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Dynamics of a single particle

  • L. P. Yarin
  • G. Hetsroni
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  • 460 Downloads
Part of the Heat and Mass Transfer book series (HMT)

Abstract

The drag on a particle moving in a viscous fluid remains the greatest challenge of modern hydrodynamics. This knowledge is essential for numerous applications in engineering, in particular for the calculations of the atomized fuel distribution in combustion chambers, as well as for heating, ignition and combustion of a single particle and a spray.

Keywords

Nusselt Number Drag Coefficient Burning Rate Mass Transfer Coefficient Particle Temperature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Arpaci VS (1997) Microscales of turbulence heat and mass transfer Correlations. Gordon and Breach, AmsterdamGoogle Scholar
  2. Auton TR (1987) The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183: 199–21. 8CrossRefGoogle Scholar
  3. Babii VI, Kuvaev JaF (1986) Combustion of coal dust and coal dust flame calculation. (in Russian) Energoatomizdat, MoscowGoogle Scholar
  4. Barenblatt GI (1996) Scaling, self-similarity and intermediate asymptotics. Cambridge University Press, CambridgeGoogle Scholar
  5. Barkla HM, Auchterlonie LJ (1971) The Magnus or Robins effect on rotating spheres. J. Fluid Mech. 47: 437–447CrossRefGoogle Scholar
  6. Basset AB (1961) A treatise on hydrodynamics, vol. 2. Dover, New YorkGoogle Scholar
  7. Batchelor GK (1967) An introduction to fluid dynamics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  8. Berlemont A, Desjonqueres P, Gouesbet G (1990) Particle Lagrangian simulation in turbulent flows. Int. J. Multiphase Flow 16: 19–34zbMATHCrossRefGoogle Scholar
  9. Bolt JA, and Saad MA (1957) Combustion rates of freely falling fuel drops in a hot atmosphere. The Sixth Symposium (International) on Combustion. The Combustion Institute, Reinhold, New York, pp. 717–725Google Scholar
  10. Boothroyd RG (1971) Following gas-solids suspensions. Charman and Hall, LondonGoogle Scholar
  11. Boussinesq J (1903) Theorie analytique de la chaleur. L’Ecole Polytechnique, ParisGoogle Scholar
  12. Brabston DC, Keller HB (1975) Viscous flows past spherical gas bubbles. J. Fluid Mech. 69: 179–189zbMATHCrossRefGoogle Scholar
  13. Briffa FEJ (1981). Transient drag in sprays. The Eighteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 307–319Google Scholar
  14. Chan PC-H, Leal LG (1979) The motion of a deformable drop in a second-order fluid. J. Fluid Mech. 92: 131–170zbMATHCrossRefGoogle Scholar
  15. Chang EJ, Maxey MR (1994) Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion. J. Fluid Mech. 277: 347–379zbMATHCrossRefGoogle Scholar
  16. Chang EJ, Maxey MR (1995) Unsteady flow about a sphere at low to moderate Reynolds number. Part 2. Accelerated motion. J. Fluid Mech. 303: 133–153zbMATHCrossRefGoogle Scholar
  17. Chester W, Breach DR (with an Appendix by Proudman I.). (1969) On the flow past a sphere at low Reynolds number. J. Fluid Mech. 37: 751–760zbMATHGoogle Scholar
  18. Clamen A, Gauvin WH (1969) Effect of turbulence on the drag coefficient of spheres in a supercritical flow regime. AIChE J. 15: 184–189CrossRefGoogle Scholar
  19. Clift R, Grace JR, Weber ME (1978) Bubbles, drops and particles. Academic Press. New YorkGoogle Scholar
  20. Crowe CT, Nicholls JA, Morrison RB (1963) Drag coefficients of inert and burning particles accelerating in gas streams. The Ninth Symposium (International) on Combustion. The Combustion Institute. Academic Press, New York, 395–406Google Scholar
  21. Crowe CT, Sommerfeld M, Tsuji Y (1998) Multiphase flows with droplets and particles. CRC Press, New YorkGoogle Scholar
  22. Dandy DS, Dwyer HA (1990) A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag and heat transfer. J. Fluid Mech. 216: 381–410CrossRefGoogle Scholar
  23. Davies JM (1949) The aerodynamics of golf balls. J. Appl. Phys. 20: 821–828CrossRefGoogle Scholar
  24. Dennis SCR, Walker JDA (1971) Calculation of the steady flow past a sphere at low and moderate Reynolds numbers. J. Fluid Mech. 48: 771–789zbMATHCrossRefGoogle Scholar
  25. Dwyer HA (1989) Calculations of droplet dynamics in high temperature environments. Prog. Energ. Combust. Sci. 15: 131–158CrossRefGoogle Scholar
  26. Eastop TD (1973) The influence of rotation on the heat transfer from a sphere to an air stream. Int. J. Heat Mass Transfer 16: 1954–1957CrossRefGoogle Scholar
  27. Eisenkalm, P., and Arunachalam, S.A. 1966. The drag resistance of burning drops. Combust. Flame, 10: 171–181CrossRefGoogle Scholar
  28. Eisenklam P, Arunachalam SA, Weston JA (1967) Evaporation rates and drag resistance of burning drops. The Eleventh Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 715–728Google Scholar
  29. Fendell FE, Coats DE, Smith EB (1968) Compressible slow viscous flow past a vaporizing droplet. AIAA J. 6: 1953–1960zbMATHCrossRefGoogle Scholar
  30. Fendell FE, Sprankle ML, Dodson DS (1966). Thin-flame theory for a fuel droplet in slow viscous flow. J. Fluid Mech. 26: 267–280zbMATHCrossRefGoogle Scholar
  31. Gal-Or B, Yaron I (1973) Diffusion drag upon slowly evaporating droplets. Phys. Fluids. 16: 1826–1829CrossRefGoogle Scholar
  32. Genkin AL, Gnatyuk TA, Yarin LP (1981) Distribution of concentration of particles polydispersed material in technological cyclone chambers. Theor. Found. Chem. Technol. 5: 787–791 (in Russian)Google Scholar
  33. Gogos G, Ayyaswamy PS (1988) A model for the evaporation of a slowly moving droplet. Combust. Flame. 74: 111–129CrossRefGoogle Scholar
  34. Gogos G, Sadhal SS, Ayyaswamy PS, Sundararajan T (1986) Thin-flame theory for the combustion of a moving liquid drop: effects due to variable density. J. Fluid Mech. 171: 121–144zbMATHCrossRefGoogle Scholar
  35. Goldshtik MA (1972) The elementary theory of pulverized layer. Zh. Prikl. Mekh. Tekhn. Fiz. 6: 106–112 (in Russian)Google Scholar
  36. Goldstein S (1938) Modern developments in fluid dynamics. Oxford University Press, OxfordGoogle Scholar
  37. Haber S, Hetsroni G (1971) The dynamics of a deformable drop suspended in an unbounded Stoks flow. J. Fluid Mech. 49: 257–277zbMATHCrossRefGoogle Scholar
  38. Hadamard JS (1911) Mouvement permanent lend d’une sphere liquid et visqueuse dans un liquid visqueux. C.R. Acad. Sci. Paris 152: 1735–1738zbMATHGoogle Scholar
  39. Happel J, Brenner H (1983) Low Reynolds number hydrodynamics. Martinus Nijhoff, The HagueGoogle Scholar
  40. Harper JF, Moore DW (1968) The motion of a spherical liquid drop at high Reynolds number. J. Fluid Mech. 32: 367–391zbMATHCrossRefGoogle Scholar
  41. Hetsroni G (1982) Handbook of multiphase systems. Hemisphere, New YorkzbMATHGoogle Scholar
  42. Hjelmfelt AT, Mockros LF (1966) Motion of discrete particles in a turbulent fluid. Appl. Sci. Res. 16: 149–164CrossRefGoogle Scholar
  43. Ingebo RD (1957) Atomization, acceleration, and vaporization of liquid fuels. The Sixth Symposium (International) on Combustion. The Combustion Institute. Reinhold, New York, pp. 684–687Google Scholar
  44. Ingebo RD (1962) Heat-transfer and drag coefficients for ethanol drops in a rocket chamber burning ethanol and liquid oxygen. The Eighth Symposium (International) on Combustion. The Combustion Institute. Williams and Wilkins, Baltimore, pp. 1104–1113Google Scholar
  45. Kang SW, Sarofim AF, Beer JM (1988) Particle rotation in coal combustion: statistical experimental and theoretical studies. The Twenty-second Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 145–152.Google Scholar
  46. Karanfilian SK, Kotas TJ (1978) Drag on a sphere in unsteady motion in a liquid at rest. J. Fluid Mech. 87: 85–96CrossRefGoogle Scholar
  47. Kassoy DR, Adamson TCJr, Messiter AF (1966). Compressible low Reynolds number, flow around a sphere. Phys. Fluids. 9: 671–681zbMATHCrossRefGoogle Scholar
  48. Khudyakov GN (1947) On the combustion of liquid droplets in flight. Isvest. Akad. Nauk SSSR Otdel. Tekn. Nauk. 4: 508–513 (in Russian)Google Scholar
  49. Kim I, Elghobashi S, Sirignano WA (1998) On the equation for spherical-particle motion: effect of Reynolds and acceleration numbers. J. Fluid Mech. 367: 221–253MathSciNetzbMATHCrossRefGoogle Scholar
  50. Kim S, Karrila SJ (1991) Microhydrodynamics: Principles and Selected Applications. Butterworth — Heinemann, BostonGoogle Scholar
  51. Kuchling H (1980) Nachschlagebucher fur Grundlagenfacher Physik. VERB Fachbuchverlag, LeipzigGoogle Scholar
  52. Kurose R, Komori S (1999) Drag and lift forces on a rotating sphere in a linear shear flow. J. Fluid Mech. 384: 183–206MathSciNetzbMATHCrossRefGoogle Scholar
  53. Landau LD, Lifschitz EM (1959) Fluid mechanics, 2nd edn. Pergamon, New YorkGoogle Scholar
  54. Leal LG (1980) Particle motions in a viscous fluid. In: Van Dyke M, Wehausen JV Lumley JL (eds), Annu. Rev. Fluid Mech. 12: 435–476Google Scholar
  55. Legendre D, Magnaudet J (1998) The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech. 368: 81–126MathSciNetzbMATHCrossRefGoogle Scholar
  56. Levich VG (1949) Motion of gaseous bubbles with high Reynolds numbers Zh. Eksper. Teoret. Fiz. 19: 18–24. (in Russian), 1962. Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  57. Lozinski D, Matalon M (1992) Vapaorization of a spinning fuel droplet. The Twenty-fourth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1483–1491Google Scholar
  58. Maccoll JH (1928) Aerodynamics of a spinning sphere. J.R. Aero. Soc. 32: 777–798Google Scholar
  59. Magnaudet J, Rivero M, Fabre J (1995) Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow. J. Fluid Mech. 284: 97–135MathSciNetzbMATHCrossRefGoogle Scholar
  60. Makino A (1992) Drag coefficient of a slowly moving carbon particle undergoing combustion. Combust. Sci. Techol. 81: 169–192CrossRefGoogle Scholar
  61. Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids. 26: 863–889CrossRefGoogle Scholar
  62. McLaughlin JB (1991) Inertial migration of small sphere in linear shear flows. J. Fluid Mech. 224: 261–274zbMATHCrossRefGoogle Scholar
  63. Mei R (1992) An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Int. J. Multiphase Flow 18: 145–147zbMATHCrossRefGoogle Scholar
  64. Mei R (1994) Flow due to an oscillating sphere and an expression for unsteady drag on the sphere at finite Reynolds number. J. Fluid Mech. 270: 133–174zbMATHCrossRefGoogle Scholar
  65. Mei R, Lawrence CJ, Adrian RJ (1991) Unsteady drag on a sphere at finite Reynolds num- ber with small fluctuations in the free-stream velocity. J. Fluid Mech. 233: 613–631zbMATHCrossRefGoogle Scholar
  66. Mitchell RE (1986) Experimentally determined overall burning rates of coal chars. In: The spring meeting of the west states section. The Combustion Institute, Banff, Canada. April 27–30Google Scholar
