From a steady plume to periodic puffs during confined carbon dioxide dissolution

Abstract

In this paper, the stability of a laminar plume due to solutal convection is addressed from experimental, numerical and theoretical points of view. A topless vertical tube containing water is put in a pressure cell filled with carbon dioxide ( $\text{CO}_{2}$ ). The diffusion of $\text{CO}_{2}$ at the free surface creates a thin layer of heavy fluid underneath the surface. This unstable density gradient generates a steady laminar plume which goes downward through the entire tube. A quasi-steady flow settles in the tube, filling gradually the bottom of the tube with heavy fluid. During this laminar regime, the velocity of the plume slowly decreases due to the build-up of the background density gradient. Surprisingly, despite the decrease of the Reynolds number, the laminar plume suddenly destabilises via a varicose mode into periodic pulsed puffs after an onset time which depends on the height of the tube and on the solutal Rayleigh number $Ra$ . This periodic regime is followed by an aperiodic regime, which lasts until the complete saturation of the solution. The observed destabilisation is explained as a result of the interplay between the feedback of the global recirculating flow and the progressive density stratification of the background fluid. The wavelength, frequency, onset time and phase velocity of the instability are explored using particle image velocimetry (PIV) measurements over two decades of Rayleigh number. The characteristics of the instability appear to be almost independent of the Bond number but strongly dependent on the solutal Rayleigh number and the aspect ratio. The phase velocity is very close to the fluid velocity of the plume before the instability, which has been predicted in various works to scale as $Ra^{2/3}(\ln \,Ra)^{1/3}$ . The wavelength is close to 4.5 times the radius of the cylinder (independent of aspect ratio, Bond number and Rayleigh number) such that the frequency scales as the phase velocity. The onset time, which is proportional to the height of the cylinder, scales as $Ra^{-0.55}$ and depends on the Bond number. A simplified model inspired from Lorenz’ waterwheel is proposed to explain the destabilisation process after partial fill-up of the cylinder. Although very qualitative, the model captures the key features of the experimental observations.