We present results of a theoretical study aimed at understanding melt extraction from the upper mantle. Specifically, we address mechanisms for focusing of porous how of melt into conduits beneath mid-ocean ridges in order to explain the observation that most oceanic residual peridotites are not in equilibrium with mid-ocean ridge basalt. The existence of such conduits might also explain geological features, termed replacive dunites, that are observed in exposed mantle sections. We show here, by linear analysis, that flow in a chemically reactive porous media is unstable in the presence of a solubility gradient, such as induced by adiabatic ascent of melt underneath mid-ocean ridges. The initially homogeneous flow becomes focused in time to produce elongated high-porosity fingers that act as conduits for transport of fast flowing melt. This instability arises due to a positive feedback mechanism in which a region of slightly higher than average porosity causes increased influx of unsaturated flow, leading to increased dissolution which further reduces the porosity. Even in the presence of matrix compaction and chemical diffusion the instability is demonstrated to be robust. Our analysis also indicates the existence of growing, traveling waves which transport and amplify porosity and concentration perturbations.
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