  67. Moore DW (1959) The rise of a gas bubble in viscous liquid. J. Fluid Mech. 6: 113–130zbMATHCrossRefGoogle Scholar
  68. Moore DW (1963) The boundary layer on a spherical gas bubble. J. Fluid Mech. 16: 161–176MathSciNetzbMATHCrossRefGoogle Scholar
  69. Moore DW (1965) The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23: 749–766CrossRefGoogle Scholar
  70. Morsi SA, Alexander AJ (1972) An investigation of particle trajectories in two-phase flow systems. J. Fluid Mech. 55: 193–208zbMATHCrossRefGoogle Scholar
  71. Muggia A (1956) Speed of evaporation and drag coefficient for a droplet in a gas stream. Aerotecnica Roma 36: 127–131MathSciNetGoogle Scholar
  72. Natarajan R (1973) Experimental drag coefficients for evaporating and burning drops at elevated pressure. Combust. Flame 20: 199–209CrossRefGoogle Scholar
  73. Niksa S, Mitchell RE, Hencken KP, Tichenor DA (1984) Optically determined temperatures, sizes, and velocities of individual carbon particles under typical combustion conditions. Combust. Flame 60: 183–193CrossRefGoogle Scholar
  74. Odar F (1966) Verification of the proposed equation for calculation of the forces on a sphere accelerating in a viscous fluid. J. Fluid Mech. 25: 591–592CrossRefGoogle Scholar
  75. Odar F, Hamilton WS (1964) Forces on a sphere accelerating in viscous fluid. J. Fluid Mech. 18: 302–314zbMATHCrossRefGoogle Scholar
  76. Oesterle B, Dinh TB (1998) Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers. Exp. Fluid 25: 16–22CrossRefGoogle Scholar
  77. Ogasawara M, Adachi T, Yashiki T (1967) Study on the drag of cylinder and sphere with flames supported in air stream. Bull. JSME. 10: 825–832CrossRefGoogle Scholar
  78. Oliver DLP, Chung JN (1985) Steady flows inside and around a fluid sphere at low Reynolds numbers. J. Fluid Mech. 154: 215–230zbMATHCrossRefGoogle Scholar
  79. Oliver DLR, Chung JN (1987) Flow about a fluid sphere at low to moderate Reynolds numbers. J. Fluid Mech. 177: 1–18zbMATHCrossRefGoogle Scholar
  80. Oseen CW a. (1910). Über die Stoke’s Formel, and über eine verwendte Aufgabe in der Hydrodynamik. Ark. Math. Astronom. Fys. 6: 29, 1–20;Google Scholar
  81. Oseen CW (1927) Hydrodynamik. Akademische Verlagsgesellschaft LeipzigGoogle Scholar
  82. Pearlman HG, Sohrab SH (1991) The role of droplet rotation in turbulent spray combustion modeling. Combust. Sci. Technol. 76: 321–334CrossRefGoogle Scholar
  83. Proudman J, Pearson JRA (1957) Expansions at small Reynolds numbers for the flow past a sphere and circular cylinder. J. Fluid Mech. 2: 237–367MathSciNetzbMATHCrossRefGoogle Scholar
  84. Renksizbulut M, Haywood RJ (1988) Transient droplet evaporation with variable properties and internal circulation at intermediate Reynolds numbers. Int. J. Multiphase Flow 14: 189–202zbMATHCrossRefGoogle Scholar
  85. Renksizbulut M, Yuen MC (1983a). Numerical study of droplet evaporation in a high temperature stream. J. Heat Transfer 105: 389–397CrossRefGoogle Scholar
  86. Renksizbulut M, Yuen MC (1983b) Experimental study of droplet evaporation in a high temperature air stream. J. Heat Transfer 105: 384–388CrossRefGoogle Scholar
  87. Rubinow SI, Keller JB (1961) The transverse force on a spinning sphere moving in a viscous fluid. J. Fluid Mech. 11: 447–459MathSciNetzbMATHCrossRefGoogle Scholar
  88. Rudinger G (1980) Fundamentals of gas-particle flow. Handbook of powder technology vol. 2. Elsevier, AmsterdamGoogle Scholar
  89. Rudoff RR, Bachalo WD (1988) Measurements of droplet drag coefficient in polydispersed turbulent field. AIAA Paper 88–0235Google Scholar
  90. Rybczynski W (1911) Jber die fortschreitende Bewegung einer flussingen Kugel in einem zahen Medium. Bull. Inst. Acad. Sci. Cracovie. ser A. 133: 40–46Google Scholar
  91. Sadhal SS, Ayyaswamy PS (1983). Flow past a liquid drop with a large non-uniform radial velocity. J. Fluid Mech. 133: 65–81zbMATHCrossRefGoogle Scholar
  92. Sadhal SS, Ayyaswamy PS, Chung JN (1997) Transport phenomena with drops and bubbles. Springer, New YorkGoogle Scholar
  93. Saffman PG (1965) The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22: 385–400zbMATHCrossRefGoogle Scholar
  94. Saffman PG (1968) Corrigendum to “The lift on a small sphere in a slow shear flow”. J. Fluid Mech. 31: 624CrossRefGoogle Scholar
  95. Schiller L, Naumann A (1933) Uber die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Ver. Deut. Ind. 77: 318–320Google Scholar
  96. Schlichting H (1960) Boundary layer theory. McGraw Hill, New YorkzbMATHGoogle Scholar
  97. Sedov LI (1993) Similarity and dimensional methods in mechanics, 10th edn., Boca Raton, Fla CRC Pres.Google Scholar
  98. Soo SL (1990) Multiphase fluid dynamics. Science Press and Gower Technical, BeijingGoogle Scholar
  99. Spalding DB (1954) Mass transfer in laminar flow. Proc. R. Soc. London, Ser. A. 221: 78–88MathSciNetzbMATHCrossRefGoogle Scholar
  100. Stokes GG (1851) On the effect of internal friction of fluids on the motion of pendulums. Trans Cambridge Philos. Soc. 9: 8–106Google Scholar
  101. Taylor TD, Acrivos AS (1964) On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18: 466–476MathSciNetzbMATHCrossRefGoogle Scholar
  102. Torobin LB, Gauvin WH (1961) The drag coefficient of single spheres moving in steady and accelerated motion in a turbulent fluid. AIChE J. 7: 615–619CrossRefGoogle Scholar
  103. Tsuji Y, Morikawa Y, Mizuno O (1985) Experimental measurement of the Mangus force on a rotating sphere at low Reynolds numbers. Trans. ASME, J. Fluids Eng. 107: 484–488Google Scholar
  104. Uhlherr PHT, Sinclair CG (1970) The effect of free stream turbulence on the drag coefficient of spheres. Proc. Chemea. A conference convened by Australian National Committee of the Institution of Chemical Engineers and the Australian Academy of Science. Chatwood, Australia: Butterworths of Australia and the Institution of Chemical Engineers 70: 1–13Google Scholar
  105. Voir DJ, Michaelides EE (1994) The effect of the history term on the motion of rigid spheres in a viscous fluid. Int. J. Multiphase Flow 20: 547–556CrossRefGoogle Scholar
  106. Warnica WD, Renksizbulut M, Strong AB (1994) Drag coefficients of spherical liquid droplets. Part 2. Turbulent gaseous fields. Exp. Fluids 18: 265–276Google Scholar
  107. Williams A (1973) Combustion of droplets of liquid fuels: a review. Combust. Flame 21: 131CrossRefGoogle Scholar
  108. Wohl PR, Rubinov SI (1974) The transfer force on a drop in an unbounded parabolic flow. J. Fluid. Mech. 62: 185–207zbMATHCrossRefGoogle Scholar
  109. Yang JC (1993) Heterogeneous combustion. Environmental implications of combustion processes. In: Puri 1K (ed) CBC Press, London 97–137Google Scholar
  110. Yarin LP, Sukhov GS (1987) Fundamentals of combustion theory of two-phase media. Energoatomizdat, Leningrad (in Russian).Google Scholar
  111. Yuen MC, Chen LW (1976) On drag of evaporating liquid droplets. Combust. Sci. Technol. 14: 147–154CrossRefGoogle Scholar
  112. Zarin NA, Nicholls JA (1971) Sphere drag in solid rockets non-continuum and turbulence effects. Combust. Sci. Technol. 3: 273–285CrossRefGoogle Scholar
  113. Abramzon B, Borde I (1980) Conjugate unsteady heat transfer from a droplet in creeping flow. AIChE J. 26: 536–544CrossRefGoogle Scholar
  114. Abramzon B, Elata C (1984) Unsteady heat transfer from a single sphere in Stokes flow. Int. J. Heat Mass Transfer 27: 687–695CrossRefGoogle Scholar
  115. Acrivos A (1966) On the combined effect of forced and free convection heat transfer in laminar boundary layer flows. Chem. Eng. Sci. 21: 343–352CrossRefGoogle Scholar
  116. Acrivos A (1971) Heat transfer at high Peclet number from a small sphere freely rotating in a simple shear field. J. Fluid Mech. 46: 233–240zbMATHCrossRefGoogle Scholar
  117. Acrivos A (1980). Note on the rate of heat or mass transfer from a small particle freely suspended in a linear shear field. J. Fluid Mech. 98: 299–304MathSciNetzbMATHCrossRefGoogle Scholar
  118. Acrivos A, Goddard JD (1965) Asymptotic expressions for laminar forced-convection heat and mass transfer. Part 1. Low speed flows. J. Fluid Mech. 23: 273–271MathSciNetCrossRefGoogle Scholar
  119. Acrivos A, Taylor TD (1962) Heat and mass transfer from single spheres in Stokes flow. Phys. Fluids. 5: 378–394MathSciNetCrossRefGoogle Scholar
  120. Anthony DB, Howard JB (1976) Coal devolatilization and hydrogasification. AIChE J. 22: 625–656CrossRefGoogle Scholar
  121. Anthony DB, Howard JB, Hottel HC, Meissner HP (1975) Rapid devolatilization of pulverized coal. The Fifteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1303–1317Google Scholar
  122. Badzioch S, Hawksley PGW (1970) Kinetics of thermal decomposition of pulverized coal particle. Ind. Eng. Chem. Process Desing Develop. 9: 521–530CrossRefGoogle Scholar
  123. Banks WHH (1965) The thermal laminar boundary layer on a rotating sphere. J. Appl. Math. Phys. 16: 780–788CrossRefGoogle Scholar
  124. Batchelor GK (1979) Mass transfer from a particle suspended in fluid with a steady linear ambient velocity distribution. J. Fluid Mech. 95: 369–400MathSciNetzbMATHCrossRefGoogle Scholar
  125. Batchelor GK (1980) Mass transfer from small particle suspended in turbulent fluid. J. Fluid Mech. 98: 609–623MathSciNetzbMATHCrossRefGoogle Scholar
  126. Beck NC, Hayhurst AN (1990) The early stages of the combustion of pulverized coal at high temperatures 1: the kinetics of devolatilization. Combust. Flame. 79: 47–74CrossRefGoogle Scholar
  127. Birouk M, Chauveau C, Sarh B, Quilgars X, Gokalp I (1996) Turbulence effects on the vaporization of monocomponent single droplets. Combust. Sci. Tech. 113: 413–428CrossRefGoogle Scholar
  128. Boothroyd RG (1971) Following gas-solids suspensions. Chapman and Hall. LTD. LondonGoogle Scholar
  129. Burdukov AP, Nakoryakov VE (1965) On mass transfer in an acoustic field. J. Appl. Mech. Tech. Phys. 6: 51–55CrossRefGoogle Scholar
  130. Burdukov AP, Nakoryakov VE (1967) Effect of vibrations on mass transfer from a sphere at high Prandtl numbers. J. Appl. Mech. Tech. Phys. 8: 111–113CrossRefGoogle Scholar
  131. Carey VP (1992) Liquid—vapor phases-change phenomena. Hemisphere, Bristol, PAGoogle Scholar
  132. Chao BT (1969) Transient heat and mass transfer to a translating droplet. ASME J. Heat Mass Transfer, 91: 273–281Google Scholar
  133. Chao BT, Greif R (1974) Laminar forced convection over rotating bodies. Trans. ASME. 96: 463–466CrossRefGoogle Scholar
  134. Chen TS, Mucoglu A (1977) Analysis of mixed forced and free convection about a sphere. Int. J. Heat Mass Transf. 20: 867–875zbMATHCrossRefGoogle Scholar
  135. Chiang T, Ossin A, Tien CL (1964) Laminar free convection from a sphere. Trans. ASME. J. Heat Transf. 86: 537–542CrossRefGoogle Scholar
