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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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.).
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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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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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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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DOI: https://doi.org/10.1038/s41567-023-02354-3