Mass transfer rates along vertical walls in magma chambers and marginal upwelling

The origin of compositional zonation in magma chambers^1-11 has created much interest. Observed chemical, mineralogical and thermal gradients in many ash flow deposits are widely believed to indicate pre-eruptive zonations within the magma reservoir^7,12,13. By analogy with laboratory experiments involving salt crystallization and the concomitant release of chemically-induced buoyancy, it has been suggested that compositionally evolved magma might accumulate at the top of a magma chamber. Crystallization of mafic phases along the chamber margins would produce a residual melt which is more silicic than the bulk composition. Marginal upwelling of buoyant melt could then lead to vertical compositional stratification underneath the roof of the chamber^{1,3,6,7,14-16}. Here we show that analysis of laminar boundary layer flows driven by thermal and/or chemical buoyancy indicates that, for physical parameters characteristic of magma, the rate of enriched magma accumulation is small compared with geologically-inferred rates. Furthermore, the effect of a temperature-dependent rheology is to suppress the marginal upwelling effect⁸. Even for the extreme case of an isothermal chamber, sidewall upwellings can only be quantitatively significant for highly mobile species (chemical diffusion, D>10^-11 m² s ^-1) located in low-viscosity basaltic chambers with a high surface area-to-volume ratio.