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How to make micromagnetic balls swim in the magnetic field

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This is a paramagnetic microsphere. Put it in an aqueous solution. If you add a magnetic field around the rectangle, how to simulate the movement of this microsphere in the magnetic field? Mainly consider the situation that the microsphere is subjected to magnetic force and the velocity distribution of the flow field.

The size of this microsphere is about 500 nanometers. Consider a two-dimensional model simulation. The simple geometric model is shown below:

model

I have been researching for more than a week, and still very troubled. Thank you for your help and guidance


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