Three-dimensional aspects of fluid flows in channels. I. Meniscus and Thin Film regimes

TL;DR

This study investigates the dynamics of fluid-fluid interfaces in three-dimensional channels, focusing on the transition between meniscus and thin film regimes influenced by capillary and Peclet numbers, using Lattice-Boltzmann simulations.

Contribution

It introduces a detailed numerical analysis of interface displacement regimes in 3D channels, highlighting the effects of slip velocity, capillary number, and viscosity contrast on interface morphology.

Findings

Transition from meniscus to thin film controlled by capillary and Peclet numbers.

Narrow fingers observed at zero viscosity contrast.

Universal shape of the advancing finger.

Abstract

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a Lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Peclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, Lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.