Capillary imbibition in a diverging flexible channel

TL;DR

This study investigates how the flexibility and initial tilt of diverging sheets affect capillary imbibition, revealing that elasticity can enhance liquid spreading and identifying optimal conditions for fastest filling.

Contribution

It demonstrates that elasticity in diverging sheets can reverse traditional imbibition speed trends and introduces a scaling law for filling time near collapse thresholds.

Findings

Flexible diverging sheets can prevent collapse and improve imbibition speed.

An optimal tilt angle exists that minimizes filling time.

Elasticity reverses the slower imbibition trend of rigid diverging plates.

Abstract

We study the imbibition of a wetting liquid between flexible sheets that are fixed on both ends. Assuming a narrow gap between the sheets, we solve the lubrication equation coupled with slender body deformation. When the sheets are parallel, we find that the deformation initially speeds up the flow, as shown in previous studies, but only up to the middle of the channel. As the channel contracts, the hydrodynamic resistance increases and ultimately slows down the filling process. Below a threshold stiffness, the channel collapses and imbibition stops. We propose a scaling of the filling duration near this threshold. Next we show that if the sheets are initially tilted with a minimal angle, the channel avoids collapse. The liquid front pulls the diverging sheets and spreads in a nearly parallel portion, which maintains the capillary propulsion and enhances the wicking. Therefore, while it is established that diverging rigid plates imbibe liquids slower than parallel ones, we show that elasticity reverses this principle: diverging flexible sheets imbibe liquids faster than parallel ones. We find an optimal tilt angle that gives the shortest filling time.