On the stability of the μ(I) rheology for granular flow
On the stability of the μ(I) rheology for granular flow
复制标题
颗粒流μ(I)流变学的稳定性
DOI：
--
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
Jaesung Lee
中科院分区：
文献类型：
--
作者：
Joe D. Goddard;Jaesung Lee
本文讨论了Barker等人最近报道的致密快速剪切颗粒流的所谓$unicode[STIX]{x1D707}(I)$模型的Hadamard不稳定性。， vol. 779, 2015, pp. 794-818)。本文对平面单纯剪切流和纯剪切流的线性稳定性进行了较为全面的研究，并考虑了基底流对对流开尔文波的拉伸。我们为线性稳定性问题提供了一个封闭形式的解，并证明了波矢量拉伸导致Barker等人发现的非对流不稳定性的渐近稳定(J.流体力学。， vol. 779, 2015, pp. 794-818)。我们还探讨了基于范德华斯-坎-希利亚德平衡热力学方程耗散模拟的增强连续体模型所实现的高速度梯度的稳定效应。该模型涉及一个耗散超应力，作为一个特殊的Korteweg应力的模拟，表面粘度代表弹性表面张力的对应。在增强连续介质模型的基础上，提出了稳定剪切带及其在平行剪切作用下的非线性稳定性模型。最后，我们提出了Barker等人（J.流体力学）的非对流不稳定性之间的理论联系。准静态场方程中广义椭圆性的损失，vol. 779, 2015, pp. 794-818)。除了理论兴趣之外，本工作可能为涉及$unicode[STIX]{x1D707}(I)$流变及其变体的连续统场方程的数值模拟提供策略。
This article deals with the Hadamard instability of the so-called $unicode[STIX]{x1D707}(I)$ model of dense rapidly sheared granular flow, as reported recently by Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818). The present paper presents a more comprehensive study of the linear stability of planar simple shearing and pure shearing flows, with account taken of convective Kelvin wavevector stretching by the base flow. We provide a closed-form solution for the linear-stability problem and show that wavevector stretching leads to asymptotic stabilization of the non-convective instability found by Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818). We also explore the stabilizing effects of higher velocity gradients achieved by an enhanced-continuum model based on a dissipative analogue of the van der Waals–Cahn–Hilliard equation of equilibrium thermodynamics. This model involves a dissipative hyperstress, as the analogue of a special Korteweg stress, with surface viscosity representing the counterpart of elastic surface tension. Based on the enhanced-continuum model, we also present a model of steady shear bands and their nonlinear stability against parallel shearing. Finally, we propose a theoretical connection between the non-convective instability of Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) and the loss of generalized ellipticity in the quasi-static field equations. Apart from the theoretical interest, the present work may suggest stratagems for the numerical simulation of continuum field equations involving the $unicode[STIX]{x1D707}(I)$ rheology and variants thereof.