The possibility of imposing a given shape to a liquid metal column or to guide it without contact with walls, by using high frequency alternating magnetic fields is proved both experimentally and theoretically.Two types of inductor are tested on an experimental setup using the mercury as the test metal. The first, able to impose a cross shape as cross section of an initially circular mercury vein, may also act as a guide. The second, also tested on molten tin, stretches a circular vein in the form of a sheet.The free boundary problem regarding the theoretical prediction of the forms of equilibrium is analyzed. The calculation is based on the exploitation of complex potentials and conformal mapping used alone in the case of pure magnetic balance and in combination with energy variational methods when additional constrain (eg surface tension) is involved.
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