Permeability of a bubble assembly: From the very dry to the wet limit

Abstract

Bubble assemblies offer the remarkable property of adjusting their packing fraction over three orders of magnitude, thus providing an interesting system for the study of liquid flows through granular matter. Although significant work has been done in several fields of research, e.g., foams, porous media, and suspensions, a complete set of data over such a wide range of porosity ε is still lacking. In this paper, we measure the permeability of a bubbly system in the range 0.1<ε<0.8 and we connect these new data with a recently published set obtained for foams corresponding to ε<0.2 [E. Lorenceau et al., Eur. Phys. J. E 28, 293 (2009)]. Moreover, measurements performed with two different surfactants, the so-called “mobile” and “nonmobile” interfaces, allow us to determine the influence of the bubbles’ surface mobility, which is proved to be a significant parameter up to ε≈0.6, thus well above the bubbles packing fraction. Above ε≈0.6, surface elasticity is fully mobilized over the bubbles’ surface and the behavior of rigid spheres is observed for both solutions. We show that all the permeability values obtained for the bubble assembly with “nonmobile” interfaces are properly described with the Carman–Kozeny model.