The compressibility of foamy sands

The compressibility of a two-dimensional dispersion of solids, liquid and bubbles, stabilized by surfactant and of size comparable with the solids, is calculated. For sufficiently small solids and bubbles, the capillarity significantly alters the compressibility from that for the same volume of ideal gas and for a dispersion of bubbles of the same size without solid present. There is a second-order phase transition at the point where the bubbles touch each other between the solid particles.