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Atomization and Sprays
Fator do impacto: 1.737 FI de cinco anos: 1.518 SJR: 0.814 SNIP: 1.18 CiteScore™: 2.2

ISSN Imprimir: 1044-5110
ISSN On-line: 1936-2684

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Atomization and Sprays

DOI: 10.1615/AtomizSpr.2020031712
pages 913-935


Walter Oswald
Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany
Lutz Gödeke
Fluid Mechanics, Biochemical and Chemical Engineering, TU Dortmund, Dortmund, Germany
Peter Ehrhard
Fluid Mechanics, Biochemical and Chemical Engineering, TU Dortmund, Dortmund, Germany
Norbert Willenbacher
Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Institute of Technology, Karlsruhe, Germany


High-speed rotary bell atomization is the key coating technology in the automotive industry. We investigated the atomization behavior of shear-thinning fluids emphasizing the contributions of elon-gational flow resistance and the presence of anisotropic particles. Mixtures of two commercial acrylic thickener solutions allowed for a variation of elongational relaxation time λe by almost two orders of magnitude. Suspending different fractions of highly anisotropic, flake-shaped particles in such thickener solutions resulted in a fourfold increase of λe. In both series of model fluids, shear viscosity remained essentially unchanged. Light-scattering techniques were used to determine the droplet size. The length of the ligaments formed at the bell edge during an important intermediate step preceding droplet formation was obtained from high-speed videos in combination with a customized image analysis code. For the pure thickener solutions, an increase in the elongational relaxation time resulted in an increase in the ligament length but did not affect the droplet size, since drops were not only formed from primary ligaments but were also formed after further fragmentation downstream. Suspended glass flakes accelerated ligament disintegration despite the increasing λe but, again, did not affect droplet size. The flake-shaped particles appear to act as predetermined breaking points disturbing the flow inside the ligaments. This phenomenon was verified using an industrial automotive basecoat including different amounts of aluminum flakes. These new insights regarding the high-speed atomization of complex fluids may support the targeted formulation of coating fluids.


  1. Ahmed, M. and Youssef, M.S., Characteristics of Mean Droplet Size Produced by Spinning Disk Atomizers, J. Fluids Eng., vol. 134, no. 7, p. 071103, 2012.

  2. Albrecht, H.-E., Borys, M., Damaschke, N., and Tropea, C., Laser Doppler and Phase Doppler Measurement Techniques, Berlin: Springer, 2003.

  3. Batchelor, G.K., The Stress Generated in a Non-Dilute Suspension of Elongated Particles by Pure Straining Motion, J. Fluid Mech, vol. 46, no. 4, pp. 813-829,1971.

  4. Bayvel, L. and Orzechowski, Z., Liquid Atomization, Washington DC: Taylor & Francis, 1993.

  5. Bazilevsky, A.V., Entov, V.M., and Rozhkov, A.N., Breakup of an Oldroyd Liquid Bridge as a Method for Testing the Rheological Properties of Polymer Solutions, Polym. Sci., vol. 43, no. 7, pp. 716-726,2001.

  6. Bizjan, B., Sirok, B., Hocevar, M., and Orbanic, A., Ligament-Type Liquid Disintegration by a Spinning Wheel, Chem. Eng. Sci., vol. 116, pp. 172-182, 2014a.

  7. Bizjan, B., Sirok, B., Hocevar, M., and Orbanic, A., Liquid Ligament Formation Dynamics on a Spinning Wheel, Chem. Eng. Sci., vol. 119, pp. 187-198, 2014b.

  8. Boize, L.M. and Dombrowski, N., The Atomization Characteristics of a Spinning Disc Ultra-Low Volume Applicator, J. Agri. Eng. Res., vol. 21, no. 1, pp. 87-99, 1976.

  9. Bruin, S., Velocity Distribution in a Liquid Film Flowing over a Rotating Conical Surface, Chem. Eng. Sci, vol. 24, no. 11, pp. 1647-1654, 1969.

