Skip to Main content Skip to Navigation

Contact lines on soft solids with uniform surface tension: analytical solutions and double transition for increasing deformability

Abstract : Using an exact Green function method, we calculate analytically the substrate deformations near straight contact lines on a soft, incompressible solid, having a uniform surface tension γ s . This generalized Flamant-Cerruti problem of a single contact line is regularized by introducing a finite width 2a for the contact line. We then explore the dependance of the substrate deformations upon the softness ratio l s /a, where l s = γ s /(2µ) is the elastocapillary length built upon γ s and on the elastic shear modulus µ. We discuss the force transmission problem from the liquid surface tension to the bulk and surface of the solid, and show that Neuman condition of surface tension balance at the contact line is only satisfied in the asymptotic limit a/l s → 0, Young condition holding in the opposite limit. We then address the problem of two parallel contact lines separated from a distance 2R, and we recover analytically the "double transition" upon the ratios l s /a and R/l s identified recently by Karpitschka et al, when one increases the substrate deformability. We also establish a simple analytic law ruling the contact angle selection upon R/l s in the limit a/l s ≪ 1, that is the most common situation encountered in problems of wetting on soft materials.
Document type :
Journal articles
Complete list of metadatas

Cited literature [26 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01079623
Contributor : Julien Dervaux <>
Submitted on : Friday, January 9, 2015 - 2:00:07 PM
Last modification on : Friday, March 27, 2020 - 3:08:05 AM
Document(s) archivé(s) le : Friday, April 10, 2015 - 10:06:45 AM

Files

elastomouille-arxiv (1).pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01079623, version 1

Collections

Citation

Julien Dervaux, Laurent Limat. Contact lines on soft solids with uniform surface tension: analytical solutions and double transition for increasing deformability. Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences, Royal Society, The, 2015, 471 (2176), https://doi.org/10.1098/rspa.2014.0813. ⟨hal-01079623⟩

Share

Metrics

Record views

693

Files downloads

645