Nanodrop of an Ising magnetic fluid on a solid surface

The density functional theory of inhomogeneous simple fluids is extended to an Ising magnetic fluid in contact with a solid surface, which is subjected to an external uniform or nonuniform magnetic field. The system is described by two coupled integral equations regarding the magnetic moment and fluid density distributions. The dependence of the contact angle that a nanodrop makes with the solid surface on the parameters involved in the magnetic interactions between the molecules of fluid and between the molecules of fluid and an external magnetic field is calculated. For the uniform magnetic field, the contact angle increases with increasing magnetic field, approaching an asymptotic value that depends on the strength of the fluid-fluid magnetic interactions. In the nonuniform field generated by a permanent magnet, the contact angle first increases with increasing magnetic field B(M) and then decreases, with the decrease being almost linear for large values of B(M). The obtained results are in qualitative agreement with the experimental data on the contact angle of magnetic drops on a solid surface available in the literature.