The bending of an elastic beam by a liquid drop: A variational approach

TL;DR

This paper investigates how a liquid drop causes an elastic beam to bend, using a variational approach to derive equilibrium equations that account for gravity, contact line pinning, and forces at the triple line.

Contribution

It introduces a variational method to derive equilibrium equations for liquid-elastic beam interactions, including effects of gravity and contact line pinning.

Findings

Equilibrium equations reveal external forces on the beam from liquid and vapor phases.

Force at the triple line aligns with the liquid-vapor interface.

The approach clarifies the force distribution at the contact line.

Abstract

We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or absence of contact line pinning. We show that the derived equilibrium equations for the beam subsystem reveal the external forces applied on the beam by the liquid and vapor phases. Among these, the force applied at the triple line (the curve where the three phases meet) is found to lie along the liquid-vapor interface.