Bubble fragmentation in a 2D foam flowing through a porous medium
Résumé
Foams have been used for decades as displacing fluids for EOR and aquifer remediation, and more recently as carriers of chemical amendments for the remediation of the vadose zone. Apart from various interesting physico-chemical and biochemical properties, foams are better injection fluids due to their low sensitivity to gravity and their peculiar rheology: for foams with bubbles on the order of at least the typical pore size, viscous dissipation arises mostly from the contact zones between the soap films and the walls.In most experimental studies no local information of the foam structure can be obtained, and only global quantities such as the effective viscosity can be measured. In a recent study [1] we investigated foam flows through a two-dimensional porous medium consisting of circular obstacles positioned randomly in a horizontal transparent Hele-Shaw cell. In this experiment we observed bubble fragmentation through lamella division, occurring when bubbles are pinched against obstacles. This phenomenon, observed at the scale of individual bubbles, drastically modifies the bubble size distribution as the foam travels in the porous medium, and, therefore, the rheology of the foam flow. We now present a detailed characterization of this fragmentation process based on experiments, theory and numerical simulations.We measure and characterize the evolution of the bubble size distributions along the porous medium for several flow parameters. The observation of the bubble fragmentation around specific obstacles provides the bubbles fragmentation rates and the fragment size probability density function. These two ingredients and the measurement of the initial bubble size distribution allow modeling the process by a fragmentation equation, which is then solved either analytically (using some simplications) or numerically [2]. The dynamics of the bubble size distribution as inferred from the models is in very good agreement with the experimental data.References :[1] Géraud, B., Jones, S. A., Cantat, I., Dollet, B., & Méheust, Y. (2016). The flow of a foam in a two‐dimensional porous medium, Water Resour. Res. 52, 773–790.[2] B. Géraud, Y. Méheust, I. Canta and B. Dollet (2016). Model fragmentation process in 2D foam flows, submitted.