  136. Clift R, Grace JR, Weber ME (1978) Bubbles, drops and particles. Academic Press, New YorkGoogle Scholar
  137. Cooper F (1972) Heat transport from a sphere to an infinite medium. Int. J. Heat Mass Transfer. 20: 991–993CrossRefGoogle Scholar
  138. Costa M, Godoy S, Lockwood FC, Zhou J (1994) Initial stages of devolatilization of pulverized–coal in a turbulent jet. Combust. Flame. 96: 150–162CrossRefGoogle Scholar
  139. Crowe CT, Sommerfeld M, Tsuji Y (1998). Multiphase flows with droplets and particles. CRC Press, New YorkGoogle Scholar
  140. Dennis SCR, Walker JDA, Hudson JD (1973) Heat transfer from a sphere at low Reynolds numbers. J. Fluid Mech. 60: 273–283zbMATHCrossRefGoogle Scholar
  141. Dorfman LA (1963) Hydrodynamic resistance and the heat loss of rotating solids. Oliver and Boyd, Edinburgh and LondonGoogle Scholar
  142. Dorfman LA, Mironova VA (1970) Solutions of equations for the thermal boundary layer of a rotating axisymmetric surface. Int. J. Heat Mass Transfer. 13: 81–92zbMATHCrossRefGoogle Scholar
  143. Dorfman LA, Serazetdinov AZ (1965) Laminar flow and heat transfer near rotating axisymmetric surface. Int. J. Heat Mass Transfer 8: 317–327zbMATHCrossRefGoogle Scholar
  144. Dudek DR, Fletcher TH, Longwell JP, Sarofim AF (1988) Natural convection induced drag forces on spheres at low Grashof numbers: comparison of theory with experiment. Int. J. Heat Mass Transfer 31: 863–873CrossRefGoogle Scholar
  145. Eastop TD (1973) The influence of rotation on the heat transfer from a sphere to an air stream. Int. J. Heat Mass Transfer 16: 1954–1957CrossRefGoogle Scholar
  146. Essenhigh RH (1976) Combustion and flame propagation in coal systems: A Review. The Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 353–374Google Scholar
  147. Faeth GM (1977) Current status of droplet and liquid combustion. Prog. Energy Combust. Sci. 3: 191–224Google Scholar
  148. Faeth GM (1983) Evaporation and combustion of sprays. Prog. Energy Combust. Sci. 9: 176Google Scholar
  149. Fendell FE (1968) Laminar natural convection about an isothermally heated sphere at small Grashof number. J. Fluid Mech. 34: 163–176zbMATHCrossRefGoogle Scholar
  150. Fletcher TH (1989) Time-resolved particle temperature and mass loss measurements of a bituminous coal during devolatilization. Combust. Flame. 78: 223–236CrossRefGoogle Scholar
  151. Frankel NA, Acrivos A (1968) Heat and mass transfer from small spheres and cylinders freely suspended in shear flow. Phys. Fluids. 11: 1913–1918zbMATHCrossRefGoogle Scholar
  152. Frank-Kamenetskii DA (1969) Diffusion and heat transfer in chemical kinetics. 2nd edn., Plenum, New York.Google Scholar
  153. Gale TK, Bartholomew CH, Fletcher TH (1995) Decreases in the swelling and porosity of bituminous coals during devolatilization at high heating rates. Combust. Flame. 100: 94–100CrossRefGoogle Scholar
  154. Gan H, Nadi SP, Walker PI (1972) Nature of the porosity in American coals. Fuel 51: 272–277CrossRefGoogle Scholar
  155. Gat N (1986) On internal temperature gradients in a pyrolysing coal particle. combust. Sci. Technol. 49: 297–303Google Scholar
  156. Gavalas GR (1981) Coal pyrolysis. Elsevier, New YorkGoogle Scholar
  157. Geoola F, Cornish ARH (1981) Numerical solution of steady-state free convective heat transfer from a solid sphere. Int. J. Heat Mass Transfer. 24: 1369–1379zbMATHCrossRefGoogle Scholar
  158. Geoola F, Cornish ARH (1982) Numerical simulation of free convective heat transfer from a sphere. Int. J. Heat Mass Transfer 25: 1677–1687zbMATHCrossRefGoogle Scholar
  159. Glassman I (1987) Combustion, 2nd edn. Academic Press, New YorkGoogle Scholar
  160. Gokalp I, Chauveau C, Simon O, Chesneau X (1992) Mass transfer from liquid fuel drops in turbulent flow. Combust. Flame. 89: 286–298CrossRefGoogle Scholar
  161. Gokalp I, Chauveau C, Berrekam H, Ramos-Arroyo NA (1994) Vaporization of miscible binary fuel droplets under laminar and turbulent convective conditions. Atomization and Sprays. 4: 661–676Google Scholar
  162. Gopinath A, Mills AF (1993) Convective heat transfer from a sphere due to acoustic streaming. Trans. ASME J. Heat Transfer 115: 332–341CrossRefGoogle Scholar
  163. Gostowski VJ, Costello FA (1970) The effect of free stream turbulence on the heat transfer from the stagnation point of a sphere. Int. J. Heat Mass Transfer. 13: 1382–1386CrossRefGoogle Scholar
  164. Gupalo YuP, Ryazantsev YuS (1974) Heat and mass transfer from a sphere with a chemical surface reaction in a laminar flow. Acta Astronaut. 1: 993–1005CrossRefGoogle Scholar
  165. Gupalo YuP, Polyanin AD, Ryazantsev YuS (1985) Mass heat transfer reactive particles with flow. (in Russian) Nauka, MoscowGoogle Scholar
  166. Hadamard JS (1911) Mouvement permanent lent d’une sphere liquid et visqueuse dans une liquid visquese. C. R. Acad. Sci. Paris, 152: 1735–1738zbMATHGoogle Scholar
  167. Hatzikonstantinou P (1990). Unsteady mixed convection about a porous rotating sphere. Int. J. Heat Mass Transfer 33: 19–27CrossRefGoogle Scholar
  168. Heritzberg M, Zlochower IA (1991) Devolatilization wave structures and temperatures for the pyrolysis of polymethylmethacrylate, ammonium perchlorate, and coal combustion level heat fluxes. Combust. Flame 84: 15–37CrossRefGoogle Scholar
  169. Hieber CA, Gebhart B (1969) Mixed convection from a sphere at small Reynolds and Grashof numbers. J. Fluid Mech. 38: 137–159zbMATHCrossRefGoogle Scholar
  170. Hossain MA (1966) Laminar free convection about an isothermal sphere at extremely small Grashof numbers. Ph.D. Thesis, Cornell UniversityGoogle Scholar
  171. Hussaini MY, Sastry MS (1976) The laminar compressible boundary layer on a rotating sphere with heat transfer. Trans. ASME. J. Heat Transfer 98: 533–535CrossRefGoogle Scholar
  172. Jafarpur K, Yovanovich MM (1992) Laminar free convection heat transfer from isothermal spheres: a new analytical method. Int. J. Heat Mass Tranfer 35: 2195–2201zbMATHCrossRefGoogle Scholar
  173. Kassoy DR, Adamson TCJr, Messiter AF (1966) Compressible low Reynolds number flow around a sphere. Phys. Fluids 9: 671–681zbMATHCrossRefGoogle Scholar
  174. Kestin J (1966) The effect of free-stream turbulence on heat transfer rates. In: Irvine TF, Hertnett (eds), Advances in heat transfer, vol. 3: pp. 1–32Google Scholar
  175. Khitrin LN (1957) The physics of combustion. (in Russian) Moscow University, MoscowGoogle Scholar
  176. Klyachko LS (1963) Heat transfer between a gas and a spherical surface with the combined action of free and forced convection. Trans. ASME. J. Heat Transfer 85C: 355–357CrossRefGoogle Scholar
  177. Kobayashi H, Howard JB, Sarofim AF (1976) Coal devolatilization at high temperatures. The Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 411–425Google Scholar
  178. Konopliv N, Sparrow EM (1972) Unsteady heat transfer and temperature for Stokesian flow about a sphere. ASME J. Heat Mass Transfer 94: 266–272Google Scholar
  179. Korn GA, Korn TM (1968) Mathematical handbook. McGraw - Hill, New YorkGoogle Scholar
  180. Kreith F (1968) Convective heat transfer in rotating systems. In: Irvine TF, Hertnett (eds), Advances in heat transfer. vol. 5: pp. 129–251Google Scholar
  181. Kreith F, Roberts LG, Sullivan JA, Sinha SN (1963) Convection heat transfer and flow phenomena of rotating sphere. Int. J. Heat Mass Transfer 6: 881–895CrossRefGoogle Scholar
  182. Kuo KK (1986) Principles of combustion. Wiley, New York.Google Scholar
  183. Landau LD, Lifshitz EM (1959) Fluid mechanics. 2nd edn. Pergamon, New YorkGoogle Scholar
  184. Lavender WJ, Pei DCT (1967) The effect of fluid turbulence on the rate of heat transfer from spheres. Int. J. Heat Mass Transfer 10: 529–539CrossRefGoogle Scholar
  185. Law CK (1982) Recent advances in droplet vaporization and combustion. Prog. Energy Combust. Sci. 8: 171–201Google Scholar
  186. Lee CK, Singer JM, Chaiken RF (1977) Coal pyrolysis at fire-level heat flux. Combust. Sci. Technol. 16: 205–213CrossRefGoogle Scholar
  187. Lee MH, Jeng DR, De Witt KJ (1978) Laminar boundary layer transfer over rotating bodies in forced flow. Trans. ASME, J. Heat Transfer 100: 497–502Google Scholar
  188. Levich VG (1962) Physicochemical hydrodynamics. Prentice-Hall, Englewood Cliffs, NJGoogle Scholar
  189. Levich VG, Krylov VS, Vorotilin VP (1965) Towards the theory of nonstationary diffusion from a moving drop. Sov. Phys. Dokl. 161: 648–652Google Scholar
  190. Lien F–S, Chen C–K, Cleaver JW (1986) Mixed and free convection over a rotating sphere with blowing and suction. Trans. ASME, J. Heat Transfer 108: 398–404CrossRefGoogle Scholar
  191. Lin FN, Chao BT (1974) Laminar free convection over two-dimensional and axisymmetric bodies of arbitrary countur. Trans. ASME. J. Heat Transfer 96: 435–442CrossRefGoogle Scholar
  192. Lozinski D, Matalon M (1992) Vaporization of a spinning fuel droplet. The Twenty-fourth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1483–1491Google Scholar
  193. Maloney DJ, Monazam ER, Woodruff SD, Lawson LO (1991) Measurements and analysis of temperature histories and size changes for single carbon and coal particles during the early stages of heating and devolatilization. Combust. Flame 84: 210–220CrossRefGoogle Scholar
  194. Mathers WG, Madden AJJr, Piret EL (1957) Simultaneous heat and mass transfer in free convection. Ind. Eng. Chem. 49: 961–968CrossRefGoogle Scholar
  195. Nguyen HD, Paik S, Chung JN (1993) Unsteady mixed convection heat transfer from a solid sphere: the conjugate problem. Int. J. Heat Mass Transfer 36: 4443–4453zbMATHCrossRefGoogle Scholar
  196. Nigmatulin RI (1991) Dynamics of multiphase media. v.1 and 2 Hemisphere, LondonGoogle Scholar
  197. Niksa S (1986). The distributed–energy chain model for rapid coal devolatilization kinetics. Part II: Transient weight loss correlations. Combust. Flame 66: 111–119CrossRefGoogle Scholar
  198. Niksa S, Kerstein AR (1986) The distributed–energy chain model for rapid coal devolatilization kinetics. Part 1: Formulation. Combust Flame 66: 95–109CrossRefGoogle Scholar
  199. Niksa S, Kerstein AR, Fletcher TH (1987) Predicting devolatilization at typical coal combustion conditions with the distributed–energy chain model. Combust. Flame 69: 221–228CrossRefGoogle Scholar
  200. Nordle RL, Kreith F (1961) Convective heat transfer from a rotating sphere. Int. Dev. in Heat Transfer. Am. Soc. Mech. Eng. New York, 461–467Google Scholar
  201. Oliver DLP, Chung JN (1986) Conjugate unsteady heat transfer from a spherical droplet at low Reynolds numbers. Int. J. Heat Mass Transfer 29: 879–887zbMATHCrossRefGoogle Scholar
  202. Palec GL, Daguenet M (1987). Laminar three-dimensional mixed convection about a rotating sphere in a stream. Int. J. Heat Mass Transfer 30: 1511–1523zbMATHCrossRefGoogle Scholar
