Transport Phenomena with Drops and Bubbles pp 443-485 | Cite as

# Special Topics

Chapter

## Abstract

The special topics considered in this chapter are concerned with: (i) transport in the presence of an electric field; (ii) transport with a slurry fuel droplet; and (iii) thermocapillary phenomena and transport under conditions of microgravity. An attempt has been made to succinctly discuss the special features that arise in consideration of these topics, and in this context, very recent studies in the published literature have been critically examined.

## Keywords

Nusselt Number Stream Function Colloid Interface Heat Mass Transfer Migration Velocity
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## References

- [1]A. Acrivos & T.D. Taylor. Heat and mass transfer from single spheres in Stokes flow.
*Phys. Fluids*, 5:387–394, 1962.MathSciNetADSMATHCrossRefGoogle Scholar - [2]J.L. Anderson. Droplet interactions in thermocapillary motion.
*Int. J. Multiphase Flow*, 11(6):813–824, 1985.MATHCrossRefGoogle Scholar - [3]P. Annamalai, N. Shankar, R. Cole, & R.S. Subramanian. Bubble migration inside a liquid drop in a space laboratory.
*Appl. Sci. Res.*, 38:179–186, 1982.CrossRefGoogle Scholar - [4]P.J. Antaki. Transient processes in a rigid slurry droplet during liquid vaporization and combustion.
*Comb. Sci. Technol.*, 46:113–135, 1986.CrossRefGoogle Scholar - [5]P.J. Antaki. Liquid vaporization and combustion from slurry fuel droplets. In
*Encyclopedia of Environmental Control Technology*(Ed.: P.N. Cheremisinoff), chapter 5, pages 179–209. Gulf Publishing, Houston, TX, 1989.Google Scholar - [6]P.J. Antaki & RA. Williams. Observations on the combustion of boron slurry droplets in air.
*Combustion and Flame*, 67:1–8, 1987.CrossRefGoogle Scholar - [7]P.S. Ayyaswamy. Direct contact transfer processes with moving liquid droplets. In
*Advances in Heat Transfer*(Eds.: J.R Hartnett, T.F. Irvine Jr., & Y.I. Cho), volume 26, pages 1–104. Academic Press, New York, 1995.Google Scholar - [8]P.S. Ayyaswamy. Mathematical methods in direct-contact transfer studies with droplets. In
*Annual Review of Heat Transfer*(Ed.: C.L. Tien), volume 7. Begell House, New York, 1996.Google Scholar - [9]P.J. Bailes & J.D. Thornton. Electrically augmented liquid-liquid extraction in a two-component system. 1. Single droplet studies. In
*Proc. Int. Solvent. Extraction Conf.*, volume 2, pages 1431–1439, The Hague, 1971.Google Scholar - [10]P.J. Bailes & J.D. Thornton. Electrically augmented liquid-liquid extraction in a two-component system. 2. Multidroplet studies. In
*Proc. Int. Solvent. Extraction Conf.*, volume 2, pages 1011–1027, Lyon, 1974.Google Scholar - [11]R. Balasubramaniam & A.T. Chai. Thermocapillary migration of droplets: An exact solution for small Marangoni numbers
*J. Colloid Interface Sci.*, 119:531–538, 1987.CrossRefGoogle Scholar - [12]R. Balasubramaniam & J.E. Lavery. Numerical simulation of thermocapillary bubble migration under microgravity for large Reynolds and Marangoni numbers.
*Numer. Heat Transfer A*, 16:175–187, 1989.ADSCrossRefGoogle Scholar - [13]K.D. Barton & R.S. Subramanian. The migration of liquid drops in a vertical temperature gradient.
*J. Colloid Interface Sci.*, 133:211–222, 1989.CrossRefGoogle Scholar - [14]K.D. Barton & R.S. Subramanian. Thermocapillary migration of a liquid drop normal to a plane surface.
*J. Colloid Interface Sci.*, 137:170–182, 1990.CrossRefGoogle Scholar - [15]K.D. Barton & R.S. Subramanian. Migration of liquid drops in a vertical temperature gradient — interaction effects near a horizontal surface.
