Granular flow and viscous fluctuations in low Bagnold number granitic magmas

Recent thermal and fluid dynamical models have shown that density-driven ascent of isoviscous granitic melt through the crust in narrow dykes is geologically instantaneous, provided the role of suspended crystals is ignored. However, it is well known that solids in suspension can affect significantly the rheology and hence flow properties of magmas, leading to the subjective criticism that granite ascent and emplacement rates based on simple dyke transport models may be unrealistic. By estimating the magntidue of shear stresses developed during continuous flow in a 6 m wide granite dyke, we show yeidl strengths in excess of 10⁴ pascals are required to stop flow entirely if the pressure gradient driving the flow is high. Using granular flow theory, we show how fluctuations in partical velocity in the shear field can be used to predict the rheological behaviour of magmas with crustal contents (solidosity) in the range 0.1<φ<0.25. Specimen calculations for the solidosity and fluctuation on particle velocity for ascending granitic magmas show that the energy associated with these irregular movements is much greater than that expected on purely Brownian grounds. We find no clear correlation between viscosity μ and the yield strength, and while it is possible that magmas has curious, unexpected bonding properties, magmatic suspensions where the grain size is on the scale of centrimetres (eg some coarsely porphyritic magams), low estimated Bagnold numbers (c. 10^-8) render Bingham flow models inappropriate. Self-organziation of the flow into a crystal-poor margin and crystal-rich core (flow differentiation) by diffusion of particles towards the region of minimal shear results in the familiar plug-type flow profiles traditionally associated with an inherent yield strength. Shear-enhanced diffusion is an inevitable consequence of granular flow that leads to flow differentiation, providing a simple mechanistic explanation for high concentrations of phenoncrysts in the cores of porphyritic dykes (Bagnold effect). Deviation from simple Newtonian flow is unlikely to be significant until the magmas has stopped ascending and emplacement begins.