Mixing and floating magnet

For a lab set up we are using a magnet to mix oil with water. A vertical positioned tube contains oil and a magnet and is moved up and down. The magnet remains at the height of the magnetic field and rotates around its axis since the field is alternating. I would like to dimension the components (magnet, magnetic field, ...) analytically but i'm not an expert at all. Can somebody provide me equations to solve this problem - the result should allow me to have an idea of magnitude.