Double-diffusive convection in partially molten silicate systems: its role during magma production and in magma chambers

Abstract In this paper, two problems involving double-diffusive convection in partially molten, silicate systems are investigated mathematically. The first problem concerns the role of double-diffusive convection during magma production. The systems Di-An and Di-An-Ab are used as examples. The calculations show that, in a growing layer of partial melt, heated from below, the thickness of the layer at which convection initiates depends strongly upon the bulk composition. For example, assuming reasonable values of the physical parameters, in a Di-rich system, convection will occur when the layer is ∼ 800 m thick, whereas in an An-rich system convection, driven by the destabilizing compositional gradient, will begin in a layer only centimeters thick. A qualitative investigation of the Di-An-Ab system suggests similar results, depending upon whether the bulk composition lies in the diopside or the plagioclase field, respectively. Moreover, if one considers a two-component, one-dimensional diapir of Di-An, an examination of the phase diagram indicates that vigorous compositional convection will occur in the partially molten diapir as it ascends, regardless of whether the bulk composition is Di-rich or An-rich. These results suggest that during magma production, convective processes will tend to homogenize the melt before it segregates from the source zone; however, the vigor of mixing is dependent upon the bulk composition of the source, among several other factors. Models of melt segregation should be modified to include double-diffusive processes. The second problem concerns the structure of a porous boundary layer that forms as a result of side-wall crystallization in a convecting magma chamber. An examination of the steady-state boundary layer equations for flow through a porous medium shows that the boundary layer structure may be of two types. If the residual melt fraction, upon crystallization at the wall, has negative compositional buoyancy, or if the negative thermal buoyancy at the cold wall exceeds the positive compositional buoyancy of the residual melt, the flow across the entire boundary layer will be downward. If the residual melt fraction has negative compositional buoyancy, the magma chamber will become stratified as a result of accumulation of a layer of dense, cold liquid on the floor; whereas if the melt fraction has positive compositional buoyancy, the boundary layer fluid will tend to be remixed into the interior of the magma chamber. If, however, the positive compositional buoyancy exceeds the negative thermal buoyancy, counterflowing boundary layers will occur; and the compositionally buoyant liquid will tend to be fractionated towards the top of the magma chamber. An examination of the Di-An and Di-An-Ab systems suggests that both types of boundary layer structures may occur in magma chambers. An approximate calculation of the rate of fractionation suggests that, for a range of parameters that may be representative of basaltic magmas, the flow in the compositional boundary layer may transport ∼ 10 −3 km 3 /yr of low-density liquid to the top of the magma chamber.