Buckling instability of squeezed droplets

TL;DR

This paper investigates the buckling instability of droplets under compression, revealing a critical shape transition at a specific contact angle, with analysis in 2D and 3D, applicable to various surface geometries.

Contribution

It provides a theoretical framework for predicting droplet shape instability under compression, including a criterion for flat surfaces and a detailed stability analysis for non-flat surfaces.

Findings

Shape instability occurs at a critical compression when the apparent contact angle is pi.

Post-critical, droplets transition from symmetric to asymmetric shapes.

Force peaks at the critical point, indicating catastrophic buckling.

Abstract

Motivated by recent experiments, we consider theoretically the compression of droplets pinned at the bottom on a surface of finite area. We show that if the droplet is sufficiently compressed at the top by a surface, it will always develop a shape instability at a critical compression. When the top surface is flat, the shape instability occurs precisely when the apparent contact angle of the droplet at the pinned surface is pi, regardless of the contact angle of the upper surface, reminiscent of past work on liquid bridges and sessile droplets as first observed by Plateau. After the critical compression, the droplet transitions from a symmetric to an asymmetric shape. The force required to deform the droplet peaks at the critical point then progressively decreases indicative of catastrophic buckling. We characterize the transition in droplet shape using illustrative examples in two dimensions followed by perturbative analysis as well as numerical simulation in three dimensions. When the upper surface is not flat, the simple apparent contact angle criterion no longer holds, and a detailed stability analysis is carried out to predict the critical compression.