1
|
Haver D, Acuña D, Janbaz S, Lerner E, Düring G, Coulais C. Elasticity and rheology of auxetic granular metamaterials. Proc Natl Acad Sci U S A 2024; 121:e2317915121. [PMID: 38536751 PMCID: PMC10998574 DOI: 10.1073/pnas.2317915121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 03/04/2024] [Indexed: 04/08/2024] Open
Abstract
The flowing, jamming, and avalanche behavior of granular materials is satisfyingly universal and vexingly hard to tune: A granular flow is typically intermittent and will irremediably jam if too confined. Here, we show that granular metamaterials made from particles with a negative Poisson's ratio yield more easily and flow more smoothly than ordinary granular materials. We first create a collection of auxetic grains based on a re-entrant mechanism and show that each grain exhibits a negative Poisson's ratio regardless of the direction of compression. Interestingly, we find that the elastic and yielding properties are governed by the high compressibility of granular metamaterials: At a given confinement, they exhibit lower shear modulus, lower yield stress, and more frequent, smaller avalanches than materials made from ordinary grains. We further demonstrate that granular metamaterials promote flow in more complex confined geometries, such as intruder and hopper geometries, even when the packing contains only a fraction of auxetic grains. Moreover, auxetic granular metamaterials exhibit enhanced impact absorption. Our findings blur the boundary between complex fluids and metamaterials and could help in scenarios that involve process, transport, and reconfiguration of granular materials.
Collapse
Affiliation(s)
- Daan Haver
- Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Institute of Physics, Universiteit van Amsterdam, Amsterdam1098 XH, The Netherlands
| | - Daniel Acuña
- Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Santiago8370458, Chile
| | - Shahram Janbaz
- Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Institute of Physics, Universiteit van Amsterdam, Amsterdam1098 XH, The Netherlands
| | - Edan Lerner
- Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Institute of Physics, Universiteit van Amsterdam, Amsterdam1098 XH, The Netherlands
| | - Gustavo Düring
- Facultad de Física, Instituto de Física, Pontificia Universidad Católica de Chile, Santiago8331150, Chile
| | - Corentin Coulais
- Faculteit der Natuurwetenschappen, Wiskunde en Informatica, Institute of Physics, Universiteit van Amsterdam, Amsterdam1098 XH, The Netherlands
| |
Collapse
|
2
|
Clemmer JT, Monti JM, Lechman JB. A soft departure from jamming: the compaction of deformable granular matter under high pressures. SOFT MATTER 2024; 20:1702-1718. [PMID: 38284215 DOI: 10.1039/d3sm01373a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2024]
Abstract
The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follow the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.
Collapse
Affiliation(s)
- Joel T Clemmer
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
| | - Joseph M Monti
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
| | - Jeremy B Lechman
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA.
| |
Collapse
|
3
|
Xie Z, Atherton TJ. Jamming on convex deformable surfaces. SOFT MATTER 2024; 20:1070-1078. [PMID: 38206105 DOI: 10.1039/d2sm01608g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
Jamming is a fundamental transition that governs the behavior of particulate media, including sand, foams and dense suspensions. Upon compression, such media change from freely flowing to a disordered, marginally stable solid that exhibits non-Hookean elasticity. While the jamming process is well established for fixed geometries, the nature and dynamics of jamming for a diverse class of soft materials and deformable substrates, including emulsions and biological matter, remains unknown. Here we propose a new scenario, metric jamming, where rigidification occurs on a surface that has been deformed from its ground state. Unlike classical jamming processes that exhibit discrete mechanical transitions, surprisingly we find that metric jammed states possess mechanical properties continuously tunable between those of classically jammed and conventional elastic media. The compact and curved geometry significantly alters the vibrational spectra of the structures relative to jamming in flat Euclidean space, and metric jammed systems also possess new types of vibrational mode that couple particle and shape degrees of freedom. Our work provides a theoretical framework that unifies our understanding of solidification processes that take place on deformable media and lays the groundwork to exploit jamming for the control and stabilization of shape in self-assembly processes.