  203. Phuoc TX, Durbetaki P (1989) Heat and mass transfer analysis of a coal particle undergoing pyrolysis. Int. J. Heat Mass Transfer 30: 2331–2339CrossRefGoogle Scholar
  204. Phuoc TX, Maloney DI (1988) Laser pyrolysis of single coal particles in an electrodynamic balance. The Twnety-second Syumposium (International) on Combustion. The Combustion Institute, Pittsburgh Pa., pp. 125–134Google Scholar
  205. Phuoc TX, Mathur MP (1991) Transient heating of coal particles undergoing pyrolysis. Combust. Flame 85: 380–388CrossRefGoogle Scholar
  206. Pitt GJ (1962) The kinetics of the evolution of volatile products from coal. Fuel 41: 267–274Google Scholar
  207. Polyanin AD (1982) On nonisothermal chemical reaction at the particle surface in a laminar flow. Int. J. Heat Mass Transfer 25: 1031–1042zbMATHCrossRefGoogle Scholar
  208. Polyanin AD (1984) An asymptotic analysis of some nonlinear boundary–value problems of convective mass and heat transfer of reacting particles with the flow. Int. J. Heat Mass Transfer 27: 163–189zbMATHCrossRefGoogle Scholar
  209. Polyanin AD, Sergeev YuA (1980) Convective diffusion to a reacting particle in a fluid. Nonlinear surface reaction kinetics. Int. J. Heat Mass Transfer 23: 1171–1182zbMATHCrossRefGoogle Scholar
  210. Potter JM, Riley N (1980) Free convection from a heated sphere at large Grashof number. J. Fluid Mech. 100: 769–783MathSciNetzbMATHCrossRefGoogle Scholar
  211. Proudman I, Pearson JRA (1957) Expansions at small Reynolds numbers for the flow past a sphere and circular cylinder. J. Fluid Mech. 2: 237–269MathSciNetzbMATHCrossRefGoogle Scholar
  212. Ragland KW, Yang JT (1989) Combustion of millimeter sized coal particles in convective flow. Combust. Flame 60: 285–297CrossRefGoogle Scholar
  213. Raithby GD, Eckert ERG (1968) The effect of turbulence parameters and support position on the heat transfer from spheres. Int. J. Heat Mass Transfer 11: 1233–1252CrossRefGoogle Scholar
  214. Rajasekaran R, Palekar MG (1985) Mixed convection about a rotating sphere. Int. J. Heat Mass Transfer 28: 956–968CrossRefGoogle Scholar
  215. Reid RC, Prausnitz JM, Poling BE (1987). The properties of gases and liquids. McGraw-Hill, New YorkGoogle Scholar
  216. Riley N (1986) The heat transfer from a sphere in free convective flow. Comput. Fluids 14: 225–237zbMATHCrossRefGoogle Scholar
  217. Rimmer PL (1968) Heat transfer from a sphere in a stream of small Reynolds number. J. Fluid Mech. 32: 1–7zbMATHCrossRefGoogle Scholar
  218. Ruckenstein E (1967) Mass transfer between a single drop and a continuous phase. Int. J. Heat Mass Transfer 10: 1785–1792zbMATHCrossRefGoogle Scholar
  219. Rybczynski W (1911) Uber die fortschreitende bewegung einer flussigen kugel in einem zahen medium. Bull. Inst. Acad. Sci. Cracovie ser. A. 10: 40–46Google Scholar
  220. Sadhal SS, Ayyaswamy PS, Chung JN (1997) Transport phenomena with drops and bubbles. Springer, New YorkGoogle Scholar
  221. Sandoval-Robles JG, Delmas H, Couders JP (1981) Influence of turbulence on mass transfer between a liquid and solid sphere. AChIE J. 27: 819–823Google Scholar
  222. Saxena SC (1990) Devolatilization and combustion characteristics of coal particles. Prog. Energy Combust. Sci. 16: 55–94Google Scholar
  223. Sayegh NN, Gauvin WH (1979) Numerical analysis of variable property heat transfer to a single sphere in high temperature surroundings. AIChE J. 25: 522–534MathSciNetCrossRefGoogle Scholar
  224. Schlichting H (1960) Boundary layer theory. McGraw-Hill, New YorkzbMATHGoogle Scholar
  225. Sirignano WA (1983) Fuel droplet vaporization and spray combustion. Prog. Energy Combust. Sci. 9: 291–322Google Scholar
  226. Sirignano WA (1999) Fluid dynamics and transport of droplets and sprays. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  227. Smith KL, Smoot LD (1990) Characteristics of commonly–used U.S. coals–towards a set of standard research coals. Prog. Energy Combust. Sci. 16: 1–53Google Scholar
  228. Solomon PR, Serio MA, Suuberg EM (1992) Coal pyrolysis: experiments, kinetic rates and mechanisms. Prog. Energy Combust. Sci. 18: 133–220Google Scholar
  229. Soo SL (1990). Multiphase fluid dynamics. Science Press and Gower Technical, BeijingGoogle Scholar
  230. Spalding DB (1955) Some fundamentals of combustion. Butterworths, LondonGoogle Scholar
  231. Suuberg EM (1988) Significance of heat transport effects in determining coal pyrolysis rate. Energy Fuel 2: 593–595CrossRefGoogle Scholar
  232. Suwono A (1980) Buoyancy effects on flow and heat transfer on rotating axisymmetric round-nosed bodies. Int. J. Heat Mass Transfer 23: 819–831zbMATHCrossRefGoogle Scholar
  233. Taylor TD (1963) Mass transfer from single spheres in Stokes flow with surface reactions. Int. J. Heat Mass Transfer 6: 993–994CrossRefGoogle Scholar
  234. Tieng SM, Yan AC (1993) Experimental investigation on convective heat transfer of heated spinning sphere. Int. J. Heat Mass Transfer 36: 599–610CrossRefGoogle Scholar
  235. Tsubouchi T, Sato S (1960) Heat transfer from fine wires and particles by natural convection. Res. Inst. High-Speed Mech., Tohoku University 12: 127–132Google Scholar
  236. Ubhayakar SK, Stickler DB, von Posenberg CWJr, Gannon RE (1976) Rapdi devolatilization of pulverized coal in hot combustion gases. The Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 427–436Google Scholar
  237. Unger PE, Suuberg EM (1981) Modeling the devolatilization behavior of a softening bituminous coal. The Eighteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1203–1211Google Scholar
  238. Williams A (1973). Combustion of droplets of liquid fuels: A Review. Combust. Flame 21: 1–31CrossRefGoogle Scholar
  239. Williams FA (1985) Combustion theory. The fundamental theory of chemically reacting flow systems, 2nd edn. Benjamin/Cummings, Menlo Park, Calif.Google Scholar
  240. Wiser WH, Hill GR, Kertamus NJ (1967) Kinetic study of the pyrolysis of high-volatile bituminous coal. Ind. Eng. Chem. Process Desing Develop. 6: 133–138CrossRefGoogle Scholar
  241. Wong K-L, Lee S-C, Chen C-K (1986) Finite element solution of laminar combined convection from a sphere. Trans. ASME. J. Heat Transfer 108: 860–865CrossRefGoogle Scholar
  242. Wood BJ, Wise H, Inami SH (1960) Heterogeneous combustion of multicomponent fuels. Combust. Flame 4: 235–242CrossRefGoogle Scholar
  243. Yarin LP, Sukhov GS (1987) Fundamentals of combustion theory of two-phase media. (in Russian) Energoatomizdat, LeningradGoogle Scholar
  244. Yarin AL, Brenn G, Kastner O, Rensink D, Tropea C (1999) Evaporation of acoustically levitated droplets. J. Fluid Mech. 399: 151–204zbMATHCrossRefGoogle Scholar
  245. Yuge T (1960) Experiments on heat transfer from spheres including combined natural and forced convection. Trans. ASME. J. Heat Transfer 82: 214–220CrossRefGoogle Scholar
  246. Annamalai K, Durbetaki P (1977) A theory on transition of ignition phase of coal particles. Combust. Flame 29: 193–208CrossRefGoogle Scholar
  247. Annamalai K, Ryan W (1992) Interactive processes in gasification and combustion. Part I. Liquid drop arrays and clouds. Prog. Energy Combust. 18: 221–295CrossRefGoogle Scholar
  248. Annamalai K, Ryan W (1993) Interactive processes in gasification and combustion–II. isolated carbon, coal and porous char particles. Prog. Energy Combust. 19: 383–446CrossRefGoogle Scholar
  249. Babii BI, Kuvaev Ja F (1986) Combustion of coal dust and coal dust flame calculation. (in Russian) Energoatomizdat, MoscowGoogle Scholar
  250. Barishnikov NN, Gerer VE, Denisova ND (1979) Metallurgy of zirconium and hafnium. (in Russian) Metallurgy, MoscowGoogle Scholar
  251. Bartlett RW, Ong JNJr, Fassele WNJr, Papp CA (1963) Estimating aluminum particle combustion kinetics. Combust. Flame 7: 227–234CrossRefGoogle Scholar
  252. Bellan J, Summerfield M (1976) Quasi-steady gas phase assumption for a burning droplet. AIAA J. 14: 973–975CrossRefGoogle Scholar
  253. Bellan J, Summerfield M (1978) A preliminary theoretical study of droplet extinction by depressurization. Combust. Flame 32: 257–270CrossRefGoogle Scholar
  254. Botros P, Law CK, Sirignano WA (1980) Droplet combustion in a aeactive environment. Combust. Sci. Technol. 21: 123–130CrossRefGoogle Scholar
  255. Buchholz EK, Tapper ML (1978) Time to extinction of liquid hydrocarbon fuel droplets burning in a transient Diesel-like environment. Combust. Flame 31: 161–171CrossRefGoogle Scholar
  256. Burke SP, Schumann TE (1928) Diffusion flames. Ind. Eng. Chem. 20: 998–1004CrossRefGoogle Scholar
  257. Cassel HM, Liebman I (1959) The cooperative mechanism in the ignition of dust dispersions. Combust. Flame 3: 467–475CrossRefGoogle Scholar
  258. Chiu HH (2000) Advances and challenges in droplet and spray combustion. I. Toward a unified theory of droplet aerothermochemistry. Prog. Energy Combust. Sci. 26: 381416Google Scholar
  259. Chiu HH, Hu LH (1998) Dynamics of ignition transience and gasification partition of a droplet. In:Burges AR, Dryer FL (eds). The Twenty-seventh Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1889–1896Google Scholar
  260. Chung SH, Law CK (1984) Importance of dissociation equilibrium and variable transport properties on estimation of flame temperature and droplet burning rate. Combust. Flame 55: 225–235CrossRefGoogle Scholar
  261. Crespo A, Linan A (1975) Unsteady effects in droplet evaporation and combustion Combust. Sci. Technol. 11: 9–18Google Scholar
  262. Dankverts PV (1973) Gas—liquid reaction. (in Russian) Chemistry, MoscowGoogle Scholar
  263. Dreizin EL (1996) Experimental study of stages in aluminium particle combustion in air. Combust. Flame 105: 541–556CrossRefGoogle Scholar
  264. Dreizin EL, Suslov AV, Trunov MA (1993) General trends in metal particle heterogeneous combustion. Combust. Sci. Technol. 90: 79–99CrossRefGoogle Scholar
  265. Dreizin EL, Berman CH, Vicenzi EP (2000) Condensed-phase modifications in magnesium particle combustion in air. Combustion Flame 122: 30–42CrossRefGoogle Scholar
  266. Du X, Annamalai K (1994) The transition ignition of isolated coal particle. Combust. Flame 97: 339–354CrossRefGoogle Scholar
  267. Essenhigh RH, Misra MK, Shaw DW (1989) Ignition of cool particles: A review. Combust. Flame 77: 3–30CrossRefGoogle Scholar
  268. Faeth GM, Lazar RS (1971) Fuel droplet burning rates in a combustion gas environment. AIAA J. 9: 2165–2171CrossRefGoogle Scholar
  269. Fendell FE (1965). Ignition and extinction in combustion of initially unmixed reactants. J. Fluid Mech. 21: 281–303MathSciNetzbMATHCrossRefGoogle Scholar
  270. Fendell FE, Sprankle ML, Dodson DS (1966) Thin-flame theory for a fuel droplet in slow viscous flow. J. Fluid Mech. 26: 267–280zbMATHCrossRefGoogle Scholar
  271. Frank-Kamenetskii DA (1969) Diffusion and heat transfer in chemical kinetics. 2nd edn. Plenum Press, New YorkGoogle Scholar
