 2
(a) Snapshots of a complete growing process. The average tower width is 6 mm and the scale bar is 10 mm. (b) $h_{f}$ vs $W$ for the different flux values used in our experiments. Each point corresponds to five repetitions and the error bars to the standard deviation. For $W < W^{*}$ the grains cannot stick and sand towers do not emerge.Reuse & Permissions
Figure 3
Growth dynamics: (a) $h$ vs $t$ , and (b) $v$ vs $h$ obtained at constant flux ( $Q = 0.166$ g/s) for different values of $W$ : dark blue line, 1; red, 0.90; green, 0.88; blue, 0.86; cyan, 0.84; magenta, 0.82; and orange, 0.78. In (a) only the first 1200 s of growing are plotted. The evolution of a dry sand pile formed with the same flux and grain properties is compared (dashed line). Inset in (b): $h$ * vs $W$ (black points) and $h$ * vs $Q$ (red points). (c) $v$ vs $h$ at constant liquid content ( $W = 0.78$ ) and different values of $Q$ : dark blue line, 0.166; violet, 0.335; red, 0.850; and green, 1.337 g/s. Inset: $v_{0}$ vs $Q$ for $W = 0.78$ . The orange line corresponds to $v_{0} / Q = (0.410 \pm 0.006)$ mm/g. (d) Sticking and suction: only the grains impacting on wet sites can be trapped.Reuse & Permissions
Figure 4
(a) $ω = m_{l} / m_{s}$ vs $h^{'}$ : Experimental measurements (red points) and the best data fit (blue line), see text. (b) $m_{T}$ vs $h_{f}$ for the experiments shown in Fig. 2b. $Q = 0.166$ g/s is used because with this flux the erosion is negligible and the cylindrical shape can be perfectly assumed. The linear fit (red line) gives a slope $ϕ_{T} ρ_{g} A_{T} = 0.050 \pm 0.003$ . (c) $P_{t}$ vs $Q$ for $W = 0.78$ . The critical values $σ_{c} = 1.87$ kPa and $Q_{\max} = 2.4$ g/s are indicated by the arrows. (d) $σ_{c}$ vs $W$ for $Q = 0.166$ g/s. The cohesive stress increases as the liquid content at the base of the tower decreases.Reuse & Permissions
Figure 5
(a) Crater or mound formed by ants in a sunny day by passive deposition of grains around the nest. (b) Top and (c) lateral views of a granular tower formed by the same kind of ants by deposition of grains after a rain. Cohesion causes some grains to stick, forming the tower.Reuse & Permissions
Figure 6
Different morphologies obtained by pouring dry grains on a flat surface depending on the liquid content of the substrate.Reuse & Permissions

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