Ferrofluid flow

Numerical methods and mathematical models of Elmer
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cdav
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Ferrofluid flow

Post by cdav »

Hello,

I am trying to simulate the flow of a ferrofluid under the influence of an applied magnetic field.
The magnetic field is created by a DC current running through a solenoid. I calculate it by using the WhitneyAVSolver and MagnetoDynamicsCalcFields from the MagnetoDynamics module, after determining the current density with the CoilSolver.

By ferrofluid I mean some fluid like (water + Fe3O4 magnetic nanoparticles) which is nonconducting, but it can move due to the applied magnetic field H (if it's not uniform). This fluid is enclosed in a horizontal tube with one opening, and the tube is surrounded by the solenoid.

I know I have to use the Navier-Stokes equation with the magnetic force as body force, where the magnetic force (per unit volume) is mu_0 * (M \dot nabla) * H. M here would be the magnetization of the fluid. With some simplifying assumptions one can rewrite it as mu_0 * M * grad(H) and maybe I can even find some cases where I know how to write M as a function of H, but I don't know how to implement this as body force.

Is the approach I'm trying to take even correct?

Is there a way to simply use a MATC or a Fortran procedure or anything to compute the magnetic force based on the magnetic field variable and use it as body force in the NS equation?

Is there any .sif dealing with ferrohydrodynamics?

Kind regards,
cdav
kevinarden
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Re: Ferrofluid flow

Post by kevinarden »

There is an example here of a magnetic force being applied as a body force to a fluid
viewtopic.php?t=7658&start=30
cdav
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Re: Ferrofluid flow

Post by cdav »

Thank you! Now I know how I should approach the problem. Unfortunately, there is still one thing I can't understand how to do:

In that example, if I understand correctly, the liquid has electrical properties, but no magnetic properties. Thus, the force results from the interaction of the external field with the moving charges in the liquid, so it is the Lorentz force. But in my case, the fluid has no electrical properties, it only has magnetic properties due to the ferromagnetic nanoparticles. In this case, the force arises from the interaction between the external field and the magnetization of the particles. If only I knew how to calculate spatial derivates of elmer field variables, I think I could easily compute it.

Is it possible to compute the spatial derivates of the magnetic field? Than I could just write mu_0 * (Mx*dH/dx + My*dH/dy + Mz*dH/dz).

Kind regards,
cdav
kevinarden
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Re: Ferrofluid flow

Post by kevinarden »

You can give the fluid material magnetic properties.
You might also be interested in this one.
http://elmerfem.org/forum/viewtopic.php?p=25516
cdav
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Re: Ferrofluid flow

Post by cdav »

Thanks!

I'll try and see what I get.
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