*J. Colloid Interface Sci.*, 141(1):146–156, 1991.CrossRefGoogle Scholar - [16]H.F. Bauer & W. Eidel. Marangoni convection in a spherical liquid system.
*Acta Astronautica*, 15:275–290, 1987.ADSMATHCrossRefGoogle Scholar - [17]Y.K. Bratukhin. Thermocapillary drift of a viscous droplet. Fluid Dynam. (English translation of:
*Izv. Akad. Nauk SSSR Mekh. Zhidk*. Gaza), 10(5):833–837, 1975.Google Scholar - [18]L.S. Chang & J.C. Berg. Fluid flow and transfer behavior of a drop translating in an electric field at intermediate Reynolds numbers.
*Int. J. Heat Mass Transfer*, 26:823–832, 1983.MATHCrossRefGoogle Scholar - [19]L.S. Chang, T.E. Carleson, & J.C. Berg. Heat and mass transfer to a translating drop in an electric field.
*Int. J. Heat Mass Transfer*, 25:1023–1030, 1982.CrossRefGoogle Scholar - [20]B.T. Chao. Transient heat and mass transfer to a translating droplet.
*ASME J. Heat Transfer*, 91:273–281, 1969.Google Scholar - [21]J.N. Chung. The motion of particles inside a droplet.
*ASME J. Heat Transfer*, 104:438–445, 1982.ADSCrossRefGoogle Scholar - [22]J.N. Chung & D.L.R. Oliver. Transient heat transfer in a fluid sphere translating in an electric field.
*ASME J. Heat Transfer*, 112:84–92, 1990.CrossRefGoogle Scholar - [23]L. Dill. On the thermocapillary migration of a growing or a shrinking drop.
*J. Colloid Interface Sci.*, 46:533–540, 1991.CrossRefGoogle Scholar - [24]F. Feuillebois. Thermocapillary migration of two equal bubbles parallel to their line of centers.
*J. Colloid Interface Sci.*, 131:267–274, 1989.CrossRefGoogle Scholar - [25]S.K. Griffiths & F.A. Morrison Jr. Low Péclet number heat and mass transfer from a drop in an electric field.
*J. Heat Transfer*, 101:484–488, 1979.CrossRefGoogle Scholar - [26]S.K. Griffiths & F.A. Morrison Jr. The transport from a drop in an alternating electric field.
*Int. J. Heat Mass Transfer*, 26:717–726, 1983.MATHCrossRefGoogle Scholar - [27]M. Hähnel, V. Delitzsch, & H. Eckelmann. The motion of droplets in a vertical temperature gradient.
*Phys. Fluids A*, 1:1460–1466, 1989.ADSCrossRefGoogle Scholar - [28]J.H. Harker & J. Ahmadzadeh. The effect of electric fields on mass transfer from falling drops.
*Int. J. Heat Mass Transfer*, 17:1219–1225, 1974.CrossRefGoogle Scholar - [29]T.B. Jones. Electrohydrodynamically enhanced heat transfer in liquids. In
*Advances in Heat Transfer*(Eds.: T.F. Irvine Jr. & J.P. Hartnett), volume 14, pages 107–148. Academic Press, New York, 1978.Google Scholar - [30]Y.S. Kao & D.B.R. Kenning. Thermocapillary flow near a hemispherical bubble on a heated wall.
*J. Fluid Mech.*, 53:715–735, 1972.ADSMATHCrossRefGoogle Scholar - [31]H.J. Keh & S.H. Chen. The axisymmetric thermocapillary motion of two fluid droplets.
*Int. J. Multiphase Flow*, 16(3):515–427, 1990.MATHCrossRefGoogle Scholar - [32]H.S. Kim & R.S. Subramanian. Thermocapillary migration of a droplet with insoluble surfactant. II: General case.
*J. Colloid Interface Sci.*, 130:112–129, 1989.CrossRefGoogle Scholar - [33]H.S. Kim & R.S. Subramanian. Thermocapillary migration of a droplet with insoluble surfactant. I: Surfactant cap.
