Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids

›› 2010, Vol. 18 ›› Issue (6): 923-930.

• FLUID FLOW AND TRANSPORT PHENOMENA • Previous Articles Next Articles

Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids

CAI Ziqi, BAO Yuyun, GAO Zhengming

State Key Laboratory of Chemical Resource Engineering, School of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China

Received:2010-04-27 Revised:2010-08-25 Online:2010-12-28 Published:2010-12-28
Supported by:
Supported by the National Natural Science Foundation of China (20821004,20990224);the National Basic Research Program of China (2007CB714300)

Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids

蔡子琦, 包雨云, 高正明

State Key Laboratory of Chemical Resource Engineering, School of Chemical Engineering, Beijing University of Chemical Technology, Beijing 100029, China

通讯作者: GAO Zhengming, E-mail: gaozm@mail.buct.edu.cn
基金资助:
Supported by the National Natural Science Foundation of China (20821004,20990224);the National Basic Research Program of China (2007CB714300)

Abstract

Abstract: The rising behavior of single bubbles has been investigated in six systems with different viscosity and Morton number(Mo) from 3.21×10^-11 to 163. Bubbles with maximum equivalent diameter of up to 16 mm were investigated. The bubble Reynolds number(Re) ranged from 0.02 to 1200 covering 3 regimes in which two functions are obtained relating the drag coefficient,C_D,with Re and Mo. It has been found that in the high Reynolds number regime the drag coefficient increases until the Reynolds number of about 1200. The classic expression of Jamialahmadi(1994) is improved and extended to high viscosity liquids. A new relationship for the aspect ratio of deformed bubbles in terms of Re,the E鰐v鰏 number and Mo,applicable to a wide range of system properties,especially in high viscosity liquids,is also suggested.

Key words: bubble, rising velocity, viscous liquid, drag coefficient, deformation

摘要： The rising behavior of single bubbles has been investigated in six systems with different viscosity and Morton number(Mo) from 3.21×10^-11 to 163. Bubbles with maximum equivalent diameter of up to 16 mm were investigated. The bubble Reynolds number(Re) ranged from 0.02 to 1200 covering 3 regimes in which two functions are obtained relating the drag coefficient,C_D,with Re and Mo. It has been found that in the high Reynolds number regime the drag coefficient increases until the Reynolds number of about 1200. The classic expression of Jamialahmadi(1994) is improved and extended to high viscosity liquids. A new relationship for the aspect ratio of deformed bubbles in terms of Re,the E鰐v鰏 number and Mo,applicable to a wide range of system properties,especially in high viscosity liquids,is also suggested.

关键词: bubble, rising velocity, viscous liquid, drag coefficient, deformation

CAI Ziqi, BAO Yuyun, GAO Zhengming. Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids[J]. , 2010, 18(6): 923-930.

蔡子琦, 包雨云, 高正明. Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids[J]. , 2010, 18(6): 923-930.

References

1 Davies, R.M., Taylor, G., “The mechanics of large bubbles rising through extended liquids and through liquids in tubes”, Proc. R. Soc. London, A200, 375-390(1950).
2 Clift, R., Grace, J.R., Weber, M.E., Bubbles, Drops and Particles, Academic Press, New York(1978).
3 Stokes, G.G., “On the effect of the internal friction of fluid on the motion of pendulums”, Trans. Cambridge Phi. Soc., 9, 8-106(1851).
4 Levich, V.G., “Bubble motion at high Reynolds numbers”, Sov. Phys. JETP, 19, 18-24(1949).
5 Peebles, F.N., Garber, H.J., “Studies on the motion of gas bubble in liquids”, Chem. Eng. Prog., 49, 79-88(1953).
6 Rodrigue, D., “A general correlation for the rise velocity of single gas bubble”, Can. J. Chem. Eng., 82, 382-386(2004).
7 Tomiyama, A., “Drag, lift and virtual mass forces acting on a single bubble”, In: 3rd International Symposium on Two-phase Flow Modeling and Experimentation, Celata, G.P., Di Marco, P., Mariani, A., Shah, R.K., eds, Edizioni ETS, Pisa, Italy, 3-12(2004).
8 Sanada, T., Sugihara, K., Shirota, M., Watanabe, M., “Motion and drag of a single bubble in super-purified water”, Fluid Dyn. Res., 40, 534-545(2008).
9 Mendelson, H.D., “The prediction of bubble terminal velocities from wave theory”, AIChE J., 13, 250-253(1967).
10 Celata, G.P., D’Annibale, F., Di Marco, P., Memoli, G., Tomiyama, A., “Measurement of rising velocity of a small bubble in a stagnant fluid in oneand two-component systems”, Exp. Therm. Fluid Sci., 31, 609-623(2007).
11 Jamialahmadi, M., Branch, C., Muller-Steinhagen, H., “Terminal bubble rise velocity in liquids”, Chem. Eng. Res. Des., 72, 119-122(1994).
12 Kalra, T.R., Uhlherr, P.H.T., “Geometry of bluff body wakes”, Can. J. Chem. Eng., 51, 655-658(1973).
13 Miyahara, T., Takahashi, T., “Drag coefficient of a single bubble rising through a quiescent liquid”, Int. Chem. Eng., 25, 146-148(1985).
14 Rodrigue, D., “Generalized correlation for bubble motion”, AIChE J., 47, 39-44(2001).
15 Bhaga, D., Weber, M.E., “Bubble in viscous-liquids-shapes, wakes and velocities”, J. Fluid. Mech., 105, 61-85(1981).
16 Takahashi, T., Miyahara, T., Izawa, H., “Drag coefficient and wake volume of single bubble rising through quiscent liquids”, Soc. Chem. Eng. Jp., 2, 480-484(1976).
17 Wellek, R.M., Agrawal, A.K., Skelland, A.H.P., “Shape of liquid drops moving in liquid media”, AIChE J., 12, 854-862(1966).
18 Okawa, T., Tanaka, T., Kataoka, I., Mori, M., “Temperature effect on single bubble rise characteristics in stagnant distilled water”, Int. J. Heat Mass Transfer, 46, 903-913(2003).
19 Vakhrushev, I.A., Efremov, G.I., “Interpolation formula for computing the velocities of single gas bubbles in liquids”, Chem. Technol. Fuels Oils, 5/6, 376-380(1970).