Collapse
Affiliation(s)
- Zhaoyu Xie
- Department of Physics & Astronomy, Tufts University, 574 Boston Ave, Medford, MA 02155, USA.
| | - Timothy J Atherton
- Department of Physics & Astronomy, Tufts University, 574 Boston Ave, Medford, MA 02155, USA.
| |
Collapse
|
4
|
Cheng Y, Treado JD, Lonial BF, Habdas P, Weeks ER, Shattuck MD, O'Hern CS. Hopper flows of deformable particles. SOFT MATTER 2022; 18:8071-8086. [PMID: 36218162 DOI: 10.1039/d2sm01079h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Numerous experimental and computational studies show that continuous hopper flows of granular materials obey the Beverloo equation that relates the volume flow rate Q and the orifice width w: Q ∼ (w/σavg - k)β, where σavg is the average particle diameter, kσavg is an offset where Q ∼ 0, the power-law scaling exponent β = d - 1/2, and d is the spatial dimension. Recent studies of hopper flows of deformable particles in different background fluids suggest that the particle stiffness and dissipation mechanism can also strongly affect the power-law scaling exponent β. We carry out computational studies of hopper flows of deformable particles with both kinetic friction and background fluid dissipation in two and three dimensions. We show that the exponent β varies continuously with the ratio of the viscous drag to the kinetic friction coefficient, λ = ζ/μ. β = d - 1/2 in the λ → 0 limit and d - 3/2 in the λ → ∞ limit, with a midpoint λc that depends on the hopper opening angle θw. We also characterize the spatial structure of the flows and associate changes in spatial structure of the hopper flows to changes in the exponent β. The offset k increases with particle stiffness until k ∼ kmax in the hard-particle limit, where kmax ∼ 3.5 is larger for λ → ∞ compared to that for λ → 0. Finally, we show that the simulations of hopper flows of deformable particles in the λ → ∞ limit recapitulate the experimental results for quasi-2D hopper flows of oil droplets in water.
Collapse
Affiliation(s)
- Yuxuan Cheng
- Department of Physics, Yale University, New Haven, Connecticut, 06520, USA.
| | - John D Treado
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut, 06520, USA
| | | | - Piotr Habdas
- Department of Physics, Saint Joseph's University, Philadelphia, PA 19131, USA
| | - Eric R Weeks
- Department of Physics, Emory University, Atlanta, GA 30322, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Department of Physics, Yale University, New Haven, Connecticut, 06520, USA.
- Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut, 06520, USA
- Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut, 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut, 06520, USA.
| |
Collapse
|
5
|
Kim S, Hilgenfeldt S. Structural Measures as Guides to Ultrastable States in Overjammed Packings. PHYSICAL REVIEW LETTERS 2022; 129:168001. [PMID: 36306772 DOI: 10.1103/physrevlett.129.168001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Revised: 05/18/2022] [Accepted: 09/19/2022] [Indexed: 06/16/2023]
Abstract
Jammed, disordered packings of given sets of particles possess a multitude of equilibrium states with different mechanical properties. Identifying and constructing desired states, e.g., of superior stability, is a complex task. Here, we show that in two-dimensional particle packings the energy of all metastable states (inherent structures) is reliably classified by simple scalar measures of local steric packing. These structural measures are insensitive to the particle interaction potential and so robust that they can be used to guide a modified swap algorithm that anneals polydisperse packings toward low-energy metastable states exceptionally fast. The low-energy states are extraordinarily stable against applied shear, so that the approach also efficiently identifies ultrastable packings.
Collapse
Affiliation(s)
- Sangwoo Kim
- Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106-5070, USA
| | - Sascha Hilgenfeldt
- Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| |
Collapse
|
6
|
Wang D, Treado JD, Boromand A, Norwick B, Murrell MP, Shattuck MD, O'Hern CS. The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions. SOFT MATTER 2021; 17:9901-9915. [PMID: 34697616 PMCID: PMC9118367 DOI: 10.1039/d1sm01228b] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
We investigate the structural, vibrational, and mechanical properties of jammed packings of deformable particles with shape degrees of freedom in three dimensions (3D). Each 3D deformable particle is modeled as a surface-triangulated polyhedron, with spherical vertices whose positions are determined by a shape-energy function with terms that constrain the particle surface area, volume, and curvature, and prevent interparticle overlap. We show that jammed packings of deformable particles without bending energy possess low-frequency, quartic vibrational modes, whose number decreases with increasing asphericity and matches the number of missing contacts relative to the isostatic value. In contrast, jammed packings of deformable particles with non-zero bending energy are isostatic in 3D, with no quartic modes. We find that the contributions to the eigenmodes of the dynamical matrix from the shape degrees of freedom are significant over the full range of frequency and shape parameters for particles with zero bending energy. We further show that the ensemble-averaged shear modulus 〈G〉 scales with pressure P as 〈G〉 ∼ Pβ, with β ≈ 0.75 for jammed packings of deformable particles with zero bending energy. In contrast, β ≈ 0.5 for packings of deformable particles with non-zero bending energy, which matches the value for jammed packings of soft, spherical particles with fixed shape. These studies underscore the importance of incorporating particle deformability and shape change when modeling the properties of jammed soft materials.
