Transport Phenomena in Functional Droplets

  • Abhishek Saha
  • P. Deepu
  • Saptarshi Basu
Part of the Energy, Environment, and Sustainability book series (ENENSU)


Liquids containing functional materials are often used in spray systems either to generate surface coating where droplets land on solid substrates or to prepare crystalline and amorphous particles where droplets are dried in-flight and then collected for mass production. Most of these applications involve spraying droplets into a hot environment, whose temperature and velocity vary depending on the application. This allows the liquid to vaporize leading to precipitation and pyrolization of the functional materials, which subsequently attain its final form before being collected or impacted with the substrate. In this chapter, we shall discuss the transport processes inside drying droplets containing functional materials to identify some critical behavior and characteristics. Fundamentally, the life of a sprayed functional droplet is influenced by several competing physical processes such as reaction kinetics, precipitation dynamics, droplet hydrodynamics, and as such a proper balance between the associated characteristic timescales is necessary to achieve desired final product. We shall discuss a large group of experimental and numerical studies performed on single droplets, either levitated or convected, that paved the way to our current understanding. By reviewing these studies on single droplet, the goal of this chapter is to highlight the importance of the thermo-physical phenomena inside the droplets for spray processes involving functional liquids.



Abhishek Saha acknowledges support from US National Science Foundation during preparation of the chapter. P. Deepu gratefully acknowledges financial support by the Indian Institute of Technology, Patna, India. Saptarshi Basu gratefully acknowledges the funding from DST Swarnajayanti Fellowship.


