The cycle of bubble production from a gas cavity in a supersaturated solution

Bubble nucleation, classified according to the review by Jones et al. (Adv. Colloid Interface Sci. 80 (1999) 27–50) as type IV non-classical, was examined in this study. Trains of bubbles were produced in carbonated water solutions at low levels of supersaturation, typically less than about 2, at specific sites on the surface of the vessel in contact with the liquid. Closer examination at a given site revealed a cycle of bubble formation, growth and detachment, defined by the growth time, tg, required for the bubble to grow to its detachment diameter, and the nucleation time, tn, required for a new bubble to appear following detachment. A relationship, representing the cycle of bubble production, was obtained by combining the bubble growth time, calculated using Scrivenʹs model (Scriven, Chem. Eng. Sci. 10(1/2) (1959) 1–13), with the bubble nucleation time. That is,1tg=Ntn+1tg*where N is a dimensionless number characterising the bubble nucleation time, and tg* is the growth time of the last possible bubble. Experiments conducted at a number of sites, and at different temperatures, produced results consistent with the above relationship. Most of the experiments were conducted with the contact angle at 65°, and these generally resulted in a bubble detachment diameter of about 600 μm, and a value of N∼0.3. It was concluded that the nucleation time was dependent on the diameter of the detaching bubble. This dependence was explained by considering the volume of liquid, partially depleted of carbon dioxide, in the boundary layer of the bubble. Some of this partially depleted liquid should leave with the departing bubble, and the rest should remain above the gas cavity, thus slowing down the rate of bubble growth in the cavity. A consideration of the critical condition for bubble detachment indicated that the bubble remained rooted at the cavity mouth during its growth. It was shown, using the growth time of the last possible bubble, that the critical radius of curvature of the meniscus in the cavity was about 3.3 μm at 16°C. The radius was also found to increase significantly with temperature, suggesting that the position of the meniscus inside the cavity moved when the system temperature was changed, and that the cavity was essentially conical.