  272. Fridman R, Macek A (1962) Ignition and combustion of aluminium particles in hot ambient gases. Combust. Flame 6: 9–19CrossRefGoogle Scholar
  273. Fridman R, Macek A (1963) Combustion studies of single aluminium particles. The ninth symposium (international) on combustion. The Combustion Institute. Academic Press, New York, pp. 703–712Google Scholar
  274. Fridman NB, Kitain MM, Shteinberg AS, Merzhanov AG (1981) On the mechanism of bubble ignition. Sov. Phys. Dokl. 258: 961–965Google Scholar
  275. Fu WB, Zeng TF (1992) A general method for determining chemical kinetic parameters during ignition of coal char particles. Combust. Flame 88: 413–424CrossRefGoogle Scholar
  276. Fu WB, Zhang EZ (1992) A universal correlation between the heterogeneous ignition temperatures of coal char particles and coals. Combust. Flame 90: 103–113CrossRefGoogle Scholar
  277. Garmata BA, Gulnitskii BS (1968) Metallurgy of titanium. (in Russian) Metallurgy, MoscowGoogle Scholar
  278. Glassman I (1989) Combustion. 2nd edn. Academic Press, New YorkGoogle Scholar
  279. Glassman I, Williams FA, Antaki PJ (1984) A physical and chemical interpretation of boron particle combustion. The Twentieth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh Pa., pp. 2057–2064Google Scholar
  280. Godsave GA (1953) Studies of the combustion of drops on a fuel spray–the burning of single drops of fuel. The Fourth Symposium (International) on Combustion. The Williams and Wilkings, Baltimore, pp. 818–830Google Scholar
  281. Gokalp I, Chauveau C, Richard JR, Kramer M, Leuckel W (1988) Observation of the low temperature vaporization and envelope or wake flame burning of n-heptane droplets at reduced gravity during parabolic flights. The Twenty-second Symposium (International) on Combustion. The Combustion Institute, Pittsburgh Pa., pp. 2027–2035Google Scholar
  282. Gol’dshtein V, Goldfarb BI, Shreiber I, Zinoviev A (1998) Oscillations in a combustible gas bubble. Combust. Theory Modeling 2: 1–17zbMATHCrossRefGoogle Scholar
  283. Golovina EC (1983) High temperature combustion and gasification of carbon. Energoatomizdat, Moscow (in Russian)Google Scholar
  284. Gurevich MA, Lapkina KI, Ozerov ES (1970) Ignition limits of aluminum particles. Combust. Explos. Shock Waves 6: 154–157CrossRefGoogle Scholar
  285. Gurevich MA, Lydkin VM, Stepanov AM (1970a). Ignition and combustion of a gas suspension of magnesium particles. Combust. Explos. Shock Waves 6: 298–303CrossRefGoogle Scholar
  286. Gurevich MA, Ozerova GE, Stepanov AM (1970b) Heterogeneous ignition of an aluminum particle in oxygen and water vapor. Combust. Explos. Shock Waves 6: 291–297CrossRefGoogle Scholar
  287. Gurevich MA, Ozerova GE, Stepanov AM (1971) Critical avtoignion conditions for a polydisperse gas suspension of solid-fuel particles. Combust. Explos. Shock Waves 7: 7–14CrossRefGoogle Scholar
  288. Gururajan VS, Wall TF, Gupta RP, Truelove JS (1990) Mechanisms for the ignition of pulverized coal particles. Combust. Flame 81: 119–132CrossRefGoogle Scholar
  289. Hara H, Kumagai S (1990). Experimental investigation of free droplet combustion under microgravity. The Twenty-third Symposium (International) on Combustion. The Combustion Institute, Pittsburgh Pa., pp. 1605–1610Google Scholar
  290. Hottel HC, Williams GS, Simpson HC (1955). Combustion of droplets of heavy liquid fuels. The Fifth Symposium (International) on Combustion. The Combustion Institute, Reinhold, New York, pp. 101–129Google Scholar
  291. Hyseyin K (1978) Vibrations and stability of multiple parameter systems. NordhoffGoogle Scholar
  292. Isoda H, Kumagai S (1959) New aspects of droplet combustion. The seventh symposium (international) on combustion. The Combustion Institute. Academic Press, New York. pp. 523–531Google Scholar
  293. Kantorovich BV (1958). Foundation of the theory of solid fuel combustion and gasification. (in Russian) AN SSSR, MoscowGoogle Scholar
  294. Kassoy DR, Williams FA (1968) Effects of chemical kinetics on near equlibrium combustion in non premixed systems. Phys. Fluids 11: 1343–1351CrossRefGoogle Scholar
  295. Kassoy DR, Williams FA (1968) Variable property effects on liquid droplet combustion. AIAA J. 6: 1961–1965CrossRefGoogle Scholar
  296. Kassoy DR, Liu MK, Williams FA (1969) Comments on effects of chemical kinetics on near equilibrium combustion in non premixed systems. Phys. Fluids 12: 265–267CrossRefGoogle Scholar
  297. Kauffman CW, Nicholls JA (1971). Shock-wave ignition of liquid fuel drops. AIAA J. 9: 880–885CrossRefGoogle Scholar
  298. Khaikin BI, Bloshenko VN, Merzhanov AG (1970) On the ignition of metal particles. Combust. Explos. Shock Waves 6: 412–422CrossRefGoogle Scholar
  299. Khitrin LN (1957a) Fundamental principles of carbon combustion and factors intensifying the burning of solid fuels. The Sixth Symposium (International) on Combustion. The Combustion Institute. Reinhold New York, pp. 565–573Google Scholar
  300. Khitrin LN (1957b) Physics of combustion and explosion. Moscow University, Moscow (in Russian)Google Scholar
  301. Klyachko LA, Kuntsev GM (1978) A Theory of ignition for solid-fuel particles in a gaseous oxidizer. Combust. Explos. Shock Waves 14: 16–22Google Scholar
  302. Kumagai S, Sakai T, Okajima S (1971) Combustion of free fuel droplets in a freely falling chamber. The Thirteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 779–785Google Scholar
  303. Kuo KR (1986) Principles of combustion. Wiley, New YorkGoogle Scholar
  304. Lasheras JC, Fernandez-Pello AC, Dryer FL (1979) Initial observations on the free droplet combustion characteristics of water-in-fuel emulsions. Combust. Sci. Technol. 21: 1–14CrossRefGoogle Scholar
  305. Lasheras JC, Fernandez-Pello AC, Dryer FL (1980) Experimental observations on the disruptive combustion of free droplets of multicomponent fuels. Combust. Sci. Technol. 22: 195–209CrossRefGoogle Scholar
  306. Lasheras JC, Fernandez-Pello AC, Dryer FL (1981a) On the disruptive burning of free droplets of ALCOHOL/n–Paraffin solutions and emulsions. The Eighteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 293–305Google Scholar
  307. Lasheras JC, Kennedy IM, Dryer FL (198 lb). Burning of distillate fuel droplets containing alcohol or water. Effect of additive concentration. Combust. Sci. Technol. 26: 161–169Google Scholar
  308. Lasheras JC, Yap LT, Dryer FL (1984). Effect of the ambient pressure on the explosive burning of emulsified and multicomponent fuel droplets. The Twentieth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1761–1772Google Scholar
  309. Law CK (1975) Asymptotic theory for ignition and extinction in droplet burning, Combust. Flame 24: 89–98CrossRefGoogle Scholar
  310. Law C K (1976) Unsteady droplet combustion with droplet heating. Combust. Flame 26: 17–22CrossRefGoogle Scholar
  311. Law CK (1977) A model for the combustion of oil/water emulsion droplets. Combust. Sci. Technol. 17: 29–38CrossRefGoogle Scholar
  312. Law CK (1978) Theory of thermal ignition in fuel droplet burning. Combust. Flame. 31: 285–296CrossRefGoogle Scholar
  313. Law CK (1982) Recent advances in droplet vaporization and combustion. Prog. Energy Combust. Sci. 8: 171–201Google Scholar
  314. Law CK, Law HK (1982) A d2-Law for multicomponent droplet vaporization and combustion. AIAA J. 20: 522–527CrossRefGoogle Scholar
  315. Law CK, Sirignano WA (1977) Unsteady droplet combustion with droplet heating II: conduction limit. Combust. Flame 28: 175–186CrossRefGoogle Scholar
  316. Law CK, Williams FA (1972) Kinetics and convection in the combustion of Alkane droplets. Combust. Flame. 19: 393–405CrossRefGoogle Scholar
  317. Law CK, Chung SH, Srinivasan N (1980) Gas-phase quasi-steadiness and fuel vapor accumulation effects in droplet burning. Combust. Flame 38: 173–198CrossRefGoogle Scholar
  318. Leal LG (1992) Laminar flow and convective transport process. Scaling principles and asymptotic analysis. Butterworth-Heinemann, Mass. BostonGoogle Scholar
  319. LeMott SR, Peskin RL, Levine DG (1971) Effect of fuel molecular weight on particle ignition. Combust. Flame 16: 17–27CrossRefGoogle Scholar
  320. Linan A (1974). The asymptotic structure of counterflow diffusion flames for large activation energies. Acta Astronaut 1: 1007–1039CrossRefGoogle Scholar
  321. Lisitsyn VI, Rumanov EN, Khaikin BI (1971) Induction period in the ignition of a particle system. Combust. Explos. Shock Waves 7: 1–6CrossRefGoogle Scholar
  322. Macek A (1967) Fundamentals of combustion of single aluminum and beryllium particles. The Eleventh Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 203–217Google Scholar
  323. Macek A (1973) Combustion of boron particles: experiment and theory. The Fourteenth Symposium (International) on Combustion. The Combustion Institute. Pittsburgh, Pa., pp. 1401–1411Google Scholar
  324. Macek A, Semple JM (1969) Experimental burning rates and combustion mechanisms of single beryllium particles. The Twelfth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 71–81Google Scholar
  325. Macek A, Semple JM (1971) Combustion of boron particles at elevated pressures. The Thirteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 859–868Google Scholar
  326. Madooglu K, Karagozian AR (1994) Burning of a spherical fuel droplet in a uniform flow-field with exact property variation. Combust. Flame 94: 321–329CrossRefGoogle Scholar
  327. Matalon M, Law CK (1983) Gas-phase transition diffusion in droplet vaporization and combustion. Combust. Flame 50: 219–229CrossRefGoogle Scholar
  328. Merzhanov AG (1973) The problem of technological combustion. In: Merzhanov AG (ed) Combustion processes in chemical technology and metallurgy. AN SSSR, Chernogolovka, pp. 5–28 (in Russian)Google Scholar
  329. Merzhanov AG, Grigorjev YuM, Gal’chenko YuA (1977) Aluminium ignition. Combustion Flame 29: 1–14CrossRefGoogle Scholar
  330. Molodetsky IE, Vicenzi EP, Dreizin EL, Law CK (1998) Phase of titaniuim combustion in air. Combust. Flame 112: 522–532CrossRefGoogle Scholar
  331. Nakoryakov VE, Pokusaev BG, Shreiber IR (1993) Wave propogation in gas-liquid media. 2nd. edn. CRC Press, Boca Raton FlaGoogle Scholar
  332. Nigmatulin RI (1991). Dynamics of multiphase media v. 1 and 2. Hemisphere, LondonGoogle Scholar
  333. Nioka T, Sato J (1986) Combustion and microexplosion behavior of miscible fuel droplets under high pressure. The Twenty-first Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 625–631Google Scholar
  334. Nishiwaki N (1955) Kinetics of liquid combustion processes: evaporation and ignition lag of fuel droplets. The Fifth Symposium (International) on Combustion. The combustion Institute. Reinhold, New York, pp. 148–158Google Scholar
