Dipole Orientations in an Applied Magnetic Field

If now a magnetic field H is applied to a suspension of spherical particles of diameter d, the orientation-dependent potential energy Wh of a particle in this field is expressed as 

Here 9 is the angle of orientation of the magnetic dipole with respect to the field, and we define 

We find that the magnetic energy equals the thermal energy ksT when a 1, or 

in a field /uqH of 0.1 T, with = 4.5 x 10 A/m, at room temperature, we obtain from Eq. (8-25) that particles of around diameter 10 nm and above will orient their magnetic dipoles with the field. Furthermore, if only part of the ferrofluid is exposed to the magnetic field particles larger than 10 nm will be drawn into the field and will enneentrate where the field is strongest. Thus, in practical applications of ferrofluids, the particles must be kept small to avoid field-induced particle segregation. 

If the ferrofluid is dilute, so that particle-particle interactions can be neglected, then the distribution of dipole orientations in a field H is given by the usual Boltzmann equation ----------------------------------------------------------------------------------- 

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