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What keeps sandcastles standing?


Any child playing on the beach knows that the physical properties of wet and dry sand are very different. Wet sand can be used to build sharp-featured sandcastles that would be unstable in dry sand. We have now quantified the effect of adding small quantities of liquid to a granular medium. Nanometre-scale layers of liquid on millimetre-scale grains dramatically increase the repose angle (the steepest stable slope that the substance can form) and allow the development of long-range correlations, or clumps.


Moisture-induced changes in granular media are primarily caused by adhesive forces associated with interstitial liquid bridges between grains. Such effects are significant in industries as diverse as pharmaceuticals, construction and agriculture. Liquid-induced forces also affect experimental studies of the physics of granular media1,2,3,4. Previous studies of moisture in granular media have examined only relatively large quantities of water added to highly irregular, porous or water-soluble materials such as coal5,6, sugar7, seeds or rock chips8,9. The resulting data are difficult to analyse and do not aid understanding of the physics of wetted granular media.

We have studied the effects of the addition of small quantities of corn oil and vacuum-pump oil (which both have low vapour pressures) to spherical polystyrene beads, which are insoluble in these oils. We measured the angle of repose by the draining-crater method10, with varying draining apertures and liquid content. Our maximum liquid content, (40 times less than the minimum moisture content of previous studies) corresponds to a liquid coating thickness (tliq) of less than 50 nm on the spheres. We found an enormous increase of the angle of repose (ΘR) with tliq(Fig. 1a). One surprising feature is that ΘRseems to increase linearly with tliqup to the point where clumping occurs. The results are independent of oil type and aperture (except for the largest t liq), and ΘRat tliq=0 agrees with previous measurements by this method10.

Figure 1: The angle of repose (ΘR) as a function of the average liquid-layer thickness on spheres (750 g samples, sphere diameter 0.8 ± 0.2 mm).

Draining apertures, d, are listed. Data have been corrected for changes in relative humidity (40–50%) which had a small (~1°) effect on ΘR. Experimental uncertainty is thus roughy 1°. Solid curve, one-parameter theoretical fit. Deviation from the theoretical values for small apertures and large tliq, is due to clumping. b, The distribution width of measured ΘRas a function of pump-oil layer thickness. Width corresponds to variations in roughness of the crater surface, which increases with cluster size, as seen with larger tliq.

In dry sand, ΘRis determined by the shape of the grains and by the friction forces. In wet sand, the attractive forces due to interstitial liquid bridges increase the stability of the surface particles and hence ΘR. Taking into account the observed surface roughness (˜1 μm) of the spheres, we calculated the interparticle adhesive force as a function of liquid content11. We then calculated the angle of repose for the wet material using a method based on the stability of the surface particles12. This model fits the data with a single free parameter corresponding to the volume of liquid in a typical bridge. The fit indicates that the typical volume of a liquid bridge is ~3×10-17 m3 for our maximum tliq, implying that 99.9% of the liquid does not contribute to the adhesive force, possibly because of the surface roughness.

As liquid was added to the spheres, correlated particle clusters (clumps) formed, the size of which increased with liquid content. The presence of such clusters leads to the appearance of an aperture dependence in ΘRfor the largest values of tliq. The development of clustering is also shown by increases in the width of the distribution of values of ΘRwith increasing tliq(Fig. 1b). The width corresponds to variations in the roughness of the crater surface (for tliq20 nm the craters were noticeably asymmetrical whereas for smaller tliqthe surfaces were essentially conical with roughness equivalent to a few sphere diameters).

The development of such clusters appears to be rather sudden, suggesting a transition from a situation where the bulk properties are associated with the dynamics of individual grains to a situation where long-range correlations dominate. Our apparatus entirely failed to drain for larger tliq( 40 nm) when the size of the clusters approached the aperture size.

Small quantities of wetting liquid can thus dramatically change the properties of granular media, leading to a large increase in the repose angle, clustering and correlation in grain motion. Our results indicate that interstitial liquids can alter many aspects of pattern formation, self-organization1,4 and segregation13 in granular materials, potentially leading to new physical phenomena not encountered in dry matter.


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Hornbaker, D., Albert, R., Albert, I. et al. What keeps sandcastles standing?. Nature 387, 765 (1997).

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