Melt flow in a variable viscosity matrix

Abstract

Abstract. It is often assumed that the molten regions of planetary interiors can be modeled as a compacting viscous matrix permeated by a less viscous melt phase. In order to assess the true behaviour, it is important to test as many different aspects of these models as possible. In the calculations presented here, the matrix viscosity is made to decrease as the proportion of melt increases. New results in two dimensions show that if only gravity drives the flow, pockets of melt travel u•)wards as solitary waves, and the behaviour is similar to the well known constant viscosity case. However, when an external shear strain is applied, an instability occurs and melt flows into elongated pockets, or veins, perpendicular to the least compressive stress. Whilst veins much greater than a compaction length in width are suppressed, their minimum width is not clearly constrained. The growth rate of veins is directly proportional to the applied strain rate, so that their degree of development is proportional to the total strain. It is suggested that under mid-ocean ridges, the total strain may be enough for such veins to be important.

Physics and Chemistry of Partially Molten Rocks

“…2 shows the rise of a porosity wave obtained with the CBA. This behaviour has also been observed by Richardson [1998]. 2a).…”

Stress‐driven melt segregation in partially molten rocks

“…The resulting equations are nondimensionalized using a characteristic length scale called the compaction length, δ c . The compaction length of a partially molten sample is determined by the permeability, k , the melt viscosity, μ, the bulk viscosity, λ, and the shear viscosity, η, of the partially molten rock as expressed by the relation [ McKenzie , 1984; Scott and Stevenson , 1986] We use the simplified form δ c = [ k (4/3)η]/μ] 1/2 [ Daines and Kohlstedt , 1993], assuming that λ ≪ η [ Richardson , 1998; McKenzie and Holness , 2000]. To extrapolate viscosity to higher and lower melt fractions, an expression of the form was suggested by Kelemen et al [1997], with α = 45, based on a compilation of published experimental creep data, and where η 0 , the pre‐exponential factor, is a function of temperature and pressure (see section 5.4).…”

“…However, upward scaling to anything other than a homogenous mantle is a difficult problem, partly because of the necessarily small scale of experimental samples and the difficulty of finding evidence for the mesoscale processes in the field. A few theoretical models have demonstrated that deviatoric stress can drive mesoscale melt segregation in pure water [e.g., Stevenson , 1989; Richardson , 1998; Hall and Parmentier , 2000]. However, these studies did not address the interaction of melt segregation and strain partitioning in the weaker melt‐rich zones; the only interactions between the melt and solid flow fields were due to compaction, not shear.…”

A model of episodic melt extraction for plumes

“…If a partially molten rock is subjected to deviatoric stresses, porosity mediated weakening may lead to a channeling instability with channels oriented perpendicular to the direction of minimum compressive stress [ Stevenson , 1989]. To obtain melt channels at moderate finite strains, higher initial melt factions (1–3%) are required [ Richardson , 1998; Müller , 2005]. …”