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Winters A, Öttinger HC, Vermant J. Comparative analysis of fluctuations in viscoelastic stress: A comparison of the temporary network and dumbbell models. J Chem Phys 2024; 161:014901. [PMID: 38949587 DOI: 10.1063/5.0213660] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 06/11/2024] [Indexed: 07/02/2024] Open
Abstract
Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as "noise," hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work, a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the hydrodynamic dumbbell model. Despite both models conforming to the upper convected Maxwell model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at the local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure-flow coupling, beyond what is captured by macroscopically averaged stresses.
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Affiliation(s)
- Arturo Winters
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 5, Zurich 8093, Switzerland
| | | | - Jan Vermant
- Department of Materials, ETH Zurich, Vladimir-Prelog-Weg 5, Zurich 8093, Switzerland
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2
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Chakraborty S, Ramola K. Long-range correlations in elastic moduli and local stresses at the unjamming transition. SOFT MATTER 2024; 20:4895-4904. [PMID: 38860707 DOI: 10.1039/d4sm00328d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
We explore the behaviour of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic p2 dependence of the correlations as the pressure p approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.
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Affiliation(s)
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500046, India.
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Mangal D, Vera GS, Aime S, Jamali S. Small variations in particle-level interactions lead to large structural heterogeneities in colloidal gels. SOFT MATTER 2024; 20:4692-4698. [PMID: 38787743 DOI: 10.1039/d4sm00316k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Colloidal gels typically exhibit mechanical properties akin to a viscoelastic solid, influenced by their underlying particulate network. Hence, the structural and morphological characteristics of the colloidal network have a significant effect on the rigidity of the gel. In this study, we show how seemingly small variations in the particle-level interactions throughout the system result in larger scale structural heterogeneities. While the microscale particle level descriptors of the colloidal network remain largely unaffected by heterogeneous interactions, larger scale properties of a colloidal gel change appreciably. The overall cluster-level mesostructure of a colloidal gel is found to be sensitive to the small variations in the interaction potential at the particle level.
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Affiliation(s)
- Deepak Mangal
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, 02115, USA.
| | | | - Stefano Aime
- Molecular, Macromolecular Chemistry, and Materials, ESPCI Paris, France
| | - Safa Jamali
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, 02115, USA.
- Department of Chemical Engineering, Northeastern University, Boston, 02115, USA
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Maharana R, Das D, Chaudhuri P, Ramola K. Universal stress correlations in crystalline and amorphous packings. Phys Rev E 2024; 109:044903. [PMID: 38755843 DOI: 10.1103/physreve.109.044903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Accepted: 02/20/2024] [Indexed: 05/18/2024]
Abstract
We present a universal characterization of stress correlations in athermal systems, across crystalline to amorphous packings. Via numerical analysis of static configurations of particles interacting through harmonic as well as Lennard-Jones potentials, for a variety of preparation protocols and ranges of microscopic disorder, we show that the properties of the stress correlations at large lengthscales are surprisingly universal across all situations, independent of structural correlations, or the correlations in orientational order. In the near-crystalline limit, we present exact results for the stress correlations for both models, which work surprisingly well at large lengthscales, even in the amorphous phase. Finally, we study the differences in stress fluctuations across the amorphization transition, where stress correlations reveal the loss of periodicity in the structure at short lengthscales with increasing disorder.