*J. Colloid Interface Sci.*, 127:417–428, 1989.CrossRefGoogle Scholar - [34]B.K. Larkin. Thermocapillary flow around a hemispherical bubble.
*AIChE J.*, 16(1): 101–107, 1970.MathSciNetCrossRefGoogle Scholar - [35]C.K. Law, H.K. Law, & C.H. Lee. Combustion characteristics of coal/oil and coal/oil/water mixtures.
*Energy*, 4:329–339, 1979.ADSCrossRefGoogle Scholar - [36]J.J. Lorenz & B.B. Mikic. Effect of thermocapillary flow on heat transfer in dropwise condensation.
*ASME J. Heat Transfer*, 92:46–52, 1970.CrossRefGoogle Scholar - [37]M. Lowenberg & R.H. Davis. Near-contact thermocapillary motion of two nonconducting drops.
*J. Fluid Mech.*, 256:107–131, 1993.MathSciNetADSCrossRefGoogle Scholar - [38]R.R Manohar & S.R.K. Iyengar. Transient heat transfer to a droplet suspended in an electric field.
*Numer. Heat Transfer*, 14:499–510, 1988.ADSMATHCrossRefGoogle Scholar - [39]D.M. Mattox, H.D. Smith, W.R. Wilcox, & R.S. Subramanian. Thermal-gradient-induced migration of bubbles in molten glass.
*J. Amer. Ceramic Soc*, 65:437–442, 1982.CrossRefGoogle Scholar - [40]R.M. Merritt & R.S. Subramanian. Migration of a gas bubble normal to a plane horizontal surface in a vertical temperature gradient.
*J. Colloid Interface Sci.*, 131:514–525, 1989.CrossRefGoogle Scholar - [41]R.M. Merritt, D.S. Morton, & R.S. Subramanian. Flow structures in bubble migration under the combined action of buoyancy and thermocapillarity.
*J. Colloid Interface Sci.*, 155:200–209, 1993.CrossRefGoogle Scholar - [42]R.M. Merritt & R.S. Subramanian. The migration of isolated gas bubbles in a vertical temperature gradient.
*J. Colloid Interface Sci.*, 125:333–339, 1988.CrossRefGoogle Scholar - [43]M. Meyyappan & R.S. Subramanian. The thermocapillary motion of two bubbles oriented arbitrarily relative to a thermal gradient.
*J. Colloid Interface Sci.*, 97(1):291–294, 1984.CrossRefGoogle Scholar - [44]M. Meyyappan & R.S. Subramanian. Thermocapillary migration of a gas bubble in an arbitrary direction with respect to a plane surface.
*J. Colloid Interface Sci.*, 115(1):206–219, 1987.CrossRefGoogle Scholar - [45]M. Meyyappan, W.R. Wilcox, & R.S. Subramanian. Thermocapillary migration of a bubble normal to a plane surface.
*J. Colloid Interface Sci.*, 83:199–208, 1981.CrossRefGoogle Scholar - [46]M. Meyyappan, W.R. Wilcox, & R.S. Subramanian. The slow axisymmetric motion of two bubbles in a thermal gradient.
*J. Colloid Interface Sci.*, 94(l):243–257, 1983.CrossRefGoogle Scholar - [47]K. Miyasaka & C.K. Law. Combustion and agglomeration of coal-oil mixtures in furnace environments.
*Combust. Sci. Technol.*, 24:71–82, 1980.CrossRefGoogle Scholar - [48]F.A. Morrison Jr. Transient heat and mass transfer to a translating droplet.
*ASME J. Heat Transfer*, 99:269–273, 1977.CrossRefGoogle Scholar - [49]D.S. Morton, R.S. Subramanian, & R. Balasubramaniam. The migration of a compound drop due to thermocapillarity.
*Phys. Fluids A*, 12:2119–2133, 1990.ADSCrossRefGoogle Scholar - [50]M. Nallani & R.S. Subramanian. Migration of methanol drops in a vertical temperature gradient in a silicone oil.
*J. Colloid Interface Sci.*, 157:24–31, 1993.CrossRefGoogle Scholar - [51]A.B. Newman. The drying of porous solids: Diffusion and surface emission equations.
