Interactions between two in-line drops rising in pure glycerin

doi:10.1016/j.cjche.2016.05.027

›› 2016, Vol. 24 ›› Issue (10): 1325-1334.DOI: 10.1016/j.cjche.2016.05.027

• Fluid Dynamics and Transport Phenomena • 上一篇下一篇

Interactions between two in-line drops rising in pure glycerin

Li Rao, Zhengming Gao, Ziqi Cai, Yuyun Bao

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

收稿日期:2015-12-18 修回日期:2016-04-29 出版日期:2016-10-28 发布日期:2016-11-19
通讯作者: Ziqi Cai,E-mail address:caiziqi@mail.buct.edu.cn;Yuyun Bao,E-mail address:baoyy@mail.buct.edu.cn.
基金资助:
Supported by the National Natural Science Foundation of China (21376016, 21506005).

Interactions between two in-line drops rising in pure glycerin

Li Rao, Zhengming Gao, Ziqi Cai, Yuyun Bao

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

Received:2015-12-18 Revised:2016-04-29 Online:2016-10-28 Published:2016-11-19
Supported by:
Supported by the National Natural Science Foundation of China (21376016, 21506005).

摘要/Abstract

摘要： The behaviors of time-dependent interaction between two buoyancy-driven in-line deformable drops rising in pure glycerin at Re<1 were studied, where the diameter for the leading drops ranged from 9.51 mm to 12.6 mm and for trailing drops from 12.7 mm to 15.8 mm. The situation while a larger drop chasing a smaller onewas specifically consideredwhich typically led to the smaller drop "coating" the larger one. Two approaches, the geometric feature approach and the energy change one, were used to judge the starting and ending times of the interaction between twodrops. Based on a conicalwakemodel, the drag coefficient of twoapproaching drops was calculated. Due to the approaching effect of the trailing drop, the leading drop was accelerated and the average drag coefficientwas smaller than that for a free rising single drop. The frequency spectrums of the lateral oscillation of two drops during the interaction were obtained by using Fourier analysis. The oscillation frequency of the interactional drops was also different from that for a free rising single drop because of the wake effect produced by the leading drop. Due to a superposition of the drop shape oscillation and the drop internal circulation, the transverse oscillation frequencies of two drops have the same trend during the approaching process.

关键词: Two in-line drops, Oscillation, Fourier analysis, Energy analysis

Abstract: The behaviors of time-dependent interaction between two buoyancy-driven in-line deformable drops rising in pure glycerin at Re<1 were studied, where the diameter for the leading drops ranged from 9.51 mm to 12.6 mm and for trailing drops from 12.7 mm to 15.8 mm. The situation while a larger drop chasing a smaller onewas specifically consideredwhich typically led to the smaller drop "coating" the larger one. Two approaches, the geometric feature approach and the energy change one, were used to judge the starting and ending times of the interaction between twodrops. Based on a conicalwakemodel, the drag coefficient of twoapproaching drops was calculated. Due to the approaching effect of the trailing drop, the leading drop was accelerated and the average drag coefficientwas smaller than that for a free rising single drop. The frequency spectrums of the lateral oscillation of two drops during the interaction were obtained by using Fourier analysis. The oscillation frequency of the interactional drops was also different from that for a free rising single drop because of the wake effect produced by the leading drop. Due to a superposition of the drop shape oscillation and the drop internal circulation, the transverse oscillation frequencies of two drops have the same trend during the approaching process.

Key words: Two in-line drops, Oscillation, Fourier analysis, Energy analysis

Li Rao, Zhengming Gao, Ziqi Cai, Yuyun Bao. Interactions between two in-line drops rising in pure glycerin[J]. , 2016, 24(10): 1325-1334.

