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Heinze K, Frank X, Lullien-Pellerin V, George M, Radjai F, Delenne JY. Stress transmission in cemented bidisperse granular materials. Phys Rev E 2020; 101:052901. [PMID: 32575325 DOI: 10.1103/physreve.101.052901] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2019] [Accepted: 04/08/2020] [Indexed: 11/07/2022]
Abstract
We analyze stress distributions in a two-dimensional bidisperse cemented granular packing for a broad range of the values of particle-size ratio, the volumes of large and small particles, and the amount of cementing matrix. In such textured porous materials, the stress concentration, which controls the fracture and fragmentation of the material under tensile loading or in grinding processes, reflects not only the porosity but also the contact network of the particle phase and the resulting stress chains. By means of peridynamic simulations under tensile loading, we show how both the texture and stress distribution depend on size ratio, volume ratio, and the amount of the cementing matrix. In particular, the volume fraction of the class of small particles plays a key role in homogenizing stresses across the system by reducing porosity. Interestingly, the texture controls not only the porosity but also the distribution of pores inside the system with its statistical variability, found to be strongly correlated with the homogeneity of stresses inside the large particles. The most homogeneous stress distribution occurs for the largest size ratio and largest volume fraction of small particles, corresponding to the lowest pore size dispersion and the cushioning effect of small particles and its similar role to the binding matrix for stress redistribution across the packing. At higher porosity, the tensile stresses above the mean stress fall off exponentially in all phases with an exponent that strongly depends on the texture. The exponential part broadens with decreasing matrix volume fraction and particle-size ratio. These correlations reveal the strong interplay between size polydispersity and the cohesive action of the binding matrix for stress distribution, which is significant for the behavior of textured materials in grinding operations.
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Affiliation(s)
- K Heinze
- IATE, Université de Montpellier, INRA, CIRAD, Montpellier SupAgro, Montpellier, France.,L2C, Université de Montpellier, CNRS, Montpellier, France
| | - X Frank
- IATE, Université de Montpellier, INRA, CIRAD, Montpellier SupAgro, Montpellier, France
| | - V Lullien-Pellerin
- IATE, Université de Montpellier, INRA, CIRAD, Montpellier SupAgro, Montpellier, France
| | - M George
- L2C, Université de Montpellier, CNRS, Montpellier, France
| | - F Radjai
- LMGC, Université de Montpellier, CNRS, Montpellier, France
| | - J-Y Delenne
- IATE, Université de Montpellier, INRA, CIRAD, Montpellier SupAgro, Montpellier, France
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Mayer-Laigle C, Barakat A, Barron C, Delenne J, Frank X, Mabille F, Rouau X, Sadoudi A, Samson MF, Lullien-Pellerin V. DRY biorefineries: Multiscale modeling studies and innovative processing. INNOV FOOD SCI EMERG 2018. [DOI: 10.1016/j.ifset.2017.08.006] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Frank X, Li HZ, Funfschilling D. An analytical approach to the rise velocity of periodic bubble trains in non-Newtonian fluids. Eur Phys J E Soft Matter 2005; 16:29-35. [PMID: 15688138 DOI: 10.1140/epje/e2005-00004-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2004] [Indexed: 05/24/2023]
Abstract
The present study aims at providing insight into the acceleration mechanism of a bubble chain rising in shear-thinning viscoelastic fluids. The experimental investigation by the Particle Image Velocimetry (PIV), birefringence visualisation and rheological simulation shows that two aspects are central to bubble interactions in such media: the stress creation by the passage of bubbles, and their relaxation due to the fluid's memory forming an evanescent corridor of reduced viscosity. Interactions between bubbles were taken into account mainly through a linear superposition of the stress evolution behind each bubble. An analytical approach together with the rheological consideration was developed to compute the rise velocity of a bubble chain in function of the injection period and bubble volume. The model predictions compare satisfactorily with the experimental investigation.
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Affiliation(s)
- X Frank
- Laboratoire des Sciences du Génie Chimique (CNRS, BP 451, UPR 6811), ENSIC-INPL, 1, rue Grandville, 54001, Nancy Cedex, France
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