Mass transport in confinement: CO2 convection and diffusion in a narrow cylindrical liquid barrier

In this thesis we study the dissolution of carbon dioxide and the subsequent mass transfer mechanisms in a liquid barrier confined to a narrow cylindrical cell, focusing both on the short-time transient behaviour and on the long-time, steady mass transfer processes under different experimental conditions. Due to the strong confinement, we force the formation of only a single convective plume after the onset of convection, allowing us to discriminate the initial diffusive behaviour, the moment of the onset of convection, and the propagation of the carbon dioxide into and through the liquid barrier. Furthermore, by trapping a slug bubble underneath the liquid barrier, we were able to quantify the quasi steady-state mass transfer in and through the liquid barrier.

In Chapter 2 we begin by quantifying the long-time mass transfer transport by trapping a slug bubble in a narrow vertical cylinder underneath short liquid barriers. We study the growth of the slug bubble after replacing the outer air atmosphere with a pure CO2 atmosphere and compare the experimental results with simple numerical and analytical models to predict the bubble growth dynamics. We observe that the asymmetric exchange of the gaseous solutes between the CO2-rich water barrier and the air-rich bubble always results in net bubble growth, a process we refer to as solute exchange. We conclude that the mass transport is convective rather than diffusive, consistent with a power-law in which the Sherwood number depends on the Rayleigh number to the power one fourth. Furthermore, we derive an analytical solutions that accurately predict the bubble growth dynamics, in which the effect of convective dissolution across the water layer is treated as a reduction of the effective diffusion length, in accordance with the mass transfer scaling observed in laminar or natural convection. Finally, we place a n-hexadecane layer underneath the trapped slug bubble in order to extend the binary water--bubble system to a ternary water--bubble--alkane system. We find that n-hexadecane layer bestows a buffering (hindering) effect on bubble growth and dissolution.

In Chapter 3 we shift our focus from the long-time mass transfer mechanics to the short-time transient behaviour. By adding sodium fluorescein, a pH sensitive fluorophore, to the liquid barrier we directly visualise the dissolution and propagation of the CO2 and as a result can study the initial dissolution, onset of convection, and the CO2 propagation throughout the barrier in great detail. Once the CO2 comes into contact with the water barrier a CO2-rich water layer forms at the top gas-liquid interface, which is denser in comparison to pure water. Continued dissolution of CO2 into the water barrier results in the layer becoming gravitationally unstable, leading to the onset of buoyancy-driven convection and, consequently, the shedding of a buoyant plume. Tracking the CO2 front propagation in time results in the discovery of two distinct transport regimes, a purely diffusive regime and a convective regime where the CO2 front nevertheless propagates in a diffusive manner, but with an effective diffusion coefficient that is substantially larger than the ordinary molecular diffusion coefficient. This is the enhanced diffusive regime. Using direct numerical simulations, we explain the propagation dynamics of these two transport regimes in this laterally strongly confined geometry, namely by disentangling the contributions of diffusion and convection to the propagation of the CO2 front.

In Chapter 4 we expand on our findings from chapters 2 and 3 by varying the degree of confinement. In the first part of the chapter we focus on expanding our understanding of the short-time, transient diffusion of CO2 into a vertical water barrier confined to a narrow cylindrical cell by varying the cylinder diameter and CO2 pressure. We combine fluorescence and particle tracking experiments to quantify the effects of the cylinder width and CO2 pressure on the initial diffusive behaviour, the onset of convection, and the enhancement of the buoyancy driven convection of the subsequent transport. In the second part, we investigate the long-time, steady mass transfer dynamics in the liquid barrier by trapping a slug bubble underneath the liquid barrier and varying the barrier height and partial CO2 pressure.

In Chapter 5 we investigate the effect of a tilt angle on the dissolution and subsequent propagation dynamics of carbon dioxide gas into a water barrier confined to a glass cylinder. By adding sodium fluorescein, we directly visualise the dissolution, onset of convection, and propagation of the CO2 across the water barrier. In the convective stage, we find that increasing the tilt angle results in enhancement of the propagation dynamics of the CO2 until an optimum is reached around 45 degrees. Increasing the tilt angle past 45 degrees diminishes this enhancement effect, even slowing down the mass transfer dynamics in comparison to 0 degrees when the tilt angle reaches 90 degrees. Additionally, we find that increasing the tilt angle leads to a decrease in the effective critical Rayleigh number.

In Chapter 6, by using mixtures of water and various alcohols, we investigate the effect of the liquid properties on the propagation dynamics of carbon dioxide through a liquid barrier confined to a vertical, cylindrical cell in order to investigate the influence of the physical parameters, such as the viscosity and CO2 solubility, on the short-time transient diffusion of CO2 into the liquid barrier. The addition of methanol, ethanol, 1-propanol, and 2-propanol to water causes a decrease in viscosity, while the diffusion coefficient and solubility increase. For the ethylene glycol experiment we obtain the predicted results, which visualise the effect of viscosity on the propagation dynamics of the CO2. For the other alcohols, we observe non-monotonic behaviour which cannot simply be explained by the changes in viscosity, solubility and diffusivity. This is most likely due to the solutal expansion coefficient changing with the alcohol mole fraction, however reliable literature values are not available.

Finally, in Chapter 7 we add various salts to the water barrier at varying salinities to investigate the effects on the dissolution and propagation dynamics of carbon dioxide through a liquid barrier consisting of these aqueous salt solutions confined to a glass cylinder. We conduct experiments in an inverted (180 degrees) and an upright configuration, at a tilt angle of either 0 degrees or 30 degrees. When inverted, the front propagation is purely driven by diffusion and the obtained front trajectories are highly reproducible, regardless of the salt or salinity. The obtained diffusion coefficients are in good agreement with the literature. When the system is upright and untilted (0 degrees), the experimental results become highly irreproducible, with the observation of the simultaneous shedding of multiple convection rolls, and the propagation dynamics widely vary. Applying a tilt angle of 30 degrees to the upright system, we slightly improve the reproducibility of the experiments but still find it to be less reproducible compared to pure water. We conclude that this behaviour is most likely caused by an additional factor contributing to the gravitational forcing of the solutions, like the production of insolvable solids. This additional gravitational forcing may result in the highly irreproducible behaviour observed in the convective experiments.