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Heyden S, Bain N. From a distance: Shuttleworth revisited. SOFT MATTER 2024; 20:5592-5597. [PMID: 38973537 DOI: 10.1039/d4sm00078a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/09/2024]
Abstract
The Shuttleworth equation: a linear stress-strain relation ubiquitously used in modeling the behavior of soft surfaces. Its validity in the realm of materials subject to large deformation is a topic of current debate. Here, we allow for large deformation by deriving the constitutive behavior of the surface from the general framework of finite kinematics. We distinguish cases of finite and infinitesimal surface relaxation preceding an infinitesimal applied deformation. The Shuttleworth equation identifies as the Cauchy stress measure in the fully linearized setting. We show that both in finite and linearized cases, measured elastic constants depend on the utilized stress measure. In addition, we discuss the physical implications of our results and analyze the impact of surface relaxation on the estimation of surface elastic moduli in the light of two different test cases.
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Affiliation(s)
- Stefanie Heyden
- ETH Zürich, Institute for Building Materials, 8093 Zürich, Switzerland.
| | - Nicolas Bain
- Universite Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, UMR5306, F-69100, Villeurbanne, France.
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2
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Wang L, Liu Q. Deformation-dependent gel surface topography due to the elastocapillary and osmocapillary effects. SOFT MATTER 2024; 20:3676-3684. [PMID: 38623818 DOI: 10.1039/d4sm00139g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/17/2024]
Abstract
Actively tuning surface topography is crucial for the design of smart surfaces with stimuli-responsive friction, wetting, and adhesion properties. This paper studies how elastocapillary deformation and osmocapillary phase separation can lead to rich deformation-dependent surface topography in polymeric gels. In a purely elastic material, stretching always flattens the surface due to the Poisson effect. We show that stretching can roughen the surface due to the elastocapillary and osmocapillary effects. The roughening can be tuned by the gel stiffness, the gel osmotic pressure, the deformation mode, and the initial amplitude of surface roughness. The rich deformation-dependent behavior of gel surface topography points to a new direction in designing smart surfaces.
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Affiliation(s)
- Luochang Wang
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15213, USA.
| | - Qihan Liu
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15213, USA.
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3
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Oléron M, Limat L, Dervaux J, Roché M. Morphology and stability of droplets sliding on soft viscoelastic substrates. SOFT MATTER 2024; 20:762-772. [PMID: 38165773 DOI: 10.1039/d3sm01197f] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2024]
Abstract
We show that energy dissipation partition between a liquid and a solid controls the shape and stability of droplets sliding on viscoelastic gels. When both phases dissipate energy equally, droplet dynamics is similar to that on rigid solids. When the solid is the major contributor to dissipation, we observe an apparent contact angle hysteresis of viscoelastic origin. We find excellent agreement between our data and a non-linear model of the wetting of gels of our own that also indicates the presence of significant slip. Our work opens general questions on the dynamics of curved contact lines on compliant substrates.
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Affiliation(s)
- Mathieu Oléron
- Matière et Systèmes Complexes, Université Paris Cité, CNRS UMR 7057, Paris, France.
| | - Laurent Limat
- Matière et Systèmes Complexes, Université Paris Cité, CNRS UMR 7057, Paris, France.
| | - Julien Dervaux
- Matière et Systèmes Complexes, Université Paris Cité, CNRS UMR 7057, Paris, France.
| | - Matthieu Roché
- Matière et Systèmes Complexes, Université Paris Cité, CNRS UMR 7057, Paris, France.
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Zhu J, Yang C, Liu Q. Experimental characterization of elastocapillary and osmocapillary effects on multi-scale gel surface topography. SOFT MATTER 2023; 19:8698-8705. [PMID: 37938918 DOI: 10.1039/d3sm01147j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/10/2023]
Abstract
Surface topography significantly affects various surface properties of polymer gels. Unlike conventional materials where surface topography is largely a geometric property, the surface topography of a polymer gel is governed by the competition between capillary, elastic, and osmotic effects, which leads to complex stimuli-responsive effects. Elastocapillary deformation and osmocapillary phase separation are two phenomena that are known to flatten gel surface topography. Here we experimentally quantify how osmocapillary phase separation affects gel surface topography by fabricating ionogels with multi-scale topography and characterizing the swelling-dependent surface flattening. Our observation confirms the vital role of the osmocapillary length in governing the surface behavior of swollen ionogels. This study provides the first quantitative experimental verification of the osmocapillary phase separation and shows the insufficiency of the previous studies based on elastocapillary deformation alone.
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Affiliation(s)
- Jie Zhu
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15213, USA.
| | - Canhui Yang
- Shenzhen Key Laboratory of Soft Mechanics & Smart Manufacturing, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, P. R. China
| | - Qihan Liu
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA 15213, USA.
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5
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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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Khattak HK, Lu G, Dutcher LA, Brook MA, Dalnoki-Veress K. Preparation of ultra-thin elastomeric films. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2023; 46:33. [PMID: 37171676 DOI: 10.1140/epje/s10189-023-00291-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2023] [Accepted: 04/11/2023] [Indexed: 05/13/2023]
Abstract
When polydimethylsiloxane elastomers are produced, in the absence of great care, chains remain that are unbound to the cross-linked matrix. Due to the unbound chains swelling the crosslinked matrix, these materials are gels. We have developed a simple process to prepare well-controlled elastomeric thin films which do not rely on unknown commercial formulations.
