Elastocapillary instability under partial wetting conditions: bending versus buckling

TL;DR

This paper theoretically analyzes elastocapillary instability of a flexible plate in a liquid bath, revealing two distinct destabilizing mechanisms—bending and buckling—dependent on contact angle and capillary forces.

Contribution

It identifies and characterizes two separate elastocapillary instability mechanisms under partial wetting, providing analytical conditions for their onset.

Findings

Buckling occurs for contact angles greater than π/2.

Bending mechanism induces instability for all contact angles greater than zero.

Two dimensionless parameters govern the stability and bifurcation scenarios.

Abstract

The elastocapillary instability of a flexible plate plunged in a liquid bath is analysed theoretically. We show that the plate can bend due to two separate destabilizing mechanisms, when the liquid is partially wetting the solid. For contact angles $\theta_e > \pi/2$, the capillary forces acting tangential to the surface are compressing the plate and can induce a classical buckling instability. However, a second mechanism appears due to capillary forces normal to surface. These induce a destabilizing torque that tends to bend the plate for any value of the contact angle $\theta_e > 0$. We denote these mechanisms as "buckling" and "bending" respectively and identify the two corresponding dimensionless parameters that govern the elastocapillary stability. The onset of instability is determined analytically and the different bifurcation scenarios are worked out for experimentally relevant conditions.