Collapse
Affiliation(s)
- Dong Wang
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA.
| | - John D Treado
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA.
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
| | - Arman Boromand
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA.
| | - Blake Norwick
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Michael P Murrell
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Biomedical Engineering, Yale University, New Haven, Connecticut 06520, USA
- Systems Biology Institute, Yale University, West Haven, Connecticut, 06516, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA.
- Integrated Graduate Program in Physical and Engineering Biology, Yale University, New Haven, Connecticut 06520, USA
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|
7
|
Kim S, Pochitaloff M, Stooke-Vaughan GA, Campàs O. Embryonic Tissues as Active Foams. NATURE PHYSICS 2021; 17:859-866. [PMID: 34367313 PMCID: PMC8336761 DOI: 10.1038/s41567-021-01215-1] [Citation(s) in RCA: 43] [Impact Index Per Article: 14.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but it is unclear how cells control these emergent tissue states and transitions, including tissue fluidization. Combining computational and experimental methods, here we show that tissue fluidization in posterior zebrafish tissues is controlled by the stochastic dynamics of tensions at cell-cell contacts. We develop a computational framework that connects cell behavior to embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and cortical tension dynamics. We predict that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively-generated tension fluctuations controlling stress relaxation and tissue fluidization. By directly measuring strain and stress relaxation, as well as the dynamics of cell rearrangements, in elongating posterior zebrafish tissues, we show that tension fluctuations drive active cell rearrangements that fluidize the tissue. These results highlight a key role of non-equilibrium tension dynamics in developmental processes.
Collapse
Affiliation(s)
- Sangwoo Kim
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
| | - Marie Pochitaloff
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
| | | | - Otger Campàs
- Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
- Center for Bioengineering, University of California, Santa Barbara, CA 93106, USA
- Department of Molecular, Cellular and Developmental Biology, University of California, Santa Barbara, CA 93106, USA
- California NanoSystems Institute, University of California, Santa Barbara, CA 93106, USA
- Cluster of Excellence Physics of Life, TU Dresden, 01062 Dresden, Germany
- Correspondence should be addressed to Otger Camps ()
| |
Collapse
|
8
|
Shewan HM, Yakubov GE, Bonilla MR, Stokes JR. Viscoelasticity of non-colloidal hydrogel particle suspensions at the liquid-solid transition. SOFT MATTER 2021; 17:5073-5083. [PMID: 33929481 DOI: 10.1039/d0sm01624a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Suspensions of soft particles transition from a viscous fluid to a soft material upon increases in phase volume. The criteria defining the transition to this jammed state are difficult to define due to the porous and deformable nature of soft particles. Here, we characterise the rheology of aqueous suspensions of industrially relevant non-colloidal, polydisperse, frictional agarose microgels and evaluate shear and viscoelastic behaviour across a range of phase volumes from the dilute regime to the highly concentrated regime. In order to model the viscoelastic response of suspensions without free fitting parameters, the random close packing volume fraction (φrcp) and the particle modulus are determined, respectively, from particle size distribution measurements and direct measurements of reduced elastic modulus of individual particles (Erp) using Atomic Force Microscopy. It is found that at φrcp, previously shown to correspond to divergence of the viscosity, also corresponds to the suspension transition from a viscous to viscoelastic fluid. However, the transition to a jammed solid-like state (φj) occurs at phase volumes exceeding this value (i.e. φj > φrcp). The suspension modulus and its sudden growth at φj are well-predicted by the Evans and Lips model that incorporates the Erp of the hydrogel particles. This rheological behaviour showing a dual transition is reminiscent of two families of systems: (i) colloidal suspensions and (ii) frictional-adhesive non-colloidal suspensions. However, it does not strictly follow either case. We propose that the width of the transition region is dictated by frictional contact, particle size distribution and particle modulus, and plan to further probe this in future work.