  10. Burns, J., Ramshaw, C., and Jachuck, R., Measurement of Liquid Film Thickness and the Determination of Spin-Up Radius on a Rotating Disc Using an Electrical Resistance Technique, Chem. Eng. Sci, vol. 58, no. 11, pp. 2245-2253,2003.

  11. Charwat, A.F., Kelly, R.E., and Gazley, C., The Flow and Stability of Thin Liquid Films on a Rotating Disk, J. Fluid Mech, vol. 53, no. 2, pp. 227-255, 1972.

  12. Corbeels, P.L., Senser, D.W., and Lefebvre, A.H., Atomization Characteristics of a High-Speed Rotary-Bell Paint Applicator, Atomization Sprays, vol. 2, no. 2, pp. 87-99, 1992.

  13. Dexter, R.W., Measurement of Extensional Viscosity of Polymer Solutions and Its Effects on Atomization from a Spray Nozzle, Atomization Sprays, vol. 6, no. 2, pp. 167-191, 1996.

  14. Einstein, A., Eine Neue Bestimmung der Molekuldimensionen, Ann. Phys., vol. 324, no. 2, pp. 289-306, 1906.

  15. Ellwood, K.R.J., Tardiff, J.L., and Alaie, S.M., A Simplified Analysis Method for Correlating Rotary Atomizer Performance on Droplet Size and Coating Appearance, J. Coatings Technol. Res., vol. 11, no. 3, pp. 303-309,2014.

  16. Espig, H. and Hoyle, R., Waves in a Thin Liquid Layer on a Rotating Disk, J. Fluid Mech., vol. 22, no. 4, pp. 671-677,1965.

  17. Frost, A.R., Rotary Atomization in the Ligament Formation Mode, J. Agri. Eng. Res., vol. 26, no. 1, pp. 63-78, 1981.

  18. Gramlich, S. and Piesche, M., Numerical and Experimental Investigations on the Breakup of Particle Laden Liquid Jets in the Centrifugal Field, Chem. Eng. Sci., vol. 84, pp. 408-416, 2012.

  19. Hewitt, A., Droplet Size Spectra Produced by Air-Assisted Atomizers, J. Aerosol Sci., vol. 24, no. 2, pp. 155-162, 1993.

  20. Hinch, E.J. and Leal, L.G., The Effect of Brownian Motion on the Rheological Properties of a Suspension of Non-Spherical Particles, J. Fluid Mech, vol. 52, no. 4, pp. 683-712,1972.

  21. Hinze, J. andMilborn, H., Atomization of Liquids by Means of a Rotating Cup, ASMEJ. Appl. Mech., vol. 17, pp. 145-153, 1950.

  22. Horn, A.F. and Merrill, E.W., Midpoint Scission of Macromolecules in Dilute Solution in Turbulent Flow, Nature, vol. 312, no. 5990, pp. 140-141, 1984.

  23. Jones, D.M., Walters, K., and Williams, P.R., On the Extensional Viscosity of Mobile Polymer Solutions, Rheol. Acta, vol. 26, no. 1, pp. 20-30, 1987.

  24. Kamiya, T. and Kayano, A., Film-Type Disintegration by Rotating Disk, J. Chem. Eng. Jpn., vol. 5, no. 2, pp. 174-182,1972.

  25. Keller, A. and Odell, J.A., The Extensibility of Macromolecules in Solution: A New Focus for Macro-molecular Science, ColloidPolym. Sci., vol. 263, no. 3, pp. 181-201,1985.

  26. Kheirandish, S., Gubaydullin, I., and Willenbacher, N., Shear and Elongational Flow Behavior of Acrylic Thickener Solutions. Part II: Effect of Gel Content, Rheol. Acta, vol. 48, no. 4, pp. 397-407,2009.

  27. Kheirandish, S., Guybaidullin, I., Wohlleben, W., and Willenbacher, N., Shear and Elongational Flow Behavior of Acrylic Thickener Solutions, Rheol. Acta, vol. 47, no. 9, pp. 999-1013,2008.

