Rigidity loss transition in a disordered 2D froth

Abstract

Disordered two-dimensional soap froth has been simulated, with a gas fraction \ensuremath{\varphi} less than unity. Upon decreasing \ensuremath{\varphi}, it is found that the system loses its rigidity at ${\mathrm{\ensuremath{\varphi}}}_{\mathit{c}}$=0.84. This value is identified with the dense random packing of hard disks. Results are presented for the variation of yield stress and shear modulus, the latter being tentatively related to elastic-network theory.