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Effect of processing conditions on drop behavior in an electromagnetic levitator

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Abstract

A mathematical model, which can predict the electromagnetic and temperature fields and also the shape of a molten silicon drop, has been developed for the improvement and determination of the optimal processing conditions in an electromagnetic levitation (EML) device recently developed to accurately measure the thermophysical properties of molten silicon. As a result, it was found that there exists an unstable state in which the drop was squeezed and then might be collapsed due to the electromagnetic force acting on the sample’s surface. Also, the results suggest that the shape of the molten material is not necessarily a perfect sphere under the microgravity environment because of the electromagnetic force due to the heating coil current.

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Abbreviations

A′:

magnetic vector potential

B′:

magnetic flux density

A φ :

dimensionless azimuthal component of vector potential, A φ ′/(μ′0 J′ref r′ 2ref )

Bo g :

Bond number, (ρ′g′r′ 2ref )/γ′

Bo m :

electromagnetic Bond number, (μ′0 J′ref r′ 3ref )/γ′

B S :

dimensionless magnetic intensity tangential to the surface of molten sample, B′ S /(μ′0 J′ref r′ref)

f :

dimensionless radial distance, f′/r′ref

2H :

dimensionless mean curvature, 2H′r′ref

h :

dimensionless relative position between coils and sample, h′/r′ref

J :

dimensionless current density, J′/J′ ref

k :

dimensionless thermal conductivity, k′/k′ ref

N A :

dimensionless number defined by μ′0 θ′ f σ′ ref r′ 2ref

N Q :

dimensionless number defined by (σ′ref θ′ 2 f ′ 20 J′ 2ref r′ 2ref )/(k′ref T′m)

n :

dimensionless normal direction, n′/r′ ref

Ra:

Radiation number, (ε′ σ′ref T′ 3 m r′ref)/k′ref

r :

dimensionless radial coordinate, r′/r′ ref

T :

dimensionless temperature, T′/T′ m

T′ m :

melting temperature of silicon

t′:

time

z :

dimensionless axial coordinate, z′/r′ ref

α :

dimensionless electric conductivity, σ′/σ′ ref

γ′:

surface tension

ε′:

emissivity

ϑ′:

polar angle

λ :

dimensionless reference pressure difference, (r′ref ΔP′)/γ′

μ′0 :

magnetic permeability

σ′:

electric conductivity

ρ′:

density

ω′:

angular frequency

C :

coil

a :

environment

f :

frequency

ref:

reference value

φ:

azimuthal component

′:

dimensional value

*:

complex conjugate

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Authors and Affiliations

  1. the Institute for Chemical Reaction Science, Tohoku University, 980, Sendai, Japan

    S. H. Hahn (Postdoctoral Fellow), Y. Sakai (Student), T. Tsukada (Associate Professor) & M. Hozawa (Professor)

  2. the Institute for Advanced Materials Study, Kyushu University, 816, Kasuga, Japan

    M. Imaishi (Professor)

  3. the Japan Space Utilization Promotion Center, 169, Tokyo, Japan

    S. Kitagawa (Senior Research Engineer)

Authors
  1. S. H. Hahn
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  2. Y. Sakai
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  3. T. Tsukada
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  4. M. Hozawa
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  5. M. Imaishi
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  6. S. Kitagawa
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Hahn, S.H., Sakai, Y., Tsukada, T. et al. Effect of processing conditions on drop behavior in an electromagnetic levitator. Metall Mater Trans B 29, 223–228 (1998). https://doi.org/10.1007/s11663-998-0025-y

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  • DOI: https://doi.org/10.1007/s11663-998-0025-y

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