Title: Shape and fission instabilities of ferrofluids in non-uniform magnetic fields,
Abstract: We study static distributions of ferrofluid submitted to non-uniform magnetic
fields. We show how the normal-field instability is modified in the presence of
a weak magnetic field gradient. Then we consider a ferrofluid droplet and show
how the gradient affects its shape. A rich phase transitions phenomenology is
found. We also investigate the creation of droplets by successive splits when a
magnet is vertically approached from below and derive theoretical expressions
which are solved numerically to obtain the number of droplets and their aspect
ratio as function of the field configuration. A quantitative comparison is
performed with previous experimental results, as well as with our own
experiments, and yields good agreement with the theoretical modeling.