*Trans. AIChE*, 27:203–220, 1931.Google Scholar - [52]H.D. Nguyen & J.N. Chung. Flows inside and around a vaporizing/condensing drop translating in an electric field.
*ASME J. Appl. Mech.*, 57:1044–1055, 1990.ADSCrossRefGoogle Scholar - [53]H.D. Nguyen & J.N. Chung. Conjugate heat transfer from a translating drop in an electric field at low Péclet number.
*Int. J. Heat Mass Transfer*, 35:443–456, 1992.MATHCrossRefGoogle Scholar - [54]H.D. Nguyen & J.N. Chung. Evaporation from a translating drop in an electric field.
*Int. J. Heat Mass Transfer*, 36:3797–3812, 1993.MATHCrossRefGoogle Scholar - [55]D.L.R. Oliver, T.E. Carleson, & J.N. Chung. Transient heat transfer to a fluid sphere suspended in an electric field.
*Int. J. Heat Mass Transfer*, 28:1005–1009, 1985.CrossRefGoogle Scholar - [56]D.L.R. Oliver & K.J. De Witt. Surface tension driven flows in a micro-gravity environment.
*Int. J. Heat Mass Transfer*, 31:1534–1537, 1988.CrossRefGoogle Scholar - [57]D.L.R. Oliver & K.J. De Witt. High Péclet number heat transfer from a droplet suspended in an electric field: Interior problem.
*Int. J. Heat Mass Transfer*, 36:3153–3155, 1993.MATHCrossRefGoogle Scholar - [58]S.S. Sadhal. A note on the thermocapillary migration of a bubble normal to a plane surface.
*J. Colloid Interface Sci.*, 95:283–286, 1983.CrossRefGoogle Scholar - [59]S.S. Sadhal & P.S. Ayyaswamy. Row past a liquid drop with a large non-uniform radial velocity.
*J. Fluid Mech.*, 133:65–81, 1983.ADSMATHCrossRefGoogle Scholar - [60]S.S. Sadhal & R.E. Johnson. Stokes flow past drops and bubbles coated with thin films. Part 1: Stagnant cap of surfactant film — exact solution.
*J. Fluid. Mech.*, 126:237–250, 1983.ADSMATHCrossRefGoogle Scholar - [61]S.S. Sadhal & H.N. Oğuz. Stokes flow past compound multiphase drops: Cases of completely engulfed drops/bubbles.
*J. Fluid Mech.*, 160:511–529, 1985.MathSciNetADSMATHCrossRefGoogle Scholar - [62]S.S. Sadhal, E.H. Trinh, & P. Wagner. Unsteady spot heating of a drop in a microgravity environment. In
*Fluid Mechanics Phenomena in Microgravity*, volume No. AMD-154, pages 105–110. ASME, 1992.Google Scholar - [63]T. Sakai & M. Saito. Single droplet combustion of coal slurry fuels.
*Combustion and Flame*, 51:141–154, 1983.CrossRefGoogle Scholar - [64]J.A. Satrape. Interactions and collisions of bubbles in thermocapillary motion.
*Phys. Fluids A*, 4(9): 1883–1900, 1992.ADSMATHCrossRefGoogle Scholar - [65]T.C. Scott. Surface area generation and droplet size control using pulsed electric fields.
*AIChE J.*, 33:1557–1559, 1987.CrossRefGoogle Scholar - [66]N. Shankar, R. Cole, & R.S. Subramanian. Thermocapillary migration of a fluid droplet inside a drop in a space laboratory.
*Int. J. Multiphase Flow*, 7:581–594, 1981.MATHCrossRefGoogle Scholar - [67]N. Shankar & R.S. Subramanian. The slow axisymmetric thermocapillary migration of an eccentrically placed bubble inside a drop in zero gravity.
*J. Colloid Interface Sci.*,94(1):258–275, 1983.CrossRefGoogle Scholar - [68]L. Sharpe & F.A. Morrison Jr. Numerical analysis of heat and mass transfer from fluid spheres in an electric field.
*ASME J. Heat Transfer*, 108:337–342, 1986.CrossRefGoogle Scholar - [69]M.B. Stewart & F.A. Morrison Jr. Small Reynolds number electro-hydrodynamic flow around drops and the resulting deformation.
