# Frictional drag reduction by bubble injection

- First Online:

- Received:
- Revised:
- Accepted:

## Abstract

The injection of gas bubbles into a turbulent boundary layer of a liquid phase has multiple different impacts on the original flow structure. Frictional drag reduction is a phenomenon resulting from their combined effects. This explains why a number of different void–drag reduction relationships have been reported to date, while early works pursued a simple universal mechanism. In the last 15 years, a series of precisely designed experimentations has led to the conclusion that the frictional drag reduction by bubble injection has multiple manifestations dependent on bubble size and flow speed. The phenomena are classified into several regimes of two-phase interaction mechanisms. Each regime has inherent physics of bubbly liquid, highlighted by keywords such as bubbly mixture rheology, the spectral response of bubbles in turbulence, buoyancy-dominated bubble behavior, and gas cavity breakup. Among the regimes, bubbles in some selected situations lose the drag reduction effect owing to extra momentum transfer promoted by their active motions. This separates engineers into two communities: those studying small bubbles for high-speed flow applications and those studying large bubbles for low-speed flow applications. This article reviews the roles of bubbles in drag reduction, which have been revealed from fundamental studies of simplified flow geometries and from development of measurement techniques that resolve the inner layer structure of bubble-mixed turbulent boundary layers.

### References

- Adrian RJ (2007) Hairpin vortex organization in wall turbulence. Phys Fluids 19:041301Google Scholar
- Aliseda A, Lasheras JC (2006) Effect of buoyancy on the dynamics of a turbulent boundary layer laden with microbubbles. J Fluid Mech 559:307–334MATHGoogle Scholar
- Amromin E, Mizine I (2003) Partial cavitation as drag reduction technique and problem of active flow control. Mar Technol 40:181–188Google Scholar
- Amromin E, Karafiath G, Metcalf B (2011) Ship drag reduction by air bottom ventilated cavitation in calm water and in waves. J Ship Res 55:196–207Google Scholar
- Andereck CD, Liu SS, Swinny HL (1986) Flow regimes in a circular Couette system with independently rotating cylinders. J Fluid Mech 164:155–183Google Scholar
- Atkhen K, Fontaine J, Wesfreid JE (2002) Highly turbulent Couette–Taylor bubbly flow patterns. J Fluid Mech 422:55–68Google Scholar
- Batchelor GK (1967) Effective viscosity of dilute dispersion: an introduction to fluid dynamics. Cambridge University Press, Cambridge, pp 246–255Google Scholar
- Biesheuvel A, van Wijngaaden L (1984) Two-phase flow equations for a dilute dispersion of gas bubbles in liquid. J Fluid Mech 148:301–318MATHGoogle Scholar
- Boffetta G, Celani A, Vergassola M (2000) Inverse energy cascade in two-dimensional turbulence: deviations from Gaussian behavior. Phys Rev E 61:29–32Google Scholar
- Brücker C (1999) Structure and dynamics of the wake of bubbles and its relevance for bubble interaction. Phys Fluids 11:1781–1796MATHMathSciNetGoogle Scholar
- Bunner B, Tryggvason G (2003) Effect of bubble deformation on the properties of bubbly flow. J Fluid Mech 495:77–118MATHMathSciNetGoogle Scholar
- Callenaere M, Franc JP, Michel JM, Riondet M (2001) The cavitation instability induced by the development of a re-entrant jet. J Fluid Mech 444:223–256MATHGoogle Scholar
- Ceccio S (2010) Frictional drag reduction of external flows with bubble and gas injection. Annu Rev Fluid Mech 42:183–203Google Scholar
- Chouippe A, Climent E, Legendre D, Gabillet C (2014) Numerical simulation of bubble dispersion in turbulent Taylor–Couette flow. Phys Fluids 26:043304Google Scholar
- Climent E, Simonnet M, Magnaudet J (2007) Preferential accumulation of bubbles in Couette–Taylor flow patterns. Phys Fluids 19:083301Google Scholar
- Crowe CT, Troutt TR, Chung JN (1996) Numerical models for two-phase turbulent flows. Annu Rev Fluid Mech 28:11–43MathSciNetGoogle Scholar