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Affiliation(s)
- Hamza K Khattak
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada
| | - Guanhua Lu
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada
| | - Lauren A Dutcher
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada
| | - Michael A Brook
- Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada
| | - Kari Dalnoki-Veress
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada.
- UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005, Paris, France.
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Henkel C, Essink MH, Hoang T, van Zwieten GJ, van Brummelen EH, Thiele U, Snoeijer JH. Soft wetting with (a)symmetric Shuttleworth effect. Proc Math Phys Eng Sci 2022; 478:20220132. [PMID: 35937429 PMCID: PMC9347665 DOI: 10.1098/rspa.2022.0132] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Accepted: 07/04/2022] [Indexed: 11/12/2022] Open
Abstract
The wetting of soft polymer substrates brings in multiple complexities when compared with the wetting on rigid substrates. The contact angle of the liquid is no longer governed by Young’s Law, but is affected by the substrate’s bulk and surface deformations. On top of that, elastic interfaces exhibit a surface energy that depends on how much they are stretched—a feature known as the Shuttleworth effect (or as surface-elasticity). Here, we present two models through which we explore the wetting of drops in the presence of a strong Shuttleworth effect. The first model is macroscopic in character and consistently accounts for large deformations via a neo-Hookean elasticity. The second model is based on a mesoscopic description of wetting, using a reduced description of the substrate’s elasticity. While the second model is more empirical in terms of the elasticity, it enables a gradient dynamics formulation for soft wetting dynamics. We provide a detailed comparison between the equilibrium states predicted by the two models, from which we deduce robust features of soft wetting in the presence of a strong Shuttleworth effect. Specifically, we show that the (a)symmetry of the Shuttleworth effect between the ‘dry’ and ‘wet’ states governs horizontal deformations in the substrate. Our results are discussed in the light of recent experiments on the wettability of stretched substrates.
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Affiliation(s)
- C. Henkel
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany
| | - M. H. Essink
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, Enschede 7500 AE, The Netherlands
| | - T. Hoang
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, Enschede 7500 AE, The Netherlands
| | | | - E. H. van Brummelen
- Multiscale Engineering Fluid Dynamics Group, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, Eindhoven 5600 MB, The Netherlands
| | - U. Thiele
- Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Str. 9, Münster 48149, Germany
- Center for Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, Münster 48149, Germany
| | - J. H. Snoeijer
- Physics of Fluids Group, Faculty of Science and Technology, Mesa+ Institute, University of Twente, Enschede 7500 AE, The Netherlands
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Khattak HK, Karpitschka S, Snoeijer JH, Dalnoki-Veress K. Direct force measurement of microscopic droplets pulled along soft surfaces. Nat Commun 2022; 13:4436. [PMID: 35907882 PMCID: PMC9338979 DOI: 10.1038/s41467-022-31910-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 07/08/2022] [Indexed: 11/21/2022] Open
Abstract
When a droplet is placed on a soft surface, surface tension deforms the substrate, creating a capillary ridge. We study how the motion of the ridge dissipates energy in microscopic droplets. Using a micropipette based method, we are able to simultaneously image and measure forces on a microscopic droplet moving at a constant speed along a soft film supported on a rigid substrate. Changing the thickness of the thin film tunes the effective stiffness of the substrate. Thus we can control the ridge size without altering the surface chemistry. We find that the dissipation depends strongly on the film thickness, decreasing monotonically as effective stiffness increases. This monotonic trend is beyond the realm of small deformation theory, but can be explained with a simple scaling analysis. Elastic deformation of soft substrates occurs upon wetting, yet it is challenging to follow its dynamics at a microscale. Khattak et al. show that the force required to pull a droplet along a soft surface decreases monotonically as the film thickness decreases and explain the phenomenon using a scaling analysis.
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Affiliation(s)
- Hamza K Khattak
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada
| | - Stefan Karpitschka
- Max Planck Institute for Dynamics and Self-Organization, 37077, Göttingen, Germany
| | - Jacco H Snoeijer
- Physics of Fluids Group, Mesa+ Institute, University of Twente, 7500, AE Enschede, The Netherlands
| | - Kari Dalnoki-Veress
- Department of Physics and Astronomy, McMaster University, 1280 Main Street West, Hamilton, Ontario, L8S 4M1, Canada. .,UMR CNRS Gulliver 7083, ESPCI Paris, PSL Research University, 75005, Paris, France.
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Bain N, Heyden S, Xu Q, Style RW, Dufresne ER. Reply to the 'Comment on "Surface elastic constants of a soft solid"' by E. Gutman, Soft Matter, 2022, 18, DOI: 10.1039/D1SM01412A. SOFT MATTER 2022; 18:4641-4642. [PMID: 35678167 DOI: 10.1039/d2sm00249c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
In response to Gutman's comment, we clarify the derivation of the Shuttleworth equation. In addition, we discuss the findings of our original paper in light of recent theoretical and experimental work on surface elasticity in soft solids.
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Affiliation(s)
- Nicolas Bain
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Stefanie Heyden
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Qin Xu
- Department of Physics, The Hong Kong University of Science and Technology, Hong Kong, China.
| | - Robert W Style
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Eric R Dufresne
- Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
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