2nd Sino-German Workshop on

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FREE SURFACE INSTABILITIES PRODUCED BY
HIGH-FREQUENCY MAGNETIC FIELDS
Christian KarcherTechnische Universität Ilmenau

• Motivation
• Model Experiments, Analytical Model
• Results
• Conculsions
• Proposals for Collaboration within Common Project

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Motivation Electromagnetic Shaping
Forming of a stable dome during electron beam
evaporation
Supporting meniscus during spin casting of strips
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Experimental ans Analytical Modelling
Electromagnetic Shaping of Drops Experiments
Vaclav Kocourek Theory Michael Conrath
Electromagnetic Sealing of Slits Experiments
Jens-Uwe Mohring Theory Ch. Karcher, A. Potherat
Galinstan
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Model Experiment Drop

• PARAMETERS
• drop Galinstan
• current 0 - 320 A
• frequency 2- 50 kHz
• drop volume 0.2 - 11 ml

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Static Drop Deformation for I lt IC
Results of analytical model (Conrath, Karcher
EJM B/Fluids 2004)
Sketch of squeezing
Experimental results (Kocourek, Karcher, Conrath
Phys. Rev.E 2005)
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Drop Instability for I gt IC (m 3)
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Stability Diagram
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Annulus
Control parameters I0, w, L, H, a
I0coswt
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Karcher, Mohring in MHD (2003), Mohring, Karcher,
Schulze in Phys. Rev. E (2005)
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Small surface waves 1
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Dynamics of the free surface 1
a 3 mm, H 24 mm, L 17 mm, f 21.9 kHz, I
120 A

• Spectrum of different wavelengths (gravity,
  capillary)
• Amplitudes increase upon increasing I0

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Static surface deformation 1
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Dynamics of the free surface 2
a 3 mm, H 24 mm, L 17 mm, f 21.9 kHz, I
127 A

• Wavelength corresponding to skin depth ?1 2p d

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Pinch
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Pinch development
a 3 mm, H 24 mm, L 17 mm, f 47.2 kHz, I
123 A
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Theoretical Model
Cartesian geometry
Hele Shaw approximation
I coswt
I coswt
h(y,t)
z,w
z
pa, pM
L
p
x
y,v
n
Liquid metal r,u,s
H
g
Skin depth approximation
2d
magnetic pressure
Lorentz force
j, B from vector potentials Ai, Aa
Magnetohydrodynamics 2003
Karcher, Mohring
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governing equations
boundary conditions
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Linear stabilty analysis for basic state
evolution equation
Most dangerous mode
Neutral instability H??
Physical interpretation
Conclusions
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Measurement vs. theory
a 3 mm, H 30 mm
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Conclusions

• Electromagnetic shaping with high-frequency
  magnetic fields
• Squeezing of drops up to 15 possible
• Onset of drop instabilities critical parameters
  depending on drop volume and inductor current
  frequeny
• 3 Types of surface instabilities small surface
  waves, large-amplitude static deformation,
  electromagnetic pinch
• First instability well-predicted by simple model
  based on Hele Shaw and skin depth approximation
• High-frequency fields not suited for sealing
  purposes

Acknoledgements
DFG Research Group Magnetofluiddynamics DAAD
PROCOPE program with EPM Grenoble (Professor Yves
Fautrelle)
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Proposal for Collaboration I

• Lorentz force velocimetry (Thess, Kolesnikov,
  Karcher Patent 2005)
• BMBF project start 01.07.2006
• Measurement of mass flow in liquid aluminum,
  steel, glass, semiconductor melts

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Proposal for Collaboration II