  28. Kizior, T.E. and Seyer, F.A., Axial Stress in Elongational Flow of Fiber Suspension, Trans. Soc. Rheol., vol. 18, no. 2, pp. 271-285,1974.

  29. Kuhnhenn, M., Joensen, T.V., Reck, M., Roisman, I.V., and Tropea, C., Study of the Internal Flow in a Rotary Atomizer and Its Influence on the Properties of the Resulting Spray, Int. J. Multiphase Flow, vol. 100, pp. 30-40,2018.

  30. Leshev, I. and Peev, G., Film Flow on a Horizontal Rotating Disk, Chem. Eng. Process. Process Intensif., vol. 42, no. 11, pp. 925-929, 2003.

  31. Lin, S.P. and Reitz, R.D., Drop and Spray Formation From a Liquid Jet, Annu. Rev. FluidMech., vol. 30, no. 1,pp. 85-105,1998.

  32. Liu, Y., Lai, M., and Im, K., An Experimental Investigation of Spray Transfer Processes in an Electrostatic Rotating Bell Applicator, SAE Tech. Papers, vol. 107, no. 5, pp. 1235-1243, 1999.

  33. Liu, J., Yu, Q., and Guo, Q., Experimental Investigation of Liquid Disintegration by Rotary Cups, Chem. Eng. Sci., vol. 73, pp. 44-50, 2012a.

  34. Liu, J., Yu, Q., Li, P., and Du, W., Cold Experiments on Ligament Formation for Blast Furnace Slag Granulation, Appl. Therm. Eng., vol. 40, pp. 351-357, 2012b.

  35. Mansour, A. and Chigier, N., Air-Blast Atomization of Non-Newtonian Liquids, J. Non-Newtonian Fluid Mech., vol. 58, pp. 161-194,1995.

  36. Mantripragada, V.T. and Sarkar, S., Prediction of Drop Size from Liquid Film Thickness during Rotary Disc Atomization Process, Chem. Eng. Sci., vol. 158, pp. 227-233,2017.

  37. Matsumoto, S., Saito, K., and Takashima, Y., The Thickness of Aviscous Liquid Film on a Rotating Disk, J. Chem. Eng. Jpn., vol. 6, no. 6, pp. 503-507, 1974.

  38. Matsumoto, S., Takashima, Y., Kamlya, T., Kayano, A., and Ohta, Y., Film Thickness of a Bingham Liquid on a Rotating Disk, Ind. Eng. Chem. Fundam., vol. 21, no. 3, pp. 198-202, 1982.

  39. McKinley, G.H. and Tripathi, A., How to Extract the Newtonian Viscosity from Capillary Breakup Measurements in a Filament Rheometer, J. Rheol., vol. 44, no. 3, pp. 653-670, 2000.

  40. Mescher, A. and Walzel, P., Breakup of Stretched Liquid Threads at Low Gas Relative Velocities - Comparison of the Laminar Rotary Atomization to the Gravity Condition, ILASS-Europe 2010, Proc. of 23rd Annual Conf. on Liquid Atomization and Spray Systems, Brno, Czech Republic, 2010.

  41. Mewis, J. and Metzner, A.B., The Rheological Properties of Suspensions of Fibres in Newtonian Fluids Subjected to Extensional Deformations, J. Fluid Mech., vol. 62, no. 3, pp. 593-600, 1974.

  42. Mulhem, B., Schulte, G., and Fritsching, U., Solid-Liquid Separation in Suspension Atomization, Chem. Eng. Sci., vol. 61, no. 8, pp. 2582-2589,2006.

  43. Nguyen, T.Q. and Kausch, H.-H., Macromolecules: Synthesis, Order and Advanced Properties, Macro-molecules: Synthesis, Order and Advanced Properties, Berlin: Springer, pp. 73-182, 2006.

  44. Ochowiak, M., Broniarz-Press, L., Rozanska, S., and Rozanski, J., The Effect of Extensional Viscosity on the Effervescent Atomization of Polyacrylamide Solutions, J. Ind. Eng. Chem.., vol. 18, no. 6, pp. 2028-2035,2012.

