Rotational diffusion of colloidal particles near confining walls

We study the rotational diffusion of a spherical colloid confined in a narrow channel between parallel plane hard walls. The walls damp translational diffusion much more than rotational diffusion so that there is expected to be little translation-rotation coupling. Using a recent calculation of the nonisotropic rotational mobilities arising from the hydrodynamic interactions with the walls, we set up the rotational Smoluchowski equation for either a particle with a permanent dipole moment or a polarizable particle with axisymmetric polarizabilities subject to an external electric field. Using the Smoluchowski equation dynamics we calculate the time-correlation functions of orientation that are measured in depolarized light scattering for the cases of no external field, external field normal to the walls, and external field parallel to the walls. The decay of correlations is shown to be given by a weighted sum of decaying exponentials and can be characterized by an initial and a mean characteristic decay time. The weights and decay rates of each component and the characteristic decay times are studied numerically for a range of field strengths. The nonisotropic rotational mobilities make these decay times highly sensitive to the distance of the particle from the confining walls. This position dependence can be used as a method of measuring the rotational mobilities or, conversely, the rate of decay of correlations can be used as a probe of particle position between the confining walls.