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Numerical analysis of the deformation and solidification of a single droplet impinging onto a flat substrate

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Abstract

An existing model has been modified to explore the deformation and solidification of a single droplet impinging on a substrate. The modification accounts for possible solid fraction of material at impact. Numerical results predict that the kinetic energy dominates the process at impinging velocities greater than about 100 m s−1. In addition, the thermal diffusivity of the solidifying material controls the process, but the temperature of the substrate relative to the melting temperature of the material must be considered when comparing materials. It is believed that droplets solidifying into thinner, wider discs would reduce porosity; therefore, dense materials accelerated to high speed would solidify into masses with the highest bulk density.

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Abbreviations

a l :

Thermal diffusivity of the liquid (cm2 s−1)

a s :

Thermal diffusivity of the solid (cm2 s−1)

b :

Thickness of the molten metal (cm)

c l :

Specific heat of the liquid (J g−1 K−1)

c s :

Specific heat of the solid (J g−1 K−1)

D :

Diameter of the droplet (D = 2R 0) (cm)

E k :

Kinetic energy (J)

E p :

Potential energy (J)

L f :

Work of the friction forces (W)

Δh :

Enthalpy of fusion (J g−1)

k l :

Thermal conductivity of the liquid (W cm−1K−1)

k s :

Thermal conductivity of the solid (W cm−1 K−1)

R :

Radius of the solidified disc (cm)

t * :

Real time (s)

τ * :

Real time from solidification (s)

T l :

Temperature of the molten metal (K)

T m :

Melting temperature (K)

T s :

Temperature of the substrate (K)

V s :

Volume of the solid (cm3)

y :

Thickness of the solidified layer (cm)

y o :

Thickness of the solidified layer at impact (cm)

μ:

Viscosity of the molten metal (mN s m−2)

χ :

Mass fraction of the solid at impact

ϱl :

Density of the molten metal (g cm−3)

ϱs :

Density of the solid metal (g cm−3)

σ:

Surface tension of the molten metal (mN m−1)

ω:

Velocity of the liquid droplet at impact (cm s−1)

t :

Dimensionless time

τ:

Dimensionless time from solidification

T o :

Dimensionless temperature of the substrate

T p :

Dimensionless temperature of the droplet

φ:

Dimensionless thickness

ξ:

Dimensionless radius

Pe:

Peclet number

Re:

Reynolds number

We:

Weber number

κ:

Constant (Equation 13)

ɛ:

Constant (=0.5)

U :

Freezing constant (Equation 1)

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, 92717, Irvine, CA, USA

    C. San Marchi, H. Liu, E. J. Lavernia & R. H. Rangel

  2. Electroplasma Inc., 16842 Milliken Ave., 92714, Irvine, CA, USA

    A. Sickinger & E. Muehlberger

Authors
  1. C. San Marchi
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  2. H. Liu
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  3. E. J. Lavernia
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  4. R. H. Rangel
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  5. A. Sickinger
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  6. E. Muehlberger
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Marchi, C.S., Liu, H., Lavernia, E.J. et al. Numerical analysis of the deformation and solidification of a single droplet impinging onto a flat substrate. JOURNAL OF MATERIALS SCIENCE 28, 3313–3321 (1993). https://doi.org/10.1007/BF00354253

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