- Cui Z, Fan JM, Park AH (2003) Drag coefficients for a settling sphere with microbubble drag reduction effects. Power Technol 138:132–134Google Scholar
- Djeridi H, Gabillet C, Billard Y (2004) Two-phase Couette–Taylor flow: arrangement of the dispersed phase and effect on the flow structure. Phys Fluids 16:128–139Google Scholar
- Doi M, Ohta T (1991) Dynamics and rheology of complex interfaces I. J Chem Phys 95(2):1242–1247Google Scholar
- Dominguez-Lerma MA, Ahlers G, Channell DS (1985) Effects of Kalliroscope flow visualization particles on rotating Couette–Taylor flow. Phys Fluids 28:1204–1206Google Scholar
- Einstein A (1906) Eine neue Bestimmung der Molekuldimensionen. Ann Phys 19:289–306MATHGoogle Scholar
- Elbing BR, Winkel ES, Lay KA, Ceccio SL, Dowling DR, Perlin M (2008) Bubble-induced skin-friction drag reduction and the abrupt transition to air-layer drag reduction. J Fluid Mech 612:201–236MATHGoogle Scholar
- Elbing BR, Mäkiharju S, Wiggins A, Perlin M, Dowling DR, Ceccio SL (2013) On the scaling of air layer drag reduction. J Fluid Mech 717:484–513MATHGoogle Scholar
- Felton K, Loth E (2001) Spherical bubble motion in a turbulent boundary layer. Phys Fluids 13:2564–2577Google Scholar
- Felton K, Loth E (2002) Diffusion of spherical bubbles in a turbulent boundary layer. Int J Multiph Flow 28:69–92MATHGoogle Scholar
- Ferrante A, Elghobashi S (2004) On the physical mechanism of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J Fluid Mech 503:345–355MATHGoogle Scholar
- Ferrante A, Elghobashi S (2005) Reynolds number effect of drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J Fluid Mech 543:93–106Google Scholar
- Fischer F, Hampel U (2010) Ultra fast electron beam X-ray computed tomography for two-phase flow measurement. Nuclear Eng Des 240(9):2254–2259Google Scholar
- Foeth EJ, Eggers R, Quadvlieg EHHA (2010) The efficiency of air-bubble lubrication for decreasing friction resistance. Prof. int. conf. ship drag reduction (SMOOTH-SHIPS), Instanbul, Turkey. Paper No. 12, pp 9Google Scholar
- Frankel NA, Acrivos A (1970) The constitutive equation for a dilute emulsion. J Fluid Mech 44:65–78MATHGoogle Scholar
- Fujikawa S, Yano Y, Watanabe M (2011) Vapor–liquid interfaces, bubbles and droplets: fundamentals and applications. Series of heat and mass transfer. Springer, BerlinGoogle Scholar
- Fujiwara A, Minato D, Hishida K (2004) Effect of bubble diameter on modification of turbulence in an upward pipe flow. Int J Heat Fluid Flow 25:481–488Google Scholar
- Fukagata K, Iwamoto K, Kasagi N (2002) Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys Fluids 14:L73–L76Google Scholar
- Fukuda K, Tokunaga J, Nobunaga T, Nakatani T, Iwasaki T (2000) Frictional drag reduction with air lubricant over a super-water-repellent surface. J Mar Sci Technol 5:123–130Google Scholar
- Gabillet C, Colin C, Fabre J (2002) Experimental study of bubble injection in a turbulent boundary layer. Int J Multiph Flow 28:553–578MATHGoogle Scholar
- Gao T, Hu HH, Castaneda PP (2011) Rheology of a suspension of elastic particles in a viscous shear flow. J Fluid Mech 687:209–237MATHMathSciNetGoogle Scholar
- Gore RA, Crowe CT (1989) Effect of particle size on modulating turbulent intensity. Int J Multiph Flow 15:279–285Google Scholar
- Gore RA, Crowe CT (1991) Modulation of turbulence by a dispersed phase. J Fluids Eng 113:304–307Google Scholar
- Guin MM, Kato H, Yamaguchi H, Maeda M, Miyanaga M (1996) Reduction of skin friction by microbubbles and its relation with near wall bubble concentration in a channel. J Mar Sci Technol 1:241–254Google Scholar
- Hara K, Suzuki T, Yamamoto F (2011) Image analysis applied to study on frictional drag reduction by electrolytic microbubbles in a turbulent channel flow. Exp Fluids 50:715–727Google Scholar
- Hardalupas A, Sahu S, Taylor AMKP, Zarogoulidis K (2010) Simultaneous planer measurement of droplet velocity and size with gas phase velocities in a spray by combined ILIDS and PIV techniques. Exp Fluids 49:417–434Google Scholar
