Silvana S. S. Cardoso

From Chemical Gardens to Chemobrionics

Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap.

Mixing by a Turbulent Plume in a Confined Stratified Region

An experimental and theoretical study of the mixing produced by a plume rising in a confined stratified environment is presented. As a result of the pre-existing stable stratification, the plume penetrates only part way into the region; at an intermediate level it intrudes laterally forming a horizontal layer. As time evolves, this layer of mixed fluid is observed to increase in thickness. The bottom front advects downward in a way analogous to the first front in the filling box of Baines & Turner (1969), while the lateral spreading of the plume occurs at an ever-increasing level and an ascending top front results. We develop a model of this stratijiedfilling box; the model predicts the rate at which the two fronts advance into the environment. It is found that stratification in the environment, when smooth, has no significant influence on the dynamics of the descending front. We show that the rate of rise of the ascending front is determined by the turbulent mixing occurring at the spreading level. Entrainment of environmental fluid from above into the overshooting plume is significant; as a result, a density interface develops at this level. Asymptotically, the system reaches a state in which a bottom convecting layer, with an almost homogeneous density, deepens in a stratified background. The model proposed for this large-time behaviour is based on the simple energetic formulation that a constant fraction of the kinetic energy supplied by the plume, for mixing across the interface, is converted into potential energy of the convective layer. Our experimental results suggest an efficiency of approximately 50 % for this conversion. We discuss our results in the light of previous studies on turbulent penetrative convection and conclude that the theory developed should be valid for an intermediate range of values of the Richardson number characterizing the dynamic conditions at the interface. The model is applied quantitatively to the process of cooling of a room wherein stratification is relevant. The geological problem of replenishment of a magma chamber by a light input of magma is also analysed.

On convection in a volatile-saturated magma

When a saturated basaltic magma cools and crystallises in a shallow magma reservoir, gas bubbles may be exsolved from solution, thereby influencing the density, convective mixing and pressure evolution of the melt. In wet basaltic magmas, saturated with H2O, the production of small bubbles may dominate the density evolution of the mixture, causing a gradual decrease of the bulk density with cooling. Cool upper boundaries of the chamber may therefore become stable to convection while vigorous convection may develop as the bubbly-mixture rises from cold lower boundaries. The intensity of such bubble-driven convection may be an order of magnitude greater than purely thermal or compositional convection which arises in unsaturated melt. New laboratory experiments of such bubble-driven convection suggest that after a transient, an equilibrium bubble concentration is attained, and subsequently bubble-magma separation leads to build up of a layer of bubbles above the well-mixed bubble-laden melt [1]. These results have some important implications for mixing when a volatile rich mafic magma is intruded below an evolved, less dense body of silicic magma. When the mafic magma becomes volatile saturated, then owing to cooling at its upper boundary, the bulk density in the upper boundary layer of the mafic magma will decrease owing to the exsolution of gas. If the density falls below that of the overlying silicic magma, then small plumes of buoyant bubble-rich mafic magma may rise from the boundary into the upper silicic layer. In addition, on saturation of the mafic magma, cooling at the lower boundary will begin to drive convection of bubble-rich melt. The mafic magma may eventually reach an equilibrium bubble concentration and, subsequently, the bubbles produced at the base of the layer will be supplied to the interface between the silicic and mafic layers. Large scale overturn of the mafic and silicic magmas can therefore only occur if, at the equilibrium bubble concentration, the bulk density of the bubbly mafic magma is smaller than that of the overlying magma; otherwise mixing continues through small plumes of vesicular mafic melt rising from the upper boundary layer. For basaltic magma in which CO2 is the dominant volatile phase, the generation of bubbles does not typically dominate the density evolution and the convective flows are similar to those in an unsaturated melt.

Geochemistry of silicate-rich rocks can curtail spreading of carbon dioxide in subsurface aquifers

Pools of carbon dioxide are found in natural geological accumulations and in engineered storage in saline aquifers. It has been thought that once this CO2 dissolves in the formation water, making it denser, convection streams will transport it efficiently to depth, but this may not be so. Here, we assess theoretically and experimentally the impact of natural chemical reactions between the dissolved CO2 and the rock formation on the convection streams in the subsurface. We show that, while in carbonate rocks the streaming of dissolved carbon dioxide persists, the chemical interactions in silicate-rich rocks may curb this transport drastically and even inhibit it altogether. These results challenge our view of carbon sequestration and dissolution rates in the subsurface, suggesting that pooled carbon dioxide may remain in the shallower regions of the formation for hundreds to thousands of years. The deeper regions of the reservoir can remain virtually carbon free.

Frontiers of chaotic advection

This work reviews the present position of and surveys future perspectives in the physics of chaotic advection: the field that emerged three decades ago at the intersection of fluid mechanics and nonlinear dynamics, which encompasses a range of applications with length scales ranging from micrometers to hundreds of kilometers, including systems as diverse as mixing and thermal processing of viscous fluids, microfluidics, biological flows, and oceanographic and atmospheric flows.

