Capillary filling with randomly coated walls

TL;DR

This paper investigates how an air-fluid interface moves through a capillary with randomly coated walls, revealing intermittent dynamics and providing methods to predict experimental outcomes.

Contribution

It introduces a model incorporating random capillary forces into the Lucas-Washburn equation, capturing pinning effects and power-law waiting time distributions.

Findings

Pinning probability varies with interface speed.

Distribution of waiting times shows a power-law tail $ au^{-2}$.

Method to predict average interface trajectory and pinning lengths.

Abstract

The motion of an air-fluid interface through an irregularly coated capillary is studied by analysing the Lucas-Washburn equation with a random capillary force. The pinning probability goes from zero to a maximum value, as the interface slows down. Under a critical velocity, the distribution of waiting times $\tau$ displays a power-law tail $\sim \tau^{-2}$ which corresponds to a strongly intermittent dynamics, also observed in experiments. We elaborate a procedure to predict quantities of experimental interest, such as the average interface trajectory and the distribution of pinning lengths.