Capillary Rise in Tubes with Sharp Grooves

TL;DR

This paper investigates the behavior of liquids in sharp-grooved capillaries, revealing a thermodynamic instability that causes a tongue of liquid to rise and analyzing the dynamics and shape of this phenomenon.

Contribution

It provides an analytical description of the equilibrium shape and dynamic behavior of liquid rise in sharp-grooved capillaries, highlighting the role of the opening angle and wetting properties.

Findings

Liquid exhibits a tongue-like rise along the groove.

The rise follows a t^{1/2} law for the meniscus and t^{1/3} for the tongue.

Sharp grooves aid in releasing trapped gas bubbles.

Abstract

Liquid in grooved capillaries, made by e.g. inserting a plate in a cylindrical tube, exhibits unusual spreading and flow properties. One example is capillary rise, where a long, upward tongue on top of the usual meniscus has been observed along the groove. We attribute the underlying mechanism to a thermodynamic instability against spreading for a (partial or complete wetting) liquid in a sharp groove whose opening angle $\alpha$ is less than a critical value $\alpha_c=\pi-2\theta$. The equilibrium shape of the tongue is determined analytically. The dynamics of liquid rising is studied in the viscous regime. When the diameter of the tube is smaller than the capillary length, the center part of the meniscus rises with time $t$ following a $t^{1/2}$-law, while the tongue is truncated at a height which grows following a $t^{1/3}$-law. Sharp groove also facilitates release of gas bubbles trapped inside a capillary under the action of gravity.