Abstract
Taylor finger is characterized by a single elongated air bubble that grows upward during the drainage of liquid from closed top vertical tubes. The characteristic of the Taylor finger is similar to the Taylor bubble commonly observed in gas–liquid two-phase flow. During the upward growth of the Taylor finger, liquid from the tube drains as a thin film around it. The exact prediction of film thickness is important in several engineering designs and process calculations such as the design of contacting devices, two-phase flow through porous media, boiling in tubes, and monolith reactors. The present study proposes an experimental technique to estimate the thickness of the draining liquid film. Based on experiments an empirical model has been proposed for non-dimensional film thickness in the inviscid region. The proposed model agrees well with the experimental data and equation proposed in published literatures (Davies, R. M., and G. Taylor. 1950. “The Mechanics of Large Bubbles Rising Through Extended Liquids and Through Liquids in Tubes.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 200, 375–90; Dukler, A. E., and J. Fabre. 1994. “Gas-Liquid Slug Flow.” Multiphase Science and Technology 8: 1–4; Fabre, J., and A. Liné. 1992. “Modeling of Two-Phase Slug Flow.” Annual Review of Fluid Mechanics 24: 21–46).
Acknowledgements
We are grateful to Professor Gargi Das for his generous support of our experimental activity. The authors are thankful to Professor Subhabrata Ray for his help in preparing this paper.
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Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
References
Aussillous, P., and D. Quere. 2000. “Quick Deposition of a Fluid on the Wall of a Tube.” Physics of Fluids 12: 2367–71, https://doi.org/10.1063/1.1289396.Search in Google Scholar
Biswas, K. G., G. Das, S. Ray, and J. K. Basu. 2015. “The Use of Bends for Enhanced Mass Transfer During Liquid-Liquid Flow Through Milli Channels.” International Journal of Heat and Mass Transfer 84: 876–92, https://doi.org/10.1016/j.ijheatmasstransfer.2015.01.085.Search in Google Scholar
Brady, P. T., M. Herrmann, and J. M. Lopez. 2011. “Confined Thermocapillary Motion of a Three-Dimensional Deformable Drop.” Physics of Fluids 23: 22101, https://doi.org/10.1063/1.3529442.Search in Google Scholar
Bretherton, F. 1961. “The Motion of Long Bubbles in a Network of Tubes.” Journal of Fluid Mechanics 10: 166–88, https://doi.org/10.1017/s0022112061000160.Search in Google Scholar
Brown, R. A. S. 1965. “The Mechanics of Large Gas Bubbles in Tubes: I. Bubble Velocities in Stagnant Liquids.” The Canadian Journal of Chemical Engineering 43: 217–23, https://doi.org/10.1002/cjce.5450430501.Search in Google Scholar
Davies, R. M., and G. Taylor. 1950. “The Mechanics of Large Bubbles Rising Through Extended Liquids and Through Liquids in Tubes.” Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences 200, 375–90.10.1016/B978-0-08-092523-3.50041-1Search in Google Scholar
de Azevedo, M. B., D. dos Santos, J. L. H. Faccini, and J. Su. 2017. “Experimental Study of the Falling Film of Liquid Around a Taylor Bubble.” International Journal of Multiphase Flow 88: 133–41, https://doi.org/10.1016/j.ijmultiphaseflow.2016.09.021.Search in Google Scholar
Ding, Z., R. Liu, T. N. Wong, and C. Yang. 2018. “Absolute Instability Induced by Marangoni Effect in Thin Liquid Film Flows on Vertical Cylindrical Surfaces.” Chemical Engineering Science 177: 261–9, https://doi.org/10.1016/j.ces.2017.11.039.Search in Google Scholar
Drosos, E.I.P., S.V. Paras, and A.J. Karabelas. 2004. “Characteristics of developing free falling films at intermediate Reynolds and high Kapitza numbers.” International Journal of Multiphase Flow 30: 853–876.10.1016/j.ijmultiphaseflow.2004.03.003Search in Google Scholar
Dukler, A. E., and J. Fabre. 1994. “Gas-Liquid Slug Flow.” Multiphase Science and Technology 8: 1–4, https://doi.org/10.1615/multscientechn.v8.i1-4.80.Search in Google Scholar
Dumitrescu, D. T. 1943. “Flow on an Air Bubble in the Vertical Tube.” Journal of Applied Mathematics and Mechanics 23: 139–49, https://doi.org/10.1002/zamm.19430230303.Search in Google Scholar
Fabre, J., and A. Liné. 1992. “Modeling of Two-Phase Slug Flow.” Annual Review of Fluid Mechanics 24: 21–46, https://doi.org/10.1146/annurev.fl.24.010192.000321.Search in Google Scholar
Goldsmith, H. L., and S. G. Mason. 1962. “The Movement of Single Large Bubbles in Closed Vertical Tubes.” Journal of Fluid Mechanics 14: 42–58, https://doi.org/10.1017/s0022112062001068.Search in Google Scholar