- Hassan YA, Ortiz-Villafuerte J (2003) Investigation of microbubble boundary layer using particle image velocimetry. In: Proceedings of ASME FEDSM’03 -45639 [CD-ROM], Fourth ASME-JSME Joint Fluids Engineering Conference, Honolulu, HIGoogle Scholar
- Hassan YA, Gutierrez Torres CC, Jimenez-Bernal JA (2005) Temporal correlation modification by microbubbles injection in a channel flow. Int Commun Heat Mass Transf 32:1009–1015Google Scholar
- Hesketh RP, Etchells AW, Russell TWF (1991) Bubble breakage in pipeline flow. Chem Eng Sci 46:1–9Google Scholar
- Higuchi M, Saito T (2010) Quantitative characterizations of long-period fluctuations in a large-diameter bubble column based on point-wise void fraction measurements. Chem Eng J 160:284–292Google Scholar
- Hinze JO (1955) Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J 1:289–295Google Scholar
- Hirata M, Nishiwaki N (1963) Skin friction and heat transfer for liquid flow over a porous wall with gas injection. Int J Heat Mass Transf 6:941–949Google Scholar
- Hosokawa S, Tomiyama A (2004) Turbulence modification in gas–liquid and solid–liquid dispersed two-phase pipe flows. Int J Heat Fluid Flow 25:489–498Google Scholar
- Hosokawa S, Tomiyama A (2009) Multi-fluid simulation of turbulent bubbly pipe flows. Chem Eng Sci 64:5308–5318Google Scholar
- Hosokawa S, Tomiyama A (2013) Bubble-induced pseudo turbulence in laminar pipe flows. Int J Heat Fluid Flow 40:97–105Google Scholar
- Hosokawa S, Fukunaga T, Tomiyama (2009) Application of photobleaching molecular tagging velocimetry to turbulent bubbly flow in a square duct. Exp Fluids 47:745–754Google Scholar
- Huang J, Murai Y, Yamamoto F (2008) Shallow DOF-based particle tracking velocimetry applied to horizontal bubbly wall turbulence. Flow Meas Instrum 19:93–105Google Scholar
- Huang J, Murai Y, Yamamoto F (2009) Quadrant analysis of bubble induced velocity fluctuation in a transitional boundary layer. J Hydrodyn 21:93–99Google Scholar
- Hubacz R, Wronski S (2004) Horizontal Couette–Taylor flow in a two-phase gas–liquid system: flow patters. Exp Therm Fluid Sci 28:457–472Google Scholar
- Ishii M, Hibiki T (2011) Drift-flux model: thermo-fluid dynamics of two-phase flow. Springer, BerlinGoogle Scholar
- Iwasaki T, Nishimura K, Tanaka M, Hagiwara Y (2001) Direct numerical simulation of turbulent Couette flow with immiscible droplets. Int J Heat Fluid Flow 22:332–342Google Scholar
- Jacob B, Olivieri A, Miozzi M, Campana EF, Piva R (2010) Drag reduction by microbubbles in a turbulent boundary layer. Phys Fluids 22:115104Google Scholar
- Jimenez J (2012) Cascades in wall-bounded turbulence. Annu Rev Fluid Mech 44:27–45Google Scholar
- Kameda M, Matsumoto Y (1996) Shock waves in a liquid containing small gas bubbles. Phys Fluids 8:322–335MathSciNetGoogle Scholar
- Kato H, Iwashina T, Miyanaga M, Yamaguchi H (1999) Effect of microbubbles on the structure of turbulence in a turbulent boundary layer. J Mar Sci Technol 4:115–162Google Scholar
- Katsui T, Okamoto Y, Kasahara Y, Shimoyama N, Iwasaki Y, Soejima S (2003) A study of air lubrication method to reduce frictional resistance of ship: experimental investigation by tanker form model ship and estimation of full scale ship performance. J Kansai Soc Nav Archit Jpn 239:45–53 (in Japanese)Google Scholar
- Kawaguchi T, Akasaka Y, Maeda M (2002) Size measurement of droplets and bubbles by advanced interferometric laser imaging technique. Meas Sci Technol 13:308Google Scholar
- Kawamura T, Kodama Y (2002) Numerical simulation method to resolve interactions between bubbles and turbulence. Int J Heat Fluid Flow 23:627–638Google Scholar
- Kim J (2003) Control of turbulent boundary layers. Phys Fluids 15:1093–1106MathSciNetGoogle Scholar
- Kim SY, Cleaver JW (1995) The persistence of drag reduction following the injection of microbubbles into a turbulent boundary layer. Int Commun Heat Mass Transf 22:353–357Google Scholar
- Kitagawa A, Murai Y (2013) Natural convection heat transfer from a vertical heated plate in water with microbubble injection. Chem Eng Sci 99:215–224Google Scholar
