ALBERT

Description: Gravity currents created by the release of a fixed volume of a suspension into a lighter ambient fluid are studied theoretically and experimentally. The greater density of the current and the buoyancy force driving its motion arise primarily from dense particles suspended in the interstitial fluid of the current. The dynamics of the current are assumed to be dominated by a balance between inertial and buoyancy forces; viscous forces are assumed negligible. The currents considered are two-dimensional and flow over a rigid horizontal surface. The flow is modelled by either the single- or the two-layer shallow-water equations, the two-layer equations being necessary to include the effects of the overlying fluid, which are important when the depth of the current is comparable to the depth of the overlying fluid. Because the local density of the gravity current depends on the concentration of particles, the buoyancy contribution to the momentum balance depends on the variation of the particle concentration. A transport equation for the particle concentration is derived by assuming that the particles are vertically well-mixed by the turbulence in the current, are advected by the mean flow and settle out through the viscous sublayer at the bottom of the current. The boundary condition at the moving front of the current relates the velocity and the pressure head at that point. The resulting equations are solved numerically, which reveals that two types of shock can occur in the current. In the late stages of all particle-driven gravity currents, an internal bore develops that separates a particle-free jet-like flow in the rear from a dense gravity-current flow near the front. The second type of bore occurs if the initial height of the current is comparable to the depth of the ambient fluid. This bore develops during the early lock-exchange flow between the two fluids and strongly changes the structure of the current and its transport of particles from those of a current in very deep surroundings. To test the theory, several experiments were performed to measure the length of particle-driven gravity currents as a function of time and their deposition patterns for a variety of particle sizes and initial masses of sediment. The comparison between the theoretical predictions, which have no adjustable parameters, and the experimental results are very good. © 1993, Cambridge University Press

Description: Intense fluid motions can be generated by the solidification of a binary liquid. This review paper describes systematically some of the concepts involved in the fluid mechanics of solidification. It also presents quantitative calculations for the fluid motion, the rate of growth of solid and the evolution of both the thermal and the compositional fields in various geometries. The results of many of the calculations are favourably compared with data from laboratory experiments using aqueous solutions. © 1990, Cambridge University Press. All rights reserved.

Description: This is the third of a series of papers which investigates the evolution of a binary alloy that is cooled from above and releases buoyant residual fluid as one component of the alloy is preferentially incorporated within the solid. This paper focuses on the compositional zonation that is produced when the melt is completely solidified. Parts 1 and 2 considered the temperature of the cooled boundary to be greater than the eutectic temperature of the alloy so that only partial solidification of the alloy could occur. Here we extend the study by investigating the effects that arise when the cooling temperature is less than the eutectic temperature. The formation of a completely solid layer results, which extends from the cooling plate down to a mushy zone of dendritic crystals and interstitial melt. The melt below this mushy layer is convectively unstable because it is cooled from above. This generates vigorous thermal convection. Eventually the melt becomes completely solidified and a compositionally zoned solid is formed. The solid below the cooling plate is shown to be of fixed bulk composition until it reaches the depth that the interface between the mushy layer and melt occupied when the melt first became saturated. Below this level, the composition of the solid decreases with depth until it merges into the solid growing from the floor, whose composition is nearly equal to that of the heavier component of the alloy. Results of laboratory experiments with aqueous solutions of sodium sulphate are in good agreement with our quantitative predictions. The model is used to give an interpretation of profiles of the composition of magnesium oxide found within solidified komatiite lavas. © 1990, Cambridge University Press. All rights reserved.

Description: When a suspension of small particles is overlain by a clear fluid whose density is greater than that of the interstitial fluid, but less than that of the bulk suspension, the settling of the dense suspended particles can lead to vigorous convection in the overlying fluid. This novel situation is investigated experimentally and theoretically. A sharp interface is observed between the convecting upper region and a stagnant lower region in which there is unimpeded sedimentation at low Reynolds number. There is no transport of fluid from the upper region into the lower, though there is mixing of both buoyant fluid and entrained particles from the lower region into the upper. The interface between the two regions is found to descend at a constant velocity. Systematic laboratory measurements have determined how this velocity depends on the densities of the layers and the distributions of settling velocities of the particles. A theoretical description is developed which calculates the evolution of the density of the lower region due to differential sedimentation of polydisperse particles. Buoyancy arguments based on the calculated density profile are used to place upper and lower bounds on the amount of particle entrainment into the upper layer and on the rate of fall of the interface between the convecting and sedimenting regions. The theoretical predictions are in good agreement with the experimental observations. The analysis of the interaction between convection and sedimentation in the system considered here may be particularly relevant to the description of evolving crystal-rich layers in magma chambers and of silt-laden outflow from rivers, and has a wide range of other industrial, environmental and geological applications. © 1991, Cambridge University Press. All rights reserved.

Description: The model developed in Part 1 for the solidification and convection that occurs when an alloy is cooled from above is extended to investigate the role of disequilibrium at the mush—liquid interface. Small departures from equilibrium are important because in a convecting system an interfacial temperature below its equilibrium value can drive the bulk temperature of the melt below its liquidus. This behaviour is observed in experiments and can result in crystallization within and at the base of the convecting melt. The additional crystals formed in the interior can settle to the base of the fluid and continue to grow, causing the composition of the melt to change. This ultimately affects the solidification at the roof. The effects of disequilibrium are explored in this paper by replacing the condition of marginal equilibrium at the interface used in the model of Part 1 with a kinetic growth law of the form ht= &8T, where hi is the rate of advance of the mush-liquid interface, ST is the amount by which the interfacial temperature is below the liquidus temperature of the melt and is an empirical constant. This modification enables the model to predict very accurately both the growth of the mushy layer and the development of supersaturation in the isopropanol experiments described in Part 1. An additional series of experiments, using aqueous solutions of sodium sulphate, is presented in which the development of supersaturation leads to the internal nucleation and growth of crystals. A further extension of the model is introduced which successfully accounts for this internal crystal growth and the changing composition of the melt. We discuss the implications of this work for geologists studying the formation of igneous rocks. Important conclusions include the facts that cooling the roof of a magma chamber can lead to crystallization at its floor and that vigorous convection can occur in a magma chamber even when there is no initial superheat. © 1990, Cambridge University Press. All rights reserved.

Description: The interaction between the solidification and convection that occurs when a melt is cooled from above is investigated in a series of three papers. In these papers we consider a two-component melt that partially solidifies to leave a buoyant residual fluid. The solid forms a mushy layer of dendritic crystals, the interstices of which accommodate the residual fluid. The heat extraction through the upper boundary, necessary to promote solidification, drives convection at high Rayleigh numbers in the melt below the mushy layer. The convection enhances the heat transfer from the melt and alters the rate of solidification. In this paper the various phenomena are studied in a series of laboratory experiments in which ice is frozen from aqueous solutions of isopropanol. The experiments are complemented by the development of a general theoretical model in which the mush is treated as a continuum phase with thermodynamic properties that are functions of the local solid fraction. The model, which is based upon principles of equilibrium thermodynamics and local conservation of heat and solute, produces results in good agreement with the experimental data. Careful comparisons between this theory and experiments suggest the need to explore non-equilibrium effects, which are investigated in Parts 2 and 3. © 1990, Cambridge University Press. All rights reserved.