THE SOLIDIFICATION OF BUOYANCY-DRIVEN FLOW IN A FLEXIBLE-WALLED CHANNEL .1. CONSTANT-VOLUME RELEASE

The solidification of hot fluid flowing in a thin buoyancy-driven laye r between cold solid boundaries is analysed in a series of two papers. As an approximation to flow in a crack in a weakly elastic solid or t o free-surface flow beneath a thin solidified crust, the boundaries ar e considered to be flexible and to exert negligible resistance to late ral deformation. The resultant equations of continuity and motion redu ce to a kinematic-wave equation with a loss term corresponding to the accumulation of solidified material at the boundaries. The Stefan prob lem for the solidification is coupled back to the flow through the adv ection of heat by the fluid, which competes with lateral heat loss by conduction to the solid. Heat and mass conservation are used to derive boundary conditions at the propagating nose of the flow. In this pape r the two-dimensional flow produced by a line release of a given volum e of fluid is investigated. It is shown that at short times the flow s olidifies completely only near the point of release where the flow is thinnest, at later times complete solidification also occurs near the nose of the flow where the cooling rates are greatest and, eventually, the flow is completely solidified along its depth. Some transient mel ting of the boundaries can also occur if the fluid is initially above its solidification temperature. The dimensionless equations are parame terized only in terms of a Stefan number S and a dimensionless solidif ication temperature THETA. Asymptotic solutions for the flow at short times and near the source are derived by perturbation series and simil arity arguments. The general evolution of the flow is calculated numer ically, and the scaled time to final solidification, the length and th e thickness of the solidified product are determined as functions of S and THETA. The theoretical solutions provide simple models of the rel ease of a pulse of magma into a fissure in the Earth's lithosphere or of lava flow on the flanks of a volcano after a brief eruption. Other geological events are better modelled as flows fed by a continual supp ly of hot fluid. The solidification of such flows will be investigated in Part 2.