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FREE SURFACE INSTABILITIES PRODUCED BY HIGH-FREQUENCY MAGNETIC FIELDS

This study explores the electromagnetic shaping and instabilities of liquid metal drops caused by high-frequency magnetic fields. Focusing on electron beam evaporation and spin casting, we present both experimental and analytical models that identify critical parameters affecting drop stability. Our findings highlight three types of surface instabilities—small surface waves, large-amplitude static deformations, and electromagnetic pinch effects. Additionally, we propose collaboration opportunities within the framework of the 2nd Sino-German Workshop on Electromagnetic Processing of Materials to advance research in magnetofluid dynamics.

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FREE SURFACE INSTABILITIES PRODUCED BY HIGH-FREQUENCY MAGNETIC FIELDS

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  1. 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 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  2. Motivation: Electromagnetic Shaping Forming of a stable dome during electron beam evaporation Supporting meniscus during spin casting of strips 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  3. 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 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  4. Model Experiment Drop PARAMETERS • drop Galinstan • current 0 - 320 A • frequency 2- 50 kHz • drop volume 0.2 - 11 ml 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  5. I=100A I=0A I Rmin R0 Static Drop Deformation for I < IC Results of analytical model (Conrath, Karcher: EJM B/Fluids 2004) Sketch of squeezing Experimental results (Kocourek, Karcher, Conrath: Phys. Rev.E 2005) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  6. Drop Instability for I > IC (m = 3) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  7. Stability Diagram 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  8. Annulus Control parameters I0, w, L, H, a I0coswt 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  9. Karcher, Mohring in MHD (2003), Mohring, Karcher, Schulze in Phys. Rev. E (2005) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  10. Small surface waves 1 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  11. 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 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  12. Static surface deformation 1 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  13. Dynamics of the free surface 2 21 1 cm a = 3 mm, H = 24 mm, L = 17 mm, f = 21.9 kHz, I = 127 A • Wavelength corresponding to skin depth: 1 ~ 2p d 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  14. Pinch 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  15. 21 1 cm Pinch development a = 3 mm, H = 24 mm, L = 17 mm, f = 47.2 kHz, I = 123 A 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  16. 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 Karcher, Mohring Magnetohydrodynamics 2003 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  17. governing equations boundary conditions 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  18. Linear stabilty analysis for basic state evolution equation Most dangerous mode Neutral instability H Physical interpretation Conclusions 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  19. measured: Icp  -0.218 a = 1 mm, H = 24 mm, L = 22 mm Measurement vs. theory a = 3 mm, H = 30 mm 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  20. 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) 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  21. 1 3 4 2 Proposal for CollaborationI 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 2nd Sino-German Workshop on Electromagnetic Processing of Materials

  22. Proposal for Collaboration II 2nd Sino-German Workshop on Electromagnetic Processing of Materials

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