Collapse
Affiliation(s)
- Heather M Shewan
- School of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia.
| | - Gleb E Yakubov
- School of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia.
| | - Mauricio R Bonilla
- School of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia.
| | - Jason R Stokes
- School of Chemical Engineering, The University of Queensland, Brisbane, QLD 4072, Australia.
| |
Collapse
|
9
|
Golovkova I, Montel L, Pan F, Wandersman E, Prevost AM, Bertrand T, Pontani LL. Adhesion as a trigger of droplet polarization in flowing emulsions. SOFT MATTER 2021; 17:3820-3828. [PMID: 33725054 DOI: 10.1039/d1sm00097g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Tissues are subjected to large external forces and undergo global deformations during morphogenesis. We use synthetic analogues of tissues to study the impact of cell-cell adhesion on the response of cohesive cellular assemblies under such stresses. In particular, we use biomimetic emulsions in which the droplets are functionalized in order to exhibit specific droplet-droplet adhesion. We flow these emulsions in microfluidic constrictions and study their response to this forced deformation via confocal microscopy. We find that the distributions of avalanche sizes are conserved between repulsive and adhesive droplets. However, adhesion locally impairs the rupture of droplet-droplet contacts, which in turn pulls on the rearranging droplets. As a result, adhesive droplets are a lot more deformed along the axis of elongation in the constriction. This finding could shed light on the origin of polarization processes during morphogenesis.
Collapse
Affiliation(s)
- Iaroslava Golovkova
- Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP), F-75005, Paris, France.
| | | | | | | | | | | | | |
Collapse
|
10
|
Hernandez A, Marchetti MC. Poisson-bracket formulation of the dynamics of fluids of deformable particles. Phys Rev E 2021; 103:032612. [PMID: 33862788 DOI: 10.1103/physreve.103.032612] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2020] [Accepted: 02/25/2021] [Indexed: 01/13/2023]
Abstract
Using the Poisson-bracket method, we derive continuum equations for a fluid of deformable particles in two dimensions. Particle shape is quantified in terms of two continuum fields: an anisotropy density field that captures the deformations of individual particles from regular shapes and a shape tensor density field that quantifies both particle elongation and nematic alignment of elongated shapes. We explicitly consider the example of a dense biological tissue as described by the Vertex model energy, where cell shape has been proposed as a structural order parameter for a liquid-solid transition. The hydrodynamic model of biological tissue proposed here captures the coupling of cell shape to flow and provides a starting point for modeling the rheology of dense tissue.
Collapse
Affiliation(s)
- Arthur Hernandez
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
| |
Collapse
|
11
|
Chen Y, Yuan M, Wang Z, Zhao Y, Li J, Hu B, Xia C. Structural characterization and statistical properties of jammed soft ellipsoid packing. SOFT MATTER 2021; 17:2963-2972. [PMID: 33595009 DOI: 10.1039/d0sm01699c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The jamming transition and jammed packing structures of hydrogel soft ellipsoids are studied using magnetic resonance imaging techniques. As the packing fraction increases, the fluctuation of local free volume decreases and the fluctuation of particle deformation increases. Effective thermodynamic quantities are obtained by characterizing these fluctuations using k-gamma distributions based on an underlying statistical model for granular materials. Surprisingly, the two granular temperatures measuring the relative fluctuations of both free volume and particle deformation remain basically unchanged as the packing fraction increases. The total configurational entropy is also approximately constant for packing with different packing fractions. The significantly different behaviors of these effective thermodynamic quantities compared with hard sphere systems are further attributed to a statistically affine structural transformation of the packing structures along with particle deformations when the packing fraction changes.
Collapse
Affiliation(s)
- Yinfei Chen
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Ming Yuan
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Zhichao Wang
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Yu Zhao
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Jianqi Li
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Bingwen Hu
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| | - Chengjie Xia
- Shanghai Key Laboratory of Magnetic Resonance, Institute of Materials, School of Physics and Electronic Science, East China Normal University, Shanghai 200241, P. R. China.
| |
Collapse
|
12
|
Yanagisawa N, Kurita R. Size distribution dependence of collective relaxation dynamics in a two-dimensional wet foam. Sci Rep 2021; 11:2786. [PMID: 33531566 PMCID: PMC7854744 DOI: 10.1038/s41598-021-82267-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Accepted: 01/18/2021] [Indexed: 11/09/2022] Open
Abstract
Foams can be ubiquitously observed in nature and in industrial products. Despite the relevance of their properties to deformation, fluidity, and collapse, all of which are essential for applications, there are few experimental studies of collective relaxation dynamics in a wet foam. Here, we directly observe how the relaxation dynamics changes with increasing liquid fraction in both monodisperse and polydisperse two-dimensional foams. As we increase the liquid fraction, we quantitatively characterize the slowing-down of the relaxation, and the increase of the correlation length. We also find two different relaxation modes which depend on the size distribution of the bubbles. It suggests that the bubbles which are simply near to each other play an important role in large rearrangements, not just those in direct contact. Finally, we confirm the generality of our experimental findings by a numerical simulation for the relaxation process of wet foams.