  335. Okajima S, Kumagai S (1974) Further investigations of combustion of free droplets in a freely falling chamber including moving droplets. The Fifteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 401–407Google Scholar
  336. Peskin RL, Wise H (1966) A theory for ignition and deflagration of fuel drops. AIAA J. 4: 1646–1650CrossRefGoogle Scholar
  337. Peskin RL, Polymeropoulos CE, Yeh PS (1967) Results from a theoretical study of fuel drop ignition and extinction. AIAA J. 5: 2173–2178CrossRefGoogle Scholar
  338. Pindera MZ, Brzustowski TA (1984) A model for the ignition and extinction of liquid fuel droplets. Combust. Flame 55: 79–91CrossRefGoogle Scholar
  339. Polymeropoulos CE, Peskin RL (1969) Ignition and extinction of liquid fuel drops–numerical computations. Combust. Flame 13: 166–172CrossRefGoogle Scholar
  340. Predvoditelev AS, Khitrin LN, Tsukhanova OA, Kolodtsev KI, Grodzovsky MK (1949) Carbon combustion. (in Russian) AN SSSR, MoscowGoogle Scholar
  341. Puri JK, Libby PA (1991) The influence of transport properties on droplet burning. Combust. Sci. Technol. 76: 67–80CrossRefGoogle Scholar
  342. Rosser WAJr, Rajapakse Y (1969) Thermal stability of a reactive spherical shell. Combust. Flame 13: 311–317CrossRefGoogle Scholar
  343. Saitoh T, Ishiguro S, Niioka T (1982) An experimental study of droplet ignition characteristics near the ignitable limit. Combus. Flame. 48: 27–32CrossRefGoogle Scholar
  344. Schvab BA (1948) Connection between temperature and velocity fields in gaseous flame. In: Investigation of processes of fossil fuel combustion. Gosenergoizdat, Moscow Leningrad, pp. 231–248 (in Russian).Google Scholar
  345. Semenov NN (1935) Chemical kinetics and chain reactions. Oxford University Press, LondonGoogle Scholar
  346. Shafirovich , Goldshleger VI (1992) The superheat phenomenon in the combustion of magnesium particles. Combust. Flame 88: 425–42CrossRefGoogle Scholar
  347. Shaygan N, Prakash S (1995) Droplet ignition and combustion including liquid-phase heating. Combust. Flame 102: 1–10CrossRefGoogle Scholar
  348. Sirignano WA (1999) Fluid dynamics and transport of droplets and sprays. Cambridge. University Press, CambridgeGoogle Scholar
  349. Solomon PR, Chien PL, Carangelo RM Serio MA, Markham JR, (1990) New ignition phenomenon in coal combustion. Combust. Flame 79: 214–215CrossRefGoogle Scholar
  350. Spalding DB (1953) The Combustion of liquid fuels. The Fourth Symposium (International) on Combustion. Williams and Wilkings, Baltimore, Md., pp. 847–864Google Scholar
  351. Spalding DB (1955) Some fundamentals of combustion. Butterworth, LondonGoogle Scholar
  352. Spalding DB (1951) A theory of the extinction of diffusion flames Fuel 33: 255–273Google Scholar
  353. Spalding DB, Jain VK (1962) A theoretical study of the effects of chemical kinetics on onedimensional diffusion. Combust. Flame 6: 265–273CrossRefGoogle Scholar
  354. Takei M, Tsukamoto T, Niioka T (1993). Ignition of blended-fuel droplet in high temperature atmosphere. Combust. Flame 93: 149–156CrossRefGoogle Scholar
  355. Tarifa CS, Notario PP, Moreno FG (1962) Comustion of liquid monopropellants and bipropellants in droplets. The Eighth Symposium (International) on Combustion. The Combustion Institute. Williams and Wilkins, Baltimore, Md., pp. 1035–1056Google Scholar
  356. Varshayskii GA (1945) Burning of the droplet of liquid fuel. Diffusion theory. BNT MAP. Moscow (in Russian) (see also Khitrin LN (1957) The physics of combustion and ex196 1 Dynamics of a single particle 1.3 Ignition and combustion of a single particle plosion. pp. 347–349. Moscow University, Israel Program for Scientific Translations. Jerusalem, 1962 )Google Scholar
  357. Vol’fkovich CI, Egorov AP, Epshtein DA (1952) General chemical technology. (in Russian) Chemistry, Moscow LeningradGoogle Scholar
  358. Vulis LA (1961) Thermal regimes of combustion. McGraw-Hill, New YorkGoogle Scholar
  359. Vulis LA, Yarin LP (1970). Combustion of unmixed gases at a finite reaction rate. Combust. Explos. Shock Waves 6: 423–428CrossRefGoogle Scholar
  360. Vulis LA, Yarin LP (1978). Aerodynamics of a torch. (in Russian) Energia, LeningradGoogle Scholar
  361. Vulis LA, Ershin ShA, Yarin LP (1968) Foundations of the theory of gas torch. (in Russian) Energia, LeningradGoogle Scholar
  362. Waldman CH (1974a) Theory of non-steady state droplet combustion. The Fifteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 429–442Google Scholar
  363. Wang CH, Liu XQ, Law CK (1984) Combustion and microexplosion of freely falling multicomponent droplets. Combust. Flame 56: 175–197CrossRefGoogle Scholar
  364. Willems JL (1970) Stability theory of dynamical systems. Thomas NelsonGoogle Scholar
  365. Williams A (1973) Combustion of droplets of liquid fuels: a review. Combust. Flame 21: 1–31CrossRefGoogle Scholar
  366. Williams FA (1985) Combustion theory. 2nd edn. Benjamin/Cummings, Menlo Park, Calif.Google Scholar
  367. Wise H, Agoston GA (1958) Burning of a ignition droplet. In: Advances in chemistry, Ser. 20 American Chemical Society, New York, pp. 116–135Google Scholar
  368. Wise H, Lorell J, Wood BJ (1955) The effects of chemical and physical parameters on the burning rate of a liquid droplet. The Fifth Symposium (International) on Combustion. The Combustion Institute. Reinhold, New York, pp. 132–141Google Scholar
  369. Wood BJ, Rosser WAJr (1969) An experimental study of fuel droplet ignition. AIAA J. 7: 2288–2292CrossRefGoogle Scholar
  370. Wood BJ, Wise H, Inami SH (1960) Heterogeneous combustion of multicomponent fuels. Combust. Flame 4: 235–242CrossRefGoogle Scholar
  371. Yang JC (1993) Heterogeneous combustion. In: Puri JK (ed) Environmental Implications of Combustion Processes. CRC Press, London, pp. 97–137Google Scholar
  372. Yang JC, Jackson GS, Avedisian CT (1990) Combustion of unsupported Methanol/Dedecanol mixture droplets at low gravity. The Twenty-third Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1619–1625Google Scholar
  373. Yap LT, Kennedy IM, Dryer FL (1984) Disruptive and micro-explosive combustion of free droplets in highly convective environment. Combust. Sci. Technol. 41: 291–313CrossRefGoogle Scholar
  374. Yarin LP (1961) Thermal regime of combustion of unpremixed gases. In: Acad. Sci. of Kazakhstan. Energetics. Alma-Ata, 19: 47–55 (in Russian)Google Scholar
  375. Yeh CL, Kuo KK (1996) Ignition and combustion of boron particles. Prog. Energy Combust. Sci. 22: 511–541Google Scholar
  376. Zel’dovich YaB (1939). Towards the theory of reaction on porous or powder-like material. J. Phys. Chem. 13:163–168. (see Zel’dovich YaB ( 1984 ) Selected papers chemical physics and gas dynamics, (in Russian) Nauka, Moscow )Google Scholar
  377. Zel’dovich YaB (1948). Toward the theory of unmixed gases combustion. J. Tech. Phys. 19: 1199–1210 (in Russian). (see also Zel’dovich YaB, Barenblatt GI, Librovich VB, and Makhviladze GM ( 1985 ) Mathematical theory of combustion and explosion. Plenum, New York )Google Scholar
  378. Aminzadeh K, Taha TRAI, Cornish ARH, Kolansky MS, Pfeffer R (1974) Mass transport around two spheres at low Reynolds numbers. Int. J. Heat Mass Transfer 17: 14251436Google Scholar
  379. Bard E (1968) The slow unsteady settling of a fluid sphere towards a flat fluid interface. Chem Eng. Sci. 23: 193–210CrossRefGoogle Scholar
  380. Boothroyd RG (1974) Following gas-solid suspensions. Chapman and Hall, LondonGoogle Scholar
  381. Brzustowski TA, Twardus EM, Wojcicki S, Sobiesiak A (1979) Interaction of two burning fuel droplets of arbitrary size. AIAA J. 17: 1234–1242CrossRefGoogle Scholar
  382. Cooley MDA, O’Neill ME (1969) On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere. Mathematika 16: 37–49CrossRefGoogle Scholar
  383. Crowe CT, Sommerfeld M, Tsuji Y (1997) Multiphase flows with droplets and particles. CPC Press, New YorkGoogle Scholar
  384. Davis MH (1969) The slow translation and rotation of two unequal spheres in a viscous fluid. Chem. Eng. Sci. 24: 1769–1776CrossRefGoogle Scholar
  385. Faxen H (1927) Die geschwindigkeit zwen kugeln, die unter ein wirkung der schwere in einen zahen flussigkeit fallen. ZAMM 7: 79–80zbMATHCrossRefGoogle Scholar
  386. Goldman AJ, Cox RG, Brenner H (1967) Slow viscous motion of a sphere parallel to a plane wall. Part I. Motion through a quiescent fluid Chem. Eng. Sci. 22: 637–651 Part II 22: 653CrossRefGoogle Scholar
  387. Gupalo YuP, Polyanin AD, Ryazantsev YuS (1985) Mass transfer reactive particles with flow. (in Russian) Nauka, MoscowGoogle Scholar
  388. Haber S, Hetsroni G, Solan A (1973) On the low Reynolds number motion of two droplets. Int. J. Multiphase Flow 1: 57–71zbMATHCrossRefGoogle Scholar
  389. Happel J, Brenner H (1983) Low reynolds number hydrodynamics. Martinus Nijhoff, The HagueGoogle Scholar
  390. Hasimoto H (1959) On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5: 317–328MathSciNetzbMATHCrossRefGoogle Scholar
  391. Hetsroni G, Haber S (1970) The flow fields in and around a droplet or bubble submerged in an unbounded arbitrary velocity field. Rheol. Acta 9: 488–496zbMATHCrossRefGoogle Scholar
  392. Hetsroni G, Haber S (1971) Low Reynolds number motion of raindrops in the atmosphere. Department of Mechanical Engineering, Technion, HaifaGoogle Scholar
  393. Hetsroni G, Haber S (1978) Low Reynolds number motion of two drops submerged in an unbounded arbitrary velocity field. Int. J. Multiphase Flow 4: 1–17zbMATHCrossRefGoogle Scholar
  394. Hetsroni G, Haber S, Wacholder E (1970) The flow fields in an around a droplet moving axially within a tube. J. Fluid Mech. 41: 689–705zbMATHCrossRefGoogle Scholar
  395. Jeffery G B (1915) On the steady rotation of a solid of revolution in a viscous field. Proc. London Math. Soc. (Ser 2) 14: 327–338Google Scholar
  396. Kim I, Elghobashi S, Siriganano WA (1993) Three-dimensional flow over two spheres placed side by side. J Fluid Mech. 246: 465–488zbMATHCrossRefGoogle Scholar
  397. Kim S (1987) Stokes flow past three spheres: an analytic solution. Phys. Fluids 30: 2309–2314zbMATHCrossRefGoogle Scholar
  398. Kim S, Karrila SJ (1991) Microhydrodynamics: principles and selected applications. Butterworth — Heinemann, Boston MassGoogle Scholar
  399. Labowsky M (1978) A formalism for calculating the evaporation rates of rapidly evaporating interacting particles. Combust. Sci. Technol. 18: 145–151CrossRefGoogle Scholar
  400. Labowsky M (1980) Calculation of burning rates of interacting fuel droplets. Combust. Sci. Technol. 22: 217–226CrossRefGoogle Scholar
  401. Lee KC (1979) Aerodynamic interaction between two spheres at Reynolds numbers about 104. Aero. Q. 30: 371–385Google Scholar
  402. Liang S-C, Hong T, Fan L-S (1996) Effects of particle arrangements on the drag force of a particle in intermediate flow regime. Int. J. Multiphase Flow 22: 285–306zbMATHCrossRefGoogle Scholar
