Drop Size Distributions

  • A. Déchelette
  • E. Babinsky
  • P. E. SojkaEmail author


Drop size distributions are at least as important as mean drop sizes. Some spray applications require narrow size distributions (paint and respirable sprays), while some need wide ones (gas turbine engines). Other spray processes require very few small drops (agricultural or consumer product sprays) or very few large ones (waste incineration, IC engines). In this section, we discuss the concepts of drop size distributions, moments of those distributions, and characteristic drop diameters computed from them. This is followed by a summary of methods available for describing drop size distributions.


Characteristic drop diameter Cumulative volume fraction Discrete probability function (DPF) Drop size distribution Empirical drop size distribution Log-hyperbolic distribution Log-normal distribution Maximum entropy formalism (MEF) Nukiyama–Tanasawa distribution Number distribution function Probability density function (pdf) Representative diameter Root-normal distribution Rosin–Rammler distribution Upper limit distribution Volume distribution 


  1. 1.
    R. A. Mugele, H. D. Evans: Droplet Size Distributions in Sprays, Ind. Eng. Chem. 43(6), 1317–1324 (1951).CrossRefGoogle Scholar
  2. 2.
    W. A. Sowa: Interpreting Mean Drop Diameters Using Distribution Moments, Atomization Sprays 2, 1–15 (1992).Google Scholar
  3. 3.
    R. W. Sellens, T. A. Brzustowski: A Prediction of the Drop Size Distribution in a Spray from First Principles, Atomization Spray Technol. 1, 89–102 (1985).Google Scholar
  4. 4.
    X. Li, R. S. Tankin: Droplet Size Distribution: A Derivation of a Nukiyama–Tanasawa Type Distribution Function, Combust. Sci. Technol. 56, 65–76 (1987).CrossRefGoogle Scholar
  5. 5.
    S. D. Sovani, P. E. Sojka, Y. R. Sivathanu: Prediction of Drop Size Distributions from First Principles: The Influence of Fluctuations in Relative Velocity and Liquid Physical Properties, Atomization Sprays 9, 113–152 (1999).Google Scholar
  6. 6.
    S. D. Sovani, P. E. Sojka, Y. R. Sivathanu: Prediction of Drop Size Distributions from First Principles: Joint-PDF Effects, Atomization Sprays 10, 587–602 (2000).Google Scholar
  7. 7.
    Y. R. Sivathanu, J. P. Gore: A Discrete Probability Function Method for the Equation of Radiative Transfer, J. Quant. Spectrosc. Radiat. Transfer 49(3), 269–280 (1993).CrossRefGoogle Scholar
  8. 8.
    T. Paloposki: Drop Size Distributions in Liquid Sprays, Acta Polytechnica Scandinavica, Mech. Eng. Series 114, Helsinki, Finland (1994).Google Scholar
  9. 9.
    E. L. Crow, K. Shimizu: Lognormal Distributions: Theory and Applications, Marcel Dekker, New York (1988).zbMATHGoogle Scholar
  10. 10.
    R. W. Tate, W. R. Marshall Jr.: Atomization by Centrifugal Pressure Nozzles, Chem. Eng. Prog. 49, 169–174 (1953).Google Scholar
  11. 11.
    S. Nukiyama, Y. Tanasawa: Experiments on the Atomization of Liquids in an Air Stream. Report 3: On the Droplet-Size Distribution in an Atomized Jet. Trans. Soc. Mech. Eng. Jpn. 5, 62–67 (1939).Google Scholar
  12. 12.
    J. C. Bhatia, J. Dominick, F. Durst: Phase-Doppler-Anemometry and the Log-Hyperbolic Distribution Applied to Liquid Sprays, Part. Part. Syst. Char. 5, 153–164 (1988).CrossRefGoogle Scholar
  13. 13.
    J. C. Bhatia, F. Durst: Comparative Study of Some Probability Distributions Applied to Liquid Sprays, Part. Part. Syst. Char. 6, 151–162 (1989).CrossRefGoogle Scholar
  14. 14.
