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The hidden hierarchical nature of soft particulate gels

Nature Physics volume 19, pages 1178–1184 (2023)Cite this article

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Abstract

Soft particulate gels are composed of a small amount of particulate matter dispersed in a continuous fluid phase. The solid components assemble to form a porous matrix, providing rigidity and control of the mechanical response, despite being the minority constituent. The rheological response and gel elasticity are direct functions of the particle volume fraction. However, the diverse range of different functional dependencies reported experimentally has challenged efforts to identify general scaling laws. Here we reveal a hidden hierarchical organization of fractal elements that controls the viscoelastic spectrum, and which is associated with the spatial heterogeneity of the solid matrix topology. The fractal elements form the foundations of a viscoelastic master curve, constructed using large-scale three-dimensional (3D) microscopic simulations of model gels, which can be described by a recursive rheological ladder model over a range of particle volume fractions and gelation rates. The hierarchy of the fractal elements provides the missing general framework required to predict the gel elasticity and the linear viscoelastic response of these complex materials.

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Fig. 1: Microstructural and viscoelastic properties of networks having different connectivity.
Fig. 2: Rheological master curves and constitutive model for particulate gels.
Fig. 3: Structural characterization of gel networks.
Fig. 4: Scaling of viscoelastic parameters and connection to the ladder model.

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Data availability

We have deposited the manuscript data in a public repository (https://doi.org/10.5281/zenodo.7580589). Additional data supporting the manuscript data are available from the authors upon request.

Code availability

The codes used in this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We acknowledge support from the National Science Foundation, under grants nos. NSF DMR-2026842 (M. Bantawa and E.D.G.) and NSF DMREF CBET—2118962 (E.D.G.). This research was supported in part by the National Science Foundation under grant no. NSF PHY-1748958 through the KITP programme on the Physics of Dense Suspensions.

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Authors and Affiliations

  1. Department of Physics, Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC, USA

    Minaspi Bantawa & Emanuela Del Gado

  2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA

    Bavand Keshavarz, Michela Geri & Gareth H. McKinley

  3. Univ. Grenoble Alpes, CNRS, Grenoble INP, 3SR, Grenoble, France

    Mehdi Bouzid

  4. ENSL, CNRS, Laboratoire de physique, Lyon, France

    Thibaut Divoux

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  1. Minaspi Bantawa
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Contributions

M. Bantawa and B.K. contributed equally to this work. M. Bantawa performed simulations. B.K. developed the viscoelastic master curve and the rheological ladder model. All authors analysed data and wrote the paper.

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Correspondence to Emanuela Del Gado.

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Supplementary Figs. 1–8, discussions (sections 1–12) and references.

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Bantawa, M., Keshavarz, B., Geri, M. et al. The hidden hierarchical nature of soft particulate gels. Nat. Phys. 19, 1178–1184 (2023). https://doi.org/10.1038/s41567-023-01988-7

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