  45. Ochowiak, M., Broniarz-Press, L., and Woziwodzki, S., The Analysis of Silica Suspensions Atomization, Int. J. Heat Fluid Flow, vol. 32, no. 6, pp. 1208-1215, 2011.

  46. Ogasawara, S., Daikoku, M., Shirota, M., Inamura, T., Saito, Y., Yasumara, K., Shoji, M., Aoki, H., and Miura, T., Liquid Atomization Using a Rotary Bell Cup Atomizer, J. Fluid Sci. Technol, vol. 5, no. 3, pp. 464-474,2010.

  47. Oswald, W., Godeke, L., Ehrhard, P., and Willenbacher, N., Effect of Elongational Flow Behavior on Ligament Disintegration and Drop Formation by Means of a High-Speed Rotary Bell Atomizer, ICLASS 2018, Proc. of 14th Triennial Int. Conf. on Liquid Atomization and Spray Systems, Chicago, 2018.

  48. Oswald, W. and Willenbacher, N., Controlling the Elongational Flow Behavior of Low Viscosity Complex Fluids at Constant Shear Viscosity, Rheol. Acta, vol. 58, no. 10, pp. 687-698, 2019.

  49. Ryley, D.J., Analysis of a Polydisperse Aqueous Spray from a High-Speed Spinning Disk Atomizer, Br. J. Appl. Phys, vol. 10, no. 4, pp. 180-186, 1959.

  50. Shirota, M., Hatayama, Y., Haneda, T., Inamura, T., Daikoku, M., Saito, Y., and Aoki, H., Formation and Breakup of Ligaments from a Rotary Bell Cup Atomizer, ICLASS 2012, Proc. of 12th Triennial Int. Conf. on Liquid Atomization and Spray Systems, Heidelberg, 2012.

  51. Soma, T., Katayama, T., Tanimoto, J., Saito, Y., Matsushita, Y., Aoki, H., Nakai, D., Kitamura, G., Miura, M., Asakawa, T., Daikoku, M., Haneda, T., Hatayama, Y., Shirota, M., and Inamura, T., Liquid Film Flow on a High Speed Rotary Bell-Cup Atomizer, Int. J. Multiphase Flow, vol. 70, pp. 96-103, 2015.

  52. Stelter, M. and Brenn, G., Elongational Rheometry for the Characterization of Viscoelastic Liquids, Chem. Eng. Technol, vol. 25, no. 1, pp. 30-35,2002.

  53. Thompson, J.C. and Rothstein, J.P., The Atomization of Viscoelastic Fluids in Flat-Fan and Hollow-Cone Spray Nozzles, J. Non-Newtonian Fluid Mech., vol. 147, nos. 1-2, pp. 11-22, 2007.

  54. Trouton, F.T., On the Coefficient of Viscous Traction and Its Relation to that of Viscosity, Proc. R. Soc. A, vol. 77, no. 519, pp. 426-440, 1906.

  55. Weinberger, C.B. and Goddard, J.D., Extensional Flow Behavior of Polymer Solutions and Particle Suspensions in a Spinning Motion, Int. J. Multiphase Flow, vol. 1, no. 3, pp. 465-486, 1974.

  56. Williams, P.A., English, R.J., Blanchard, R.L., Rose, S.A., Lyons, L., and Whitehead, M., The Influence of the Extensional Viscosity of Very Low Concentrations of High Molecular Mass Water-Soluble Polymers on Atomisation and Droplet Impact, Pest Man. Sci., vol. 64, no. 5, pp. 497-504, 2008.

  57. Xing, L.L., Glass, J.E., and Fernando, R.H., Parameters Influencing the Spray Behavior of Waterborne Coatings, J. Coatings Technol., vol. 71, no. 3, pp. 37-50, 1999.

  58. Yarin, A.L., Strong Flows of Polymeric Liquids, J. Non-Newtonian Fluid Mech., vol. 37, nos. 2-3, pp. 113-138, 1990.

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