Skip to main content

Part of the book series: Mechanical Engineering Series ((MES))

  • 531 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Acrivos & T.D. Taylor. Heat and mass transfer from single spheres in Stokes flow. Phys. Fluids, 5:387–394, 1962.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. J.L. Anderson. Droplet interactions in thermocapillary motion. Int. J. Multiphase Flow, 11(6):813–824, 1985.

    Article  MATH  Google 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.

    Article  Google Scholar 

  4. P.J. Antaki. Transient processes in a rigid slurry droplet during liquid vaporization and combustion. Comb. Sci. Technol., 46:113–135, 1986.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  ADS  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google Scholar 

  16. H.F. Bauer & W. Eidel. Marangoni convection in a spherical liquid system. Acta Astronautica, 15:275–290, 1987.

    Article  ADS  MATH  Google 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.

    Article  MATH  Google 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.

    Article  Google 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.

    Article  ADS  Google 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.

    Article  Google Scholar 

  23. L. Dill. On the thermocapillary migration of a growing or a shrinking drop. J. Colloid Interface Sci., 46:533–540, 1991.

    Article  Google Scholar 

  24. F. Feuillebois. Thermocapillary migration of two equal bubbles parallel to their line of centers. J. Colloid Interface Sci., 131:267–274, 1989.

    Article  Google 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.

    Article  Google 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.

    Article  MATH  Google Scholar 

  27. M. Hähnel, V. Delitzsch, & H. Eckelmann. The motion of droplets in a vertical temperature gradient. Phys. Fluids A, 1:1460–1466, 1989.

    Article  ADS  Google 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.

    Article  Google 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.

    Article  ADS  MATH  Google 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.

    Article  MATH  Google 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.

    Article  Google 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.

    Article  Google Scholar 

  34. B.K. Larkin. Thermocapillary flow around a hemispherical bubble. AIChE J., 16(1): 101–107, 1970.

    Article  MathSciNet  Google 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.

    Article  ADS  Google 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.

    Article  Google Scholar 

  37. M. Lowenberg & R.H. Davis. Near-contact thermocapillary motion of two nonconducting drops. J. Fluid Mech., 256:107–131, 1993.

    Article  MathSciNet  ADS  Google 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.

    Article  ADS  MATH  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  Google Scholar 

  47. K. Miyasaka & C.K. Law. Combustion and agglomeration of coal-oil mixtures in furnace environments. Combust. Sci. Technol., 24:71–82, 1980.

    Article  Google Scholar 

  48. F.A. Morrison Jr. Transient heat and mass transfer to a translating droplet. ASME J. Heat Transfer, 99:269–273, 1977.

    Article  Google 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.

    Article  ADS  Google 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.

    Article  Google 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.

    Article  ADS  Google 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.

    Article  MATH  Google 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.

    Article  MATH  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  MATH  Google 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.

    Article  Google 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.

    Article  ADS  MATH  Google 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.

    Article  ADS  MATH  Google 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.

    Article  MathSciNet  ADS  MATH  Google 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.

    Article  Google Scholar 

  64. J.A. Satrape. Interactions and collisions of bubbles in thermocapillary motion. Phys. Fluids A, 4(9): 1883–1900, 1992.

    Article  ADS  MATH  Google Scholar 

  65. T.C. Scott. Surface area generation and droplet size control using pulsed electric fields. AIChE J., 33:1557–1559, 1987.

    Article  Google 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.

    Article  MATH  Google 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.

    Article  Google 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.

    Article  Google 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.

    MATH  Google Scholar 

  70. R.S. Subramanian. Slow migration of a gas bubble in a thermal gradient. AIChE J., 27:646–654, 1981.

    Article  Google Scholar 

  71. R.S. Subramanian. Thermocapillary migration of bubbles and droplets. Adv. Space Res., 3:145–153, 1983.

    Article  MathSciNet  ADS  Google 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.

    Article  ADS  MATH  Google 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.

    ADS  Google 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.

    ADS  Google 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.

    Article  Google 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.

    Article  ADS  Google 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.

    Article  MathSciNet  ADS  MATH  Google 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.

    Article  Google 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.

    Article  ADS  Google 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.

    Article  ADS  Google 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.

    Article  Google 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.

    Article  Google 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.

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Sadhal, S.S., Ayyaswamy, P.S., Chung, J.N. (1997). Special Topics. In: Transport Phenomena with Drops and Bubbles. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4022-8_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-4022-8_9

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8470-3

  • Online ISBN: 978-1-4612-4022-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics