Bendocapillary Instability of Liquid in a Flexible-Walled Channel

TL;DR

This paper investigates the bendocapillary instability in flexible-walled microchannels, revealing how liquid volume and wetting properties influence instability growth, with implications for microfabrication processes.

Contribution

The study develops a mathematical model combining numerical and asymptotic analysis to characterize bendocapillary instability in deformable channels, highlighting conditions for instability onset.

Findings

Configurations are always unstable to small-wavenumber perturbations.

Instability growth rate depends strongly on liquid volume.

Both wetting and non-wetting states are susceptible to instability.

Abstract

We study the bendocapillary instability of a liquid droplet that part fills a flexible walled channel. Inspired by experiments in which a `weaving' pattern emerges as droplets of liquid are condensed slowly into deformable microchannels, we develop a mathematical model of this instability. We describe equilibria of the system, and use a combination of numerical methods, and asymptotic analysis in the limit of small channel wall deflections, to elucidate the key features of this instability. We find that configurations are always unstable to perturbations of sufficiently small wavenumber, that the growth rate of the instability is highly sensitive to the volume of liquid in the channel, and that both wetting and non-wetting configurations are susceptible to the instability in the same channel. Insight into novel interfacial instabilities opens the possibility for their control and thus exploitation in processes such as microfabrication.