- Kitagawa A, Murai Y (2014) Pulsatory rise of microbubble swarm along a vertical wall. Chem Eng Sci 116:694–703Google Scholar
- Kitagawa A, Murai Y, Yamamoto F (2001) Two-way coupling of Eulerian–Lagrangian model for dispersed multiphase flows using filtering functions. Int J Multiph Flow 27:2129–2153MATHGoogle Scholar
- Kitagawa A, Sugiyama K, Murai Y (2004) Experimental detection of bubble–bubble interactions in a wall-sliding bubble swarm. Int J Multiph Flow 30:1213–1234MATHGoogle Scholar
- Kitagawa A, Hishida K, Kodama Y (2005) Flow structure of microbubble-laden turbulent channel flow measured by PIV combined with the shadow image technique. Exp Fluids 38:466–475Google Scholar
- Kitagawa A, Kosuge K, Uchida K, Hagiwara Y (2008) Heat transfer enhancement for laminar natural convection along a vertical plate due to sub-millimeter-bubble injection. Exp Fluids 45:473–484Google Scholar
- Kodama Y, Kakugawa A, Takahashi T, Kawashima H (2000) Experimental study on microbubbles and their applicability to ships for skin friction reduction. Int J Heat Fluid Flow 21:582–588Google Scholar
- Kramer MO (1960) Boundary layer stabilization by distributed damping. J Am Soc Nav Eng 72:25–34Google Scholar
- Kulick JD, Fessler JR, Eaton JK (1994) Particle response and turbulence modification in fully developed channel flow. J Fluid Mech 277:109–134Google Scholar
- Kumagai, I, Nakamura N, Murai Y, Tasaka Y, Takeda Y, Takahashi Y (2010) A new power-saving device for air bubble generation: hydrofoil air pump for ship drag reduction. In: Proceedings of international conference on ship drag reduction, Istanbul (Smooth), pp 95–102 Google Scholar
- Kwon BH, Kim HH, Jeon HJ, Kim MC, Lee I, Chun S, Go JS (2014) Experimental study on the reduction of skin frictional drag in pipe flow by using convex air bubbles. Exp Fluids 55:1772Google Scholar
- L’vov VS, Pomyalov A, Procaccia I, Tiberkevich V (2005) Drag reduction by microbubbles in turbulent flows: the limit of minute bubbles. Phys Rev Let 94:174502Google Scholar
- La Porta A, Voth GA, Crawford AM, Alexander J, Bodenschatz E (2001) Fluid particle accelerations in fully developed turbulence. Nature 409:1017–1019Google Scholar
- Lance M, Bataille J (1991) Turbulence in the liquid phase of a uniform bubbly air–water flow. J Fliud Mech 222:95–118Google Scholar
- Latorre R (1997) Ship hull drag reduction using bottom air injection. Ocean Eng 24:161–175Google Scholar
- Latorre R, Miller A, Philips R (2003) Micro-bubble resistance reduction on a model SES catamaran. Ocean Eng 30:2297–2309Google Scholar
- Lay KA, Yakushiji R, Makiharju S, Perlin M, Ceccio SL (2010) Partial cavity drag reduction at high Reynolds number. J Ship Res 54:109–119Google Scholar
- Lee CY, Kim CJ (2011) Underwater restoration and retention of gases on superhyrdophibic surfaces for drag reduction. Phys Rev Lett 106:014502Google Scholar
- Legner HH (1984) Simple model for gas bubble drag reduction. Phys Fluids 27:2788–2790Google Scholar
- Lelouvetel J, Tanaka T, Sato Y, Hishida K (2014) Transport mechanisms of the turbulent energy cascade in upward/downward bubbly flows. J Fluid Mech 741:514–542MathSciNetGoogle Scholar
- Li FC, Kawaguchi Y, Yu B, Wei JJ, Hishida K (2008) Experimental study of drag-reduction mechanism for a dilute surfactant solution flow. Int J Heat Mass Transf 51:835–843Google Scholar
- Liu TJ (1997) Investigation of the wall shear stress in vertical bubbly flow under different bubble size conditions. Int J Multiph Flow 23:1085–1109MATHGoogle Scholar
- Llewellin EW, Manga M (2005) Bubble suspension rheology and implications for conduit flow. J Volcanol Geotherm Res 143:205–217Google Scholar
- Lockhart RW, Martinelli RC (1949) Proposed correlation of data for isothermal two-phase two-component flow in pipes. Chem Eng Process 45:39–48Google Scholar
- Lu J, Tryggvason G (2007) Effect of bubble size in turbulent bubbly downflow in a vertical channel. Chem Eng Sci 62:3008–3018Google Scholar
