Critical dynamics governing the lateral flow of magmatic slurries

Magmas are particle-fluid mixtures and as such governed by the physical laws that determine flow and deformation in granular slurries. However, developing quantitative models that combine conduit-scale flow properties with the local generation of flow instabilities that lead to pattern formation, for example layering, segregation or clumping/jamming of crystals during transit, remains a challenge.

Here we provide a detailed theoretical analysis of the lateral flow of a granular magmatic slurry, with application to flow differentiation and layering in mafic sill complexes. The slurry rheology is decomposed into scalar and vector components of the fluctuations in the time-dependent configuration of the particles, which although operating on different scales, together give rise to fluctuations in velocity and particle concentrations that may impart considerable heterogeneity during flow.

A key determinant in the development of geological features of interest is the ratio of flow velocity to the gravitational settling rates of crystals in suspension.  Equations are derived that explore the relative contribution of lateral, pressure gradient or volume-driven lateral conduit flow (G) to rates of crystal settling (H). The key ratio G/H ~ D is defined for both symmetrical and non-symmetrical flow as a function of particle pressure, the latter key in controlling crystal-liquid segregation. Two regimes are identified, D < 1 (crystal settling/sedimentation dominates) and D > 1 where differentiation and layering are emergent properties intrinsic to the flow.  Sensitivity analysis reveals the upper and lower boundary conditions at the magma-country rock interface play a critical (and unique) role in controlling velocity fluctuations that impact on local flow segregation and layering.

Lack of experimental evidence, or real-time observations of magmatic intrusions, means critical open questions remain concerning the precise thermo-mechanical conditions (density contrasts, crystallinity and pressure gradients), needed to match theory with the natural world. However, theoretical treatment sets the scene for follow-up numerical work and experimental verification while providing new insight into factors contributing to chemical diversity and textural heterogeneity in igneous rocks.