Impact-activated solidification of dense suspensions via dynamic jamming fronts

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Abstract

Although liquids typically flow around intruding objects, a counterintuitive phenomenon occurs in dense suspensions of micrometre-sized particles: they become liquid-like when perturbed lightly, but harden when driven strongly1,2,3,4,5. Rheological experiments have investigated how such thickening arises under shear, and linked it to hydrodynamic interactions1,3 or granular dilation2,4. However, neither of these mechanisms alone can explain the ability of suspensions to generate very large, positive normal stresses under impact. To illustrate the phenomenon, such stresses can be large enough to allow a person to run across a suspension without sinking, and far exceed the upper limit observed under shear or extension2,4,6,7. Here we show that these stresses originate from an impact-generated solidification front that transforms an initially compressible particle matrix into a rapidly growing jammed region, ultimately leading to extraordinary amounts of momentum absorption. Using high-speed videography, embedded force sensing and X-ray imaging, we capture the detailed dynamics of this process as it decelerates a metal rod hitting a suspension of cornflour (cornstarch) in water. We develop a model for the dynamic solidification and its effect on the surrounding suspension that reproduces the observed behaviour quantitatively. Our findings suggest that prior interpretations of the impact resistance as dominated by shear thickening need to be revisited.

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Figure 1: Impact into a cornflour and water suspension.
Figure 2: Suspension solidification and surface dynamics.
Figure 3: Displacement field of suspension interior during impact.
Figure 4: Added mass model for impact.

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Acknowledgements

We thank E. Brown, J. Burton, J. Ellowitz, Q. Guo, W. Irvine, M. Miskin, S. Nagel, C. Orellana, V. Vitelli, T. Witten and W. Zhang for discussions and J. Burton for his PIV code. This work was supported by NSF through its MRSEC programme (DMR-0820054) and by the US Army Research Office through grant number W911NF-12-1-0182. S.R.W. acknowledges support from a Millikan fellowship.

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Authors

Contributions

S.R.W. and H.M.J. conceived the study and wrote the paper. S.R.W. performed the experimental work, analysed results and created the model.

Corresponding author

Correspondence to Scott R. Waitukaitis.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Discussions I-III, Supplementary Figures 1-4 and an additional reference. (PDF 811 kb)

41586_2012_BFnature11187_MOESM303_ESM.mov

This file contains a high-speed video of rod (mrod = 0.368 kg, rrod = 0.93 cm) impact into a cornstarch and water suspension (Φ = 0.49, μ = 1.0 cP) at v = 0~0.5 m-1. Video covers ~10 ms before to 50 ms after impact. Rather than penetrating and creating a splash, the rod pushes the surface downward, causing a growing depression around the impact site. (MOV 975 kb)

Supplementary Movie 1

This file contains a high-speed video of rod (mrod = 0.368 kg, rrod = 0.93 cm) impact into a cornstarch and water suspension (Φ = 0.49, μ = 1.0 cP) at v = 0~0.5 m-1. Video covers ~10 ms before to 50 ms after impact. Rather than penetrating and creating a splash, the rod pushes the surface downward, causing a growing depression around the impact site. (MOV 975 kb)

41586_2012_BFnature11187_MOESM304_ESM.mov

This file contains a high-speed video of depression evolution via laser-line projection. The rod (centred on left edge of field of view) and suspension are black, while the laser on the suspension surface creates the bright line. Video covers ~10 ms before to 50 ms after impact. The maximum radial extent of the depression grows with the distance travelled by the rod. (MOV 517 kb)

Supplementary Movie 2

This file contains a high-speed video of depression evolution via laser-line projection. The rod (centred on left edge of field of view) and suspension are black, while the laser on the suspension surface creates the bright line. Video covers ~10 ms before to 50 ms after impact. The maximum radial extent of the depression grows with the distance travelled by the rod. (MOV 517 kb)

41586_2012_BFnature11187_MOESM305_ESM.mov

This file contains an X-ray video of suspension interior during impact. Duration is ~0.67 s. Tracer particles loaded into the central plane below the rod are displaced by the dynamic solidification, while outside this the suspension responds in a fluid-like manner to ensure global volume conservation. (MOV 942 kb)

Supplementary Movie 3

This file contains an X-ray video of suspension interior during impact. Duration is ~0.67 s. Tracer particles loaded into the central plane below the rod are displaced by the dynamic solidification, while outside this the suspension responds in a fluid-like manner to ensure global volume conservation. (MOV 942 kb)

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Waitukaitis, S., Jaeger, H. Impact-activated solidification of dense suspensions via dynamic jamming fronts. Nature 487, 205–209 (2012). https://doi.org/10.1038/nature11187

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