Magnetic properties of ferrofluid emulsions
Ferrofluid emulsions are the colloidal suspensions of droplets, filled with a ferrofluid and suspended in neutral nonmiscible liquids. Typical droplet diameter is of the order 1 – 10 micrometers; and they are spherical in a field absence. An externally applied magnetic field induces the droplet magnetic moments and tends to elongation of droplets along a field direction.
Recently the nonmonotonic magnetic response was experimentally reported for the emulsions of kerosene-based ferrofluid in nonmiscible aviation oil. Under the action of a uniform external magnetic field the magnetic permeability of such ferrofluid emulsion demonstrates the rapid weak field growth and further log-tail decay in stronger magnetic fields. The effect could be observed only for emulsions with a rather weak interfacial tension (~ 10-5 N/m and less), and it is more pronounced for emulsions with higher values of the droplet volume fraction.
The effect could be theoretically explained on the basis of the following physical idea. In weak fields the magnetization of ferrofluid inside the droplets might be considered as being linearly dependent on a magnetic field strength with a constant value of the ferrofluid magnetic susceptibility. Simultaneously, the droplet elongation results in the decrease of demagnetizing field inside the droplets. So, in weak magnetic field one could expect more rapid growth of the induced droplet magnetic moment than the linear dependence on external field strength; and, thus, the emulsion magnetic permeability is an increasing function of field strength.
In stronger magnetic field the droplets are already highly elongated. So, the field strengthening is not accompanied by further significant decrease of the demagnetizing field; and the further droplet elongation terminates. On the other hand the magnetic susceptibility of the ferrofluid reduces with a field. Thus, the effective magnetic permeability of the ferrofluid suspension becomes decreasing.
The theoretical model, combining the known magnetization behaviour of the ferrofluid, the solution of magnetostatic problem for the magnetic field geometry inside and outside the elongated droplet, and the droplet energy minimization approach for obtaining the droplet elongation at moderate value of an externally applied uniform magnetic field, fully substantiate the described physical conception.