Three-dimensional rotational relaxation in external fields

The Fokker–Planck equation provides a unified basis for studying three-dimensional Brownian rotation in external fields, beginning with the kinetic stage – the relaxation of the angular velocities. The information contained in the Fokker–Planck equation enables one to take into account after the reduction of the description to the level of angular distributions the memory effects associated with the inertia of the particles in the process of orientational relaxation during the hydrodynamic stage. These effects become important in strong external fields, which appreciably accelerate the relaxation. The generalized equation of rotational diffusion that is obtained takes into account consistently retardation and it is solved analytically by the reference equation method for the case of a strong rigid-dipole interaction of the particles with a stationary (in time) external field. The spectrum of orientational relaxation times and the relaxation distribution functions are found. The inertialess contributions are calculated in two orders in the interaction, while the retardation corrections are calculated in the principal order in the interaction and the basic parameter of the nonequilibrium theory.