参考文献

[1] R.V. Chaudhari, H. Hofmann, Coalescence of gas bubbles in liquids, Rev. Chem. Eng. 10(2) (1994) 131-190.
[2] G.F. Scheele, D.E. Leng, An experimental study of factors which promote coalescence of two colliding drops suspended in water-I, Chem. Eng. Sci. 26(11) (1971) 1867-1879.
[3] A.K. Chesters, The modelling of coalescence processes in fluid-liquid dispersions:A review of current understanding, Trans. Inst. Chem. Eng. 69(A4) (1991) 259-270.
[4] V.G. Levich, S. Technica, Physiochemical hydrodynamics, vol. 689, Prentice Hall, Englewood Cliffs, NJ, 1962.
[5] C.A. Coulaloglou, L.L. Tavlarides, Description of interaction processes in agitated liquid-liquid dispersions, Chem. Eng. Sci. 32(11) (1977) 1289-1297.
[6] A.K. Chesters, G. Hohan, Bubble coalescence in pure liquids, Appl. Sci. Res. 38(1982) 353-361.
[7] S.A.K. Jeelani, S. Hartland, Effect of approach velocity on binary and interfacial coalescence, Trans. Inst. Chem. Eng. 69(A4) (1991) 271-281.
[8] S.A.K. Jeelani, S. Hartland, Collision of oscillating liquid drops, Chem. Eng. Sci. 46(7) (1991) 1807-1814.
[9] D. Jeffrey, Conduction through a random suspension of spheres, Proc. R. Soc. Lond. A 335(1973) 355-367.
[10] L.V.Wijngaarden, D.J. Jeffrey, Hydrodynamic interaction between gas bubbles in liquid, J. Fluid Mech. 77(01) (1976) 27-44.
[11] J.B.W. Kok, Dynamics of a pair of gas bubbles moving through liquid. Part 1. Theory, Eur. J. Mech. B Fluids 12(4) (1993) 515-540.
[12] J.F. Harper, Growing bubbles rising in line, J. Appl. Math. Decis. Sci. 5(2) (2001) 65-73.
[13] J. Zhang, L.-S. Fan, On the rise velocity of an interactive bubble in liquids, Chem. Eng. J. 92(1) (2003) 169-176.
[14] J. Zhang, L.-S. Fan, A semianalytical expression for the drag force of an interactive particle due to wake effect, Ind. Eng. Chem. Res. 41(20) (2002) 5094-5097.
[15] W. Myint, S. Hosokawa, A. Tomiyama, Shapes of single drops rising through stagnant liquids, JFST 2(1) (2007) 184-195.
[16] Z.M. Gao, L. Rao, Y.Y. Bao, Z.Q. Cai, Hydrodynamics and deformation of single drop rising in Newtonian fluids, JCEJ 48(5) (2015) 345-352.
[17] C.J. Koh, L.G. Leal, The stability of drop shapes for translation at zero Reynolds number through a quiescent fluid, Phys. Fluids A 1(8) (1989) 1309-1313.
[18] C. Pozrikidis, The instability of a moving viscous drop, J. Fluid Mech. 210(1990) 1-21.
[19] H. Luo, H.F. Svendsen, Modeling and simulations of binary approach by energy conservation analysis, Chem. Eng. Commun. 145(1) (1996) 145-153.
[20] D. Bhaga, M.E.Weber, In-line interaction of a pair of bubble in a viscous liquid, Chem. Eng. Sci. 35(12) (1980) 2467-2474.
[21] T. Miyahara, K. Tsuchiya, L.-S. Fan, Effect of turbulent wake on bubble-bubble interaction in a gas-liquid-solid fluidized bed, Chem. Eng. Sci. 46(9) (1991) 2368-2373.
[22] Z.Q. Cai, Z.M. Gao, Y.Y. Bao,G.M. Evans, E. Doroodchi, Formation and motion of conjunct bubbles in glycerol-water solutions, Ind. Eng. Chem. Res. 51(4) (2011) 1990-1996.
[23] T. Otake, S. Tone, K. Nakao, Y.Mitsuhashi, Coalescence and breakup of bubbles in liquids, Chem. Eng. Sci. 32(4) (1977) 377-383.
[24] C.W. Stewart, Bubble interaction in low-viscosity liquids, Int. J. Multiphase Flow 21(6) (1995) 1037-1046.
[25] H.K. Tsao, D.L. Koch, Observations of high Reynolds number bubbles interacting with a rigid wall, Phys. Fluids 9(1) (1997) 44-56.
[26] J.R. Crabtree, J. Bridgewater, Bubble coalescence in viscous liquids", Chem. Eng. Sci. 26(6) (1971) 839-851.
[27] F.A. Morrison Jr.,M.B. Stewart, Small bubble motion in an accelerating liquid", ASME J. 43(3) (1976) 399-403.
[28] N. de Nevers, J.-L. Wu, Bubble coalescence in viscous fluid, AIChE J. 17(1) (1971) 182-186.
[29] D. Legendre, J. Magnaudet, G. Mougin, Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid, J. Fluid Mech. 497(2003) 133-166.
[30] R. Clift, J.R. Grace, M.E. Weber, Bubbles, drops and particles, Academic Press, New York, U.S.A., 1978210.

Interactions between two in-line drops rising in pure glycerin

Interactions between two in-line drops rising in pure glycerin

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