    J. C. Bhatia, F. Durst: Description of Sprays Using Joint Hyperbolic Distribution in Particle Size and Velocity, Combust. Flame 81, 203–218 (1990).CrossRefGoogle Scholar
  15. 15.
    L. Griffith: A Theory of the Size Distribution of Particles in a Comminuted System, Can. J. Res. 21(A), 57–64 (1943).MathSciNetGoogle Scholar
  16. 16.
    X. Li, R. S. Tankin: Derivation of Droplet Size Distribution in Sprays by Using Information Theory, Combust. Sci. Technol. 60, 345–357 (1988).CrossRefGoogle Scholar
  17. 17.
    M. Ahmadi, R. W. Sellens: A Simplified Maximum-Entropy-Based Drop Size Distribution, Atomization Sprays 3, 291–310 (1993).Google Scholar
  18. 18.
    C. W. M. van der Geld, H. Vermeer: Prediction of Drop Size Distributions in Sprays Using the Maximum Entropy Formalism: The Effect of Satellite Formation, Int. J. Multiphase Flow 20(2), 363–381 (1994).zbMATHCrossRefGoogle Scholar
  19. 19.
    J. Cousin, S. J. Yoon, C. Dumouchel: Coupling of Classical Linear Theory and Maximum Entropy Formalism for Prediction of Drop Size Distribution in Sprays: Application to Pressure-Swirl Atomizers, Atomization Sprays 6, 601–622 (1996).Google Scholar
  20. 20.
    C. Dumouchel: A New Formulation of the Maximum Entropy Formalism to Model Liquid Spray Drop-Size Distribution, Part. Part. Syst. Char. 23, 468–479 (2006).CrossRefGoogle Scholar
  21. 21.
    M. Lecompte, C. Dumouchel: On the Capability of the Generalized Gamma Function to Represent Spray Drop-Size Distribution, Part. Part. Syst. Char. 25, 154–167 (2008).CrossRefGoogle Scholar
  22. 22.
    X. Li, M. Li, H. Fu: Modeling the Initial Droplet Size Distribution in Sprays Based on the Maximization of Entropy Generation, Atomization Sprays 15, 295–321 (2005).CrossRefGoogle Scholar
  23. 23.
    E. Babinsky, P. E. Sojka: Modeling Drop Size Distributions from First Principles for Non-Newtonian Fluids, Atomization Sprays 11, 597–617 (2001).Google Scholar
  24. 24.
    S. Apte, M. Gorokhovski, P. Moin: LES of Atomizing Spray with Stochastic Modeling of Secondary Break-Up, Int. J. Multiphase Flow 29, 1503–1522 (2003).zbMATHCrossRefGoogle Scholar
  25. 25.
    M. Gorokhovski, V. Saveliev: Further Analyses of Kolmogorov’s Model of Breakup, Phys. Fluids 15, 184–192 (2003).CrossRefGoogle Scholar
  26. 26.
    N. Rimbert, O. Sero-Guillaume: Log-Stable Laws as Asymptotic Solutions to a Fragmentation Equation: Application to the Distribution of Droplet in a High-Weber-Number Spray, Phys. Rev. E: Stat. Nonlinear Soft Matter Phys. 69, 056316 (2004).CrossRefGoogle Scholar
  27. 27.
    I. Vinkovic, C. Agguire, S. Simoens, M. Gorokhovski: Large Eddy Simulations of Droplet Dispersion for Inhomogeneous Turbulent Wall Flow, Int. J. Multiphase Flow 32, 344–364 (2006).zbMATHCrossRefGoogle Scholar
  28. 28.
    M. Gorokhovski, M. Herrman: Modeling Primary Atomization, Annu. Rev. Fluid Mech. 40, 343–366 (2008).CrossRefGoogle Scholar
  29. 29.
    H. F. Liu, X. Gong, W. F. Li, F. C. Wang, Z. H. Yu: Prediction of Droplet Size Distribution in Sprays of Prefilming Air-Blast Atomizers, Chem. Eng. J. 61, 1741–1747 (2006).CrossRefGoogle Scholar
  30. 30.
    W. X. Zhou, T. J. Zhao, T. Wu, Z. H. Yu: Application of Fractal Geometry to Atomization Process, Chem. Eng. J. 78, 193–197 (2000).CrossRefGoogle Scholar

Copyright information

© Springer US 2011

Authors and Affiliations

  1. 1.Maurice J. Zucrow Laboratories, School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA

Personalised recommendations