Materials Science and Engineering, A178 (1994) 73-76 73
Containerless processing of undercooled melts: measurements of
surface tension and viscosity
Ivfin Egry and Stefan Sauerland
Institute of Space Simulation, DLR, 51140, Cologne (Germany)
Abstract
Electromagnetic levitation is an elegant way of processing highly reactive liquid metals. It avoids contact with any
container walls and thus protects the sample's surface from contamination. This is important not only for obtaining
reliable surface tension data for the pure metals or alloys, but also for accessing the metastable, undercooled regime. With
electromagnetic levitation, the undercooled state can be maintained for extended periods of time, allowing in sire
diagnostics, i.e. non-contact measurements of thermophysical properties. The oscillating drop technique can be used to
determine surface tension and viscosity as a function of temperature. The frequencies of the oscillations of liquid drops
are related to the restoring force, the surface tension, while the damping of the oscillations is related to the viscosity.
1. Electromagnetic levitation
An inhomogeneous, alternating electromagnetic
field has two effects on a conducting, diamagnetic
body: firstly, it induces eddy currents within the
material, which, owing to ohmic losses, eventually heat
up the sample (inductive heating) and, secondly, it
exerts a force on the body pushing it towards regions of
lower field strength (Lorentz force). The latter effect
can be used to compensate the gravitational force
acting on the body.
The fundamental parameter of levitation theory is
q =R/a (1)
Here R is the radius of the sample and 6 is the skin
depth, given by
~ ) 1/2
a = (2)
where o is the electrical conductivity and w is the
angular frequency of the electromagnetic field. For
frequencies in the megahertz range, the skin depth is
about 0.1 mm for most metals, whereas usually
R=3-5 mm.
The time-averaged absorbed power by a sample of
radius R in a homogeneous magnetic field of amplitude
B is given by [1]
P=3~R 2 H(q)B 2 (3)
oflo
where
sinh(2q) + sin(2q)
H (q) = q cosh(2q)- cos(2q)
- 1 (4)
For a weakly non-homogeneous magnetic field, the
time-averaged force acting on a conducting sample can
be calculated from
~R ~
F = --- G(q)VB 2 (5)
2~,
where
3 sinh(2q)-sin(2q)
C(q)=l (6)
2q cosh(2q)- cos(2q)
Equations (3) and (5) are the (approximate)working
relations of electromagnetic levitation. Figure 1 shows
the field distribution inside a typical conical levitation
coil.
1. I. Microgravity
On earth, strong magnetic fields are needed to
compensate the lg gravitational force. The micro-
gravity environment offers the unique possibility of
minimizing the magnetic positioning fields. Therefore,
after melting, in the cooling phase, only negligible
forces act on the sample. There is practically no defor-
mation of the sample, and the spherical shape is main-
tained. This is important for measurements of the
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