On the breakup of an air bubble injected into a fully developed turbulent flow. Part 1. Breakup frequency

Abstract

The transient evolution of the bubble-size probability density functions resulting from the breakup of an air bubble injected into a fully developed turbulent water ow has been measured experimentally using phase Doppler particle sizing (PDPA) and image processing techniques. These measurements were used to determine the breakup frequency of the bubbles as a function of their size and of the critical diameter D_c defined as D_c = 1.26 (σ/ρ)^3/5ε^−2/5, where ε is the rate of dissipation per unit mass and per unit time of the underlying turbulence. A phenomenological model is proposed showing the existence of two distinct bubble size regimes. For bubbles of sizes comparable to D_c, the breakup frequency is shown to increase as (σ/ρ)^−2/5ε^−3/5 √D/D_c−1, while for large bubbles whose sizes are greater than 1.63D_c, it decreases with the bubble size as ε^1/3D^−2/3. The model is shown to be in good agreement with measurements performed over a wide range of bubble sizes and turbulence intensities.