The origin of compositional zonation in magma chambers1-11 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 reservoir7,12,13. 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 chamber1,3,6,7,14-16. 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.