Thermal and dynamical regimes of single‐ and two‐phase magmatic flow in dikes

Abstract

Finite element calculations of magma flow in dikelike channels with length‐to‐width ratios of 1000:1 or more have been used to investigate the coupling between thermal and dynamical regimes due to temperature‐dependent viscosity and dissipation. Steady state solutions with realistic thermal and dynamical parameter values have been obtained. The models show that the onset of solidification on the boundaries of a basaltic or andesitic dike, as predicted by idealized laminar flow models, can be prevented or significantly delayed by a small amount of transverse flow induced by rising bubbles, boundary roughness, or turbulence. This effect will reduce the critical initial widths of dikes estimated by Bruce and Huppert (1989). In the absence of transverse flow, the bulk temperature of the magma may actually increase slightly with distance along the dike as a result of viscous dissipation even while solidification is occurring on the walls of the dike. With converging or necking dike walls it is found that boundary temperatures fall to a minimum and then increase with distance along a dike even if viscous heating is neglected. For viscous heating to offset significant rates of heat loss (2 kW/m2) in a plane‐parallel 1‐m‐wide basaltic dike, an average flow velocity of 2.7 m/s driven by a pressure gradient of 1.7 MPa/km is required. A 7% void fraction caused by exsolution of volatiles or chamber gas in the magma will produce this pressure gradient. The ease of producing such a gradient by reducing the density of the magmatic column with addition of a gas phase makes it likely that flows of basaltic magma could be maintained in dikes tens of kilometers long. Furthermore, a gas phase may be important for the propagation of the fracture prior to the initial injection of magma during dike emplacement. Rapid transport of more silicic magmas through dikes is inhibited by the requirement of large driving pressure gradients exceeding several hundred megapascals per kilometer. However, the pressure gradient can be substantially reduced if the magma is a heterogenous mixture of a predominantly silicic component with a more mafic component. Pipe flow experiments involving molten polymers that exhibit dynamical similarity to magmas strongly suggest that unmixing occurs when a two‐component magma mixture, in which the components have different viscosities, rises within a dike. Within a few dike widths of the inlet the less viscous mafic component encapsulates the more viscous silicic part, effectively lubricating the passage of the more viscous component. Compositional variations in the Obsidian Dome volcano support the occurrence of this pressure reduction or self‐lubrication mechanism. Such a self‐lubrication process often may be necessary to permit very viscous magmas to reach Earth's surface. If so, chemical and lithologic zoning would be anticipated as a common feature of near‐surface intrusions or lava flows that are characterized by a high silica and/or high crystal content such as at Deadman Dome in Long Valley, California.