  403. Marberry M, Ray AK, Leung K (1984) Effect of multiple particle interactions on burning droplets. Combust. Flame 57: 237–245CrossRefGoogle Scholar
  404. Miyasaka K, Law CK, (1981) Combustion of strongly — interacting linear droplet arrays. The Eighteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 283–292Google Scholar
  405. Morrison FAJr, Reed LD (1978) The slow motion of two touching fluid spheres along their line of centers: addendum. Int. J. Multiphase Flow 4: 433–434CrossRefGoogle Scholar
  406. Mulholland JA, Srivastava RK, Wendt JOL (1988) Influence of droplet spacing on drag coefficient in nonevaporating, monodisperse streams. AIAA J. 26: 1231–1237CrossRefGoogle Scholar
  407. Ramachandran RS, Wang T-Y, Kleinstreuer C, Chiang H (1991) Laminar flow past three closely spaced monodisperce spheres or nonvaporating droplets. AIAA. J. 29: 43–51CrossRefGoogle Scholar
  408. Reed L, Morrison FAJr (1974) The slow motion of two touching fluid spheres along their line of centers. Int. J. Multiphase Flow 1: 573–584CrossRefGoogle Scholar
  409. Rushton E, Davies G A (1978) The slow motion of two spherical particles along their line of centers. Int. J. Multiphase Flow 4: 357–381CrossRefGoogle Scholar
  410. Sadhal SS, Ayygawamy PS, Chung JN (1997) Transport phenomena with drops and bubbles. Springer, New YorkGoogle Scholar
  411. Sangiovanni JJ, Labowsky M (1982) Burning times of linear fuel droplet arrays: a comparison of experiment and theory. Combust. Flame 47: 15–30CrossRefGoogle Scholar
  412. Siriganano WA (1999) Fluid dynamics and transport of droplets and sprays. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  413. Soo SL (1998) Multiphase fluid dynamics. Science Press and Gower Technical, BejingGoogle Scholar
  414. Stimson M, Jeffery GB (1926) The motion of two spheres in viscous fluid. Proc. R. Soc. London, Ser. A 111: 110–116zbMATHCrossRefGoogle Scholar
  415. Subramanian RS, Balasubramaniam R (2001) The motion of bubbles and drops in reduced gravity. Cambridge University Press, CambridgezbMATHGoogle Scholar
  416. Tsuji Y, Morikawa Y, Terashima K (1982) Fluid–dynamic interaction between two spheres. Int. J. Multiphase Flow 8: 71–82CrossRefGoogle Scholar
  417. Tsuji Y, Morikawa Y, Fujiwara Y (1985) Pipe flow with solid particles fixed in space. Int. J. Multiphase Flow 11: 177–188CrossRefGoogle Scholar
  418. Umemura A, Ogawa S, Oshima N ( 1981 a) Analysis of the interaction between two burning fuel droplets with different sizes. Combust. Flame 43: 111–119Google Scholar
  419. Umemura A, Ogawa S, Oshma N (1981b) Analysis of the interaction between two burning droplets. Combust. Flame 41: 45–55CrossRefGoogle Scholar
  420. Wacholder E, Weihs D (1972) Slow motion of a fluid sphere in the vicinity of another sphere or a plane boundary. Chem. Eng. Sci. 27: 1817–1828CrossRefGoogle Scholar
  421. Yarin AL (1987). Collective effect in disperse systems. J. Exp. Theor. Phys. 93: 1256–1259 (in Russian)Google Scholar
  422. Yarin LP, Sukhov GS (1987) Fundamentals of combustion theory of two-phase media. (in Russian) Energoatomizdat, LeningradGoogle Scholar
  423. Zhu C, Liang S-C, Fan L-S (1994) Particle wake effects on the drag force of an interactive particle. Int. J. Multiphase Flow 20: 117–129zbMATHCrossRefGoogle Scholar
  424. Zick AA, Homsy GM (1982) Stokes flow through periodic arrays of spheres. J. Fluid Mech. 115: 13–26zbMATHCrossRefGoogle Scholar
  425. Zinchenko AZ (1979) Calculation of hydrodynamic interaction between drops at low Reynolds number. Appl. Math. Mech. 42: 1046–1051zbMATHGoogle Scholar
  426. Zinchenko AZ (1981) The slow asymmetric motion of two drops in a viscous medium. Appl. Math. Mech. 44: 30–37Google Scholar
  427. Zinchenko AZ (1982) Calculation of close interaction between drops, with internal circulation and slip effect taken into account. Appl. Math. Mech. 45: 564–567Google Scholar
  428. Zinchenko AZ (1984) Hydrodynamic interaction of two identical spheres in linear flow field. Appl. Math. Mech. 47: 37–43zbMATHGoogle Scholar
  429. Abou-Arab TW, Roco MC (1988) Solid phase contribution in the two-phase turbulence kinetic energy equation. The 3rd International Symposium on Liquid-Solid Flows. ASME, New York, pp. 13–28Google Scholar
  430. Abramovich GN (1970) The effect of admixture of solid particles or droplets on the structure of a turbulent gas jet. Sov. Phys. Dokl. 190: 1052–1055Google Scholar
  431. Abramovich GN, Girshovich TA (1973) Diffusion of heavy particles in turbulent gas flows. Soy. Phys. Dokl. 212: 573–576Google Scholar
  432. Abramovich GN, Girshovich TA, Krasheninnikov S Yu, Sekundov AN, Smirnova IP (1984) Theory of turbulent jet. (in Russian) Science, MoscowGoogle Scholar
  433. Achenbach E (1974) Vortex shedding from spheres. J. Fluid Mech. 62: 209–221CrossRefGoogle Scholar
  434. Alajbegovich A, Assad A, Bonetto F, Lahey RT Jr (1994) Phase distribution and turbulence structure for solid/fluid upflow in a pipe. Int. J. Multiphase Flow 20: 453–479CrossRefGoogle Scholar
  435. Al-Tawell AM, Landau J (1977) Turbulence modulation in two-phase jet. Int. J. Multiphase Flow 3: 341–351CrossRefGoogle Scholar
  436. Ballantyne A, Bray KNC (1976) Investigations into the structure of jet diffusion flames using time-resolved optical measuring techniques. The Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 777–787Google Scholar
  437. Ballantyne A, Moss JB (1977) Fine wire thermocouple measurements of fluctuating temperature. Combust. Sci. Technol. 17: 63–72CrossRefGoogle Scholar
  438. Berlow RS, Morrison CQ (1990) Two-phase velocity measurements in dense particle-laden jets. Exp. Fluids 9: 93–104CrossRefGoogle Scholar
  439. Boivin M, Simonin O, Squires KD (1998) Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J. Fluid Mech. 375: 235–263zbMATHCrossRefGoogle Scholar
  440. Boothroyd RG (1971). Flowing gas-solid suspensions. Chapman and Hall, LondonGoogle Scholar
  441. Bray KNC (1978) The interaction between turbulence and combustion. The SeventeenthGoogle Scholar
  442. Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 223–233Google Scholar
  443. Bray KNC, Libby PA, Moss JB (1984) Flamelet crossing frequencies and mean reaction rates in premixed turbulent combustion. Combust. Sci. Technol. 41: 143–172CrossRefGoogle Scholar
  444. Bray KNC, Champion M, Libby PA (1988) Mean reaction rates in premixed turbulent flames. The Twenty-second Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 763–769Google Scholar
  445. Crowe CT (2000) On models for turbulence modulation in fluid-particle flows. Int. J. Multiphase Flow 26: 719–729zbMATHCrossRefGoogle Scholar
  446. Crowe CT, Troutt TR, Chung JN (1996) Numerical models for two-phase turbulent flows. In: Lumley L, Van Dake M, Reed HL (eds) Annu. Rev. Fluid Mech. 28: 11–43Google Scholar
  447. Danon H, Wolfshtein M, Hetsroni G (1974) Numerical calculations of two-phase turbulent jets. Int. J. Multiphase Flow 3: 223–234CrossRefGoogle Scholar
  448. Derevich IV (2001) Influence of internal turbulent structure on intensity of velocity and temperature fluctuations of particles. Int. J. Heat Mass Transfer 44: 4505–4521zbMATHCrossRefGoogle Scholar
  449. Elghobashi SE, Abou-Arab TW (1983) A two-equation turbulent model for two-phase flows. Phys. Fluids 26: 931–938zbMATHCrossRefGoogle Scholar
  450. Elghobashi S, Truesdell GC (1992) Direct simulation of particle dispersion in a decaying isotrorpic turbulence. J. Fluid Mech. 242: 655–700CrossRefGoogle Scholar
  451. Elghobashi S, Truesdell GC (1993) On the two-way interaction between homogeneous turbulence and dispersed solid particles. 1: Turbulence modulation. Phys. Fluids A, 5: 1790–1801zbMATHCrossRefGoogle Scholar
  452. Frank-Kamenetskii DA (1969) Diffusion and heat transfer in chemical kinetics. 2nd edn., Plenum, New YorkGoogle Scholar
  453. Frishman FM (1979) Effect of phase relative motion on turbulence intensity. In: Turbulent two-phase flows. (in Russian) A.N. ESSR, Tallinn, pp. 134–136Google Scholar
  454. Girshovich TA, Leonov BA (1979) On the effect of admixture weight on the turbulent structure of vertical two-phase jet. In: Laats MK (ed) The III All-Union cConference in Theoretical and Applied Aspects of Turbulent Flows. Part II turbulent two-phase flows. (in Russian) AN ESSR, Talllinn, pp. 127–133Google Scholar
  455. Gore RA, Crowe CT (1989) Effect of particle size on modulating turbulent intensity. Int. J. Multiphase Flow 15: 279–285CrossRefGoogle Scholar
  456. Haam SJ, Brodkey RS (2000) Laser Droplet anemometry measurements in an index of refraction column in the presence of dispersed beads. Part II. Motions of dispersed beads obtained by particle tracking velocimetry measurements. Int. J. Multiphase Flow 26: 1419–1438zbMATHCrossRefGoogle Scholar
  457. Hetsroni G (1989) Particle-turbulence interaction. Int. J. Multiphase Flow 15: 735–746CrossRefGoogle Scholar
  458. Hetsroni G, Rozenblit R (1994) Heat transfer to a liquid-solid mixture in a flume. Int. J. Multiphase Flow 20: 671–689zbMATHCrossRefGoogle Scholar
  459. Hetsroni G, Sokolov M (1971) Distribution of mass, velocity and intensity of turbulence in a two-phase turbulent jet. Trans. ASME. J. Appl. Mech. 38: 315–327CrossRefGoogle Scholar
  460. Hetsroni G, Rozenblit R, Lu DM (1995) Heat transfer enhancement by a particle on the bottom of a flume. Int. J. Multiphase Flow 21: 963–984zbMATHCrossRefGoogle Scholar
  461. Hetsroni G, Rozenblit R, Yarin LP (1997) The effect of coarse particles on the heat transfer in a turbulent boundary layer. Int. J. Heat Mass Transfer 40: 2201–2217Google Scholar
  462. Hinze JO (1972) Turbulent fluid and particle interaction. In: Hetsroni G, Sideman S, Hartnett JP (eds) Prog. Heat Mass Transfer 6: 433–452Google Scholar
  463. Jaberi FA (1998) Turbulence fluctuations in particle-laden homogeneous turbulent flows. Int. J. Heat Mass Transfer 41: 4081–4090zbMATHCrossRefGoogle Scholar
  464. Jaberi FA, Mashayek F (2000) Temperature decay in two-phase turbulent flows. Int. J. Heat Mass Transfer 43: 993–1005zbMATHCrossRefGoogle Scholar
  465. Jones WP, Whitelaw JH (1982) Calculation methods for reacting turbulent flows. A review. Combust. Flame 48: 1–26CrossRefGoogle Scholar
  466. Kenning VM, Crowe CT (1977) On the effect of particles on carrier phase turbulence in gas-particle flows. Int. J. Multiphase Flow 23: 405–408Google Scholar
  467. Kent JH, Bilger RW (1976) The prediction of turbulent diffusion flame fields and nitric oxide formation. The Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 1643–1656Google Scholar
  468. Kolmogorov AN (1942) Equations of turbulent motion of incompressible fluid. Jzv. Akad. Nauk SSSR, Phys. Ser. 1–2, 56–58 (in Russian)Google Scholar
