Abstract
When a gas bubble grows by diffusion in a gas–liquid solution, it affects the distribution of gas in its surroundings. If the density of the solution is sensitive to the local amount of dissolved gas, there is the potential for the onset of natural convection, which will affect the bubble growth rate. The experimental study of the successive quasi-static growth of many bubbles from the same nucleation site described in this paper illustrates some consequences of this effect. The enhanced growth due to convection causes a local depletion of dissolved gas in the neighbourhood of each bubble beyond that due to pure diffusion. The quantitative data of sequential bubble growth provided in the paper show that the radius-versus-time curves of subsequent bubbles differ from each other due to this phenomenon. A simplified model accounting for the local depletion is able to collapse the experimental curves and to predict the progressively increasing bubble detachment times.
Highlights
Diffusive processes leading to bubble formation are present in many different situations, such as gas-driven volcanic eruptions (Liu & Zhang 2000), bubble growth in porous media (Li & Yortsos 1995) affecting, among others, oil production (Akin & Kovscek 2002), bubbles emerging in carbonated beverages (Bisperink & Prins 1994; Liger-Belair, Voisin & Jeandet 2005; Uzel, Chappell & Payne 2006) such as beer (Lee, McKechnie & Devereux 2011) and the recently discovered nanobubbles (Lohse & Zhang 2015)
We will find that convective effects, which less surprisingly appear in strongly supersaturated gas–liquid solutions (Kuchmaand, Gor & Kuni 2009; Kuni, Kuchma & Adjemyan 2009), play a very subtle but dominant role towards the end of the bubble growth for a weak supersaturation level
By the definition (4.2b) and the results in figure 6(b), we find that the maximum local Rayleigh number Ran attained before detachment decreases for successive bubbles, which is an indicator that convection diminishes, which agrees with the decrease of mass transfer as subsequent bubbles keep growing and detaching, together with the diminishing slope represented in figure 5(b)
Summary
Diffusive processes leading to bubble formation are present in many different situations, such as gas-driven volcanic eruptions (Liu & Zhang 2000), bubble growth in porous media (Li & Yortsos 1995) affecting, among others, oil production (Akin & Kovscek 2002), bubbles emerging in carbonated beverages (Bisperink & Prins 1994; Liger-Belair, Voisin & Jeandet 2005; Uzel, Chappell & Payne 2006) such as beer (Lee, McKechnie & Devereux 2011) and the recently discovered nanobubbles (Lohse & Zhang 2015). The long-term effects due to the gas depletion of the volume surrounding a bubble nucleation site have not been studied in detail This depletion has limited effects on electrolytic bubble growth (Verhaart et al 1979; Sillen et al 1982), where gas is continuously generated, it has very marked consequences in the situation in which the overall initial dissolved gas concentration in the liquid is fixed. From a modelling point of view, the pure diffusion-driven growth of a spherical gas bubble in an infinite supersaturated liquid is a well-known problem whose dynamical equation has the following form (Epstein & Plesset 1950): dR dt. Lohse and D. van der Meer diffuses into the bubble In their experiment, the bubble grew out of a pit of radius Rp on the solid surface. Since the parameter S∗ is smaller than S, the bubble is predicted to grow on a solid surface at a smaller rate in comparison to a bubble in an unbounded liquid
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call