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Molefe L, Kolinski JM. Elastocapillary menisci mediate interaction of neighboring structures at the surface of a compliant solid. Phys Rev E 2023; 108:L043001. [PMID: 37978591 DOI: 10.1103/physreve.108.l043001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 08/25/2023] [Indexed: 11/19/2023]
Abstract
Surface stress drives long-range elastocapillary interactions at the surface of compliant solids, where it has been observed to mediate interparticle interactions and to alter transport of liquid drops. We show that such an elastocapillary interaction arises between neighboring structures that are simply protrusions of the compliant solid. For compliant micropillars arranged in a square lattice with spacing p less than an interaction distance p^{*}, the distance of a pillar to its neighbors determines how much it deforms due to surface stress: Pillars that are close together tend to be rounder and flatter than those that are far apart. The interaction is mediated by the formation of an elastocapillary meniscus at the base of each pillar, which sets the interaction distance and causes neighboring structures to deform more than those that are relatively isolated. Neighboring pillars also displace toward each other to form clusters, leading to the emergence of pattern formation and ordered domains.
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Affiliation(s)
- Lebo Molefe
- Institute of Mechanical Engineering (IGM), School of Engineering (STI), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
| | - John M Kolinski
- Institute of Mechanical Engineering (IGM), School of Engineering (STI), Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
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Pandey A, Kansal M, Herrada MA, Eggers J, Snoeijer JH. Elastic Rayleigh-Plateau instability: dynamical selection of nonlinear states. SOFT MATTER 2021; 17:5148-5161. [PMID: 33950047 DOI: 10.1039/d0sm02195d] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A slender thread of elastic hydrogel is susceptible to a surface instability that is reminiscent of the classical Rayleigh-Plateau instability of liquid jets. The final, highly nonlinear states that are observed in experiments arise from a competition between capillarity and large elastic deformations. Combining a slender analysis and fully three-dimensional numerical simulations, we present the phase map of all possible morphologies for an unstable neo-Hookean cylinder subjected to capillary forces. Interestingly, for softer cylinders we find the coexistence of two distinct configurations, namely, cylinders-on-a-string and beads-on-a-string. It is shown that for a given set of parameters, the final pattern is selected via a dynamical evolution. To capture this, we compute the dispersion relation and determine the characteristic wavelength of the dynamically selected profiles. The validity of the "slender" results is confirmed via simulations and these results are consistent with experiments on elastic and viscoelastic threads.
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Affiliation(s)
- Anupam Pandey
- Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
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Pandey A, Nawijn CL, Snoeijer JH. Hydrogel menisci: Shape, interaction, and instability. ACTA ACUST UNITED AC 2018. [DOI: 10.1209/0295-5075/122/36006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Chakrabarti A, Porat A, Raphaël E, Salez T, Chaudhury MK. Elastowetting of Soft Hydrogel Spheres. LANGMUIR 2018; 34:3894-3900. [DOI: 10.1021/acs.langmuir.8b00368] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
Affiliation(s)
- Aditi Chakrabarti
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
| | - Amir Porat
- Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, Paris, France
| | - Elie Raphaël
- Laboratoire de Physico-Chimie Théorique, UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, Paris, France
| | - Thomas Salez
- CNRS, LOMA, UMR 5798, Univ. Bordeaux, F-33405 Talence, France
- Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan
| | - Manoj K. Chaudhury
- Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, Pennsylvania 18015, United States
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Pandey A, Karpitschka S, Lubbers LA, Weijs JH, Botto L, Das S, Andreotti B, Snoeijer JH. Dynamical theory of the inverted cheerios effect. SOFT MATTER 2017; 13:6000-6010. [PMID: 28776051 DOI: 10.1039/c7sm00690j] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Recent experiments have shown that liquid drops on highly deformable substrates exhibit mutual interactions. This is similar to the Cheerios effect, the capillary interaction of solid particles at a liquid interface, but now the roles of solid and liquid are reversed. Here we present a dynamical theory for this inverted Cheerios effect, taking into account elasticity, capillarity and the viscoelastic rheology of the substrate. We compute the velocity at which droplets attract, or repel, as a function of their separation. The theory is compared to a simplified model in which the viscoelastic dissipation is treated as a localized force at the contact line. It is found that the two models differ only at small separation between the droplets, and both of them accurately describe experimental observations.
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Affiliation(s)
- Anupam Pandey
- Physics of Fluids Group, Faculty of Science and Technology, University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands.