Hayashi, K., and A. Tomiyama. 2012. “Effects of Surfactant on Terminal Velocity of a Taylor Bubble in a Vertical Pipe.” International Journal of Multiphase Flow 39: 78–87, https://doi.org/10.1016/j.ijmultiphaseflow.2011.11.001.Search in Google Scholar
Hu, P., X. Huang, K. Bao, and G. Zhu. 2020. “Experiment Study on Film Width and Thickness of Free-Falling Water Film on a Large Inclined Plate.” Nuclear Engineering and Design 358: 110445, https://doi.org/10.1016/j.nucengdes.2019.110445.Search in Google Scholar
Irandoust, S., and B. Andersson. 1989a. “Liquid Film in Taylor Flow Through a Capillary.” Industrial & Engineering Chemistry Research 28: 1684–8, https://doi.org/10.1021/ie00095a018.Search in Google Scholar
Irandoust, S., and B. Andersson. 1989b. “Simulation of Flow and Mass Transfer in Taylor Flow Through a Capillary.” Computers & Chemical Engineering 13: 4–5, https://doi.org/10.1016/0098-1354(89)85034-3.Search in Google Scholar
Jana, A. K., T. K. Mandal, D. P. Chakrabarti, G. Das, and P. K. Das. 2007. “An Optical Probe for Liquid–Liquid Two-phase Flows.” Measurement Science and Technology 18: 1563, https://doi.org/10.1088/0957-0233/18/5/048.Search in Google Scholar
Kang, C. W., S. Quan, and J. Lou. 2010. “Numerical Study of a Taylor Bubble Rising in Stagnant Liquids.” Physical Review E 81: 066308, https://doi.org/10.1103/PhysRevE.81.066308.Search in Google Scholar PubMed
Kumar, A., G. Das, and S. Ray. 2017. “Void fraction and pressure drop in gas-liquid downflow through narrow vertical conduits-experiments and analysis.” Chemical Engineering Science 171: 117–130.10.1016/j.ces.2017.05.027Search in Google Scholar
Kumar, A., G. Das, S. Ray, J. M. Jha, A. K. Thakur, and S. R. Panda. 2021a. “Gas-liquid Downward Flow Through Narrow Vertical Conduits: Effect of Angle of Entry and Tube-Diameter on Flow Patterns.” International Journal of Chemical Reactor Engineering 19: 655–62, https://doi.org/10.1515/ijcre-2020-0164.Search in Google Scholar
Kumar, A., S. Ray, and G. Das. 2018. “Draining Phenomenon in Closed Narrow Tubes Pierced at the Top: An Experimental and Theoretical Analysis.” Scientific Reports 8: 1–11, https://doi.org/10.1038/s41598-018-32359-5.Search in Google Scholar PubMed PubMed Central
Kumar, A., A. K. Thakur, R. Kumar, P. Chaudhari, M. D. Aurangzeb, and G. K. Gaurav. 2021b. “Experimental investigation on in-situ void fraction of air-water co-current flow-through milli-channels.” Materials Today: Proceedings.10.1016/j.matpr.2021.12.317Search in Google Scholar
Llewellin, E. W., E. Del Bello, J. Taddeucci, P. Scarlato, and S. Lane. 2012. “The Thickness of the Falling Film Ff Liquid Around a Taylor Bubble.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1041–64, https://doi.org/10.1098/rspa.2011.0476.Search in Google Scholar
Mandal, S., P. K. Das, and K. Biswas. 2021. “Reconstruction of the Shape of a Taylor Bubble Rising Through a Circular Tube Using Parallel Wire Conductivity Probes.” In 2021 IEEE Second International Conference on Control, Measurement and Instrumentation (CMI), 178–83.10.1109/CMI50323.2021.9362868Search in Google Scholar
Picchi, D., A. Ullmann, N. Brauner, and P. Poesio. 2021. “Motion of a Confined Bubble in a Shear-Thinning Liquid.” Journal of Fluid Mechanics: 918, https://doi.org/10.1017/jfm.2021.321.Search in Google Scholar
Thakur, A. K., S. K. Gupta, and P. Chaudhari. 2020 In press. “Slurry-phase ethylene polymerization processes: a review on multiscale modeling and simulations.” Reviews in Chemical Engineering, https://doi.org/10.1515/revce-2020-0048.Search in Google Scholar
Viana, F., R. Pardo, R. Yánez, J. L. Trallero, and D. D. Joseph. 2003. “Universal Correlation for the Rise Velocity of Long Gas Bubbles in Round Pipes.” Journal of Fluid Mechanics 494: 379–98, https://doi.org/10.1017/s0022112003006165.Search in Google Scholar
Wallis, G. B. 1969. One-Dimensional Two-Phase Flow. New York: McGraw-Hill.Search in Google Scholar
Ye, X., T. Hao, Y. Chen, X. Ma, and R. Jiang. 2020. “Liquid Film Transport Around Taylor Bubble in a Microchannel with Gas Cavities.” Chemical Engineering and Processing-Process Intensification 148: 107828, https://doi.org/10.1016/j.cep.2020.107828.Search in Google Scholar
Young, N. O., J. S. Goldstein, and M. J. Block. 1959. “The Motion of Bubbles in a Vertical Temperature Gradient.” Journal of Fluid Mechanics 6: 350–6, https://doi.org/10.1017/s0022112059000684.Search in Google Scholar
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