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Kopecz-Muller C, Bertin V, Raphaël E, McGraw JD, Salez T. Mechanical response of a thick poroelastic gel in contactless colloidal-probe rheology. Proc Math Phys Eng Sci 2023. [DOI: 10.1098/rspa.2022.0832] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/10/2023] Open
Abstract
When a rigid object approaches a soft material in a viscous fluid, hydrodynamic stresses arise in the lubricated contact region and deform the soft material. The elastic deformation modifies in turn the flow, hence generating a soft-lubrication coupling. Moreover, soft elastomers and gels are often porous. These materials may be filled with solvent or uncrosslinked polymer chains, and might be permeable to the surrounding fluid, which further complexifies the description. Here, we derive the point-force response of a semi-infinite and permeable poroelastic substrate. Then, we use this fundamental solution in order to address the specific poroelastic lubrication coupling associated with contactless colloidal-probe methods. In particular, we derive the conservative and dissipative components of the force associated with the oscillating vertical motion of a sphere close to the poroelastic substrate. Our results may be relevant for dynamic surface force apparatus and contactless colloidal-probe atomic force microscopy experiments on soft, living and/or fragile materials, such as swollen hydrogels and biological membranes.
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Affiliation(s)
- Caroline Kopecz-Muller
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400 Talence, France
- Gulliver, CNRS UMR 7083, ESPCI Paris, Université PSL, 75005 Paris, France
- Institut Pierre-Gilles de Gennes, ESPCI Paris, Université PSL, 75005 Paris, France
| | - Vincent Bertin
- Physics of Fluids, Faculty of Sciences and Technology, University of Twente, 7500AE Enschede, The Netherlands
| | - Elie Raphaël
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400 Talence, France
| | - Joshua D. McGraw
- Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33400 Talence, France
- Gulliver, CNRS UMR 7083, ESPCI Paris, Université PSL, 75005 Paris, France
| | - Thomas Salez
- Institut Pierre-Gilles de Gennes, ESPCI Paris, Université PSL, 75005 Paris, France
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Liu Z, Hui CY, Jagota A, Gong JP, Kiyama R. A surface flattening method for characterizing the surface stress, drained Poisson's ratio and diffusivity of poroelastic gels. SOFT MATTER 2021; 17:7332-7340. [PMID: 34286785 DOI: 10.1039/d1sm00513h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
When a poroelastic gel is released from a patterned mold, surface stress drives deformation and solvent migration in the gel and flattens its surface profile in a time-dependent manner. Specifically, the gel behaves like an incompressible solid immediately after removal from the mold, and becomes compressible as the solvent is able to squeeze out of the polymer network. In this work, we use the finite element method (FEM) to simulate this transient surface flattening process. We assume that the surface stress is isotropic and constant, the polymer network is linearly elastic and isotropic, and that solvent flow obeys Darcy's law. The short-time and long-time surface profiles can be used to determine the surface stress and drained Poisson's ratio of the gel. Our analysis shows that the drained Poisson's ratio and the diffusivity of the gel can be obtained using interferometry and high-speed video microscopy, without mechanical measurement.
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Affiliation(s)
- Zezhou Liu
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.
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Hui CY, Liu Z, Bain N, Jagota A, Dufresne ER, Style RW, Kiyama R, Gong JP. How surface stress transforms surface profiles and adhesion of rough elastic bodies. Proc Math Phys Eng Sci 2020; 476:20200477. [PMID: 33362416 DOI: 10.1098/rspa.2020.0477] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Accepted: 10/06/2020] [Indexed: 01/07/2023] Open
Abstract
The surface of soft solids carries a surface stress that tends to flatten surface profiles. For example, surface features on a soft solid, fabricated by moulding against a stiff-patterned substrate, tend to flatten upon removal from the mould. In this work, we derive a transfer function in an explicit form that, given any initial surface profile, shows how to compute the shape of the corresponding flattened profile. We provide analytical results for several applications including flattening of one-dimensional and two-dimensional periodic structures, qualitative changes to the surface roughness spectrum, and how that strongly influences adhesion.
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Affiliation(s)
- Chung-Yuen Hui
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA.,Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan
| | - Zezhou Liu
- Field of Theoretical and Applied Mechanics, Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
| | - Nicolas Bain
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Anand Jagota
- Departments of Bioengineering and of Chemical and Biomolecular Engineering, Lehigh University, 111 Research Drive, Bethlehem, PA 18015, USA
| | - Eric R Dufresne
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Robert W Style
- Laboratory of Soft and Living Materials, Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
| | - Ryuji Kiyama
- Graduate School of Life Science, Hokkaido University, Sapporo 001-0021, Japan
| | - Jian Ping Gong
- Global Station for Soft Matter, GI-CoRE, Hokkaido University, Sapporo, Japan.,Faculty of Advanced Life Science, Hokkaido University, Sapporo 001-0021, Japan.,WPI-ICReDD, Hokkaido University, Sapporo 001-0021, Japan
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