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Chakrabarti A, Chaudhury MK, Mora S, Pomeau Y. Elastobuoyant Heavy Spheres: A Unique Way to Study Nonlinear Elasticity. PHYSICAL REVIEW X 2016; 6:041066. [DOI: 10.1103/physrevx.6.041066] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
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Abstract
Solid particles floating at a liquid interface exhibit a long-ranged attraction mediated by surface tension. In the absence of bulk elasticity, this is the dominant lateral interaction of mechanical origin. Here, we show that an analogous long-range interaction occurs between adjacent droplets on solid substrates, which crucially relies on a combination of capillarity and bulk elasticity. We experimentally observe the interaction between droplets on soft gels and provide a theoretical framework that quantitatively predicts the interaction force between the droplets. Remarkably, we find that, although on thick substrates the interaction is purely attractive and leads to drop-drop coalescence, for relatively thin substrates a short-range repulsion occurs, which prevents the two drops from coming into direct contact. This versatile interaction is the liquid-on-solid analog of the "Cheerios effect." The effect will strongly influence the condensation and coarsening of drops on soft polymer films, and has potential implications for colloidal assembly and mechanobiology.
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Chakrabarti A, Ryan L, Chaudhury MK, Mahadevan L. Elastic Cheerios effect: Self-assembly of cylinders on a soft solid. EPL (EUROPHYSICS LETTERS) 2015; 112:54001. [DOI: 10.1209/0295-5075/112/54001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
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Liu T, Jagota A, Hui CY. Adhesive contact of a rigid circular cylinder to a soft elastic substrate--the role of surface tension. SOFT MATTER 2015; 11:3844-3851. [PMID: 25857676 DOI: 10.1039/c5sm00008d] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This article studies the effects of surface tension on the adhesive contact mechanics of a long rigid cylinder on an infinite half space comprising an incompressible elastic material. We present an exact solution based on small strain theory. The relationship between the indentation force and contact width was found to depend on a single dimensionless parameter ω = σ/[4(μR)(2/3)(W(ad)/2π)(1/3'), where R is the cylinder radius, Wad is the interfacial work of adhesion, and σ and μ are the surface tension and shear modulus of the half space, respectively. For small ω the solution reduces to the classical Johnson-Kendall-Roberts (JKR) theory, whereas for large ω the solution reduces to the small slope version of the Young-Dupre equation. The pull-off phenomenon was carefully examined and it was found that the contact width at pull-off reduces to zero when surface tension is larger than a critical value.
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Affiliation(s)
- Tianshu Liu
- Field of Theoretical & Applied Mechanics, Dept. of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
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Chinomona R, Lajeunesse J, Mitchell WH, Yao Y, Spagnolie SE. Stability and dynamics of magnetocapillary interactions. SOFT MATTER 2015; 11:1828-1838. [PMID: 25611298 DOI: 10.1039/c4sm02189d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9, 2420]. Dynamic activity arises from a periodically induced dipole-dipole repulsion between the beads acting in concert with capillary attraction. We investigate analytically and numerically the stability and dynamics of this magnetocapillary swimming, and explore other related topics including the steady and periodic equilibrium configurations of two and three beads, and bead collisions. The swimming speed and system stability depend on a dimensionless measure of the relative repulsive and attractive forces which we term the magnetocapillary number. An oscillatory magnetic field may stabilize an otherwise unstable collinear configuration, and striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound micro-particles.
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Affiliation(s)
- Rujeko Chinomona
- Department of Computational and Applied Mathematics, Rice University, 6100 Main MS-134, Houston, TX 77005, USA
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Chakrabarti A, Chaudhury MK. Attraction of mesoscale objects on the surface of a thin elastic film supported on a liquid. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2015; 31:1911-1920. [PMID: 25069091 DOI: 10.1021/la502236r] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
We study the interaction of two parallel rigid cylinders on the surface of a thin elastic film supported on a pool of liquid. The excess energy of the surface due to the curvature of the stretched film induces attraction of the cylinders that can be quantified by the variation of their gravitational potential energies as they descend into the liquid while still floating on the film. Although the experimental results follow the trend predicted from the balance of the gravitational and elastic energies of the system, they are somewhat underestimated. The origin of this discrepancy is the hysteresis of adhesion between the cylinder and the elastic film that does not allow the conversion of the total available energy into gravitational potential energy, as some part of it is recovered in stretching the film behind the cylinders while they approach each other. A modification of the model accounting for the effects of adhesion hysteresis improves the agreement between theoretical and experimental results. The contribution of the adhesion hysteresis can be reduced considerably by introducing a thin hydrogel layer atop the elastic film that enhances the range of attraction of the cylinders (as well as rigid spheres) in a dramatic way. Morphological instabilities in the gel project corrugated paths to the motion of small spheres, thus leading to a large numbers of particles to aggregate along their defects. These observations suggest that a thin hydrogel layer supported on a deformable elastic film affords an effective model system to study elasticity and defects mediated interaction of particles on its surface.
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Affiliation(s)
- Aditi Chakrabarti
- Department of Chemical Engineering Lehigh University , Bethlehem, Pennsylvania 18015, United States
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Chakrabarti A, Chaudhury MK. Vibrations of sessile drops of soft hydrogels. EXTREME MECHANICS LETTERS 2014; 1:47-53. [DOI: 10.1016/j.eml.2014.12.002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
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