Equilibrium states of a liquid bridge between flexible sheets

TL;DR

This paper investigates the equilibrium configurations of a liquid drop between flexible sheets, revealing multiple stable states, hysteresis effects, and mechanisms that prevent collapse, with implications for micro-device design.

Contribution

It introduces a comprehensive analysis of liquid bridges between flexible sheets, including classification of equilibria, hysteresis, and collapse prevention mechanisms, extending beyond rigid plate models.

Findings

Multiple equilibrium states exist for liquid drops between flexible sheets.

Hysteresis cycles and abrupt transitions are identified in the solution space.

Flexible sheets can delay or prevent collapse compared to rigid channels.

Abstract

We study equilibrium states of a drop between flexible sheets clamped on both ends. Revisiting first the case of parallel sheets, we find multiple equilibria which we classify in a parameter space. In solution branching diagrams we identify hysteresis cycles and folds indicating abrupt transitions, yet not necessarily leading to channel collapse. Between nonparallel sheets, a drop can stay in equilibrium away from the ends even when the liquid is totally wetting, which is impossible between nonparallel rigid plates. We also show that nonparallel sheets can delay or prevent collapse in comparison to straight channels, suggesting thus a mechanism that protects slender structures inside micro-devices from damage by surface tension.