Collapse
Affiliation(s)
- Naoya Yanagisawa
- Department of Physics, Tokyo Metropolitan University, 1-1 Minamioosawa, Hachiouji-shi, Tokyo, 192-0397, Japan.
| | - Rei Kurita
- Department of Physics, Tokyo Metropolitan University, 1-1 Minamioosawa, Hachiouji-shi, Tokyo, 192-0397, Japan.
| |
Collapse
|
13
|
Tsuritani K, Inasawa S. Scaling law for the kinetics of water imbibition in polydisperse foams. RSC Adv 2021; 11:33093-33101. [PMID: 35493588 PMCID: PMC9042101 DOI: 10.1039/d1ra06392h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2021] [Accepted: 09/26/2021] [Indexed: 11/26/2022] Open
Abstract
We investigated the kinetics of water imbibition in polydisperse foams. We used a Hele-Shaw cell, and horizontal imbibition was observed for a timescale of up to 103 s in which the gravity effect was negligible. While several papers have reported kinetics for imbibition in foams, imbibition kinetics in polydisperse foams and its variations in longer timescales are not well understood. The tip position of imbibition was proportional to the square root of time in the initial stage of imbibition, but it showed plateauing in the late stage of imbibition. We evaluated the proportional constant A in the initial stage of imbibition as a kinetic constant for the time-dependent increase in the tip position, which showed a clear dependency on the initial and final water volume fractions in the foams. Conversely, the mean initial radius of the curvature and the channel length in the Plateau borders did not show any clear correlations with A, although both valuables are frequently used in modeling for liquid imbibition in foams. On the basis of the t1/2 dependence, the correlation of A with the water volume fraction and the increase in the water volume fraction during imbibition, we proposed a simple equation to describe the tip position over the entire period of imbibition. We used them to scale all of the experimental data, which showed good agreement with the theoretical line. This clearly showed that the water volume fraction in the foams during imbibition was the key factor to quantitatively describe the rate of water imbibition. Features in the kinetics of imbibition were discussed. Horizontal imbibition of water in foams is scaled well by a simple mathematical expression that considers t1/2 dependence and changes in volume fraction of water in foams.![]()
Collapse
Affiliation(s)
- Kanoko Tsuritani
- Graduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan
| | - Susumu Inasawa
- Graduate School of Bio-Applications and Systems Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan
- Department of Applied Physics and Chemical Engineering, School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan
- Department of Chemical Engineering, School of Engineering, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588, Japan
| |
Collapse
|
14
|
Xiao H, Ivancic RJS, Durian DJ. Strain localization and failure of disordered particle rafts with tunable ductility during tensile deformation. SOFT MATTER 2020; 16:8226-8236. [PMID: 32935714 DOI: 10.1039/d0sm00839g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Quasi-static tensile experiments were performed for a model disordered solid consisting of a two-dimensional raft of polydisperse floating granular particles with capillary attractions. The ductility is tuned by controlling the capillary interaction range, which varies with the particle size. During the tensile tests, after an initial period of elastic deformation, strain localization occurs and leads to the formation of a shear band at which the pillar later fails. In this process, small particles with long-ranged interactions can endure large plastic deformation without forming significant voids, while large particles with short-range interactions fail dramatically by fracturing at small deformation. Particle-level structure was measured, and the strain-localized region was found to have higher structural anisotropy than the bulk. Local interactions between anisotropic sites and particle rearrangements were the main mechanisms driving strain localization and the subsequent failure, and significant differences of such interactions exist between ductile and brittle behaviors.