[1]	Hae-Kyun Park, Dong-Hyuk Park, Bum-Jin Chung. Influence of the electrolyte conductivity on the critical current density and the breakdown voltage [J]. Chinese Journal of Chemical Engineering, 2023, 59(7): 169-175.
[2]	Weikai Ren, Runsong Dai, Ningde Jin. Modeling of liquid film thickness around Taylor bubbles rising in vertical stagnant and co-current slug flowing liquids [J]. Chinese Journal of Chemical Engineering, 2023, 58(6): 179-194.
[3]	Hongwei Liang, Wenling Li, Zisheng Feng, Jianming Chen, Guangwen Chu, Yang Xiang. Numerical simulation of gas-liquid flow in the bubble column using Wray-Agarwal turbulence model coupled with population balance model [J]. Chinese Journal of Chemical Engineering, 2023, 58(6): 205-223.
[4]	Qi Han, Xin-Yuan Zhang, Hai-Bo Wu, Xian-Tai Zhou, Hong-Bing Ji. Different efficiency toward the biomimetic aerobic oxidation of benzyl alcohol in microchannel and bubble column reactors: Hydrodynamic characteristics and gas–liquid mass transfer [J]. Chinese Journal of Chemical Engineering, 2023, 55(3): 84-92.
[5]	Qinyan Wang, Yang Jin, Jun Li, Yongbo Zhou, Ming Chen. Study on liquid–liquid two-phase mass transfer characteristics in the microchannel with deformed insert [J]. Chinese Journal of Chemical Engineering, 2023, 54(2): 114-126.
[6]	Chao Zhang, Youzhi Liu, Weizhou Jiao, Hongyan Shen, Xigang Yuan, Shengkun Jia. An optimization method for enhancement of gas–liquid mass transfer in a bubble column reactor based on the entropy generation extremum principle [J]. Chinese Journal of Chemical Engineering, 2023, 53(1): 83-88.
[7]	Xibao Zhang, Zhenghong Luo. Bubble size modeling approach for the simulation of bubble columns [J]. Chinese Journal of Chemical Engineering, 2023, 53(1): 194-200.
[8]	Nouman Ahmad, Jianqiang Deng, Muhammad Adnan. Numerical investigation for the suitable choice of bubble diameter correlation for EMMS/bubbling drag model [J]. Chinese Journal of Chemical Engineering, 2022, 47(7): 254-270.
[9]	Yaran Yin, Xianming Zhang, Chunying Zhu, Taotao Fu, Youguang Ma. Formation characteristics of Taylor bubbles in a T-junction microchannel with chemical absorption [J]. Chinese Journal of Chemical Engineering, 2022, 46(6): 214-222.
[10]	Wenjuan Bai, Dianming Chu, Kuanxin Tang, Lei Geng, Yan Li, Yan He. The motion mechanism and characteristic of bubble in a pseudo-2D tapered fluidized bed [J]. Chinese Journal of Chemical Engineering, 2022, 46(6): 255-270.
[11]	Zhen Chen, Chunying Zhu, Taotao Fu, Xiqun Gao, Youguang Ma. Formation dynamics and size prediction of bubbles for slurry system in T-shape microchannel [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 153-161.
[12]	Shenglin Yan, Yan Zhang, Chong Peng, Xiaoyong Yang, Yuan Huang, Zhishan Bai, Xiao Xu. Oil droplet movement and micro-flow characteristics during interaction process between gas bubble and oil droplet in flotation [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 229-237.
[13]	Tao Sun, Mingjun Pang, Yang Fei. Numerical study on hydrodynamic characteristics of spherical bubble contaminated by surfactants under higher Reynolds numbers [J]. Chinese Journal of Chemical Engineering, 2022, 45(5): 268-283.
[14]	He Yang, Aqiang Chen, Shujun Geng, Jingcai Cheng, Fei Gao, Qingshan Huang, Chao Yang. Influences of fluid physical properties, solid particles, and operating conditions on the hydrodynamics in slurry reactors [J]. Chinese Journal of Chemical Engineering, 2022, 44(4): 51-71.
[15]	Teng Wang, Zihong Xia, Caixia Chen. Computational study of bubble coalescence/break-up behaviors and bubble size distribution in a 3-D pressurized bubbling gas-solid fluidized bed of Geldart A particles [J]. Chinese Journal of Chemical Engineering, 2022, 44(4): 485-496.

Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids

Hydrodynamic Behavior of a Single Bubble Rising in Viscous Liquids

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments