Novel Cooling Rate Correlations in Molten Metal Gas Atomization

  • N. Ciftci
  • N. Ellendt
  • G. Coulthard
  • E. Soares Barreto
  • L. Mädler
  • V. UhlenwinkelEmail author


The cooling rate in molten metal gas atomization is the key determining factor for the microstructure of metal powders. Mathematical expressions for cooling rates often include the melt droplet diameter and a pre-exponential factor describing the materials and gas properties. A new mathematical cooling rate correlation for rapidly solidified melt droplets is proposed based on heat flow considerations during gas atomization. The model approach takes process conditions such as gas-to-melt mass flow ratio and the initial gas temperature into account. The mathematical formulation was experimentally developed using secondary dendrite arm spacing method. For this purpose, a Cu-6wt pct Sn alloy was atomized with close-coupled (CCA) and free-fall atomization (FFA). A novel approach was made to predict the pre-exponential factor that allows the transferability to other materials. Our correlation for the cooling rate and the pre-exponential factor was validated by experimental data from the literature. The novel correlation type is valid for two different atomizing systems (FFA and CCA), suggesting that it may be applicable to entirely different gas atomization systems.



Constant to calculate the cooling rate through SDAS


Model parameters


Specific heat capacity of the gas, J kg−1 K−1

\( c_{{{\text{p}}_{\text{L}} }} \)

Specific heat capacity of the liquid melt droplet, J kg−1 K−1

\( c_{{{\text{p}}_{\text{S}} }} \)

Specific heat capacity of the solid melt droplet, J kg−1 K−1


Cooling rate, K s−1


Nozzle outlet diameter, m


Droplet diameter, m


Mass median particle diameter, m


Solid fraction


Heat transfer coefficient, W m−2 K−1


Thermal conductivity of the gas, W m−1 K−1


Thermal conductivity of the melt droplet, W m−1 K−1


Distance between first adjacent arm to the last, m


Constant to calculate the SDAS

\( \dot{m}_{G} \)

Gas mass flow rate, kg s−1

\( \dot{m}_{L} \)

Melt mass flow rate, kg s−1


Constant to calculate the cooling rate through SDAS


Number of counted arms to calculate SDAS, #


Atomization pressure, MPa


Heat flux, W m−2


r-axis, m




Ambient gas temperature (293 K)


Gas temperature, K

\( T_{{G_{0} }} \)

Initial gas temperature, K


Liquidus temperature, K


Temperature of the melt droplet at solid fraction = 0.5, K


Melt temperature, K


Solidus temperature, K


Droplet velocity, m s−1


Gas velocity, m s−1


z-axis, m

Greek Symbols


Latent heat of fusion, J kg−1


Solidification time, s


Temperature difference between melt droplet and surrounding gas, K


Superheated melt temperature, K


Relative velocity m s−1


Dynamic viscosity of the gas, N s m−2


Primary dendrite arm spacing, m


Secondary dendrite arm spacing, m


Density of the gas, kg m−3


Density of the melt droplet at solid fraction = 0.5 kg m−3


Geometric standard deviation


Materials and gas properties



Biot number


Close-coupled atomization


Free-fall atomization


Gas-to-melt mass flow ratio


Hot gas atomization


Nusselt number


Prandtl number


Reynolds number


Atomization at ambient temperature


Secondary dendrite arm spacing, m



Financial support of subprojects S01 ‘Process to Generate Rapidly Cooled, Homogenous Samples’ and U01 ‘Generation of spherical microscopic samples with single droplet solidification’ of the Collaborative Research Center SFB 1232 “Farbige Zustände” by the German Research Foundation (DFG) is gratefully acknowledged. We also thank F. Peschel, R. Lehmann, S. Evers for their experimental support. Additionally, the authors wish to thank F. Mostaghimi, J. Eitzen, C. O’Fuarthain for useful discussions and their helpful comments on this work.


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Copyright information

© The Minerals, Metals & Materials Society and ASM International 2019

Authors and Affiliations

  • N. Ciftci
    • 2
  • N. Ellendt
    • 1
    • 2
  • G. Coulthard
    • 1
    • 2
  • E. Soares Barreto
    • 1
    • 2
  • L. Mädler
    • 1
    • 2
  • V. Uhlenwinkel
    • 1
    • 2
    Email author
  1. 1.Faculty of Production EngineeringUniversity of BremenBremenGermany
  2. 2.Leibniz Institute for Materials Engineering IWTBremenGermany

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