Convection and reaction in a diffusive boundary layer in a porous medium: Nonlinear dynamics

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

The formation of drops through viscous instability

The stability of an immiscible layer of fluid bounded by two other fluids of different viscosities and migrating through a porous medium is analysed, both theoretically and experimentally. Linear stability analyses for both one-dimensional and radial flows are presented, with particular emphasis upon the behaviour when one of the interfaces is highly stable and the other is unstable. For one-dimensional motion, it is found that owing to the unstable interface, the intermediate layer of fluid eventually breaks up into drops. However, in the case of radial flow, both surface tension and the continuous thinning of the intermediate layer as it moves outward may stabilize the system. We investigate both of these stabilization mechanisms and quantify their effects in the relevant parameter space. When the outer interface is strongly unstable, there is a window of instability for an intermediate range of radial positions of the annulus. In this region, as the basic state evolves to larger radii, the linear stability theory predicts a cascade to higher wavenumbers. If the growth of the instability is sufficient that nonlinear effects become important, the annulus will break up into a number of drops corresponding to the dominant linear mode at the time of rupture. In the laboratory, a Hele-Shaw cell was used to study these processes. New experiments show a cascade to higher-order modes and confirm quantitatively the prediction of drop formation. We also show experimentally that the radially spreading system is stabilized by surface tension at small radii and by the continual thinning of the annulus at large radii.

The mixing of liquids by a plume of low-Reynolds number bubbles

Abstract When bubbles are continuously released from a localised source at the bottom of a liquid layer, a plume is produced. As the bubble plume rises due to its buoyancy, it entrains surrounding liquid, which is carried upward with the stream of bubbles. In the present work, we investigate the motion of a plume of low-Reynolds number bubbles in a stratified liquid consisting of two homogeneous layers of different densities. The liquid environment is of finite lateral extent. We develop a theoretical model for the flow of the bubble plume and the surrounding liquid. The full equations are solved numerically. The mixing at the interface is quantified and the time-evolution of the density profiles in both layers is calculated. The model also predicts the rate of rise of the density interface. We develop an analytical solution for the problem in the limit of strong stratifications. Our theoretical predictions are compared with new experimental results using plumes of small bubbles generated by electrolysis of an aqueous solution of sodium chloride and with previous experimental results (McDougall (1978), Journal of Fluid Mechanics , 85 , 655–672; Baines & Leitch (1992), Journal of Hydraulic Engineering , 118 (4), 559–577).

Turbulent plumes with heterogeneous chemical reaction on the surface of small buoyant droplets

A model is developed for a turbulent plume with heterogeneous chemical reaction rising in an unbounded environment. The chemical reaction, which may generate or deplete buoyancy in the plume, occurs at the interface between two phases, a continuous phase and a dispersed one. We study the case in which a buoyant reactant is released at the source and forms the dispersed phase, consisting of very small bubbles, droplets or particles. Once in contact with the ambient fluid, a first-order irreversible reaction takes place at the surface of the, for example, droplets. The behaviour of this plume in a uniform and stratified environment is examined. We show that the dynamics of a pure plume with such heterogeneous reaction is completely determined by the ratio of the environmental buoyancy frequency N and a frequency parameter associated with the chemical reaction, G . The group G is a measure of the ability of the reaction to generate buoyancy in the plume. In a uniform environment, the sign of parameter G fully determines the plume motion. When the reaction generates buoyancy (positive G ) the motion is unbounded, whilst when reaction depletes buoyancy (negative G ) the plume reaches a level of neutral buoyancy. A relation for this neutral buoyancy level as a function of the initial buoyancy flux of the plume and G is calculated. Our theoretical predictions compared well with experimental results using a plume of calcium carbonate particles descending in an acidic aqueous solution. In a stratified environment, the motion of the plume is always bounded, irrespective of the magnitude of G , and we determine the level of maximum buoyancy flux, as well as those of zero buoyancy and zero momentum as a function of N / G . Finally, our model is applied to study the dynamics of a localized release of carbon dioxide in the ocean.

Thermodynamics, Disequilibrium, Evolution: Far-From-Equilibrium Geological and Chemical Considerations for Origin-Of-Life Research

The 8th meeting of the NASA Astrobiology Institute’s Thermodynamics, Disequilibrium, Evolution (TDE) Focus Group took place in November 2014 at the Earth-Life Science Institute, at the Tokyo Institute of Technology, Japan. The principal aim of this workshop was to discuss the conditions for early Earth conducive for the emergence of life, with particular regard to far-from-equilibrium geochemical systems and the thermodynamic and chemical phenomena that are driven into being by these disequilibria. The TDE focus group Orig Life Evol Biosph DOI 10.1007/s11084-016-9508-z