Rigidity transition in polydisperse shear-thickening suspensions
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| Format: | Preprint |
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2025
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| _version_ | 1866917262094499840 |
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| author | Singh, Sourav Kumar Tyagi, Vishant Santra, Aritra |
| author_facet | Singh, Sourav Kumar Tyagi, Vishant Santra, Aritra |
| contents | Shear thickening suspensions of non-Brownian polydisperse particles are simulated in 2D using a discrete element method based algorithm (LF-DEM) at high packing fractions ($ϕ$) and large non-dimensional stresses ($σ$). Rigidity analysis of the stress induced particle clusters is carried out using \textit{pebble game} algorithm for polydisperse suspensions and compared with the statistically equivalent bidisperse systems. A critical value of the packing fraction, $ϕ_c$, close to the shear jamming transition, $ϕ_J^μ$, ($ϕ_c<ϕ_J^μ$) is obtained where rigid particle clusters begin to grow sharply. The growth is found to be characterized by a critical transition of an order parameter ($f_\text{rig}$), defined by the fraction of particles in rigid clusters which scales as, $f_\text{rig}\sim (ϕ-ϕ_c)^β$ for $ϕ>ϕ_c$, and by the susceptibility scaling, $χ_\text{rig}\sim|ϕ-ϕ_c |^{-γ}$, with exponents having values consistent with the critical exponents in 2D percolation transition. The variations of $f_\text{rig}$ and $χ_\text{rig}$ in polydisperse suspensions are found to be identical to that of the statistically equivalent bidisperse suspensions. Finite size scaling analysis shows a divergence of correlation length near $ϕ_{c_\infty}$ following critical exponent $ν\approx 1.33$, in agreement with the 2D percolation theory. Furthermore, $ϕ_c$ and $ϕ_J^μ$ are found to vary non-monotonically with polydispersity index and depend on the particle stiffness. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_16464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity transition in polydisperse shear-thickening suspensions Singh, Sourav Kumar Tyagi, Vishant Santra, Aritra Soft Condensed Matter Shear thickening suspensions of non-Brownian polydisperse particles are simulated in 2D using a discrete element method based algorithm (LF-DEM) at high packing fractions ($ϕ$) and large non-dimensional stresses ($σ$). Rigidity analysis of the stress induced particle clusters is carried out using \textit{pebble game} algorithm for polydisperse suspensions and compared with the statistically equivalent bidisperse systems. A critical value of the packing fraction, $ϕ_c$, close to the shear jamming transition, $ϕ_J^μ$, ($ϕ_c<ϕ_J^μ$) is obtained where rigid particle clusters begin to grow sharply. The growth is found to be characterized by a critical transition of an order parameter ($f_\text{rig}$), defined by the fraction of particles in rigid clusters which scales as, $f_\text{rig}\sim (ϕ-ϕ_c)^β$ for $ϕ>ϕ_c$, and by the susceptibility scaling, $χ_\text{rig}\sim|ϕ-ϕ_c |^{-γ}$, with exponents having values consistent with the critical exponents in 2D percolation transition. The variations of $f_\text{rig}$ and $χ_\text{rig}$ in polydisperse suspensions are found to be identical to that of the statistically equivalent bidisperse suspensions. Finite size scaling analysis shows a divergence of correlation length near $ϕ_{c_\infty}$ following critical exponent $ν\approx 1.33$, in agreement with the 2D percolation theory. Furthermore, $ϕ_c$ and $ϕ_J^μ$ are found to vary non-monotonically with polydispersity index and depend on the particle stiffness. |
| title | Rigidity transition in polydisperse shear-thickening suspensions |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2510.16464 |