Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis
Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis
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DOI：
10.1017/jfm.2013.482
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发表时间：
2013-10
影响因子：
3.7
通讯作者：
Y. Takei;R. Katz
中科院分区：
文献类型：
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作者：
Y. Takei;R. Katz
摘要在地球的部分熔融区，岩石和岩浆以两相集合体的形式共存，岩石的固体颗粒在其中形成粘性变形的骨架或基质。液态岩浆存在于颗粒间可渗透的孔隙网络中。偏应力使固体颗粒之间的接触面积分布变得各向异性，进而导致基质粘度在连续介质尺度上的各向异性。在这两篇论文的集合中，我们预测了粘性各向异性对三种构型的两相集合体流动的影响：简单剪切、泊松和扭转流动。第一部分介绍了控制方程及其线性化形式的分析。第二部分(Katz&Takei，J.Fluid Mech，Vol.734,2013，pp.456-485)给出了完整的非线性模型的数值解。在我们的理论中，各向异性粘性张量耦合了基质应力/应变率的剪切和体积分量。这种作用在剪应力梯度上的耦合导致了液体和固体的分离。液体通常朝着较高的剪应力迁移，但在特定条件下，可能会发生相反的情况。此外，众所周知，在具有孔隙率弱化粘度的两相集料中，基质剪切导致孔隙率扰动发展为带状或片状结构。我们发现，粘性各向异性减小了这些新出现的高孔隙率特征与剪切面之间的夹角。实验室实验产生了类似的、高孔隙率的特征。我们假设，在这种实验中，孔隙带的低角度是粘性各向异性的结果。因此，我们预测，由于粘性各向异性，加入剪应力梯度的实验将在整个样品范围内形成液-固分离。
Abstract In partially molten regions of Earth, rock and magma coexist as a two-phase aggregate in which the solid grains of rock form a viscously deformable framework or matrix. Liquid magma resides within the permeable network of pores between grains. Deviatoric stress causes the distribution of contact area between solid grains to become anisotropic; in turn, this causes anisotropy of the matrix viscosity at the continuum scale. In this two-paper set, we predict the consequences of viscous anisotropy for flow of two-phase aggregates in three configurations: simple shear, Poiseuille, and torsional flow. Part 1 presents the governing equations and an analysis of their linearized form. Part 2 (Katz & Takei, J. Fluid Mech., vol. 734, 2013, pp. 456–485) presents numerical solutions of the full, nonlinear model. In our theory, the anisotropic viscosity tensor couples shear and volumetric components of the matrix stress/strain rate. This coupling, acting over a gradient in shear stress, causes segregation of liquid and solid. Liquid typically migrates toward higher shear stress, but under specific conditions, the opposite can occur. Furthermore, it is known that in a two-phase aggregate with a porosity-weakening viscosity, matrix shear causes porosity perturbations to grow into a banded or sheeted structure. We show that viscous anisotropy reduces the angle between these emergent high-porosity features and the shear plane. Laboratory experiments produce similar, high-porosity features. We hypothesize that the low angle of porosity bands in such experiments is the result of viscous anisotropy. We therefore predict that experiments incorporating a gradient in shear stress will develop sample-wide liquid–solid segregation due to viscous anisotropy.