Melt segregation inside a partially molten zone: Theory,numerical models and implications

For the problem of matrix compaction and melt segregation a general mush continuity equation is derived, which explicitly expresses the coupling between the melt percolation and the inelastic matrix deformation and closes the governing equation set. Besides, a general equation is obtained, which describes the change in the volume of pore space due to all the possible reasons (inelastic matrix deformation, the phase transitions, and the advection of porosity by the matrix flow). The features of the isothermal melt segregation inside a partially molten zone are demonstrated using one-dimensional (1D) numerical solutions. It follows from the solutions that the pattern and the characteristic time of the melt segregation inside a partially molten zone of thickness L are controlled by the segregation parameter γ _c = (L/δ _c )², where the compaction length δ _c = k(φ₀)η/(φ₀μ) depends on the permeability, k, the value of characteristic porosity, φ₀, and the viscosities of the matrix, η, and melt, μ. The solutions demonstrate that at any value of γ _c , layers that are highly enriched in melt compared to the maximum initial porosity are formed in the upper part of the zone. At the same time, the evolution of the system and the segregation time differ considerably in the limits of γ _c ≪ γ* and γ _c ≫ γ*, where γ* depends on the boundary and initial conditions of the problem, and γ* is about 80 for the problem of melt segregation inside a partially molten zone with the maximum in the initial melt distribution located in the middle of the zone. At γ _c ≪ γ*, which corresponds to the segregation of low-viscosity ultrabasic melts (kimberlites, carbonatites), all the melt accumulates to the roof of the zone, and the segregation time does not depend on the matrix permeability and melt viscosity and decreases with an increase in the thickness of the zone as L ⁻¹. The latter can be the reason for the formation of clusters of the same age and same composition eruptions characteristic of the kimberlite provinces. In the opposite limiting case, γ _c ≫ γ*, the segregation time does not depend on the matrix viscosity and scales as L with a wave sequence forming in the upper part of the zone, which, probably, elucidates the origin of the rhythmical layering of the large tholeiitic basalt plutons.