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- - **Model particle movement under magnetic force**
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Dear OpenFOAMers:
I am wondDear OpenFOAMers:
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 goal is to calculate how long does it take for the iron particle to reach the cup wall. The difficulty lies in computing magnetic force exerts on the iron particle. Any suggestion? Pei |

Dear Pei,
1) the main questDear Pei,
1) the main question is: how is the tracking of only 1 iron particle justified. If there are heavy interaction between the particles or the magnetic field B is influenced by the other particles, this will produce no useful answers to your questions. 2) The phenomenon you are looking for is Ferromagnetism. Maybe you find some useful equations via google or google scholar cheers Stefan |

Hi Pei!
There are two ways Hi Pei!
There are two ways to do that (there are more, but these are the "easier" ones): - If you can assume the velocity field and the magnetic field to be stationary (and not influenced by the particle= and if you have these fields (propably by some other solver) you can write a little utility that solves the ODE for a particle (there are capabilities for that in OF) - You can adapt a fluid solver to also solve the magnetic field (or assume it to be constant), add Lagrangian particles to it and modify the force term of the particles to take the magnetic field into account But I'm afraid there is no "add water and stirr"-solution for that readily available (but you might want to start with icoLagrangianFoam - if the magnetic field can be assumed to be constant (or some other analytical function of the position) adding the source term on the particles might only take a line or two (depending on your choice of indentation)) |

HI, Stefan and Bernhard,
ThHI, Stefan and Bernhard,
Thanks for the replies. Yes, there are interaction among the iron particles. We will glad (for now) to just get an rough idea of the time needed for 1 particle to reach the wall. I am not sure how we can deal with interaction anyway. I used GetDP to compute a static magnetic flux density field - without the particle present. So, this is static field. However, to calculate the forces acting on the particle, I belive that I need the calculate the magnetic flux density field "with" the iron particle present. The hard part is that, when the particle moves to a new position, re-mesh is needed, then, recompute the magnetic flux density and magnetic force. I have used icoLagrangianFoam - good stuff. In my problem, both magnetic field and velocity field are static. The main difficulty lies in my limited knowledge in magnetism. How to calculate magnetic foce on the particle when the particle moves in a non-uniform (but static) magnetic field? Maybe there are good simplified methods for this type of problem? Pei |

Hi Pei!
If your particles aHi Pei!
If your particles are charged, then you can easily calculate the Lorentz-Force. If they are uncharged, then you have to assume that they are dipols (otherwise the magnetic field wouldn't have any influence) - but I guess then you have to store the orientation of the particle. The magnetic field a moving charge generates can be calculated using Biot-Savart and can be added to the "static" field - just not for the particle itself. And if the particles are charged there is still the electrostatic force. Personally, I would try to justify a "particles don't influence each other" approach, everything else needs non-trivial modifications to the solver. |

If you just need a rough estimIf you just need a rough estimate of the time it takes for one particle to reach the wall, you'd do very well with only pen and paper. The particle will quickly reach a terminal velocity at which the magnetic force equals the drag force on the particle. The equations for both forces should be easy to find in introductory text books. Set the forces equal and then solve for velocity (only the drag force depend on velocity).
/Ola |

Dear Ola,
Thanks for the suDear Ola,
Thanks for the suggestion. Over the past month, I have learned a great deal about magnetism. The difficult is in calculating magnetic force. For paramagnetic particles (permability on the order of 1) + under weak inhomogenous magnetic field, then, the magnetic is ~ (H dot grad)H. In this case, it will be quite straight forward to compute the particle locations as a function of time. However, for ferromagnetic particles (permability is on the order 100s), then, interaction among the particles will needed to be considered, hence, the magnetic forces become quite complicated. Pei |

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