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Application - 1 Magnetic holes
A ferro-fluid acts as a super-paramagnetic liquid magnet when an
external magnetic field is applied. When micro-sized plastic-spheres
called Ugelstadspheres are suspended into the fluid, they act as holes
in the magnetic field with a dipolmoment in the opposite direction of
it.
The spheres will try to align in the direction of the field. If the
field is rotating the spheres will try to follow the field, but due to
the viscosity of the fluid, at a certain frequency they won't cope
with the pace.
This scenario can be analyzed in different ways, and my hope is that
we might be able to see a connection between simulation and experiment
on a braid-word-level.
Braid-words are a part of knot- and braid-theory and until recently
only theoretical mathematics.
Schematically the situation looks like this:
Ugelstad spheres in a magnetic fluid and an applied magnetic field creates
an analogue to Archimedes law, where the spheres becomes magnetic holes
and acts as magnetic dipoles with a dipolemoment in the opposite way of
the magnetic field. The strength of the dipole
sigma
is governed by the volume
displacement of the ferrofluid, the strength of the external magnetic
field and the susceptibility of the ferrofluid
is the effective susceptibility as a result of the
geometry of the Ugelstadbead, a sphere. The force on a dipole i
interacting with a dipole j of equal strength and direction is given
by
The last term acts as a torque on each pair of spheres trying to align
the spheres with the magnetic field. If the field is rotated the spheres
will try to follow the field. As a result the spheres will also feel the
viscousity-force here approximated to the stokes flow on a sphere:
d is the diameter of the sphere, v the velocity and
etha the viscosity of the fluid.
When the angular frequency of the field is fast enough the spheres
will break up in smaller groups resulting in different "modes" with drifferent
frequencies. For afew (4-8) particles acting together interesting
patterns appear, which are very unstable and almost chaotic.
The numerical simulations are carried out with ProtoMol.
In the experiments carried out to compare with the theoretical results,
the spheres and the magnetic fluid is confined between two glass-plates.
The boundary-conditions between the ferrofluid and the glassplates result
in mirrordipoles outside the sample.
Computer Simulation and Results
- 7 Spheres - Ugelstad spheres (MPEG) 7 MB, 1000 frames, A.Hellesøy.
- 7 Spheres - Ugelstad spheres with reflection (MPEG) 81 MB, 6000 frames,
A.Hellesøy.
- Ugelstad spheres (MOV) 89 MB, A.Hellesøy.
- Ugelstad spheres (MOV) 84 MB, A.Hellesøy.
Related Links
- Eksperiment og simulering av ugelstadkuler i en magnetisk væske
(PDF) (A. Hellesøy), Master's thesis, University of
Bergen, 2002.
TTP5 Presentation - Status Report
- Ugelstad spheres - Dancing with Spheres (PPT) (A. Hellesøy) 2001.
Last modified: Tuesday, 24-Sep-2002 08:33:10 CEST.
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