2D foams above the jamming transition: Deformation matters

Abstract

Jammed soft matter systems are often modelled as dense packings of overlapping soft spheres, thus ignoring particle deformation. For 2D (and 3D) soft disks packings, close to the critical packing fraction φ c , this results in an increase of the average contact number Z with a square root in φ − φ c . Using the program PLAT, we find that in the case of idealised two-dimensional foams, close to the wet limit, Z increases linearly with φ − φ c , where φ is the gas fraction. This result is consistent with the different distributions of separations for soft disks and foams at the critical packing fraction. Thus, 2D foams close to the wet limit are not well described as random packings of soft disks, since bubbles in a foam are deformable and adjust their shape. This is not captured by overlapping circular disks.

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.…”

“…Surprisingly, Z(ϕ) varies linearly close to ϕ c , in contrast with the square root variation obtained from simulations and experiments of dense packings of soft disks [9]. A detailed discussion of this matter is presented in a further paper [18].…”

“…For this system it has been suggested that a pure power-law distribution 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 [31]. Such simulations, where bubbles are modeled as overlapping disks, are successful in reproducing many rheological properties of foams, but recent work points to marked differences regarding the variation of average coordination number Z(ϕ) in the wet limit [18].…”

“…It decreases from Z = 6 for the dry limit (ϕ = 0) to Z = 4 for the wet limit (ϕ = ϕ c ) of an infinite system. The former value is essentially exact (from Euler's Theorem), the latter almost so (see [18] for details), with possible correction for occasional "rattlers" (i.e. bubbles that are free to move within the cage formed by their neighbours).…”

“…2.3.1). This results in ϕ c = 0.159 ± 0.001 [18] and it is this value that we will use when discussing large scale rearrangements in Sec. 3.…”