Partial wetting of thin solid sheets under tension

TL;DR

This paper analyzes how liquid droplets on thin elastic sheets under tension can significantly alter local stress states, especially when the tension is weak compared to an intrinsic elasto-capillary scale, challenging previous assumptions about tension measurement.

Contribution

It provides a detailed analysis using Föppl-von-Kármán equations to identify a non-perturbative regime where wetting significantly affects sheet stress, revealing limitations in current tension measurement methods.

Findings

Presence of a non-perturbative regime in wetting of thin sheets.

Measurement of contact-line tension may not reflect true pre-wetting tension.

Recent experiments may operate within this non-perturbative regime.

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 F\"{o}ppl-von-K\'{a}rm\'{a}n 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 $\gamma^{2/3}(Et)^{1/3}$ (with $\gamma$ 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.