Transient isothermal roll-cell convection in thin horizontal layers of vertically magnetized ferrofluids

A theory is presented which predicts transient roll-cell convection when a thin horizontal layer of ferrofluid at sedimentation equilibrium under the influence of gravity is subjected to a vertical external magnetic field. This field is spatially homogeneous in the absence of the ferrofluid sample. Provided that the magnetic susceptibility of the ferrofluid is sufficiently high the inhomogeneous magnetic field in the ferrofluid layer destabilizes this layer and roll-cell convection is predicted to occur at critical field strengths which can easily be achieved experimentally. Large wavenumber convection can be expected to persist until magnetodiffusion reduces the vertical gradient in the distribution of colloidal particles to a subcritical level.