Generation of micro gas bubbles of uniform diameter in an ultrasonic field

Abstract

Consecutive images of the fragmentation of capillary waves in an ultrasonic field were obtained using a high-speed video camera through a microscope at a frame rate of 500000 frames per second. The images showed that micro bubbles of uniform diameter from 4 to 15$\,\mu$m were generated at a constant periodic rate when a small amount of gas was introduced (via a needle) into a highly viscous liquid whose kinematic viscosity was between 5 and 100 mm$^{2}\,{\rm s}^{-1}$. Conditions for stable generation of micro bubbles of uniform diameter were also studied by changing the inner diameter of the needle between 0.08 and 0.34 mm, excitation frequency of around 18.77 and 42.15 kHz, kinematic viscosity of liquid between 5 and 100 mm$^{2}\,{\rm s}^{-1}$, surface tension between 20 and 34 mN m$^{-1}$, and viscosity of gas between 9.0 and 31.7$\,\mu$Pa s. Results revealed that (i) a projection is formed on the oscillatory gas–liquid interface and micro bubbles are released from the tip of the projection; (ii) gas viscosity critically affects the formation of the projection and should be around 20.0$\,\mu $Pa s for stable mother bubble oscillation; (iii) conditions for stable generation of micro bubbles are also affected by excitation frequency, surface tension and viscosity of the liquid, and dimensions of the needle; (iv) two controlling parameters for stable generation are the Weber number (${\it We}\,{=}\,\rho {f}^{2}d_{\hbox{\scriptsize{\it in}}}^{3}/\sigma $, where $\rho $ is the density of the liquid, $f$ is the excitation frequency, $d_{\hbox{\scriptsize{\it in}}}$ is the inner diameter of the needle, and $\sigma $ is the surface tension) and the Womersley number (${\it Wo}\,{=}\,d_{\hbox{\scriptsize{\it in}}}(f/{\nu })^{1 / 2}$, where $\nu $ is the kinematic viscosity of liquid); and (v) uniform-diameter micro bubbles are generated stably when ${\it We}<300$ and $2<$${\it Wo}<5$. Under the conditions where micro bubbles of uniform diameter were stably generated, the bubble diameter increased almost linearly with increasing gas pressure inside the needle. The gradient of this linear function can be expressed as a function of WoWe, and the normalized outer diameter of the needle, and decreases either with decreasing inner diameter of the needle or with increasing excitation frequency, surface tension and viscosity of the liquid, and outer diameter of the needle.