Flow of liquid foams in two-dimensional porous media

We study experimentally flows of foam in model two-dimensional porous media, where we use image analysis to quantify flow profiles and bubble size (side length a) [1]. In such confined foam flows, viscous dissipation mostly arises from the contact zones between the soap films and the walls, which gives very peculiar friction laws. In particular, foams potentially invade narrow pores much more efficiently than Newtonian fluids, which is of potential importance for enhanced oil recovery.
We first quantify the velocity (or flux) ratio between two parallel straight channels of different width b (Fig. 1, left). We show that as long as b > 3a, the two velocities are equal. In narrower channels, the foam structure is modified, which has a strong influence on the velocity. In particular, when b < a, we have a “bamboo foam” (train of films perpendicular to the channel) which can be either unfavourable or favourable depending on the ratio between b and the distance between the films. We show that another effect controlling the velocity in a narrow channel is the capillary pressure that a film has to overcome when exiting a narrow channel. We rationalise our findings in a model and propose predictions of the velocity ratio as a function of the width of the two channels [2]. Next, we show that in a convergent and a divergent channel in parallel (Fig. 1, middle), there is a coupling between the elastic stress and the dissipation in the foam, favouring the flux in the convergent channel even if the foam is not highly confined [3].
Second, we study foam flowing through a series of circular obstacles (Fig. 1, right). We show that the flow is highly intermittent, and that the bubble size distribution evolve along the porous medium by a series of fragmentation events. We study this process in details experimentally, theoretically, and numerically.

[1] B. Dollet, F. Graner, J. Fluid Mech. 585, 181 (2007).
[2] S. A. Jones, B. Dollet, Y. Méheust, S. J. Cox, I. Cantat, Phys. Fluids 25, 063101 (2013).
[3] B. Dollet, S. A. Jones, Y. Méheust, I. Cantat, Phys. Rev. E 90, 023006 (2014).