Tracer Diffusion for Rough Hard Spheres

We present a study of tracer diffusion in a rough sphere fluid. In such fluid collisions between particles exchange rotational and translational energy and momentum. As tracer particles grow in size, their diffusion constant is described by the Stokes-Einstein hydrodynamic result. In this limit, smooth hard spheres are shown to adopt ``slip'' boundary conditions. The current results show that rough hard spheres adopt boundary conditions proportional to their degree of roughness, defined by the radius of gyration. Spheres with maximum roughness adopt ``stick'' boundary conditions while those with intermediate roughness adopt values between the ``slip'' and ``stick'' limits. This dependence is found to be almost linear. Changes in the diffusion constants as a function of roughness are also examined and it is found that the dependence is stronger than suggested by the low-density, Boltzmann result. Rough hard spheres model the effect of inelasticity of a real collision and show that even without the presence of attractive forces, the boundary conditions for large particles can deviate from ``slip'' and approach ``stick.''