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Affiliation(s)
- Roshan Maharana
- Tata Institute of Fundamental Research, Hyderabad 500107, India
| | - Debankur Das
- Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37 077 Göttingen, Germany
| | - Pinaki Chaudhuri
- The Institute of Mathematical Sciences, Taramani, Chennai 600113, India
| | - Kabir Ramola
- Tata Institute of Fundamental Research, Hyderabad 500107, India
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Javerzat N. Schramm-Loewner Evolution in 2D Rigidity Percolation. PHYSICAL REVIEW LETTERS 2024; 132:018201. [PMID: 38242671 DOI: 10.1103/physrevlett.132.018201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Revised: 08/25/2023] [Accepted: 10/11/2023] [Indexed: 01/21/2024]
Abstract
Amorphous solids may resist external deformation such as shear or compression, while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid, such materials acquire a high degree of symmetry hidden in the disorder fluctuations: their microstructure becomes statistically conformally invariant. In this Letter, we exploit this finding to characterize the universality class of central-force rigidity percolation (RP), using Schramm-Loewner evolution (SLE) theory. We provide numerical evidence that the interfaces of the mechanically stable structures (rigid clusters), at the rigidification transition, are consistently described by SLE_{κ}, showing that this powerful framework can be applied to a mechanical percolation transition. Using well-known relations between different SLE observables and the universal diffusion constant κ, we obtain the estimation κ∼2.9 for central-force RP. This value is consistent, through relations coming from conformal field theory, with previously measured values for the clusters' fractal dimension D_{f} and correlation length exponent ν, providing new, nontrivial relations between critical exponents for RP. These findings open the way to a fine understanding of the microstructure in other important classes of rigidity and jamming transitions.
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Affiliation(s)
- Nina Javerzat
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy
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Thijssen K, Liverpool TB, Royall CP, Jack RL. Necking and failure of a particulate gel strand: signatures of yielding on different length scales. SOFT MATTER 2023; 19:7412-7428. [PMID: 37743690 DOI: 10.1039/d3sm00681f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2023]
Abstract
"Sticky" spheres with a short-ranged attraction are a basic model of a wide range of materials from the atomic to the granular length scale. Among the complex phenomena exhibited by sticky spheres is the formation of far-from-equilibrium dynamically arrested networks which comprise "strands" of densely packed particles. The aging and failure of such gels under load is a remarkably challenging problem, given the simplicity of the model, as it involves multiple length- and time-scales, making a single approach ineffective. Here we tackle this challenge by addressing the failure of a single strand with a combination of methods. We study the mechanical response of a single strand of a model gel-former to deformation, both numerically and analytically. Under elongation, the strand breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole strand; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different approaches gives a coherent picture of the necking and failure. The strand has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that the system loses its solid character and starts to behave more like a viscous fluid. These results will inform the development of more detailed models that incorporate the heterogeneous network structure of particulate gels.
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Affiliation(s)
- Kristian Thijssen
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | | | - C Patrick Royall
- H.H. Wills Physics Laboratory, Tyndall Avenue, Bristol, BS8 1TL, UK
- School of Chemistry, University of Bristol, Cantock's Close, Bristol, BS8 1TS, UK
- Gulliver UMR CNRS 7083, ESPCI Paris, Université PSL, 75005 Paris, France
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
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Jadrich RB, Milliron DJ, Truskett TM. Colloidal gels. J Chem Phys 2023; 159:090401. [PMID: 37668254 DOI: 10.1063/5.0170798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 08/10/2023] [Indexed: 09/06/2023] Open
Affiliation(s)
- Ryan B Jadrich
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Delia J Milliron
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
| | - Thomas M Truskett
- McKetta Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712, USA
- Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA
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Javerzat N, Bouzid M. Evidences of Conformal Invariance in 2D Rigidity Percolation. PHYSICAL REVIEW LETTERS 2023; 130:268201. [PMID: 37450798 DOI: 10.1103/physrevlett.130.268201] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2022] [Revised: 02/04/2023] [Accepted: 05/10/2023] [Indexed: 07/18/2023]
Abstract
The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid connected component, or cluster. As a second-order phase transition it exhibits a scale invariant critical point, at which the rigid clusters are random fractals. We show, using numerical analysis, that these clusters are also conformally invariant, and we use conformal field theory to predict the form of universal finite-size effects. Furthermore, although connectivity and rigidity percolation are usually thought to be of fundamentally different natures, we provide evidence of unexpected similarities between the statistical properties of their random clusters at criticality. Our work opens a new research avenue through the application of the powerful 2D conformal field theory tools to understand the critical behavior of a wide range of physical and biological materials exhibiting such a mechanical transition.
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Affiliation(s)
- Nina Javerzat
- SISSA and INFN Sezione di Trieste, via Bonomea 265, 34136, Trieste, Italy
| | - Mehdi Bouzid
- Université Grenoble Alpes, CNRS, Grenoble INP, 3SR, F-38000, Grenoble, France
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