Stationary plume induced by carbon dioxide dissolution

In this paper, laminar convection flows induced by carbon dioxide absorption are addressed from experimental, numerical and theoretical points of view. A vertical glass tube (of centimetre scale) filled with distilled water is subjected to a sudden increase in the partial pressure of carbon dioxide. As a result of the diffusion of the gas into the unsaturated solution, a thin layer of fluid located underneath the surface becomes heavier. This initial density gradient first destabilizes to form a plume, which goes downwards through the entire cell. After a first transient pulsating regime (periodic succession of such Rayleigh-Benard plumes), a stationary flow settles in the tube, which is maintained by the constant supply of gas at the surface. At late stages, this stationary regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution (thermodynamic equilibrium). The present study only focuses on the stationary regime, whose characteristics appear to be almost independent of the Bond number and the aspect ratio but strongly dependent on the chemical Rayleigh number. Three decades of Rayleigh numbers are explored using particle image velocimetry measurements, which allows for a precise determination of the scaling exponents for the vertical velocity amplitude and the plume width. The assumption that gravity and a constant pressure gradient balance the viscous effects enables us to derive an analytic expression for the stationary vertical velocity on the axis, which scales as Ra-2/3 (lnRa)(1/3). As a consequence, the width of the plume scales as Ra-1/6 (lnRa)(-1/3) and the mass Nusselt number as (Ra/lnRa)(1/3). These scalings are in excellent agreement with the experimental and numerical results. The multiplicative constants of these scalings can also be calculated and show a fairly good agreement if a rigid boundary condition (no-slip) is assumed at the free surface.