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Impact-activated solidification of dense suspensions via dynamic jamming fronts

Nature volume 487, pages 205–209 (2012)Cite this article

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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.

References

  1. Cheng, X., McCoy, J. H., Israelachvili, J. N. & Cohen, I. Imaging the microscopic structure of shear thinning and thickening colloidal suspensions. Science 333, 1276–1279 (2011)

    ADS  CAS  Article  PubMed  Google Scholar 

  2. Brown, E. et al. Generality of shear thickening in dense suspensions. Nature Mater. 9, 220–224 (2010)

    ADS  CAS  Article  Google Scholar 

  3. Wagner, N. J. & Brady, J. F. Shear thickening in colloidal dispersions. Phys. Today 62, 27–32 (2009)

    CAS  Article  Google Scholar 

  4. Fall, A., Huang, N., Bertrand, F., Ovarlez, G. & Bonn, D. Shear thickening of cornstarch suspensions as a reentrant jamming transition. Phys. Rev. Lett. 100, 018301 (2008)

    ADS  Article  PubMed  Google Scholar 

  5. Merkt, F. S., Deegan, R. D., Goldman, D. I., Rericha, E. C. & Swinney, H. L. Persistent holes in a fluid. Phys. Rev. Lett. 92, 184501 (2004)

    ADS  Article  PubMed  Google Scholar 

  6. Bischoff White, E. E., Chellamuthu, M. & Rothstein, J. P. Extensional rheology of a shear-thickening cornstarch and water suspension. Rheol. Acta 49, 119–129 (2010)

    CAS  Article  Google Scholar 

  7. Smith, M. I., Besseling, R., Cates, M. E. & Bertola, V. Dilatancy in the flow and fracture of stretched colloidal suspensions. Nature Commun. 1, 114–115 (2010)

    ADS  CAS  Article  Google Scholar 

  8. Brady, J. F. & Bossis, G. Stokesian dynamics. Annu. Rev. Fluid Mech. 20, 111–157 (1988)

    ADS  Article  Google Scholar 

  9. Maranzano, B. J. & Wagner, N. J. The effects of particle-size on reversible shear thickening of concentrated colloidal dispersions. J. Chem. Phys. 114, 10514–10527 (2001)

    ADS  CAS  Article  Google Scholar 

  10. Brown, E. et al. Shear thickening and jamming in densely packed suspensions of different particle shapes. Phys. Rev. E 84, 031408 (2011)

    ADS  Article  Google Scholar 

  11. Brown, E. & Jaeger, H. M. Dynamic jamming point for shear thickening suspensions. Phys. Rev. Lett. 103, 086001 (2009)

    ADS  Article  PubMed  Google Scholar 

  12. Bi, D., Zhang, J., Chakraborty, B. & Behringer, R. P. Jamming by shear. Nature 480, 355–358 (2011)

    ADS  CAS  Article  PubMed  Google Scholar 

  13. Cates, M. E., Haw, M. D. & Holmes, C. B. Dilatancy, jamming, and the physics of granulation. J. Phys. Condens. Matter 17, S2517–S2531 (2005)

    ADS  CAS  Article  Google Scholar 

  14. Brown, E. & Jaeger, H. M. The role of dilation and confining stresses in shear thickening of dense suspensions. J. Rheol. 56, 875–923 (2012)

    ADS  CAS  Article  Google Scholar 

  15. von Kann, S., Snoeijer, J. H., Lohse, D. & van der Meer, D. Nonmonotonic settling of a sphere in a cornstarch suspension. Phys. Rev. E 84, 060401 (2011)

    ADS  Article  Google Scholar 

  16. Liu, B., Shelley, M. & Zhang, J. Focused force transmission through an aqueous suspension of granules. Phys. Rev. Lett. 105, (2010)

  17. Royer, J. R. et al. Formation of granular jets observed by high-speed X-ray radiography. Nature Phys. 1, 164–167 (2005)

    ADS  CAS  Article  Google Scholar 

  18. Fedorchenko, A. I. & Wang, A. B. On some common features of drop impact on liquid surfaces. Phys. Fluids 16, 1349–1365 (2004)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  19. Moghisi, M. & Squire, P. T. An experimental investigation of the initial force of impact on a sphere striking a liquid surface. J. Fluid Mech. 108, 133–146 (1981)

    ADS  Article  Google Scholar 

  20. Gómez, L. R., Turner, A. M., van Hecke, M. & Vitelli, V. Shocks near jamming. Phys. Rev. Lett. 108, 058001 (2012)

    ADS  Article  PubMed  Google Scholar 

  21. Debenedetti, P. G. & Stillinger, F. H. Supercooled liquids and the glass transition. Nature 410, 259–267 (2001)

    ADS  CAS  Article  PubMed  Google Scholar 

  22. Papoular, M. Dense suspensions and supercooled liquids: dynamic similarities. Phys. Rev. E 60, 2408–2410 (1999)

    ADS  CAS  Article  Google Scholar 

  23. Ediger, M. D., Angell, C. A. & Nagel, S. R. Supercooled liquids and glasses. J. Phys. Chem. 100, 13200–13212 (1996)

    CAS  Article  Google Scholar 

  24. Graham, D. J., Magdolinos, P. & Tosi, M. Investigation of the solidification of benzophenone in the supercooled liquid state. J. Phys. Chem. 99, 4757–4762 (1995)

    CAS  Article  Google Scholar 

  25. Hocking, L. M. The effect of slip on the motion of a sphere close to a wall and of two adjacent spheres. J. Eng. Math. 7, 207–221 (1973)

    Article  Google Scholar 

  26. Davis, R. H. & Serayssol, J.-M. The elastohydrodynamic collision of two spheres. J. Fluid Mech. 163, 479–497 (1986)

    ADS  Article  Google Scholar 

  27. Glasheen, J. W. & McMahon, T. A. Vertical water entry of disks at low Froude numbers. Phys. Fluids 8, 2078–2083 (1996)

    ADS  CAS  Article  Google Scholar 

  28. Richardson, E. G. The impact of a solid on a liquid surface. Proc. Phys. Soc. 61, 352–367 (1948)

    ADS  Article  Google Scholar 

  29. Brennen, C. E. A Review of Added Mass and Fluid Inertial Forces Report CR 82.010 (Naval Civil Engineering Laboratory, 1982)

    Google Scholar 

  30. Liu, A. J. & Nagel, S. R. Jamming is not just cool any more. Nature 396, 21–22 (1998)

    ADS  CAS  Article  Google Scholar 

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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 and Affiliations

  1. James Franck Institute and Department of Physics, The University of Chicago, Chicago, 60637, Illinois, USA

    Scott R. Waitukaitis & Heinrich M. Jaeger

Authors
  1. Scott R. Waitukaitis
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  2. Heinrich M. Jaeger
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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)

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)

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)

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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