Collapse
Affiliation(s)
- Hongyi Xiao
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA.
| | - Robert J S Ivancic
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA.
| | - Douglas J Durian
- Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104, USA.
| |
Collapse
|
15
|
Cantor D, Cárdenas-Barrantes M, Preechawuttipong I, Renouf M, Azéma E. Compaction Model for Highly Deformable Particle Assemblies. PHYSICAL REVIEW LETTERS 2020; 124:208003. [PMID: 32501060 DOI: 10.1103/physrevlett.124.208003] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/13/2020] [Revised: 04/09/2020] [Accepted: 05/04/2020] [Indexed: 06/11/2023]
Abstract
The compaction behavior of deformable grain assemblies beyond jamming remains bewildering, and existing models that seek to find the relationship between the confining pressure P and solid fraction ϕ end up settling for empirical strategies or fitting parameters. Using a coupled discrete-finite element method, we analyze assemblies of highly deformable frictional grains under compression. We show that the solid fraction evolves nonlinearly from the jamming point and asymptotically tends to unity. Based on the micromechanical definition of the granular stress tensor, we develop a theoretical model, free from ad hoc parameters, correctly mapping the evolution of ϕ with P. Our approach unveils the fundamental features of the compaction process arising from the joint evolution of grain connectivity and the behavior of single representative grains. This theoretical framework also allows us to deduce a bulk modulus equation showing an excellent agreement with our numerical data.
Collapse
Affiliation(s)
- David Cantor
- Department of Mechanical Engineering, Chiang Mai University, 239 Huay Kaew Road, 50200 Chiang Mai, Thailand
| | | | - Itthichai Preechawuttipong
- Department of Mechanical Engineering, Chiang Mai University, 239 Huay Kaew Road, 50200 Chiang Mai, Thailand
| | - Mathieu Renouf
- LMGC, Université de Montpellier, CNRS, 34090 Montpellier, France
| | - Emilien Azéma
- LMGC, Université de Montpellier, CNRS, 34090 Montpellier, France
| |
Collapse
|
16
|
Golovkova I, Montel L, Wandersman E, Bertrand T, Prevost AM, Pontani LL. Depletion attraction impairs the plasticity of emulsions flowing in a constriction. SOFT MATTER 2020; 16:3294-3302. [PMID: 32173724 DOI: 10.1039/c9sm02343g] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We study the elasto-plastic behavior of dense attractive emulsions under a mechanical perturbation. The attraction is introduced through non-specific depletion interactions between the droplets and is controlled by changing the concentration of surfactant micelles in the continuous phase. We find that such attractive forces are not sufficient to induce any measurable modification on the scalings between the local packing fraction and the deformation of the droplets. However, when the emulsions are flowed through 2D microfluidic constrictions, we uncover a measurable effect of attraction on their elasto-plastic response. Indeed, we measure higher levels of deformation inside the constriction for attractive droplets. In addition, we show that these measurements correlate with droplet rearrangements that are spatially delayed in the constriction for higher attraction forces.
Collapse
Affiliation(s)
- Iaroslava Golovkova
- Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP), F-75005, Paris, France.
| | - Lorraine Montel
- Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP), F-75005, Paris, France.
| | - Elie Wandersman
- Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP), F-75005, Paris, France.
| | - Thibault Bertrand
- Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
| | - Alexis Michel Prevost
- Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP), F-75005, Paris, France.
| | - Lea-Laetitia Pontani
- Sorbonne Université, CNRS, Institut de Biologie Paris-Seine (IBPS), Laboratoire Jean Perrin (LJP), F-75005, Paris, France.
| |
Collapse
|
17
|
VanderWerf K, Boromand A, Shattuck MD, O'Hern CS. Pressure Dependent Shear Response of Jammed Packings of Frictionless Spherical Particles. PHYSICAL REVIEW LETTERS 2020; 124:038004. [PMID: 32031840 PMCID: PMC9128574 DOI: 10.1103/physrevlett.124.038004] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/25/2019] [Indexed: 05/09/2023]
Abstract
The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure p, the ensemble-averaged static shear modulus ⟨G-G_{0}⟩ scales with p^{α}, where α≈1, but above a characteristic pressure p^{**}, ⟨G-G_{0}⟩∼p^{β}, where β≈0.5. However, we find that the shear modulus G^{i} for an individual packing typically decreases linearly with p along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, ⟨G⟩ also depends on a contribution from discontinuous jumps in ⟨G⟩ that occur at the transitions between geometrical families. For p>p^{**}, geometrical-family and rearrangement contributions to ⟨G⟩ are of opposite signs and remain comparable for all system sizes. ⟨G⟩ can be described by a scaling function that smoothly transitions between two power-law exponents α and β. We also demonstrate the phenomenon of compression unjamming, where a jammed packing unjams via isotropic compression.
Collapse
Affiliation(s)
- Kyle VanderWerf
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Arman Boromand
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
| | - Mark D Shattuck
- Benjamin Levich Institute and Physics Department, The City College of New York, New York, New York 10031, USA
| | - Corey S O'Hern
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Mechanical Engineering & Materials Science, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| |
Collapse
|