无热、无摩擦、球形-圆柱形悬浮液在二维中的剪切驱动流动：应力、堵塞和接触。

Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.

Phys Rev E. 2019 Sep;100(3-1):032906. doi: 10.1103/PhysRevE.100.032906.

We use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two-dimensional spherocylinders driven by a uniform steady-state shear strain applied at a fixed finite rate. Energy dissipation occurs via a viscous drag with respect to a uniformly sheared host fluid, giving a simple model for flow in a non-Brownian suspension and resulting in a Newtonian rheology. We study the resulting pressure p and deviatoric shear stress σ of the interacting spherocylinders as a function of packing fraction ϕ, strain rate γ[over ̇], and a parameter α that measures the asphericity of the particles; α is varied to consider the range from nearly circular disks to elongated rods. We consider the direction of anisotropy of the stress tensor, the macroscopic friction μ=σ/p, and the divergence of the transport coefficient η_{p}=p/γ[over ̇] as ϕ is increased to the jamming transition ϕ_{J}. From a phenomenological analysis of Herschel-Bulkley rheology above jamming, we estimate ϕ_{J} as a function of asphericity α and show that the variation of ϕ_{J} with α is the main cause for differences in rheology as α is varied; when plotted as ϕ/ϕ_{J}, rheological curves for different α qualitatively agree. However, a detailed scaling analysis of the divergence of η_{p} for our most elongated particles suggests that the jamming transition of spherocylinders may be in a different universality class than that of circular disks. We also compute the number of contacts per particle Z in the system and show that the value at jamming Z_{J} is a nonmonotonic function of α that is always smaller than the isostatic value. We measure the probability distribution of contacts per unit surface length P(ϑ) at polar angle ϑ with respect to the spherocylinder spine and find that as α→0 this distribution seems to diverge at ϑ=π/2, giving a finite limiting probability for contacts on the vanishingly small flat sides of the spherocylinder. Finally, we consider the variation of the average contact force as a function of location on the particle surface.

我们使用数值模拟研究了无热、无摩擦、软芯二维球形棒的二相混合物在固定有限速率下施加均匀稳态剪切应变时的流动。能量耗散是通过相对于均匀剪切主体流体的粘性阻力发生的，这为非布朗悬浮液中的流动提供了一个简单的模型，并导致牛顿流变学。我们研究了相互作用的球形棒的压力 p 和偏剪切应力 σ 作为填充分数 ϕ、应变率 γ[over ̇]和一个参数 α 的函数，该参数 α 测量颗粒的非球形度；通过改变 α 来考虑从近乎圆形盘到拉长棒的范围。我们考虑了应力张量的各向异性方向、宏观摩擦 μ=σ/p 和输运系数 η_{p}=p/γ[over ̇]的散度，随着 ϕ 增加到堵塞转变 ϕ_{J}。从堵塞以上赫谢尔-布尔克利流变学的唯象分析，我们估计了 ϕ_{J}作为非球形度 α 的函数，并表明随着 α 的变化，ϕ_{J}的变化是流变学差异的主要原因；当以 ϕ/ϕ_{J}表示时，不同 α 的流变学曲线在定性上是一致的。然而，我们最拉长粒子的 η_{p}散度的详细标度分析表明，球形棒的堵塞转变可能与圆盘的堵塞转变处于不同的通用类别。我们还计算了系统中每个粒子的接触数 Z，并表明在堵塞时 Z_{J}是 α 的非单调函数，总是小于等静压值。我们测量了相对于球形棒脊柱的极角 ϑ 的单位表面长度上的接触数 P(ϑ)的概率分布，并发现当 α→0 时，该分布在 ϑ=π/2 处似乎发散，这给球形棒的微小平坦侧面上的接触提供了有限的极限概率。最后，我们考虑了平均接触力作为粒子表面位置的函数的变化。