Abstract

Despite the success of buoyancy-driven viscous compaction theory in explaining important aspects of melt extraction in the mantle, instabilities that arise where porous flow is driven primarily by external deformation of a non-viscous matrix are not so well studied. We present the results of new analytical solutions of melt extraction from a deformable, partially-molten layer sandwiched between two permeable but rigid layers, made relevant to the case of upwelling mantle trapped beneath a stiff lid. We derive estimates of the local pressure gradients driving the flow, and show that for heterogeneous porous media with a position-dependent permeability, flow of a non-Newtonian fluid (melt) results in the formation of zones of elevated permeability on the scale of the mean pore size. Whether these structures form either in the stream wise or cross stream direction depend largely on the rheology (dilatant or pseudo plastic) of the fluid phase, notably the exponents that appear in the constitutive description1. The model provides a framework for exploring melt extraction in the upper mantle driven by intraplate deformation without the need for excessively high temperatures. Whilst the geometries investigated are limited to one-dimension, this work provides the basis of more robust multiphysics models capable of predicting the mechanical response of a rigid, fluid saturated granular matrix to imposed shear, a vital step towards a quantitative understanding of melt segregation where flow is driven not only by buoyancy effects but also by deformation.