  469. Kulick JD, Fessier JR, Eaton JK (1993) On the interactions between particles and turbulence in fully-developed channel flow in air. Report No. MD-66. Standford UniversityGoogle Scholar
  470. Kunugi M, Jinno H (1959) Measurements of fluctuating flame temeprature. The Seventh Symposium (International) on Combustion. The Combustion Institute. Butterworths, pp. 942–948Google Scholar
  471. Kuznetsov VR (1969) The effect of temperature and concentration fluctuations on average rate of rection in turbulent flow. The second all-union symposiuim on combustion and explosion. (in Russian) AN SSR, Chernogolovka 99–104Google Scholar
  472. Kuznetsov VR, Sabel’nikov BA (1989) Turbulence and combustion. Hemisphere, New YorkGoogle Scholar
  473. Laats MK, Frishman FM (1973) The development of the methodics and investigation of turbulence intensity at the axis of two-phase turbulent jet. Fluid Dynam. 8: 153–157Google Scholar
  474. Lee SL, Durst F (1982) On the motion of particles in turbulent duct flow. Int. J. Multiphase Flow. 8: 125–146CrossRefGoogle Scholar
  475. Lentini D (1993) Models for Turbulent Combustion. In: Puri JK(ed). Environmental Implications of Combustion Processes. CRC Press, London, pp. 221–229Google Scholar
  476. Levy Y, Lockwood FC (1981) Velocity measurements in a particle-laden turbulent free jet. Combust. Flame 40: 333–339CrossRefGoogle Scholar
  477. Libby PA, Williams FA (1980) In: Libby PA, Williams FA (eds) Turbulent reacting flows. Springer, Berlin, p. 1zbMATHGoogle Scholar
  478. Lisin FN (1988) On temperature fluctuations in turbulent flow. J. Eng. Phys. 5: 731–735 (in Russian)Google Scholar
  479. Lockwood FC (1977) The modelling of turbulent premixed and diffusion combustion in the computation of engineering flows. Combust. Flame 29: 111–122CrossRefGoogle Scholar
  480. Lockwood FC, Odidi AOO (1974) Measurement of mean and fluctuating temperature and of ion concentration in round free-jet turbulent diffusion and premixed flames. The Fifteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 561–571Google Scholar
  481. Maeda M, Hishida K, Furutani T (1980) Optical measurements of local gas and particle velocity in an upward following dilute gas—solid suspension. In: polyphase flow and transport technology. Century 2 ETC, San Francisco Calif., pp. 216–221Google Scholar
  482. Mizukami M, Parthasarathy RN, Faeth GM (1992) Particle-generated turbulence in homogenous dilute dispersed flows. Int. J. Multiphase Flow 18: 397–412zbMATHCrossRefGoogle Scholar
  483. Moderress D, Tan H, Elghobashi S (1984a) Two-component LDA measurement in a two-phase turbulent jet. AIAA J. 22: 624–630CrossRefGoogle Scholar
  484. Moderress D, Wuerer J, Elghobashi SF (1984b) An expereimetnal study of a turbulent round two-phase jet. Chem. Eng. Commun 28: 341–354CrossRefGoogle Scholar
  485. Monin AS, Yaglom AM (1971) Statistical fluid mechanics. MIT Press, Cambridge, MassGoogle Scholar
  486. Nigmatulin RI (1991) Dynamics of multiphase media Hemisphere, London, vols. 1 and 2Google Scholar
  487. Nouri JM, Whitelaw JH, Yianneskis M (1987) Particle motion and turbulence in dense twophase flows. Int. J. Multiphase Flow 13: 729–739CrossRefGoogle Scholar
  488. Owen PR (1969) Pneumatic transport. J. Fluid Mech. 39: 407–432CrossRefGoogle Scholar
  489. Pan Y, Banerjee J (1997) Numerical investigation of the effects of large particles on wall turbulence. Phys. Fluids 9: 3786–3807CrossRefGoogle Scholar
  490. Parthasarathy RN, Faeth GM (1987) Structure of particle-laden turbulent water jets in still water. Int. J. Mutliphase Flow 13: 699–716CrossRefGoogle Scholar
  491. Parthasarathy RN, Faeth GM (1990) Turbulence modulation in homogeneous dilute particle-laden flows. J. Fluid Mech. 220: 485–537CrossRefGoogle Scholar
  492. Pope SB (1977) The implications of the probability equations for turbulent combustion models. Combust. Flame 29: 235–246CrossRefGoogle Scholar
  493. Prandtl L (1925) Ueber die ausgebildete turbulenz. Z. Angew. Math., Mech. 5: 136–139zbMATHGoogle Scholar
  494. Rashidi M, Hetsroni G, Banerjee S (1990a) Particle-turbulence interaction in a boundary layer. Int. J. Multiphase Flow 16: 935–949zbMATHCrossRefGoogle Scholar
  495. Rashidi M, Hetsroni G, Banerjee S (1990b) Mechanisms of heat and mass transport at gasliquid interfaces. Int. J. Heat Mass Transfer 34: 1799–1810CrossRefGoogle Scholar
  496. Sagara K (1980) Exact turbulence correction to Arrhenius law in the asymptotic limit of high activation energy. Sci. Technol. 21: 191–197Google Scholar
  497. Sato Y, Hishida K (1996) Transport process of turbulent energy in particle-laden turbulent flow. Int. J. Heat Fluid Flow 17: 202–210CrossRefGoogle Scholar
  498. Savolainen K, Karvinen R (1998) The effect of particles on gas turbulence in a vertical upward pipe flow. The Third International Conference on Multiphase Flow. ICMF-98, Lyon, France, June 8–12Google Scholar
  499. Schiller L, Naumann A (1933) Ueber die grundlegenden berchnungen bei der schwerkraftaufbereitung. Ver. Deut. Ing. 77: 318–320Google Scholar
  500. Schlichting H (1979) Boundary-layer theory. McGraw-Hill, New YorkzbMATHGoogle Scholar
  501. Serizawa A, Kataoka I, Michiyoshi I (1975) Turbulence structure of air-water bubbly flow. II Local properties. Int. J. Multiphase Flow 2: 235–246CrossRefGoogle Scholar
  502. Sheen HJ, Jou BH, Lee YT (1994) Effect of particle size on a two-phase turbulent jet. Exp. Thermal Fluid Sci. 8: 315–327CrossRefGoogle Scholar
  503. Shraiber AA, Gavin LB, Naumov VA, Yatsenko VP (1990) Turbulent flows in gas suspension. Hemisphere, New YorkGoogle Scholar
  504. Shuen J-S, Solomon ASP, Zhang Q-F, Faeth GM (1985) Structure of particle-laden jets: measurements and predictions. AIAI J. 23: 396–404CrossRefGoogle Scholar
  505. Soo SL (1990) Multiphase fluid dynamics. Science Press and Gover Technical, BeijingGoogle Scholar
  506. Spalding DB (1971) Concentration fluctuation in round turbulent free jet. Chem. Eng. Sci. 26: 95–107MathSciNetCrossRefGoogle Scholar
  507. Spalding DB (1976) Development of the eddy-break-up model of turbulent combustion. The Sixteenth Symposium ( International) on Combustion, Pittsburgh, Pa., pp. 1657–1663Google Scholar
  508. Squires KD, Eaton JK (1990) Particle response and turbulence modulation in isotropic turbulence. Phys. Fluids A. 2: 1191–1203CrossRefGoogle Scholar
  509. Sun TV, Faeth GM (1986) Structure of turbulent bubbly jets-1. Methods and centerline properties. Int. J. Multiphase Flow 12: 99–114CrossRefGoogle Scholar
  510. Sundaram S, Collins LA (1999) A numerical study of the modulation of isotropic turbulence by suspended particles. J. Fluid Mech. 379: 105–143zbMATHCrossRefGoogle Scholar
  511. Swain LM (1929) On the turbulent wake behind a body of revolution. Proc. R. Soc. London, Ser. A 125: 647–659zbMATHCrossRefGoogle Scholar
  512. Theofanous TG, Sullivan J (1982) Turbulence in two-phase dispersed flow: J. Fluid Mech. 116: 343–362CrossRefGoogle Scholar
  513. Townsend AA (1976) The structure of turbulent shear flow. Cambridge University Press, CambridgezbMATHGoogle Scholar
  514. Tsuge S, Sagara K (1978) Arrhenius’ law in turbulent media and an equivalent tunnel effect. Combust. Sci. Technol. 18: 179–189CrossRefGoogle Scholar
  515. Tsuji Y, Morikawa Y (1982) LDV measurements of an air-solid two-phase flow in a horizontal pipe. J. Fluid Mech. 120: 385–406CrossRefGoogle Scholar
  516. Tsuji Y, Morikawa Y, Shiomi H (1984) LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech. 139: 417–434CrossRefGoogle Scholar
  517. Tsuji Y, Morikawa Y, Tanaka T, Karimine K, Nishida S (1988) Measurements of an axisymmetric jet laden with coarse particles. Int. J. Multiphase Flow 14: 565–574CrossRefGoogle Scholar
  518. Uberoi MS, Freymuth P (1970) Turbulent energy balance and spectra of the axisymmetric wake. Phys. Fluids 13: 2203–2210MathSciNetCrossRefGoogle Scholar
  519. Varaksin AYu (1998) To questions about fluctuated velocity and temperature of the nonStokesian particles moving in the turbulent flows. Heat Transfer. In: Lee JS (ed) The 11th IHTC, Kyongju, Korea, 2, pp. 147–150Google Scholar
  520. Varaksin AYu, Kurosaki Y, Satoh I, Polezhaev YuY, Polyakov AF (1998) Experimental Study of the Direct Influence of the Small Particles on the Carrier Air Turbulence Intensity for Pipe Flow. The Third International cConference on Multiphase Flow. ICMF 98, Lyon, France, June 8–12.Google Scholar
  521. Vulis LA (1960) Towards the role of turbulent fluctuations in turbulent combustion. The 3rd All-Union Conference on Combustion Theory. (in Russian) AN SSSR, Moscow, pp. 86–90Google Scholar
  522. Vulis LA (1961) Thermal regimes of combustion. McGraw-Hill, New YorkGoogle Scholar
  523. Vulis LA (1972) On turbulent burning velocity. Combust. Explosion Shock Waves 8: 1–5CrossRefGoogle Scholar
  524. Vulis LA, Ershin ShA, Yarin LP (1968) Foundations of the theory of gas torch. (in Russian) Energia, LeningradGoogle Scholar
  525. Wang SK, Lee SJ, Jones OSJr, Lahey RTJr (1987) 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13: 327–343Google Scholar
  526. Yarin LP, Hetsroni G (1994a) Turbulence intensity in dilute two-phase flows-1. Effect of particle-size distribution on the turbulence of the carrier fluid. Int. J. Multiphase Flow 20: 1–15zbMATHCrossRefGoogle Scholar
  527. Yarin LP, Hetsroni G (1994b) Turbulence intensity in dilute two-phae flows-2. Tempera- ture fluctuations in particle-laden dilute flows. Int. J. Multiphase Flow 20: 17–25zbMATHCrossRefGoogle Scholar
  528. Yarin LP, Hetsroni G (1994c) Turbulence intensity in dilute two-phase flows-3. The particles-turbulence interaction in dilute two-phase flow. Int. J. Multiphase Flow 20: 27–44zbMATHCrossRefGoogle Scholar
  529. Yoshida A, Tsuji H (1978) Measurements of fluctuating temperature and velocity in a turbulent premixed flame. The Seventeenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, Pa., pp. 945–956Google Scholar
  530. Yuan Z, Michaelides EE (1992) Turbulence modulation in particulate flow—a theoretical approach. Int. J. Multiphase Flow 18: 779–785zbMATHCrossRefGoogle Scholar
  531. Zel’dovich YaB (1949) Towards the theory of combustion unpremixed gases. J. Tech. Phys. 19: 1199–1210 (in Russian)Google Scholar
  532. Zel’dovich YaB, Barenblatt GJ, Librovich VB, Makhviladze GM (1985) The Mathematical theory of combustion and explosion. Consultants Bureau, New YorkCrossRefGoogle Scholar
  533. Zisselmar R, Molerus O (1979) Investigation of solid-liquid pipe flow with regard to turbulence modulation. Chem. Eng. J. 18: 233–239Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • L. P. Yarin
    • 1
  • G. Hetsroni
    • 1
  1. 1.Technion CityFaculty of Mechanical EngineeringHaifaIsrael

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