Modeling of Taylor bubble rising in a vertical mini noncircular channel filled with a stagnant liquid

This paper presents a theoretical model that predicts the drift velocity of an elongated bubble (a Taylor bubble) in vertical mini triangular and square channels closed at the bottom and filled with a stagnant liquid. To facilitate the analysis, the bubble profile is divided into three zones along bubble length: the front meniscus zone, the uniform film zone in the middle of the bubble, and the rear meniscus zone. The model takes into account the effects of capillary pressure, induced by the interfacial curvature variations along bubble length, gravity, and viscous force. The interfacial profiles and the bubble drift velocities are determined by solving the conservation equations of the momentum of the liquid phase coupled with the equations of the force balance at the bubble interface. The predicted drift velocities of the bubble in both mini triangular and square channels are found to be favorably in an agreement with the experimental data in the literature. It has been revealed that the drift velocities in the triangular channel are substantially higher than those in the square channel having the same hydraulic diameter. The influences of channel size and the physical properties of the fluid on the bubble drift velocities are also examined. Finally, respective correlations for predicting the bubble drift velocities in both mini triangular and square channels are developed in terms of appropriate dimensionless parameters.