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phsieh2005 March 23, 2007 06:33

model particle movement under magnetic force
Dear CFD experts:

I am wondering whether anyone here had done anything like this and can offer some suggestion:

Problem descriptions:

iron particles suspended in water inside a cup. The dimension of the cup is on the order of 1cm x 2cm x 10cm, wheras the diameter of the iron particles are on the order of 2 micron-meter. There are thousands of iron particles in the domain, but, we will only track 1 iron particle to simplfy the problem.

At time 0+, this cup is exposed to a permanent magnet, locaed on one side of the cup. Hence, magnetic force will track the iron particle toward the magnet.

The difficulty lies in computing magnetic force exerts on the iron particle.

Any suggestion?


Harish March 23, 2007 08:30

Re: model particle movement under magnetic force
Did you try looking for papers in the field of magnetoydrodynamics. Also books on astrophysics will have some chapters on the topic.

phsieh2005 March 23, 2007 09:57

Re: model particle movement under magnetic force
Hi, Harish,

Thanks for the suggestion. I never thought about looking into Magnetohydrodynamics. I will look into it.


opaque March 23, 2007 10:19

Re: model particle movement under magnetic force
Dear phsieh,

If your problem does not include applied electric field, and the magnetic field is steady, you can model the problem as a magnetostatics problem. That is, using Ampere's law

curl H = 0

div B = 0

B = mu * H

You can simplify the problem by introducing a magnetic scalar potential, ie. H = grad Phi, then Ampere's law is automatically satisfied, and

div (mu grad Phi) = 0

must be solved for Phi.

The force on the particle due to electromagnetic effects includes several contributions: electrostatics (Coulomb), magnetohydrodynamic (Lorentz), magnetostatic/phoretic (Kelvin), etc..

In your case, I think that only the Kelvin force is needed:

F_mag = mu_o * M dot grad H

Just add this force to your particle force balance.

You should search for information on Ferrohydrodynamics. Magnetohydrodynamics is for conducting fluids. Either way, you will learn a lot of by searching on both.


phsieh2005 March 23, 2007 11:25

Re: model particle movement under magnetic force
Dear Opaque:

Thanks a LOT for the reply!

The past month, I have learned a lot about magnetostatics. I have computed the magnetic flux density field using GetDP (I have tried both scalar potential and vector potential). It looks like F_mag = mu_o * M dot gradH is what I need. But, what is M?

I just realized another problem I am facing: Although the magnetic field is static in general, when the iron particle moves to a new location, I need to re-mesh, re-calculate the magnetic flux density and magnetic force. Because the length scale of the particle is 3 order of magnitude smaller than the fluid domain, it will be a big job to remesh the magnetic field, especially for a 3D problem.

Is it possible to calculate the magnetic flux density field "without" the iron particle. Then, somehow estimate the "pull" force on the particle based on this static magnetic flux? The iron particle is very small compared to the fluid domain.


phsieh2005 March 23, 2007 17:33

Re: model particle movement under magnetic force
Dear Opaque:

Could you please post the reference that showed the Kelvin force equation (that is: "F_mag = mu_o * M dot grad H")?

I did searches for Kelvin force and was not able to find a good source for it. Thanks!


opaque March 27, 2007 09:28

Re: model particle movement under magnetic force
Dear phsieh,

M stands for Magnetization.. It is a material property, and there are different ways of how to model it as well.

For a reference on the topic try the book,

Ferrohydrodynamics R. E. Rosensweig Dover Publications Inc.,1985.

Also, you could try the following link

Hope this helps, Opaque

opaque March 27, 2007 11:35

Re: model particle movement under magnetic force
Dear phsieh

Here is another link that you may like.



phsieh2005 March 28, 2007 07:12

Re: model particle movement under magnetic force
Thanks a lot Mr. Opaque!

I quickly read through the abstract. This thesis is very helpful to me.

Best Regards,


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