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We study static distributions of ferrofluid submitted to non-uniform magneticfields. We show how the normal-field instability is modified in the presence ofa weak magnetic field gradient. Then we consider a ferrofluid droplet and showhow the gradient affects its shape. A rich phase transitions phenomenology isfound. We also investigate the creation of droplets by successive splits when amagnet is vertically approached from below and derive theoretical expressionswhich are solved numerically to obtain the number of droplets and their aspectratio as function of the field configuration. A quantitative comparison isperformed with previous experimental results, as well as with our ownexperiments, and yields good agreement with the theoretical modeling.

Shape and fission instabilities of ferrofluids in non-uniform magnetic fields