Characterization of Air Entrainment Using a Pair of Vertically Aligned Revolving Rollers

Abstract

The present study reports the characterization of air entrainment within a viscous liquid pool using a pair of revolving rollers. The rollers are aligned vertically. The top roller (first roller) is partially submerged with a fixed submergence ratio of 0.5 (equally submerged in the gas and liquid); however, the bottom roller (second roller) is fully immersed inside the liquid pool. The present computational work is carried out using open-source Gerris Solver, which discretizes the working domain adaptively based on the gradient of volume fraction. The influence of the rotational speed (described by the capillary number, Ca) and depth of immersion of the second roller (W/D) on the length and width of the entrained cusp is analyzed thoroughly. A scattered regime plot is provided to describe the different patterns of entrainment with the effect of both Ca and W/D. In addition, we have also elucidated the instantaneous (Y*) and maximum (Ymax*) vertical shift of the cusp tip by varying Ca and W/D. An interesting bubble pinch-off mechanism at the cusp tip after achieving the steady length is elucidated by characterizing the frequency and volume accumulation of the detached gaseous masses. The influence of the gravitational pull and viscous drag on the pattern of entrainment is also investigated. They play important roles in controlling the behavior of cusp entrainment. Lastly, an analytical formulation is established to predict the bent thickness of the cusp by employing a balance of the relevant influencing forces acting on the cusp. It provides an excellent agreement between the analytical solutions and computational results.