Nonlinear viscoelasticity of a dilute suspension of Brownian spheroids in oscillatory shear flow
Nonlinear viscoelasticity of a dilute suspension of Brownian spheroids in oscillatory shear flow
复制标题
振荡剪切流中布朗球体稀悬浮液的非线性粘弹性
DOI：
--
复制
发表时间：
2018
影响因子：
3.3
通讯作者：
Aditya S. Khair
中科院分区：
文献类型：
--
作者：
Toni M. Bechtel;Aditya S. Khair
数值计算了受振动剪切变形影响的布朗椭球稀薄悬浮体的非线性粘弹性。这是通过确定悬浮微结构来实现的，并通过取向分布函数将其参数化。具体地，通过将空间有限差分近似与时间傅立叶级数相结合，通过数值求解Fokker-Planck方程来获得长时间周期取向分布函数。根据取向分布函数加权的粒子应力的系综平均值，计算了整个应力张量和相关的双折射参数，即平均取向角和线性二色性；这分别在一定范围内的Weissenberg数(VI)和Deborah数(De)，或无量纲的应变率幅度和振荡频率上进行。对于长径比r=20的长椭球，给出了详细的计算；但是，我们的方法是通用的，可以应用于任意长宽比的椭球。给出了四种粘弹性状态下的结果：线性粘弹性状态(WI≪1)、拟线性粘弹性状态(WI>；1和WI/De≪1)、准稳态粘弹性状态(De→0)和非线性粘弹性状态(WI ≳ 1和WI/De ≳ 1)。在最后一个区域，当材料的非线性和非定常粘弹性被探测时，在剪应力和第一法向应力差中观察到多个超调。这些超调的机械起源可以从粒子在无布朗旋转(W I→∞)的稳态剪切下的周期取向动力学(即Jeffery轨道)中得到理解。这是通过同时分析Wi=20和De=1的微结构、剪应力、第一法向应力差和双折射参数来实现的。对于这些Wi、De和r的值，Jeffery轨道的周期与振荡周期的周期相当，从而为单个Jeffery轨道(以及随后的超调)在振荡周期中发生提供了足够的时间。我们将这一行为与凯尔[J.流体]最近的工作进行了对比。机甲。791，R5(2016)]，由于Jeffery轨道的周期较短，在振荡周期中观察到的超调要多得多。我们简要地给出了长径比r=0.05的扁球体的结果，并与r=20的结果进行了比较。最后，我们评论了本文的细观分析与其他复杂流体材料的非线性粘弹性的相关性。数值计算了受振荡剪切变形的布朗球体稀薄悬浮液的非线性粘弹性。这是通过确定悬浮微结构来实现的，并通过取向分布函数将其参数化。具体地，通过将空间有限差分近似与时间傅立叶级数相结合，通过数值求解Fokker-Planck方程来获得长时间周期取向分布函数。根据取向分布函数加权的粒子应力的系综平均值，计算了整个应力张量和相关的双折射参数，即平均取向角和线性二色性；这分别在一定范围内的Weissenberg数(VI)和Deborah数(De)，或无量纲的应变率幅度和振荡频率上进行。对长径比r=20的长椭球给出了详细的计算，但我们的方法是通用的。
The nonlinear viscoelasticity of a dilute suspension of Brownian spheroids subject to an oscillatory shear deformation is calculated numerically. This is achieved by determining the suspension microstructure, parameterized via the orientation distribution function. Specifically, the long-time periodic orientation distribution function is obtained via a numerical solution to the Fokker–Planck equation by combining a finite-difference approximation in space with a Fourier series in time. From an ensemble average of the particle stresslet, weighted by the orientation distribution function, the entire stress tensor and relevant birefringence parameters, namely, the average orientation angle and linear dichroism, are calculated; this is done over a range of the Weissenberg number ( W i) and the Deborah number ( D e), or dimensionless strain-rate amplitude and oscillation frequency, respectively. Detailed calculations are presented for prolate spheroids of aspect ratio r = 20; however, our methodology is general and can be applied to spheroids of arbitrary aspect ratio. We provide results in four viscoelastic regimes: linear viscoelastic ( W i ≪ 1), quasilinear viscoelastic ( W i > 1 and W i / D e ≪ 1), quasisteady viscoelastic ( D e → 0), and finally, the nonlinear viscoelastic regime ( W i ≳ 1 and W i / D e ≳ 1), which is our main emphasis. In this last regime, where the nonlinear and unsteady viscoelasticity of the material is probed, multiple overshoots are observed in the shear stress and first normal stress difference. The mechanistic origin of these overshoots can be understood from the periodic orientation dynamics (i.e., Jeffery orbits) of a particle under steady shear in the absence of Brownian rotation ( W i → ∞). This is achieved by simultaneously analyzing the microstructure, shear stress, first normal stress difference, and birefringence parameters specifically at W i = 20 and D e = 1. For these values of W i , D e, and r, the period of a Jeffery orbit is comparable to the period of an oscillation cycle, allowing sufficient time for a single Jeffery orbit (and subsequent overshoot) to occur during an oscillation cycle. We contrast this behavior to recent work by Khair [J. Fluid. Mech. 791, R5 (2016)] on nearly spherical particles, for which many more overshoots are observed during an oscillation cycle, due to the shorter period of the Jeffery orbit. We briefly provide results for oblate spheroids of aspect ratio r = 0.05 and compare to the results for r = 20. Finally, we comment on the relevance of the present micro-mechanical analysis to the nonlinear viscoelasticity of other complex fluid materials.The nonlinear viscoelasticity of a dilute suspension of Brownian spheroids subject to an oscillatory shear deformation is calculated numerically. This is achieved by determining the suspension microstructure, parameterized via the orientation distribution function. Specifically, the long-time periodic orientation distribution function is obtained via a numerical solution to the Fokker–Planck equation by combining a finite-difference approximation in space with a Fourier series in time. From an ensemble average of the particle stresslet, weighted by the orientation distribution function, the entire stress tensor and relevant birefringence parameters, namely, the average orientation angle and linear dichroism, are calculated; this is done over a range of the Weissenberg number ( W i) and the Deborah number ( D e), or dimensionless strain-rate amplitude and oscillation frequency, respectively. Detailed calculations are presented for prolate spheroids of aspect ratio r = 20; however, our methodology is ge...