Partial wetting of thin solid sheets under tension

Abstract

We consider the equilibrium of liquid droplets sitting on thin elastic sheets that are subject to a boundary tension and/or are clamped at their edge. We use scaling arguments, together with a detailed analysis based on the Föppl-von-Kármán equations, to show that the presence of the droplet may significantly alter the stress locally if the tension in the dry sheet is weak compared to an intrinsic elasto-capillary tension scale $γ^{2/3}(Et)^{1/3}$ (with $γ$ the droplet surface tension, $t$ the sheet thickness and $E$ its Young modulus). Our detailed analysis suggests that some recent experiments may lie in just such a "non-perturbative" regime. As a result, measurements of the tension in the sheet at the contact line (inferred from the contact angles of the sheet with the liquid--vapour interface) do not necessarily reflect the true tension within the sheet prior to wetting. We discuss various characteristics of this non-perturbative regime.

Accepted for publication in Soft Matter