- Lu J, Fernandez A, Tryggvason G (2005a) The effect of bubbles on the wall drag in a turbulent channel flow. Phys Fluids 17(095102):1–12Google Scholar
- Lu X, Hamada M, Kato H (2005b) Effect of the turbulent frictional drag reduction of microbubbles: experiments by bubbles of air and hydrogen. In: Proc. fluid eng. conf. of Japan soc. mech. eng. (JSME), Paper No. 509:69–70Google Scholar
- Lundin MD, McCready MJ (2009) Modeling of bubble coalescence in bubbly co-current flows restricted by confined geometry. Chem Eng Sci 64:4060–6067Google Scholar
- Luo R, Song Q, Yang XY, Wang Z (2002) A three-dimensional photographic method for measurement of phase distribution in dilute bubble flow. Exp Fluids 32:116–120Google Scholar
- Luther S, Rensen J, Guet S (2004) Bubble aspect ratio and velocity measurement using a four-point fiber-optical probe. Exp Fluids 36:326–333Google Scholar
- Madavan NK, Deutsch S, Merkle CL (1985) Measurements of local skin friction in microbubble-modified turbulent boundary layer. J Fluid Mech 156:237–256Google Scholar
- Magnaudet J, Eames I (2000) The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu Rev Fluid Mech 32:659–708MathSciNetGoogle Scholar
- Mäkiharju SA, Perlin M, Ceccio SL (2012) On the energy economics of air lubrication drag reduction. Int J Nav Archit Ocean Eng 4(4):412–422Google Scholar
- Mäkiharju SA, Elbing BR, Wiggins A, Schinasi S, Vanden-Broeck JM, Perlin M, Ceccio SL (2013a) On the scaling of air entrainment from a ventilated partial cavity. J Fluid Mech 732:47–76Google Scholar
- Mäkiharju SA, Gabillet C, Paik BG, Chang NA, Perlin M, Ceccio SL (2013b) Time-resolved two-dimensional X-ray densitometry of a two-phase flow downstream of a ventilated cavity. Exp Fluids 54(7):1561Google Scholar
- Marie JL (1987) A simple analytical formulation for microbubble drag reduction. J PhysicoChem Hydrodyn 13:213–220Google Scholar
- Maryami R, Farahat S, Poor MJ, Mayam MHS (2014) Bubbly drag reduction in a vertical Couette–Taylor system with superimposed axial flow. Fluid Dyn Res 46:055504. doi:10.1088/0169-5983/46/5/05504 Google Scholar
- Masliyah J, Jauhari R, Gray M (1994) Drag coefficient for air bubbles rising along an inclined surface. Chem Eng Sci 49:1905–1911Google Scholar
- Matveev KI (2007) Three dimensional wave patterns in long air cavities on a horizontal plane. Ocean Eng 34:1882–1891Google Scholar
- Maxey MR, Chang EJ, Wang LP (1996) Interaction of particles and microbubbles with turbulence. Exp Therm Fluid Sci 12:417–425Google Scholar
- McCormick M, Bhattacharyya R (1973) Drag reduction of a submersible hull by electrolysis. Nav Eng J 85:11–16Google Scholar
- Mehel A, Gabillet C, Djeridi H (2007) Analysis of the flow pattern modifications in a bubbly Couette–Taylor flow. Phys Fluids 19:118101Google Scholar
- Merkle CL, Deutsch S (1990) Drag reduction in liquid boundary layers by gas injection. Prog Astronaut Aeronaut 123:351–411Google Scholar
- Merkle CL, Deutsch S (1992) Microbubble drag reduction in liquid turbulent boundary layers. ASME Appl Mech Rev 45:103–127Google Scholar
- Michaelides EE (1997) The transient equation of motion for particles, bubbles, and droplets. J Fluids Eng 119:233–247Google Scholar
- Michel JM (1984) Some features of water flows with ventilated cavities. J Fluid Eng 106(3):319–326Google Scholar
- Mizokami S, Kawakita C, Kodan Y, Takano S, Higasa S, Shigenaga R (2010) Experimental study of air lubrication method and verification of effects on actual hull by means of sea trial. Mitsubishi Heavy Ind Techn Rev 47(3):41–47Google Scholar
- Moctezuma MF, Lima-Ochoterena R, Zenit R (2005) Velocity fluctuations resulting from the interaction of a bubble with a vertical wall. Phys Fluids 17:098106Google Scholar
- Moriguchi Y, Kato H (2002) Influence of microbubble diameter and distribution on frictional resistance reduction. J Mar Sci Technol 7:79–85Google Scholar
- Murai Y, Oiwa H (2008) Increase of effective viscosity in bubbly liquids from transient bubble deformation. Fluid Dyn Res 40:565–575MATHGoogle Scholar
