Step-Wise Velocity of an Air Bubble Rising in a Vertical Tube Filled with a Liquid Dispersion of Nanoparticles

The motion of air bubbles in tubes filled with aqueous suspensions of nanoparticles (nanofluids) is of practical interest for bubble jets, lab-on-a-chip, and transporting media. Therefore, the focus of this study is the dynamics of air bubbles rising in a tube in a nanofluid. Many authors experimentally and analytically proposed that the velocity of rising air bubbles is constant for long air bubbles suspended in a vertical tube in common liquids (e.g. an aqueous glycerol solution) when the capillary number is larger than 10^-4. For the first time, we report here a systematic study of an air bubble rising in a vertical tube in a nanofluid (e.g. an aqueous silica dioxide nanoparticle suspension, nominal particle size, 19 nm). We varied the bubble length scaled by the diameter of the tubes (L/D), the concentration of the nanofluid (10 and 12.5 v %), and the tube diameter (0.45, 0.47, and 0.50 cm). The presence of the nanoparticles creates a significant change in the bubble velocity compared with the bubble rising in the common liquid with the same bulk viscosity. We observed a novel phenomenon of a step-wise increase in the air bubble rising velocity versus bubble length for small capillary numbers less than 10^-7. This step-wise velocity increase versus the bubble length was not observed in a common fluid. The step-wise velocity increase is attributed to the nanoparticle self-layering phenomenon in the film adjacent to the tube wall. To elucidate the role of the nanoparticle film self-layering on the bubble rising velocity, the effect of the capillary number, the tube diameter (e.g. the capillary pressure), and nanofilm viscosity are investigated. We propose a model that takes into consideration the nanoparticle layering in the film confinement to explain the step-wise velocity phenomenon versus the length of the bubble. The oscillatory film interaction energy isotherm is calculated and the Frenkel approach is used to estimate the film viscosity.