Flow differentiation in dykes and sills NOT limited by intrusion width

Dispersive grain pressure (Bagnold, 1954) is commonly used to explain the observed axial concentrations of phenocrysts in dykes and sills via flow differentiation (Komar, 1972). The idea was formulated for particle fractions exceeding 0.13 by volume. A dispersive pressure is proposed that is greatest near the intrusion walls, forcing crystals to move inward, towards the centre of the magmatic flow where shear strains are low. However, Barriere (1979) argued that this phenomenological ‘Bagnold effect’ should be confined only to narrow (<<100 m) wide intrusions. His reasoning was that in larger channels, the wall effect driving the dispersive pressure diminishes swiftly, nullifying the dispersive pressure. This is true where the relevant length scale of the problem scales with the ratio W/d, where W is the full channel width and d is particle diameter.

Here we show that for congested magma (0.5 > Φ > 0.8), with the rheology decomposed into scalar and vector components, particle fluctuations (in velocity) are dependent critically on the distance gap (h) between nearest neighbour that imparts a particle pressure. Thus, the critical ratio becomes d/h. It is fluctuations in the interparticle gap distance arising during shear in the flowing suspension that causes migration, irrespective of the channel width. We show that for a fixed particle size, d/h scales with crystal fraction (Φ) and the migration effect is enhanced as W/d increases.   We focus here on particle (crystal) migration as opposed to segregation or particle size sorting, although the latter are both amenable to analysis through modifications to our mathematical model.    

Flow differentiation via particle migration is likely to be just as effective in wider channels (W >> 100m) than in narrow ones, eliminating the need to invoke other fluid dynamical or thermal explanations (convection, multiple intrusion, gravitational settling) to explain the central concentration of phenocrysts in dykes and sills exceeding several metres in width.  As the (multiphase) migration effect exerts a strong control on both magma rheology and composition, flowage differentiation as a mechanism for compositional variation during magma emplacement in large intrusions is open for re-evaluation. 

 

References

Bagnold, RA, (1954). Experiments on gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. Roy. Soc. London 225, 49-63.

Barriere, M, (1976). Flowage differentiation: limitation of the Bagnold effect to the narrow intrusions. Contrib. Min. Pet. 55, 139-145. 

Komar, P, (1972). Mechanical interactions of phenocrysts and flow differentiation of igneous dykes and sills. Geol. Soc. Amer. Bull. 83, 973-988.