- Murai Y, Matsumoto Y, Yamamoto F (2001) Three-dimensional measurement of void fraction in a bubble plume using statistic stereoscopic image processing. Exp Fluids 30:11–21Google Scholar
- Murai Y, Oishi Y, Sasaki T, Kodama Y, Yamamoto F (2005a) Turbulent shear stress profiles in a horizontal bubbly channel flow. In: Proceedings of 6th international symposium on smart control of turbulence 2005, Tokyo, 289–295Google Scholar
- Murai Y, Sasaki T, Ishikawa M, Yamamoto F (2005b) Bubble-driven convection around cylinders confined in a channel. J Fluids Eng 127:117–123Google Scholar
- Murai Y, Fujii H, Tasaka Y, Takeda Y (2006a) Turbulent bubbly channel flow investigated by ultrasound velocity profiler. J Fluid Sci Technol 1:12–23Google Scholar
- Murai Y, Oishi Y, Takeda Y, Yamamoto F (2006b) Turbulent shear stress profiles in a bubbly channel flow assessed by particle tracking velocimetry. Exp Fluids 41:343–352Google Scholar
- Murai Y, Qu JW, Yamamoto F (2006c) Three dimensional interaction of bubbles at intermediate Reynolds numbers. Multiph Sci Technol 18:175–197Google Scholar
- Murai Y, Fukuda H, Oishi Y, Kodama Y, Yamamoto F (2007) Skin friction reduction by large air bubbles in a horizontal channel flow. Int J Multiph Flow 33:147–163Google Scholar
- Murai Y, Oiwa H, Takeda Y (2008) Frictional drag reduction in bubbly Couette-Taylor flow. Phys Fluids 20:034101Google Scholar
- Murai Y, Ohta S, Shigetomi A, Tasaka Y, Takeda Y (2009) Development of an ultrasonic void fraction profiler. Meas Sci Technol 20:114003Google Scholar
- Murai Y, Tasaka Y, Nambu Y, Takeda Y, Gonzalez SR (2010) Ultrasonic detection of moving interfaces in gas–liquid two-phase flow. Flow Meas Instrum 21:356–366Google Scholar
- Narayanan C, Lakehal D (2003) Mechanism of particle deposition in a fully developed turbulent open channel flow. Phys Fluids 15:763–775Google Scholar
- Oishi Y, Murai Y (2014) Horizontal turbulent channel flow interacted by a single large bubble. Exp Therm Fluid Sci 55:128–139Google Scholar
- Oishi Y, Murai Y, Tasaka Y, Takeda Y (2009) Frictional drag reduction by wavy advection of deformable bubbles. J Phys Conf Ser 147:012020Google Scholar
- Ojima S, Hayashi K, Hosokawa S, Tomiyama A (2014) Distribution of void fraction and liquid velocity in air-water bubble column. Int J Multiph Flow 1–11. doi:10.1016/j.ijmultiphaseflow.2014.05.008
- Ortiz-Villafuerte J, Hassan YA (2006) Investigation of microbubble boundary layer using particle tracking velocimetry. J Fluids Eng 128:507–519Google Scholar
- Ouellette NT (2012) Turbulence in two dimensions. Phys Today 68–69Google Scholar
- Pang MJ, Wei JJ, Yu B (2013) Numerical study on modulation of microbubbles on turbulence frictional drag in a horizontal channel. Ocean Eng 81:58–68Google Scholar
- Park HJ, Oishi Y, Tasaka Y, Murai Y, Takeda Y (2009) Turbulent shear control with oscillatory bubble injection. J Phys Conf Ser 147:012037Google Scholar
- Park HJ, Tasaka Y, Murai Y, Oishi Y (2014) Vortical structures swept by a bubble swarm in turbulent boundary layers. Chem Eng Sci 116:486–496Google Scholar
- Piomelli U, Yuan J (2013) Numerical simulation of spatially developing, accelerating boundary layer. Phys Fluids 25:101304Google Scholar
- Poreh M, Cermak JE (1964) Study of diffusion from a line source in a turbulent boundary layer. Int J Heat Mass Transf 7:1083–1095Google Scholar
- Prasser HM, Scholz D, Zippe C (2001) Bubble size measurement using wire-mesh sensors. Flow Meas Instrum 12:299–312Google Scholar
- Prosperetti A (2012) Linear oscillations of constrained drops, bubbles, and plane liquid surfaces. Phys Fluids 24:032109MathSciNetGoogle Scholar
- Rensen J, Luther S, de Vries J, Lohse D (2005a) Hot-film anemometry in bubbly flow I: bubble–probe interaction. Int J Multiph Flow 31:285–301MATHGoogle Scholar
- Rensen J, Luther S, Lohse D (2005b) The effect of bubbles on developed turbulence. J Fluid Mech 538:153–187MATHGoogle Scholar
