Abstract.
The linear stability of the Marangoni-driven Full-Zone is investigated for low Prandtl number fluids. A constant and uniform magnetic field is applied along the axial axis of the liquid bridge to stabilize the axisymmetric base state. Dramatic contraction of the flow circulation in both radial and azimuthal directions is observed with moderate magnetic fields. The numerical solution utilizes a vorticity transport formulation and high resolution spectral collocation scheme with Chebyshev polynomial basis functions. Critical transitions to three-dimensional, stationary flows are observed up to Ha = 300 for Pr = 0.02 and Ha = 500 for Pr = 0.001. A hydrodynamically driven instability is suggested by the perturbation flows and confirmed through an energy analysis.
Similar content being viewed by others
References
T. Tanaka, E. Bannai, S. Kawai, T. Yamane, J. Crystal Growth 30, 193 (1975)
A. Eyer, R. Nitsche, H. Zimmermann, J. Crystal Growth 47, 219 (1979)
A. Cröll, P. Dold, K.W. Benz, J. Crystal Growth 137, 95 (1994)
A. Cröll, F.R. Szofran, P. Dold, K.W. Benz, S.L. Lehoczky, J. Crystal Growth 183, 554 (1998)
H. Kimura, M.F. Harvey, D.J. O’Connor, G.D. Robertson Jr, G.C. Valley, J. Crystal Growth 62, 523 (1983)
G.D. Robertson Jr, D. O’Connor, J. Crystal Growth 76, 111 (1986)
I. Martinez, A. Eyer, J. Crystal Growth 75, 535 (1986)
S. Nakamura, T. Hibiya, K. Kakimoto, N. Imaishi, S. Nishizawa, A. Hirata, K. Mukai, S. Yoda, T.S. Morita, J. Crystal Growth 186, 85 (1998)
X.F. Shen, A.V. Anilkumar, R.N. Grugel, T.G. Wang, J. Crystal Growth 165, 438 (1996)
M. Lappa, Fluid Dyn. Mater. Proc. 1, 171 (2005)
J. Baumgartl, M. Gewald, R. Rupp, J. Stierlen, G. Muller, Proc. 7th Eur. Symp. on Materials, Fluid Science in Microgravity, Oxford, ESA SP-295, 47 (1990)
T.E. Morthland, J.S. Walker, J. Crystal Growth 158, 471 (1996)
M. Lappa, Phys. Fluids 16, 331 (2004)
B.C. Houchens, J.S. Walker, J. Thermophys. Heat Transf. 137, 186 (2005)
G. Chen, A. Lizée, B. Roux, J. Crystal Growth 180, 638 (1997)
M. Lappa, Computers Fluids 34, 743 (2005)
O. Bouizi, C. Delcarte, G. Kasperski, Phys. Fluids 19, 114102 (2007)
C.W. Lan, B.C. Yeh, J. Crystal Growth 262, 59 (2004)
C.W. Lan, B.C. Yeh, Fluid Dyn. Mater. Proc. 1, 33 (2005)
M. Prange, M. Wanschura, H.C. Kuhlmann, H.J. Rath, J. Fluid Mechan. 394, 281 (1999)
E. Anderson et al. Linear Algebra PACKage (1999)
Intel ™ Intel ™ Math Kernel Library (2008)
M. Wanschura, V.M. Shevtsova, H.C. Kuhlmann, H.J. Rath, Phys. Fluids 7, 912 (1995)
SUG@R. Shared University Grid at Rice (2008)
M. Levenstam, G. Amberg, J. Fluid Mechan. 297, 357 (1995)
H.C. Kuhlmann, C. Nienhuser, Fluid Dyn. Res. 31, 103 (2002)
J. Leypoldt, H.C. Kuhlmann, H.J. Rath, J. Fluid Mechan. 414, 285 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, Y., Houchens, B. Magnetic stabilization, transition and energy analysis in the Marangoni driven Full-Zone at low Prandtl numbers. Eur. Phys. J. Spec. Top. 192, 47–61 (2011). https://doi.org/10.1140/epjst/e2011-01359-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2011-01359-5