Ostwald ripening of buoyancy-driven microbubbles

Abstract

Microbubble solutions have a wide range of industrial applications, including heat transfer, agriculture, and water treatment. Therefore, understanding and controlling the variation in bubble sizes is critical. In this study, we develop a theoretical framework for Ostwald ripening of buoyancy-driven microbubbles by introducing a height-dependent size distribution function. For the first time, we show that the population balance equation in steady state can be interpreted within the Lifshitz–Slyozov–Wagner theory when the distribution function is redefined as the density distribution of the buoyancy-induced flux. Notably, in this form of Ostwald ripening, the distribution function approaches a scaled universal distribution, not over time, but as a function of height. We analytically derive the scaled universal distribution and show that the fifth power of the mean radius of the bubbles grows linearly with height.