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Consequences of viscous anisotropy in a deforming, two-phase aggregate. Part 1. Governing equations and linearized analysis

Published online by Cambridge University Press:  11 October 2013

Yasuko Takei  and
Richard F. Katz
Yasuko Takei*
Affiliation:
Earthquake Research Institute, University of Tokyo, Tokyo 113-0032, Japan
Richard F. Katz
Affiliation:
Department of Earth Sciences, University of Oxford, Oxford OX1 3AN, UK
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Geophysical and Geological Flows: Magma and lava flow Nonlinear Dynamical Systems: Pattern formation Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 734 , 10 November 2013 , pp. 424 - 455
Copyright
©2013 Cambridge University Press 

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