Liquid-liquid capillary replacement in a horizontal geometry: universal dynamics and replacement time

TL;DR

This study investigates the dynamics of liquid-liquid capillary replacement in a horizontal tube, revealing three distinct viscous regimes and providing a unified theoretical framework that accurately predicts replacement times.

Contribution

It introduces a comprehensive theory for viscous capillary replacement in horizontal geometries, capturing multiple dynamic regimes and validating them experimentally.

Findings

Identified three viscous regimes: slowing-down, accelerating, and linear dynamics.

Developed a unified theoretical model explaining all observed regimes.

Experimentally confirmed the theory's accuracy in predicting replacement times.

Abstract

Capillary invasion of a liquid into an empty tube, which is called capillary rise when the tube axis is in the vertical direction, is one of the fundamental phenomena representing capillary effects. Usually, the tube is actually filled with another pre-existing fluid, air, whose viscosity and inertia can be practically neglected. In this study, we considered the effect of the pre-existing fluid, when its viscosity is non-negligible, in a horizontally geometry. This geometry is free from gravity and thus simpler than the geometry of capillary rise. We observed the dynamics when a capillary tube that is submerged horizontally in a liquid gets in contact with a second liquid. An appropriate combination of liquids allowed us to observe that the second liquid replaces the first without any prewetting process, thanks to a careful cleaning of capillary tubes. Furthermore, we experimentally observed three distinct viscous dynamics: (i) the conventional slowing-down dynamics, (ii) an unusual accelerating dynamics, and (iii) another unusual dynamics, which is linear in time. We developed a theory in viscous regimes, which accounts well for the observations through a unified expression describing the three distinct dynamics. We also demonstrated a thorough experimental confirmation on the initial velocity of the replacement. We further focused on the replacement time, the time required for the invading fluid to replaces completely the pre-existing fluid in the horizontal geometry, which is again well explained by the theory.