- Richter S, Aritomi M, Prasser HM, Humpel R (2002) Approach towards spatial phase reconstruction in transient bubbly flow using a wire-mesh sensor. Int J Heat Mass Transf 45:1063–1075Google Scholar
- Robinson SK (1991) Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech 23:601–639Google Scholar
- Ronen D (1982) The effect of oil price on the optimal speed of ships. J Oper Res 33:1035–1040Google Scholar
- Rust AC, Manga M (2002a) Effects of bubble deformation in the viscosity of dilute suspensions. J Non-Newton Fluid Mech 104:53–63MATHGoogle Scholar
- Rust AC, Manga M (2002b) Bubble shapes and orientations in low Re simple shear flow. J Colloid Interface Sci 249:476–480Google Scholar
- Ryskin G, Leal LG (1984) Numerical solution of free-boundary problems in fluid mechanics: part 1 the finite-difference technique. J Fluid Mech 148:1–17MATHGoogle Scholar
- Sakurai K, Tasaka Y, Murai Y (2013) Modification of effective viscosity on bubbly flows due to transient bubble deformation. Trans. Japan Soc. Mech. Eng., Ser. B, 79: 1–11 (in Japanese). English version of similar contents: Murai Y, Tasaka Y, Sakurai K, Oyama K, Takeda Y (2010) Ultrasound Doppler rheometry from spin response of viscoelastic and bubbly Liquids. In: Proceedings 7th international symposium on ultrasonic Doppler methods, Gothenburg, Sweden, 9–12Google Scholar
- Sanders WC, Winkel ES, Dowling DR, Perlin M, Ceccio SL (2006) Bubble friction drag reduction in a high-Reynolds-number flat-plate turbulent boundary layer. J Fluid Mech 552:353–380MATHGoogle Scholar
- Sangani AS, Didwania AK (1993) Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J Fluid Mech 250:307–337MATHGoogle Scholar
- Sangani AS, Kang SY, Tsao HK, Koch DL (1997) Rheology of dense bubble suspensions. Phys Fluids 9(6):1540–1561Google Scholar
- Schowalter WR, Chaffey CE, Brenner H (1968) Rheological behavior of a dilute emulsion. J Colloid Interface Sci 26:152–160Google Scholar
- Seo JH, Lele SK, Tryggvason G (2010) Investigation and modeling of bubble–bubble interaction effect in homogeneous bubbly flows. Phys Fluids 22:063302Google Scholar
- Serizawa A, Kataoka I (1990) Turbulence suppression in bubbly two-phase flow. Nuclear Eng Des 122:1–16Google Scholar
- Serizawa A, Inui T, Eguchi T (2005) Flow characteristics and pseudo-laminarization of vertically upward air–water milky bubbly flow with micro bubbles in a pipe. Jpn J Multiph Flow 19:335–340 (in Japanese)Google Scholar
- Shen X, Ceccio S, Perlin M (2006) Influence of bubble size on micro-bubble drag reduction. Exp Fluids 41:415–424Google Scholar
- Shiomi Y, Kutsuna H, Akagawa K, Ozawa M (1993) Two-phase flow in an annulus with a rotating inner cylinder (flow pattern in bubbly flow region). Nuclear Eng Des 141:27–34Google Scholar
- So S, Morikita H, Takagi S, Matsumoto Y (2002) Laser Doppler velocimetry measurement of turbulent bubbly channel flow. Exp Fluids 33:135–142Google Scholar
- Stickel J, Powell RL (2005) Fluid mechanics and rheology of dense suspensions. Annu Rev Fluid Mech 37:129–149MathSciNetGoogle Scholar
- Stutz B, Legoupil S (2003) X-ray measurements within unsteady cavitation. Exp Fluids 35(2):130–138Google Scholar
- Sugiyama K, Calzavarini E, Lohse D (2008) Microbubbly drag reduction in Taylor–Couette flow in wavy vortex regime. J Fluid Mech 608:21–41MATHGoogle Scholar
- Takagi S, Matsumoto Y (2011) Surfactant effects on bubble motion and bubbly flow. Annu Rev Fluid Mech 43:615–636Google Scholar
- Takagi S, Ogasawara T, Fukuta M, Matsumoto Y (2009) Surfactant effect on the bubble motions and bubbly flow structures in a vertical channel. Fluid Dyn Res 41:065003Google Scholar
- Takahashi T, Kakugawa A, Makino M, Kodama Y (2003) Experimental study on scale effect of drag reduction by microbubbles using very large flat plate ships. J Kansai Soc Nav Archit Jpn 239:11–20 (in Japanese)Google Scholar
- Takeda Y (2012) Ultrasonic Doppler velocity profiler for fluid flow. Fluid mechanics and its applications, Ser. 101, Springer, BerlinGoogle Scholar
- Takeda Y, Fischer WE, Sakakibara J (1994) Decomposition of the modulated waves in a rotating Couette system. Science 263:502–505Google Scholar
