Boromand Arman, Signoriello Alexandra, Lowensohn Janna, Orellana Carlos S, Weeks Eric R, Ye Fangfu, Shattuck Mark D, O'Hern Corey S
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA.
Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA.
Soft Matter. 2019 Jul 24;15(29):5854-5865. doi: 10.1039/c9sm00775j.
We perform computational studies of jammed particle packings in two dimensions undergoing isotropic compression using the well-characterized soft particle (SP) model and deformable particle (DP) model that we developed for bubbles and emulsions. In the SP model, circular particles are allowed to overlap, generating purely repulsive forces. In the DP model, particles minimize their perimeter, while deforming at fixed area to avoid overlap during compression. We compare the structural and mechanical properties of jammed packings generated using the SP and DP models as a function of the packing fraction ρ, instead of the reduced number density φ. We show that near jamming onset the excess contact number Δz = z - zJ and shear modulus G scale as Δρ0.5 in the large system limit for both models, where Δρ = ρ - ρJ and zJ ≈ 4 and ρJ ≈ 0.842 are the values at jamming onset. Δz and G for the SP and DP models begin to differ for ρ ⪆ 0.88. In this regime, Δz ∼ G can be described by a sum of two power-laws in Δρ, i.e. Δz ∼ G ∼ C0Δρ0.5 + C1Δρ1.0 to lowest order. We show that the ratio C1/C0 is much larger for the DP model compared to that for the SP model. We also characterize the void space in jammed packings as a function of ρ. We find that the DP model can describe the formation of Plateau borders as ρ → 1. We further show that the results for z and the shape factor A versus ρ for the DP model agree with recent experimental studies of foams and emulsions.
我们使用我们为气泡和乳液开发的特征明确的软颗粒（SP）模型和可变形颗粒（DP）模型，对二维各向同性压缩下的堵塞颗粒堆积进行了计算研究。在SP模型中，圆形颗粒可以重叠，产生纯排斥力。在DP模型中，颗粒在固定面积下变形以使其周长最小化，从而在压缩过程中避免重叠。我们比较了使用SP和DP模型生成的堵塞堆积的结构和力学性质，作为堆积分数ρ的函数，而不是约化数密度φ的函数。我们表明，在大系统极限下，对于这两个模型，在堵塞开始附近，过量接触数Δz = z - zJ和剪切模量G按Δρ^0.5缩放，其中Δρ = ρ - ρJ，zJ≈4且ρJ≈0.842是堵塞开始时的值。对于ρ⪆0.88，SP和DP模型的Δz和G开始出现差异。在这个区域，Δz∼G可以用Δρ的两个幂律之和来描述，即Δz∼G∼C0Δρ^0.5 + C1Δρ^1.0到最低阶。我们表明，与SP模型相比，DP模型的C1/C0比值要大得多。我们还将堵塞堆积中的空隙空间表征为ρ的函数。我们发现，随着ρ→1，DP模型可以描述普拉托边界的形成。我们进一步表明，DP模型的z和形状因子A与ρ的结果与最近关于泡沫和乳液的实验研究一致。
