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Minimally rigid clusters in dense suspension flow

Nature Physics volume 20, pages 653–659 (2024)Cite this article

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Abstract

Dense suspensions are a prototype of fluid that can dynamically enhance their viscosity to resist strong forcing. Recent work established that the key to a large viscosity increase—often in excess of an order of magnitude—is the ability to switch from lubricated, frictionless particle interactions at low stress to a network of frictional contacts at higher stress. However, to isolate network features responsible for the large viscosity has been difficult, given the lack of an appropriate physics-inspired network measure. Here we apply rigidity theory to simulations of dense suspensions in two dimensions and identify a subset of mechanically rigid clusters at each strain step from the frictional contact network. We find that rigid clusters emerge at large shear stress well before the onset of jamming and that the continual breakup and reconfiguration of system-spanning rigid clusters is responsible for the flow states of the highest viscosity. By showing how viscosity is correlated with the rigidity of the underlying network of contact forces, our results provide insights beyond mean-field models and uncover a new contribution to dissipation in dense suspensions.

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Fig. 1: Decomposition of the frictional contact network into rigid clusters.
Fig. 2: Rheology, frictional contact force networks and rigidity.
Fig. 3: Steady-state dynamics of the largest rigid clusters.
Fig. 4: System-spanning rigid cluster statistics define new regime in the suspension state diagram.

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Data availability

All data used in this Article are available via the Materials Data Facility at https://doi.org/10.18126/xpcw-kgpv.

Code availability

Simulation data used in this study were generated using LF_DEM (https://github.com/ryseto/LF_DEM). Simulation data were analysed to find rigid clusters using rigidClusterLF_DEM (https://github.com/mikevandernaald/rigidCluster_LFDEM).

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Acknowledgements

We thank S. Henkes for fruitful and illuminating discussions as well as for making their rigidLibrary code for implementing the pebble game on frictional networks freely available. We acknowledge support from the Center for Hierarchical Materials Design (CHiMaD) under award no. 70NANB19H005 (US Department of Commerce) and from the Army Research Office under grants W911NF-19-1-0245 (to A.S.), W911NF-20-2-0044 (to M.v.d.N.) and W911NF-21-2-0146 (to H.M.J.).

Author information

Author notes

  1. Abhinendra Singh

    Present address: Department of Macromolecular Science and Engineering, Case Western Reserve University, Cleveland, OH, USA

Authors and Affiliations

  1. James Franck Institute, University of Chicago, Chicago, IL, USA

    Michael van der Naald, Abhinendra Singh, Toka Tarek Eid, Kenan Tang & Heinrich M. Jaeger

  2. Department of Physics, University of Chicago, Chicago, IL, USA

    Michael van der Naald, Toka Tarek Eid, Kenan Tang & Heinrich M. Jaeger

  3. Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA

    Abhinendra Singh & Juan J. de Pablo

  4. Materials Science Division, Argonne National Laboratory, Lemont, IL, USA

    Juan J. de Pablo

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Contributions

A.S. and M.v.d.N. conceived the project. A.S. and T.T.E. ran the simulations, whereas K.T. and M.v.d.N. wrote the code to analyse the data. H.M.J. and J.J.d.P. supervised the study. M.v.d.N., A.S. and H.M.J. analysed the data and wrote the manuscript.

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Correspondence to Abhinendra Singh.

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Nature Physics thanks Silke Henkes and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Figs. 1–9 and discussion.

Supplementary Video 1

Video showing the flow of clusters.

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van der Naald, M., Singh, A., Eid, T.T. et al. Minimally rigid clusters in dense suspension flow. Nat. Phys. 20, 653–659 (2024). https://doi.org/10.1038/s41567-023-02354-3

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