Consequences of Anisotropic Permeability and Surface Tension for Magmatic Segregation in Deforming Mantle Rock

Abstract:

The mechanics of partially molten regions of the mantle are not well understood--in part due to the inaccessibility of these regions to observation. However it is widely agreed that experiments performed on synthetic mantle rocks [e.g KZK10] act as a reasonable test of theoretical models of magma dynamics. One robust feature of experiments on partially molten mantle rocks deformed under strain is the emergence of high-porosity bands at an angle of between 15° and 20° to the shear plane.

A number of theoretical approaches have been made to reproduce the formation of these low angle bands in models. The most recent approaches, for example by Takei and Katz [TK13], have involved the inclusion of anisotropic viscosity in diffusion creep arising from the grain-scale redistribution of melt as formulated in a theoretical model by Takei and Holtzman [TH09]. It is reasonable to assume that this melt-preferred orientation (MPO) that leads to anisotropy in viscosity may also lead to anisotropy in permeability. However, the effect of anisotropic permeability remains unexplored. We investigate its impact on the dynamics of partially molten rock, and specifically on its role in low-angle band formation in deformation under simple shear.

We work with the continuum model of two-phase-flow as formulated by McKenzie [M84] with the addition of anisotropic permeability. There are some apparent inconsistencies in this model. Firstly, the model predicts continued segregation of melt into bands of 100% porosity, while experiments report maximum porosities in the region of 30%. Secondly, linear stability analyses find maximal growth-rates for porosity perturbations that vary on arbitrarily small length-scales. We study how the inclusion of surface forces into the model could regulate these effects.

REFERENCES:

KZK10 = King, Zimmerman, & Kohlstedt (2010), J Pet, 10.1093/petrology/egp062. TK13 = Takei & Katz (2013), JFM, 10.1017/jfm.2013.482. TH09 = Takei & Holtzman (2009a), JGR, 10.1029/2008JB005850. M84 = McKenzie (1984), J Pet, 10.1093/petrology/25.3.713.