Rigidity loss transition in a disordered 2D froth

Abstract

Disordered two-dimensional soap froth has been simulated, with a gas fraction 0 less than unity. Upon decreasing 0, it is found that the system loses its rigidity at 0^ =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.

Statistics and topological changes in 2D foam from the dry to the wet limit

“…This value of ϕ c is consistent with other numerical results for 2D foams [8,18], and experimental [19,20] and numerical [9,21] results for random packings of disks. However, this is a 4 parameter fit.…”

“…Again, Princen may be credited with this finding [10]. This trend was also reproduced in the early simulations of Bolton and Weaire [8] and Hutzler et al [11]. An associated phenomenon was noted, which may be considered to be a third aspect of the critical behaviour associated with the wet limit: it might be termed fragility.…”

“…In the wet limit, the shear modulus goes to zero (smoothly in the case of disordered foams with polydisperse bubble sizes), as was first confirmed from experiments by Princen and Kiss [4] and tentatively identified in the early two-dimensional (2D) PLAT simulation of Bolton and Weaire [5,6,7,8] as well as in the 2D Bubble Model of Durian [9]. Also, the yield stress goes to zero.…”

“…Before proceeding to the analysis of rearrangements we shall present results for various basic quantities of interest, complementing and completing previously published data from PLAT [8,5,6,11,17].…”

“…PLAT [5,6,7,8], as the name suggests, is a software package for the simulation of a foam in 2D based on the direct implementation of Plateau's Laws, rather than an energy minimisation routine.…”