Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion.
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| Title: | Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion. |
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| Authors: | Chung-Yuen Hui1 ch45@cornell.edu, Tianshu Liu1, Salez, Thomas2, Raphael, Elie3, Jagota, Anand4 |
| Source: | Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. 3/8/2015, Vol. 471 Issue 2175, p1-16. 16p. |
| Subjects: | Surface tension, Contact mechanics, Adhesion, Elasticity, Geometric rigidity, Indentation (Materials science) |
| Abstract: | The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: ω =s(µR)-2/3((9p/4)Wad)-1/3, where s and µ are the surface tension and shear modulus of the substrate, R is the sphere radius and Wad is the interfacial work of adhesion. Our theory reduces to the Johnson-Kendall-Roberts (JKR) theory and Young-Dupre equation in the limits of small and large ω, respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by onethird compared with the JKR limit and the pull-off behaviour is completely determined by ω. [ABSTRACT FROM AUTHOR] |
| Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 108308494 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chung-Yuen+Hui%22">Chung-Yuen Hui</searchLink><relatesTo>1</relatesTo><i> ch45@cornell.edu</i><br /><searchLink fieldCode="AR" term="%22Tianshu+Liu%22">Tianshu Liu</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Salez%2C+Thomas%22">Salez, Thomas</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Raphael%2C+Elie%22">Raphael, Elie</searchLink><relatesTo>3</relatesTo><br /><searchLink fieldCode="AR" term="%22Jagota%2C+Anand%22">Jagota, Anand</searchLink><relatesTo>4</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+Royal+Society+A%3A+Mathematical%2C+Physical+%26+Engineering+Sciences%22">Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences</searchLink>. 3/8/2015, Vol. 471 Issue 2175, p1-16. 16p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Surface+tension%22">Surface tension</searchLink><br /><searchLink fieldCode="DE" term="%22Contact+mechanics%22">Contact mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Adhesion%22">Adhesion</searchLink><br /><searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+rigidity%22">Geometric rigidity</searchLink><br /><searchLink fieldCode="DE" term="%22Indentation+%28Materials+science%29%22">Indentation (Materials science)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The surface tension of compliant materials such as gels provides resistance to deformation in addition to and sometimes surpassing that owing to elasticity. This paper studies how surface tension changes the contact mechanics of a small hard sphere indenting a soft elastic substrate. Previous studies have examined the special case where the external load is zero, so contact is driven by adhesion alone. Here, we tackle the much more complicated problem where, in addition to adhesion, deformation is driven by an indentation force. We present an exact solution based on small strain theory. The relation between indentation force (displacement) and contact radius is found to depend on a single dimensionless parameter: ω =s(µR)-2/3((9p/4)Wad)-1/3, where s and µ are the surface tension and shear modulus of the substrate, R is the sphere radius and Wad is the interfacial work of adhesion. Our theory reduces to the Johnson-Kendall-Roberts (JKR) theory and Young-Dupre equation in the limits of small and large ω, respectively, and compares well with existing experimental data. Our results show that, although surface tension can significantly affect the indentation force, the magnitude of the pull-off load in the partial wetting liquid-like limit is reduced only by onethird compared with the JKR limit and the pull-off behaviour is completely determined by ω. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1098/rspa.2014.0727 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 1 Subjects: – SubjectFull: Surface tension Type: general – SubjectFull: Contact mechanics Type: general – SubjectFull: Adhesion Type: general – SubjectFull: Elasticity Type: general – SubjectFull: Geometric rigidity Type: general – SubjectFull: Indentation (Materials science) Type: general Titles: – TitleFull: Indentation of a rigid sphere into an elastic substrate with surface tension and adhesion. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chung-Yuen Hui – PersonEntity: Name: NameFull: Tianshu Liu – PersonEntity: Name: NameFull: Salez, Thomas – PersonEntity: Name: NameFull: Raphael, Elie – PersonEntity: Name: NameFull: Jagota, Anand IsPartOfRelationships: – BibEntity: Dates: – D: 08 M: 03 Text: 3/8/2015 Type: published Y: 2015 Identifiers: – Type: issn-print Value: 13645021 Numbering: – Type: volume Value: 471 – Type: issue Value: 2175 Titles: – TitleFull: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences Type: main |
| ResultId | 1 |
