Magnetic forces and the surface instability in ferromagnetic fluids

Ferromagnetic fluids are a colloidal suspension of subdomain iron particles dispersed in a carrier fluid. Experiments were performed to determine the pressure exerted by the fluid in a uniform and a gradient magnetic field. The pressure measurements were not the same as predicted by the continuum theory. An expression for the pressure jump at the surface of the fluid was proposed for the particular ferromagnetic fluid used based on the experimental measurements. This pressure jump was then used to predict the shape of the surface of the ferrofluid that results when a magnetic field is applied normal to an initially flat ferrofluid surface (ferrofluid spike). An expression for the radius of the shape ρ as a function of its distance from the base z, ρ=ρ (z), was calculated and compared to an enlarged photograph of the particular shape. In the region ρ≳0, a simple analytical solution was found. When ρ is zero or in the region close to zero, surface tension must be included and a numerical solution was necessary to determine the profile.