John R. Royer

High-speed tracking of rupture and clustering in freely falling granular streams

Thin streams of liquid commonly break up into characteristic droplet patterns owing to the surface-tension-driven Plateau–Rayleigh instability. Very similar patterns are observed when initially uniform streams of dry granular material break up into clusters of grains, even though flows of macroscopic particles are considered to lack surface tension. Recent studies on freely falling granular streams tracked fluctuations in the stream profile, but the clustering mechanism remained unresolved because the full evolution of the instability could not be observed. Here we demonstrate that the cluster formation is driven by minute, nanoNewton cohesive forces that arise from a combination of van der Waals interactions and capillary bridges between nanometre-scale surface asperities. Our experiments involve high-speed video imaging of the granular stream in the co-moving frame, control over the properties of the grain surfaces and the use of atomic force microscopy to measure grain–grain interactions. The cohesive forces that we measure correspond to an equivalent surface tension five orders of magnitude below that of ordinary liquids. We find that the shapes of these weakly cohesive, non-thermal clusters of macroscopic particles closely resemble droplets resulting from thermally induced rupture of liquid nanojets.

A rheological signature of frictional interactions in shear thickening suspensions

Colloidal shear thickening presents a significant challenge because the macroscopic rheology becomes increasingly controlled by the microscopic details of short ranged particle interactions in the shear thickening regime. Our measurements here of the first normal stress difference over a wide range of particle volume fractions elucidate the relative contributions from hydrodynamic lubrication and frictional contact forces, which have been debated. At moderate volume fractions we find N_{1}<0, consistent with hydrodynamic models; however, at higher volume fractions and shear stresses these models break down and we instead observe dilation (N_{1}>0), indicating frictional contact networks. Remarkably, there is no signature of this transition in the viscosity; instead, this change in the sign of N_{1} occurs while the shear thickening remains continuous. These results suggest a scenario where shear thickening is driven primarily by the formation of frictional contacts, with hydrodynamic forces playing a supporting role at lower concentrations. Motivated by this picture, we introduce a simple model that combines these frictional and hydrodynamic contributions and accurately fits the measured viscosity over a wide range of particle volume fractions and shear stress.

The role of interstitial gas in determining the impact response of granular beds

We examine the impact of a solid sphere into a fine-grained granular bed. Using high-speed X-ray radiography we track both the motion of the sphere and local changes in the bed packing fraction. Varying the initial packing density as well as the ambient gas pressure, we find a complete reversal in the effect of interstitial gas on the impact response of the bed: The dynamic coupling between gas and grains allows for easier penetration in initially loose beds but impedes penetration in more densely packed beds. High-speed imaging of the local packing density shows that these seemingly incongruous effects have a common origin in the resistance to bed packing changes caused by interstitial air.

Gas-Mediated Impact Dynamics in Fine-Grained Granular Materials

Noncohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material. We find a crossover from nearly incompressible, fluidlike behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated. We discuss these results in light of recent proposals for the drag force in granular media.

Rupture and clustering in granular streams

John R. Royer, Loreto Oyarte, Matthias E. Möbius, and Heinrich M. Jaeger The University of Chicago, Chicago, Illinois 60637, USA Received 30 July 2009; published online 27 October 2009 doi:10.1063/1.3211191 It is a common, well-known occurrence for a thin liquid stream to break up into droplets due to the surface tension of the liquid. Surprisingly, this effect can also occur in granular materials, where an initially uniform stream of grains breaks up into discrete clusters, or droplets, of grains, even though granular materials are generally considered to lack surface tension. Using a high-speed camera in free fall, we image the breakup in the comoving frame with the freely falling granular stream. This allows us to track the onset of clustering and the subsequent cluster evolution in detail. By eliminating gravity and performing experiments in vacuum to reduce air drag, we can minimize the external forcing so only the interactions between the grains remain. Using these free falling streams, it is possible to investigate weak forces normally masked in other granular experiments and observe the vestiges of any residual surface tension. A rough schematic diagram is shown in Fig. 1. A 9 cm diameter reservoir of grains feeds a nozzle that consists of a porous, 13 cm long, 16 mm diameter cylinder with a flat disk at the base containing a circular aperture. A remote controlled shutter beneath the nozzle is used to initiate and stop the flow, allowing the grains to be stored in the hopper under vacuum for long periods of time. The nozzle and reservoir of grains are housed in a 2.5 m high acrylic tube, which is sealed and evacuated to as low as 0.03 kPa to reduce air drag. We observe the evolution of the falling stream using a high-speed camera Phantom v7.1 falling along a low friction rail outside of the chamber. This allows us to image a 3 cm section of the stream as it falls 2 m from the nozzle to the bottom of the chamber with a resolution of 0.04 mm /pixel at a frame rate of 1000 frames per second. Figure 2 illustrates the breakup process for a stream of d=54 m diameter glass spheres emerging from a 4.0 mm diameter nozzle under vacuum Fig. 2 a . The stream maintains its sharp boundaries as it falls, with very little loss of grains to the sides. As the stream accelerates under gravity, an axial velocity gradient develops and elongates the stream as it falls. While the stream stretches, initial undulations emerge and deepen Fig. 2 b , creating clusters connected by thin bridges a few grains wide Fig. 2 c . These bridges eventually rupture as the clusters continue to separate. After the clusters have separated, the gaps between the clusters continue to grow while the clusters maintain a nearly constant size and shape. Directly measurements of grain-grain interactions using atomic force microscopy reveal that the cluster formation is driven by minute, nanoNewton cohesive forces due to a combination of van der Waals interactions and capillary bridges between nanoscale surface asperities. The shapes of these weakly cohesive, nonthermal clusters of macroscopic particles closely resemble droplets resulting from thermally induced rupture of liquid nanojets and ultralow surface tension fluids. Removing gravity and all other external forces makes these free falling streams both an exquisite probe of the weak interactions between grains and a unique system to explore the ultralow surface tension fluid regime in the absence of thermal fluctuations.