The effects of Plateau borders in the two-dimensional soap froth. II. General simulation and analysis of rigidity loss transition

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

“…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].…”

“…As the liquid fraction ϕ is increased, rearrangements are progressively triggered as the borders come into contact, forming four-sided borders. In a nearly dry foam, these immediately trigger 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 further rearrangements to complete T1 changes [6]. Such combined changes have no effect on the mean contact number Z, which remains at the value 6, but do affect the distribution f (n), see Fig.…”

“…Convergence is determined from the magnitude of the maximum change in the vertex positions. For a more detailed discussion of the PLAT representation of a foam and the equilibration process see [6].…”

“…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.…”