Microscopic boundary layer effects and rough sphere rotation

Abstract

A calculation of the rough sphere angular velocity correlation function is presented which takes into account the presence of both the microscopic boundary layer and outer hydrodynamic regions around the test particle. The boundary layer region is approximately accounted for by the slip boundary condition while generalized hydrodynamic equations (frequency dependent transport coefficients plus fluid spin variables) are used to describe the outer region. The approximate calculation of the slip coefficient and the use of the slip coefficient to account for processes occurring in the boundary layer are discussed in the context of kinetic theory results. Since a description of both regions is incorporated, the present theory contains both microscopic and collective effects. The structure of the result is compared in some detail to a recent renormalized kinetic theory calculation on the same system and various levels of approximation are examined. The results are in good agreement with the molecular dynamics calculations.