Response of a two-dimensional liquid foam to air injection: Influence of surfactants, critical velocities and branched fracture

Abstract

Experiments where air is injected into a foam confined in a Hele-Shaw cell are convenient to study the rheology of foams far from the quasistatic regime, and their limit of stability. At low overpressure, the injected air forms a ductile crack, whereas at high overpressure, it breaks the foam like a brittle material. We present new results in this configuration, complementary with previous studies. We show that air injection is slowed down for surfactants giving incompressible interfaces instead of mobile ones. The injection rate is quantitatively captured by a simple model balancing the air overpressure with known foam/wall friction laws for incompressible interfaces. We also revisit the critical velocity criteria for the injected air proposed by Arif et al. [1]. The upper bound of velocity in the ductile regime, based on the resistance of soap films against wall friction, is shown to hold much better for mobile than for incompressible interfaces. The propagation speed of shear waves is confirmed to be a good lower bound for the velocity in the brittle regime, provided the motion of all liquid within the foam is accounted for. Finally, a short description of branching in the fragile regime is given.

Microstructural effects in aqueous foam fracture

“…The versatility and generality of our model allows for a detailed discussion of the role of microstructure and defects in brittle and ductile fracture, which will be the focus of a future publication, including a systematic study of defect orientation and density. In addition, this model allows examination of the role of interfacial boundary conditions in the propagation and suppression of fracture, as investigated experimentally by Ben Salem et al (2013a) in a slightly different geometry, where they found that incompressible interfaces results in significantly slower propagation and fracture of the foam compared to mobile interfaces. Such studies will be of use not just as a general model system for crack propagation in heterogeneous media, but directly for applications where film breakage and fracture of foam are crucial phenomena, such as foam flotation or secondary oil recovery.…”

Characterization of foam flowing in a granular medium in the presence of oil by small angle neutron scattering

“…When the foam is generated, an important increase of the pressure gradient is observed, resulting from the increase of effective gas viscosity and a IFP Energies nouvelles, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison, France * E-mail: raphael.poryles@yahoo.fr and loic.barre@ifpen.fr the decrease of relative permeability leading to a reduced mobility factor 8,11,12 . Many studies have been performed in quasi 2D Hele-Shaw cells and micromodels to observe the dynamics of the foam flow at the bubble scale [13][14][15][16][17][18][19][20] . Those experiments have shown many results including that bubbles can be trapped inside a single pore and that fragmentation and coalescence processes can occur.…”

Foam trapping in a 3D porous medium: in situ observations by ultra-fast X-ray microtomography

“…In order to understand and improve the efficiency of such foam flows, studies have been performed in a 2D Hele-Shaw cell, to observe the dynamics of the bubbles at the pore scale [11][12][13][14][15][16][17][18][19] . Micromodels experiments have shown mechanisms such as bubble trapping, fragmentation and coalescence 11,12,16,19 . The trapping can be localized in a single pore or at the scale of inter connected pores 13,14 .…”