  1. Abramzon B, Sirignano WA (1989) Droplet vaporization model for spray combustion calculations. Int J Heat Mass Transf 12(9):1605–1648CrossRefGoogle Scholar
  2. Basu S, Cetegen BM (2007) Modeling of thermo-physical processes in liquid ceramic precursor droplets injected into a plasma jet. Int J Heat Mass Transf 50:3278–3290CrossRefGoogle Scholar
  3. Basu S, Cetegen BM (2008a) Modeling of liquid ceramic precursor droplets in a high velocity oxy-fuel flame jet. Acta Mater 56:2750–2759CrossRefGoogle Scholar
  4. Basu S, Cetegen BM (2008b) Modeling of thermophysical processes in liquid ceramic precursor droplets heated by monochromatic irradiation. J Heat Transf 130(7):071501CrossRefGoogle Scholar
  5. Basu S, Jordan EH, Cetegen BM (2008) Fluid mechanics and heat transfer of liquid precursor droplets injected into high-temperature plasmas. J Therm Spray Eng 17:60–72CrossRefGoogle Scholar
  6. Basu S, Saha A, Kumar R (2013a) Criteria for thermally induced atomization and catastrophic breakup of acoustically levitated droplet. Int J Heat Mass Transf 59:316–327CrossRefGoogle Scholar
  7. Basu S, Tijerino E, Kumar R (2013b) Insight into morphology changes of nanoparticle laden droplets in acoustic field. Appl Phys Lett 102(14):141602CrossRefGoogle Scholar
  8. Bremer LG, Walstra P, van Vliet T (1995) Estimations of the aggregation time of various colloidal systems. Colloids Surf, A 99(2):121–127CrossRefGoogle Scholar
  9. Clift R, Grace JR, Weber ME (1978) Bubbles drops and particles. Academic Press, New YorkGoogle Scholar
  10. Deepu P, Basu S, Kumar R (2013) Vaporization dynamics of functional droplets in a hot laminar air jet. Int J Heat Mass Transf 56(1):69–79CrossRefGoogle Scholar
  11. Hubbard HGL, Denny VE, Mills AF (1975) Droplet evaporation: effects of transients and variable properties. Int J Heat Mass Transf 18:1003–1008CrossRefGoogle Scholar
  12. Kumar R, Tijerino E, Saha A, Basu S (2010) Structural morphology of acoustically levitated and heated nanosilica droplet. Appl Phys Lett 97(12):123106CrossRefGoogle Scholar
  13. Lamb H (1993) Hydrodynamics. Cambridge University Press, New YorkzbMATHGoogle Scholar
  14. Law CK (1982) Recent advances in droplet vaporization and combustion. Prog Energy Combust Sci 8:171–201CrossRefGoogle Scholar
  15. Lierke EG (2002) Deformation and displacement of liquid drops in an optimized acoustic standing wave levitator. Acta Acustica United Acustica 88(2):206–217Google Scholar
  16. Maqua C, Castanet G, Lemoine F (2008) Bicomponent droplets evaporation: temperature measurements and modeling. Fuel 87(13–14):2932–2942CrossRefGoogle Scholar
  17. Messing GL, Zhang SC, Jayanthi GV (1993) Ceramic powder synthesis by spray pyrolysis. J Am Ceram Soc 76:2707CrossRefGoogle Scholar
  18. Miglani A, Basu S (2015) Sphere to ring morphological trans-formation in drying nanofluid droplets in a contact-free environment. Soft Matter 11(11):2268–2278CrossRefGoogle Scholar
  19. Ozturk A, Cetegen BM (2004) Modeling of plasma assisted formation of precipitates in zirconium containing liquid precursor droplets. Mater Sci Eng A 384:331–351CrossRefGoogle Scholar
  20. Ozturk A, Cetegen BM (2005a) Morphology of ceramic particulates formed in a premixed oxygen/acetylene flame from liquid precursor droplets. Acta Mater 53:2531–2544CrossRefGoogle Scholar
  21. Ozturk A, Cetegen BM (2005b) Experiments on ceramic formation from liquid precursor spray axially injected into an oxy-acetylene flame. Acta Mater 53:5203–5211CrossRefGoogle Scholar
  22. Ozturk A, Cetegen BM (2005c) Modeling of axially and transversely injected precursor droplets into a plasma environment. Int J Heat Mass Transf 48:4367–4383CrossRefGoogle Scholar
  23. Ozturk A, Cetegen BM (2006) Modeling of precipitate formation in precursor droplets injected axially into an oxygen/acetylene combustion flame. Mater Sci Eng A 422:163–175CrossRefGoogle Scholar
  24. Pathak B, Basu S (2015) Phenomenology and control of buck-ling dynamics in multicomponent colloidal droplets. J Appl Phys 117(24):244901CrossRefGoogle Scholar
  25. Pathak B, Basu S (2016) Modulation of buckling dynamics in nanoparticle laden droplets using external heating. Langmuir 32(11):2591–2600CrossRefGoogle Scholar
  26. Renksizbulut M, Yuen MC (1983) Numerical study of droplet evaporation in a high-temperature stream. J Heat Transf 105:389–397CrossRefGoogle Scholar
  27. Saha A, Basu S, Kumar R (2012a) Effects of acoustic-streaming-induced flow in evaporating nanofluid droplets. J Fluid Mech 692:207–219CrossRefGoogle Scholar
  28. Saha A, Basu S, Kumar R (2012b) Particle image velocimetry and infrared thermography in a levitated droplet with nanosilica suspensions. Exp Fluids 52(3):795–807CrossRefGoogle Scholar
  29. Saha A, Basu S, Kumar R (2012c) Scaling analysis: equivalence of convective and radiative heating of levitated droplet. Appl Phys Lett 100(3):204104CrossRefGoogle Scholar
  30. Saha A, Basu S, Suryanarayan C, Kumar R (2010a) Experimental analysis of thermo-physical processes in acoustically levitated heated droplets. Int J Heat Mass Transf 53:5663–5674CrossRefGoogle Scholar
  31. Saha A, Kumar R, Basu S (2010b) Infrared thermography and numerical study of vaporization characteristics of pure and blended bio-fuel droplets. Int J Heat Mass Transf 53:3862–3873CrossRefGoogle Scholar
  32. Saha A, Seal S, Cetegen BM, Jordan E, Ozturk A, Basu S (2008) Thermo-physical processes in cerium nitrate precursor droplets injected into high temperature plasma. Surf Coat Technol 203:2081–2091CrossRefGoogle Scholar
  33. Sazhin SS (2006) Advanced models of fuel droplet heating and evaporation. Prog Energy Combust Sci 32:162–214CrossRefGoogle Scholar
  34. Semenov SY, Cetegen BM (2001) Spectroscopic temperature measurements in direct current arc plasma jets used in thermal spray processing of materials. J Therm Spray Technol 10(2):326–336CrossRefGoogle Scholar
  35. Shaikeea A, Basu S, Hatte S, Bansal L (2016) Insights into vapor-mediated interactions in a nanocolloidal droplet system: evaporation dynamics and affects on self-assembly topologies on macro-to microscales. Langmuir 32(40):10334–10343CrossRefGoogle Scholar
  36. Sirignano WA (2010) Fluid dynamics and transport of droplets and sprays, 2nd edn. Cambridge University pressGoogle Scholar
  37. Sirignano WA, Wu G (2008) Multicomponent-liquid-fuel vaporization with complex configuration. Int J Heat Mass Transf 51:4759–4774CrossRefGoogle Scholar
  38. Sugiyama Y, Larsen RJ, Kim JW, Weitz DA (2006) Buckling and crumpling of drying droplets of colloid—polymer sus-pensions. Langmuir 22(14):6024–6030CrossRefGoogle Scholar
  39. Smoulochowski M (1917) Versuch einer mathematichen theorie der koagulationskinetic kolloider losungen. Z Phys Chem 92:129–168Google Scholar
  40. Tijerino E, Basu S, Kumar R (2013) Nanoparticle agglomeration in an evaporating levitated droplet for different acoustic amplitudes. J Appl Phys 113(3):034307CrossRefGoogle Scholar
  41. Tsapis N, Dufresne ER, Sinha SS, Riera CS, Hutchinson JW, Mahadevan L, Weitz DA (2005) Onset of buckling in drying droplets of colloidal suspensions. Phys Rev Lett 94(1):018302CrossRefGoogle Scholar
  42. Van Wylen GJ, Sonntag RE (1986) Fundamentals of classical thermodynamics. WileyGoogle Scholar
  43. Yarin AL, Brenn G, Kastner O, Rensink D, Tropea C (1999) Evaporation of acoustically levitated droplets. J Fluid Mech 399:151–204CrossRefGoogle Scholar
  44. Yuen MC, Chen LW (1976) On drag of evaporating liquid droplets. Combust Sci Technol 14(1976):147–154CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA
  2. 2.Department of Mechanical EngineeringIndian Institute of Technology PatnaBihtaIndia
  3. 3.Department of Mechanical EngineeringIndian Institute of ScienceBangaloreIndia

Personalised recommendations