Prediction of the Rise velocity of Taylor Bubble in Vertical Tube

A single gas bubble moving under the influence of gravitational, inertial, viscous and interfacial forces, relative to another fluid contained in a vertical cylindrical tube. Two-phase flows through millimeter channels may exhibit different behaviors due to the surface tension becomes significant in small - size channels. Wall effect is important for millimeter channel. As the diameter of the circular tubes became small, the upward motion of the gas bubble is slowed down, and ceases completely when the tube size was sufficiently reduced (diameter less than 5 millimeter for air - water). The sphericity of the bubble cap was enlarged about 40% due to change of the tube diameter from 6 mm to 9.5 mm. Predicted Froude number was also increased by 0.04 to 0.2 for the enhancement of tube diameter from 6 mm to 9.5 mm. Fluidsurface interaction can become dominated in small-channel. So we are interested to investigate the bubble dynamics in millimeter channel.