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.