- Tanaka M (2013) Inverse transverse migration of small bubbles in turbulence. J Phys Soc Jpn 82:044401Google Scholar
- Taniere A, Oesterle B, Monnier JC (1997) On the behavior of solid particles in a horizontal boundary layer with turbulence and saltation effects. Exp Fluids 23:463–471Google Scholar
- Taylor GI (1923) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc Lond Ser A 223:289–343MATHGoogle Scholar
- Timkin LS, Gorelik RS (2010) Specificity of laminar-turbulent transition un upward monodispersed microbubbly flow. Tech Phys Lett 36:493–495Google Scholar
- Toschi F, Bodenschartz E (2009) Lagrangian properties of particles in turbulence. Annu Rev Fluid Mech 41:375–404Google Scholar
- Tran-Cong S, Marie JL, Perkins RJ (2008) Bubble migration in a turbulent boundary layer. Int J Multiph Flow 34:786–807Google Scholar
- Tsai JF, Chen CC (2011) Boundary layer mixture model for a microbubble drag reduction technique. Int Sch Res Netw 2011:405701Google Scholar
- van den Berg TH, Luther S, Lathrop DP, Lohse D (2005) Drag reduction in bubbly Taylor–Couette turbulence. Phys Rev Lett 94:044501Google Scholar
- van den Berg TH, Luther S, Lathrop D, Lohse D (2007) Bubbly turbulent drag reduction is a boundary effect. Phys Rev Lett 98:084501Google Scholar
- van Gils DPM, Guzman DN, Sun C, Lohse D (2013) The importance of bubble deformability for strong drag reduction in bubbly turbulent Taylor–Couette flow. J Fluid Mech 722:317–347MATHGoogle Scholar
- Warsito W, Fan LS (2001) Measurement of real-time flow structures in gas–liquid and gas–liquid–solid flow systems using electrical capacitance tomography (ECT). Chem Eng Sci 56:6455–6462Google Scholar
- Watamura T, Tasaka Y, Murai Y (2013) Intensified and attenuated waves in a microbubble Taylor-Couette flow. Phys Fluids 25:054107Google Scholar
- Watanabe O, Masuko A, Shirose Y (1998) Measurements of drag reduction by microbubbles using very long ship models. J Soc Nav Archit Jpn 183:53–63Google Scholar
- Winkel ES, Ceccio SL, Dowling DR, Perlin M (2004) Bubble-size distributions produced by wall injection of air into flowing fresh water, saltwater and surfactant solutions. Exp Fluids 37:802–810Google Scholar
- Wronski S, Hubacz R, Ryszczuk T (2005) Interfacial area in a reactor with helicoidal flow for the two-phase gas–liquid system. Chem Eng J 105:71–79Google Scholar
- Wu SJ, Hsu CH, Lin TT (2007) Model test of the surface and submerged vehicles with the micro-bubble drag reduction. Ocean Eng 34:83–93Google Scholar
- Wu SJ, Ouyang K, Shiah SW (2008) Robust design of microbubble drag reduction in a channel flow using the Taguchi method. Ocean Eng 35:856–863Google Scholar
- Xu J, Maxey ML, Karniadakis GE (2002) Numerical simulation of turbulent drag reduction using micro-bubbles. J Fluid Mech 468:271–281MATHGoogle Scholar
- Yoshida K, Tasaka Y, Murai Y, Takeda Y (2009) Mode transition in bubbly Taylor–Couette flow measured by PTV. J Phys Conf Ser 147:012013Google Scholar
- Zenit R, Koch D, Sangani AS (2001) Measurements of the average properties of a suspension of bubbles rising in a vertical channel. J Fluid Mech 429:307–342MATHGoogle Scholar
- Zhang DZ, Prosperetti A (1994) Averaged equations for inviscid disperse two-phase flow. J Fluid Mech 267:185–219MATHMathSciNetGoogle Scholar
- Zhao LH, Andersson HI, Gillissen JJJ (2010) Turbulence modulation and drag reduction by spherical particles. Phys Fluids 22:081702Google Scholar
- Zhao LH, Marchioli C, Andersson HI (2012) Stokes number effects on particle slip velocity in wall-bounded turbulence and implications for dispersion models. Phys Fluids 24:021705Google Scholar
- Zhen L, Hassan YA (2006) Wavelet autocorrelation identification of the turbulent flow multi-scales for drag reduction process in microbubbly flows. Chem Eng Sci 61:7107–7114Google Scholar
- Zhen N, Handler RA, Zhang Q, Oeth C (2013) Evolution of a hairpin vortex in a shear-thinning fluid governed by a power-law model. Phys Fluids 25:110703Google Scholar