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Granular media

Structures in sand streams

Nature volume 459, pages 10641065 (25 June 2009) | Download Citation

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An ingenious experiment that involves dropping a costly, high-speed video camera from a height of several metres reveals how free-falling streams of granular matter, such as sand, break up into grain clusters.

It is common knowledge that when a stone is thrown into a pond, a jet of water shoots upwards. High-speed video imaging and even snapshots taken with short exposure times reveal that the jet breaks up into droplet patterns. Such patterns have inspired artists such as Andrew Davidhazy. What is both remarkable and intriguing is that very similar arrangements are observed in the streams that emerge when a stone is dropped into loose, fine sand1. The common view, which we have also adhered to, about the origin of this striking, liquid-like behaviour of streams of sand or other granular materials has been that the inelastic nature of collisions between the grains causes them to cluster together into larger structures2,3,4. But on page 1110 of this issue, Royer and colleagues5 show that this view is wrong, and that forces hitherto believed to be too small to cause the clustering are at work.

The formation of droplets in liquid jets (Fig. 1a) is caused by the Rayleigh–Plateau instability, which is driven by surface tension (the force that causes a liquid droplet to keep its shape). The understanding of this instability was pivotal to the conceptual development of hydrodynamics in the late nineteenth century by Joseph Plateau, Lord Rayleigh and their successors, and has since become textbook knowledge6. In contrast to liquid jets, granular streams of matter (Fig. 1b) were believed to lack surface tension. After all, granular matter such as sand is defined as a collection of grains that exert no forces on each other, with the exception of repulsive forces on collision7. It is thus surprising that streams of granular matter break up into structures that are similar to those of liquid streams.

Figure 1: Rupture of streams.
Figure 1

a, In a process caused by surface tension, a water stream breaks up into droplets (image taken from ref. 10). b, Similarly, a stream of granular media such as a sand jet — which forms, for example, after the impact of an object on loose, fine sand — breaks up into clusters of grains (image taken from ref. 1). Royer and colleagues5 show that, in granular media, the rupture and clustering process is driven by nanometre-range forces between the grains that lead to an effective surface tension that is 100,000 times weaker than in ordinary liquids. Image: a, CAMBRIDGE UNIV. PRESS; b, AM. PHYS. SOC.

Now Royer and colleagues5 demonstrate that, in granular matter, tiny nanometre-range forces between the grains lead to a minute effective surface tension that, despite being 100,000 times smaller than that in water, can explain the clustering of grains in the jet. The researchers achieved this using an ingenious combination of nanometre-scale atomic-force-microscopy measurements of the forces between the sand grains with metre-scale tracking of the evolution of the granular streams. The tracking involved letting sand (and other granular material) stream out of a funnel and following its clustering dynamics, for almost a second, in the stream's co-moving frame of reference — that is, using a high-speed video camera that moved with the stream. This means that the researchers had to drop their US$80,000 high-speed camera from a height of several metres, a heart-stopping prospect — even though the impact of the camera on the ground was adequately buffered.

In their experiment, Royer et al.5 observe a direct correlation between nanometre-range cohesive forces between the grains and the evolution of the jet structures within the first few metres of free fall. They find that modifying the nanometre-range forces — by varying the strength of intergrain cohesion through changes in the grains' surface roughness, the humidity or by using different materials — directly affects the break-up dynamics of the streams into clusters. In particular, the authors note that suppression of the nanometre-scale cohesion causes the clustering to vanish.

We would like to illustrate this striking phenomenon with two analogies. The first relates to the shapes of the grain clusters. As the authors5 themselves note, the shapes of the clusters, including the double-cone necks at rupture, resemble the droplets that form in liquid nanojets and which were first found in molecular-dynamics studies that simulated injection of molecular fluids into a vacuum through a nanoscale nozzle8. Such studies show that the small number of molecules and thermal fluctuations in the nanojets lead to irregularities in the cluster shapes, very similar to those found in Royer and colleagues' granular jets, in which the number of sand grains is also small when compared with the huge number of molecules in macroscopic liquid jets.

The second parallel that can be made is with the emergence of planetary systems from dust grains in circumstellar gas disks. In this case, the first step is the formation of metre-sized boulders, but how this process continues to form kilometre-sized planetesimals is an unsolved problem9, given that the (gravitational) attractive force between the boulders is so weak. However, Royer and colleagues' work teaches us that even minute forces can drive the formation of structures if the system is given enough time.

Traditionally, and in contrast to powders, one of the defining properties of granular matter has been the absence of cohesive forces between the grains7. But Royer and colleagues' observation of clustering in granular jets implies, conversely to what scientists have previously believed, that the distinction between powders and granular matter is much less clear-cut. Indeed, when velocity differences between the grains are small and timescales are considerable, even large grains can behave as powders.

The consequences of small, attractive forces may reach beyond the free-falling granular jets1. For example, the structures formed in the sand 'splashes' that are blown away after the impact of heavy objects on soft, fine sand1 could presumably be correlated with the same type of cohesive force. Future studies are needed to investigate whether such a correlation exists, just as Royer and colleagues have done in this pioneering study of granular jets.

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  1. Detlef Lohse and Devaraj van der Meer are in the Physics of Fluids Group, Department of Science and Technology, J. M. Burgers Center, and at the Impact and Mesa+ Institutes, University of Twente, PO Box 217, 7500 AE Enschede, the Netherlands.  d.lohse@utwente.nl

    • Detlef Lohse
    •  & Devaraj van der Meer

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