*ASME J. Heat Transfer*, 46:510–512, 1979.MATHGoogle Scholar - [70]R.S. Subramanian. Slow migration of a gas bubble in a thermal gradient.
*AIChE J.*, 27:646–654, 1981.CrossRefGoogle Scholar - [71]R.S. Subramanian. Thermocapillary migration of bubbles and droplets.
*Adv. Space Res.*, 3:145–153, 1983.MathSciNetADSCrossRefGoogle Scholar - [72]R.S. Subramanian. The Stokes force on a droplet in an unbounded fluid medium due to capillary effects.
*J. Fluid Mech.*, 153:389–400, 1985.ADSMATHCrossRefGoogle Scholar - [73]R.S. Subramanian. The motion of bubbles and drops in reduced gravity. In
*Transport Processes with Drops and Bubbles*(Eds.: R.P. Chhabra & D. De Kee), pages 1–32. Hemisphere, New York, 1992.Google Scholar - [74]J.A. Szymczyk & J. Siekmann. On the thermocapillary motion of a bubble in low gravitational environment.
*Proc. Int. Symp. Space Technol. Sci.*, 2:2137–2148, 1986.ADSGoogle Scholar - [75]J.A. Szymczyk, G. Wozniak, & J. Siekmann. On Marangoni bubble motion at higher Reynolds and Marangoni numbers under microgravity.
*Appl. Microgravity Tech.*, 1:27–29, 1987.ADSGoogle Scholar - [76]T. Takamatsu, Y. Hashimoto, M. Yamaguchi, & T. Katayama. Theoretical and experimental studies of charged drop formation in a uniform electric field.
*J. Chem. Engrg. Japan*, 14:178–182, 1981.CrossRefGoogle Scholar - [77]G.I. Taylor. Studies in electrohydrodynamics I. The circulation produced in a drop by an electric field.
*Proc. Roy. Soc. London A*, 291:159–166, 1966.ADSCrossRefGoogle Scholar - [78]T.D. Taylor & A. Acrivos. On the deformation and drag of a falling viscous drop at low Reynolds number.
*J. Fluid Mech.*, 18:466–476, 1964.MathSciNetADSMATHCrossRefGoogle Scholar - [79]R.L. Thompson.
*Marangoni Bubble Motion in Zero Gravity*. PhD thesis, University of Toledo, Toledo, Ohio, 1979.Google Scholar - [80]R.L. Thompson, K.J. De Witt, & T.L. Labus. Marangoni bubble motion phenomena in zero gravity.
*Chem. Engrg. Comm.*, 5:299–314, 1980.CrossRefGoogle Scholar - [81]S. Torza, R.G. Cox, & S.G. Mason. Electro-hydrodynamic deformation and bursts of liquid drops.
*Phil. Trans. Roy. Soc*, 269:295–319, 1971.ADSCrossRefGoogle Scholar - [82]L. Trefethen. Dropwise condensation and the possible importance of circulation within drops caused by surface tension variation. Technical Report 58GL47, General Electric Co., February 1958.Google Scholar
- [83]H. Wei & R.S. Subramanian. Interactions between two bubbles under isothermal conditions in a downward temperature gradient.
*Phys. Fluids*, 6(9):2971–2978, 1994.ADSCrossRefGoogle Scholar - [84]M. Yamaguchi, Y. Hashimoto, T. Takamatsu, & T. Katayama. Gas absorption by single charged drops during their formation in a uniform electric field.
*Int. J. Heat Mass Transfer*, 25:1631–1639, 1982.CrossRefGoogle Scholar - [85]S.C. Yao & P. Manwani. Burning of suspended coal-water slurry droplets with oil as combustion additive.
*Combustion and Flame*, 66:87–89, 1986.CrossRefGoogle Scholar - [86]N.O. Young, J.S. Goldstein, & M.J. Block. The motion of bubbles in a vertical temperature gradient.
*J. Fluid Mech.*, 6:350–356, 1959.ADSMATHCrossRefGoogle Scholar

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