A study of the motion of long bubbles in inclined tubes

The rise velocity of tube-draining bubbles in a series of inclined tubes containing Newtonian and non-Newtonian fluids has been studied. The experimental data are correlated in terms of Froude (Fr), Eotvos (Eo), and Morton (M) numbers. Froude numbers are correlated as a function of angle of inclination {dollar}(theta){dollar} and Eo to determine the effect of tube size, inclination angle, and fluid properties on the rise velocity of bubbles. As {dollar}theta{dollar} increased, Fr increased, reached a maximum, and then decreased for both Newtonian and non-Newtonian fluids. The maximum Fr value occurred at higher angles for the non-Newtonian solutions. For Newtonian and non-Newtonian solutions possessing similar values of viscosity and surface tension, the Fr values, in general, were lower for the non-Newtonian solutions in the inclined tubes. In vertical tubes, the values were similar for both types of solutions. In general, as polymer concentration increases, Fr decreases.; The interpretation of the motion of long bubbles in tubes using coating flow theory was investigated due to their physical and theoretical similarities. Studies were conducted to determine if withdrawal theory (a specific type of coating flow) could predict film thickness associated with bubble rise. A photographic study was performed in order to obtain a direct measure of the film thickness. Both the upper and lower film thickness were measured in different tube sizes at various angles of inclination.; Three methods were utilized to indirectly measure the film thickness. In the first method, an equation was developed from a material conservation approach, for both Newtonian and non-Newtonian fluids, in order to calculate the film thickness resulting from bubble rise. In vertical tubes, the film thickness values compared fairly well to those predicted from withdrawal theory for the more viscous Newtonian and non-Newtonian solutions. For dilute (low viscosity) solutions. the comparison was poor In an inclined tubes, the film thicknesses predicted by this approach compared reasonably well with the directly measured upper film thicknesses.; The second approach involved collection of the draining fluid from the tube. For vertical tubes, this yielded values of film thickness which compared fairly well with those predicted by withdrawal theory especially at higher capillary number. In inclined tubes, the film thicknesses calculated by this approach also agreed fairly well with the directly measured upper film thicknesses.; Finally, a theoretical equation was derived using a matching procedure and a modified Euler method in order to determine the film thickness in inclined tubes. The film thickness values predicted this approach did not compare well with the directly measured film thicknesses.; An error analysis indicated that some of the difference between the directly measured film thickness and the film thickness predicted from the drainage and theoretical approaches, could be attributed to experimental error. It was concluded that the drainage approach can be used to predict the upper film thickness associated with bubble rise. The theoretical approach derived in this study, which is based on withdrawal theory, is only valid for larger tubes {dollar}rm(Dgeq0.0191m){dollar} inclined at low angles of inclination {dollar}(theta<15spcirc).{dollar}...