Edge pinch instability of liquid metal sheet in a transverse high-frequency AC magnetic field

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dc.creatorPriede, J.
dc.creatorEtay, J.
dc.creatorFautrelle, Y.
dc.date2006-05-16
dc.date2006-06-01
dc.date.accessioned2026-07-07T07:15:01Z
dc.date.available2026-07-07T07:15:01Z
dc.descriptionWe analyze the linear stability of the edge of a thin liquid metal layer subject to a transverse high-frequency AC magnetic field. The layer is treated as a perfectly conducting liquid sheet that allows us to solve the problem analytically for both a semi-infinite geometry with a straight edge and a thin disk of finite radius. It is shown that the long-wave perturbations of a straight edge are monotonically unstable when the wave number exceeds some critical value $k_c,$ which is determined by the surface tension and the linear density of the electromagnetic force acting on the edge. The higher the density of electromagnetic force, the shorter the critical wavelength. The perturbations with wavelength shorter than the critical are stabilized by the surface tension, whereas the growth rate of long wave perturbations reduces as $\sim k$ for wave numbers $k\to 0$. Thus, there is the fastest growing perturbation with the wave number $k_\max=2/3 k_c$. By applying the general approach developed for the semi-infinite sheet, we find that a circular disk becomes linearly unstable with respect to exponentially growing perturbation with the azimuthal wave number $m=2$ when the magnetic Bond number exceeds $Bm_c=3π$. The instability characteristics agree well with the experimental data.
dc.description11 pages, 11 figures, minor grammatical changes; to appear in Phys. Rev. E
dc.identifierhttps://arxiv.org/abs/physics/0605132
dc.identifierhttp://arxiv.org/abs/physics/0605132
dc.identifierPhys. Rev. E 73, 066303 (2006) (10 pages)
dc.identifierdoi:10.1103/PhysRevE.73.066303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113117
dc.subjectFluid Dynamics
dc.titleEdge pinch instability of liquid metal sheet in a transverse high-frequency AC magnetic field
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