Melt segregation and matrix compaction: the mush continuity equation, compaction/segregation time, implications

Abstract

SUMMARY Two-phase aggregates, a special case of which is partially molten systems, are commonly modelled as an interpenetrating flow of two viscous liquids and are therefore described in terms of the fluid mechanics. The governing equation set of fluid mechanics describing a two-phase aggregate is incomplete as it consists of nine equations (momentum and mass conservation equations for each phase, and an energy conservation equation) in ten unknowns (six velocity components, two pressures, temperature and melt fraction). In this paper, the general equation closing the governing equation set is derived. It explicitly expresses the condition of the coupling between the liquid percolation and porosity volume change due to which the medium continuity is maintained. Therefore, the equation may be referred to as the mush continuity equation. The character of the closed set solutions is demonstrated using 1-D isothermal models by examples of melt segregation inside a bounded low-melting-degree zone and sediment compaction at the bottom of a reservoir. The compaction/segregation style and time are controlled by the compaction/segregation parameter γc= (L/δc)2 and compaction/segregation length depending on the mushy layer thickness, L, matrix permeability, k, characteristic porosity, φ0, and matrix, η, and fluid, μ, viscosities. At low γc, which approximately corresponds to low-viscosity liquids (kimberlites, carbonatites), the compaction/segregation time scales as L−1, which effectively constrains the molten region thickness at the moment of the segregation, and appears to explain the small volume and clustering of low viscosity magma eruptions characteristic of kimberlites. At high γc the porosity evolves through a formation of a series of isolated waves, which could provide an explanation for the rhythmicity observed in large layered plutons.