Rotational Brownian motion of axisymmetric particles in a Maxwell fluid

A theory of non-Markovian rotational Brownian motion is developed for axisymmetric particles moving in a Maxwell fluid in the presence of an external field. Both the inertial and viscoelastic effects are taken into account. A kinetic equation for the joint probability distribution of orientation, angular velocity, and acceleration of a particle without spin is derived starting from the rotational Langevin equation with relaxed hydrodynamic and random torques. A third-order stochastic differential equation for the particle orientation vector is also derived. Directly from this equation, the set of nonlinear evolution equations for one-time moments is derived in a noninertial approximation. The expressions for a linear response to a time-dependent external field and dynamic susceptibility of particle are obtained by direct averaging of particle orientation equation. Appendices derive the rotational mobility of axisymmetric particles in a general linear viscoelastic fluid, and the evolution equations for one-time moments of the orientation vector for axisymmetric particles moving in a Maxwell fluid in the presence of an external field.