Diffusion of dissolved CO2 in water propagating from a cylindrical bubble in a horizontal Hele-Shaw cell

Abstract

The dissolution of a gas bubble in a confined geometry is a problem of interest in technological applications such as microfluidics or carbon sequestration, as well as in many natural flows of interest in geophysics. While the dissolution of spherical or sessile bubbles has received considerable attention in the literature, the case of a two-dimensional bubble in a Hele-Shaw cell, which constitutes perhaps the simplest possible confined configuration, has been comparatively less studied. Here, we use planar laser-induced fluorescence to experimentally investigate the diffusion-driven transport of dissolved CO 2 that propagates from a cylindrical mm-sized bubble in air-saturated water confined in a horizontal Hele-Shaw cell. We observe that the radial trajectory of an isoconcentration front, r f (t), evolves in time as approximately r f − R 0 ∝ √ t,where R 0 denotes the initial bubble radius. We then characterize the unsteady CO 2 concentration field via two simple analytical models, which are then validated against a numerical simulation. The first model treats the bubble as an instantaneous line source of CO 2 , whereas the second assumes a constant interfacial concentration. Finally, we provide an analogous Epstein-Plesset equation with the intent of predicting the dissolution rate of a cylindrical bubble.

Experimental determination of gas diffusivity in liquids—A review

“…[ 50 ] Hence, in bubble dissolution method, the dissolution time and the initial bubble radius are used to estimate gas diffusivity based on an analytical solution of the gas mass balance. [ 51,52 ] A similar technique exists for gases with low solubility in which bubble radius is measured with time for diffusivity determination. [ 53 ]…”

Reaction Systems for Bubbly Flows

“…For further progress in evaluating the chemical differences when varying the solvent or the system, which is activated or changed by the gas, the basic environment of the actual multiphase system should be investigated first. Interesting factors like the bubble velocities, sizes and rising behaviour is usually measured in a water/CO 2 system …”

“…A more advanced analysis method for the CO 2 /water system in terms of bubble movement is a Hele–Shaw cell . A rising bubble with a cylindrical shape is produced between two glass walls with a gap of 1 mm.…”

“…(a) Plan view and (b) side view of the experimental setup. PLIF revealed a CO 2 ‐containing region [dark green enclosed by r f ( t )] propagating radially outward from the dissolving cylindrical bubble of radius R ( t ) . Reproduced with permission.…”

“…Comparison of (a) a raw image and (b) a processed image. The white dotted circle marks the initial bubble circumference, while the red dotted circle marks the front position . Reproduced with permission.…”