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Boundary integral simulation has been conducted to study the motion and deformation of bubbles with weak viscous and surface tension effects in fluid. Both normal and tangential stress boundary conditions are satisfied and the weak viscous effects are confined to the thin boundary layers around bubble surfaces, which is also known as boundary layer theory of bubble. By using this method, the influence of viscosity and surface tension of fluid on the motion of bubbles has been studied. Both axisymmetric and three-dimensional numerical results are compared with analytical results of Rayleigh-Plesset equation. Good agreement between them is achieved, which validates the numerical model. On this basis, interaction model between two vertically placed bubbles is established, by taking the surface tension, gravity, and viscous effects into consideration. Variations of physical quantities including bubble deformation, jet velocity, and energy of fluid are studied. Last but not least, the influence of viscosity and surface tension on the motion of a spherical bubble is investigated. It is found that viscous effects of fluid depress the pulsation of bubble and part of fluid energy is transformed into viscous dissipation energy. As a result, the development of bubble jet, the radius of the bubble, and the jet velocity are reduced gradually. On the other hand, the surface tension of fluid does not change the range of the bubble pulsation but reduces the period of the bubble pulsation and enhances the potential energy of the bubble. This model and numerical results aim to provide some references for bubble dynamics in bioengineering, chemical engineering, naval architecture, and ocean engineering, etc.
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Keywords:
- bubble /
- boundary layer /
- viscosity /
- surface tension
[1] Boulton-Stone J M, Blake J R 1993 J. Fluid Mech. 254 437
[2] Cui P, Zhang A M, Wang S P 2016 Phys. Fluids 28 117103
[3] Xue Y Z, Cui B, Ni B Y 2016 Ocean Eng. 118 58
[4] Sato K, Tomita Y, Shima A 1994 J. Acoust. Soc. Am. 95 2416
[5] Rungsiyaphornrat S, Klaseboer E, Khoo B C, Yeo K S 2003 Comput. Fluids 32 1049
[6] Chew L W, Klaseboer E, Ohl S W, Khoo B C 2011 Phys. Rev. E 84 0663078
[7] Han R, Li S, Zhang A M, Wang Q X 2016 Phys. Fluids 28 062104
[8] Guo X, Cai C, Xu G, Yang Y, Tu J, Huang P, Zhang D 2017 Ultrason. Sonoche. 39 863
[9] Zhang Y, Zhang Y, Li S 2017 Ultrason. Sonoche. 35 431
[10] Liu L T, Yao X L, Zhang A M, Chen Y Y 2017 Phys. Fluids 29 012105
[11] Miksis M J, Vanden-Broeck J M, Keller J B 1982 J. Fluid Mech. 123 31
[12] Lundgren S, Mansour N 1988 J. Fluid Mech. 194 479
[13] Boulton-Stone J M 1995 J. Fluid Mech. 302 231
[14] Georgescu S C, Achard J L, Canot E 2002 Euro. J. Mech. B-Fluids 21 265
[15] Klaseboer E, Manica R, Chan D Y C, Khoo B C 2011 Eng. Anal. Bound. Elem. 35 489
[16] Joseph D D, Wang J 2004 J. Fluid Mech. 505 365
[17] Lind S J, Phillips T N 2012 Theor. Comp. Fluid Dyn. 26 245
[18] Lind S J, Phillips T N 2013 Phys. Fluids 25 022014
[19] Ni B Y, Li S, Zhang A M 2013 Acta Phys. Sin. 62 124704 (in Chinese)[倪宝玉, 李帅, 张阿漫 2013 物理学报 62 124704]
[20] Zhang A M, Ni B Y 2014 Comput. Fluids 92 22
[21] Li S, NI B Y 2016 Eng. Anal. Bound. Elem. 68 63
[22] Lamb H 1932 Hydrodynamics (sixth Ed.) (Cambridge:Cambridge University Press) pp580-581
[23] Wu G X 1991 Appl. Ocean Res. 13 317
[24] Rayleigh J W 1917 Philos. Mag. 34 94
[25] Zhang A M, Wang S P, Wu G X 2013 Eng. Anal. Bound. Elem. 37 1179
[26] Best J P 1993 J. Fluid Mech. 251 79
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[1] Boulton-Stone J M, Blake J R 1993 J. Fluid Mech. 254 437
[2] Cui P, Zhang A M, Wang S P 2016 Phys. Fluids 28 117103
[3] Xue Y Z, Cui B, Ni B Y 2016 Ocean Eng. 118 58
[4] Sato K, Tomita Y, Shima A 1994 J. Acoust. Soc. Am. 95 2416
[5] Rungsiyaphornrat S, Klaseboer E, Khoo B C, Yeo K S 2003 Comput. Fluids 32 1049
[6] Chew L W, Klaseboer E, Ohl S W, Khoo B C 2011 Phys. Rev. E 84 0663078
[7] Han R, Li S, Zhang A M, Wang Q X 2016 Phys. Fluids 28 062104
[8] Guo X, Cai C, Xu G, Yang Y, Tu J, Huang P, Zhang D 2017 Ultrason. Sonoche. 39 863
[9] Zhang Y, Zhang Y, Li S 2017 Ultrason. Sonoche. 35 431
[10] Liu L T, Yao X L, Zhang A M, Chen Y Y 2017 Phys. Fluids 29 012105
[11] Miksis M J, Vanden-Broeck J M, Keller J B 1982 J. Fluid Mech. 123 31
[12] Lundgren S, Mansour N 1988 J. Fluid Mech. 194 479
[13] Boulton-Stone J M 1995 J. Fluid Mech. 302 231
[14] Georgescu S C, Achard J L, Canot E 2002 Euro. J. Mech. B-Fluids 21 265
[15] Klaseboer E, Manica R, Chan D Y C, Khoo B C 2011 Eng. Anal. Bound. Elem. 35 489
[16] Joseph D D, Wang J 2004 J. Fluid Mech. 505 365
[17] Lind S J, Phillips T N 2012 Theor. Comp. Fluid Dyn. 26 245
[18] Lind S J, Phillips T N 2013 Phys. Fluids 25 022014
[19] Ni B Y, Li S, Zhang A M 2013 Acta Phys. Sin. 62 124704 (in Chinese)[倪宝玉, 李帅, 张阿漫 2013 物理学报 62 124704]
[20] Zhang A M, Ni B Y 2014 Comput. Fluids 92 22
[21] Li S, NI B Y 2016 Eng. Anal. Bound. Elem. 68 63
[22] Lamb H 1932 Hydrodynamics (sixth Ed.) (Cambridge:Cambridge University Press) pp580-581
[23] Wu G X 1991 Appl. Ocean Res. 13 317
[24] Rayleigh J W 1917 Philos. Mag. 34 94
[25] Zhang A M, Wang S P, Wu G X 2013 Eng. Anal. Bound. Elem. 37 1179
[26] Best J P 1993 J. Fluid Mech. 251 79
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