Capillary imbibition in a square tube

TL;DR

This paper analyzes the capillary imbibition process in a square tube, explicitly coupling the growth of the bulk and finger-like wetting regions, and finds both grow as t^{1/2} but with different coefficients than previous models.

Contribution

It introduces coupled equations for the wetting regions in a square tube, improving upon previous separate analyses by accounting for their interaction.

Findings

Both wetting regions grow as t^{1/2} in time.

The growth coefficients differ from previous models that ignored coupling.

The analysis provides a more accurate description of capillary imbibition in square tubes.

Abstract

When a square tube is brought in contact with bulk liquid, the liquid wets the corners of the tube, and creates finger-like wetted region. The wetting of the liquid then takes place with the growth of two parts, the bulk part where the cross section is entirely filled with the liquid and the finger part where the cross section of the tube is partially filled. In the previous works, the growth of these two parts has been discussed separately. Here we conduct the analysis by explicitly accounting for the coupling of the two parts. We propose coupled equations for the liquid imbibition in both parts and show that (a) the length of each part, $h_0$ and $h_1$, both increases in time $t$ following the Lucas-Washburn's law, $h_0 \sim t^{1/2}$ and $h_1 \sim t^{1/2}$, but that (b) the coefficients are different from those obtained in the previous analysis which ignored the coupling.