Inverse Saffman-Taylor experiments with particles lead to capillarity driven fingering instabilities

TL;DR

This study investigates how particles on the walls of a Hele-Shaw cell induce capillarity-driven fingering instabilities during the inverse Saffman-Taylor experiment, revealing a new instability mechanism at low capillary numbers.

Contribution

It demonstrates that particles on the walls can cause fingering instabilities in the inverse displacement, a phenomenon not observed in the classical case, due to interfacial energy minimization.

Findings

Particles induce fingering at low capillary numbers in inverse displacement.

The instability is driven by interfacial energy minimization involving particles.

Both axisymmetric and rectangular geometries exhibit this phenomenon.

Abstract

Using air to displace a viscous fluid contained in Hele-Shaw cell can create a fingering pattern at the interface between the fluids, if the capillary number exceeds a critical value. This Saffman-Taylor instability is revisited for the inverse case of a viscous fluid displacing air, when partially wettable hydrophilic particles are lying on the walls. Though the inverse case is otherwise stable, the presence of the particles results in a fingering instability at low capillary number. This capillary-driven instability is driven-by the integration of particles into the interface which results from the minimization of the interfacial energy. Both axisymmetric and rectangular geometries are considered in order to quantify this phenomenon.