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

 

 

 

 

config, 2K archive

 

 

  • 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.

 


A Technology Transfer Project funded by NOTUR