Three-dimensional aspects of fluid flows in channels. II. Effects of Meniscus and Thin Film regimes on Viscous Fingers

TL;DR

This study uses a 3D lattice-Boltzmann approach to analyze viscous fingers in channels, revealing how meniscus and thin film regimes influence finger shape and deviations from 2D predictions.

Contribution

It introduces a 3D simulation framework to explore the effects of channel thickness and thin films on viscous finger development, extending previous 2D analyses.

Findings

Steady state fingers are effectively 2D with curved meniscus effects.

Thin films cause finger narrowing with increased aspect ratio.

Deviations from 2D predictions occur when thin films are present.

Abstract

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional Lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Secondly, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.