Impact of Inertia on the Stability of Two-phase Flow: a Pore-doublet Approach

Haine’s jumps, or rheons, occur during drainage in porous media at low capillary number and

are characterised by pinning of the interface at a constriction, before a quick and sudden

invasion of the next pore-body. During the jump, the interface’s speed is two to three orders of

magnitude above the average invasion speed. This raises the question: can inertia, usually

neglected during the invasion, play a role during those jumps? In this presentation, we will

focus on Haines jumps and the potential impact of localized inertial events on two-phase flows

in porous media.

Microfluidic devices, also called micromodels or aquifer-on-chips, are designed to mimic the

porous media and to allow for the direct observation of the fluid flow and interfacial dynamics.

In this work, particular interest is given to pore doublets, whose geometry is composed of two

parallel channels connected together at the inlet and the outlet. Their structure allows us to

reproduce the different regimes that appear during the drainage of a porous medium, as well

as to study the pore’s invasion mechanisms, such as Haine’s jumps.

We developed a pore-doublet model consisting in a set of equations resulting from the

integration of mass and momentum equations. The model accounts for inertia effects.

Simulations are then compared with experiments. The developed model, as well as the

experimental data, allows for a better understanding of the impact of inertia during two-phase flow. We

showed that, even for Reynolds numbers below one, after a jump, the menisci can oscillate

around their stable positions. If these oscillations, caused by the inertia of the fluid, are

important enough, they can help or inhibit the next Haine’s jump, altering the order in which the

pores are invaded. This can turn a stable drainage, where both channels are drained

simultaneously, to an unstable one where one pathway is preferentially invaded over the

other. We show that inertia must be considered when the density ratio or the aspect ratio

between the pore bodies and the constrictions is high.