Coupling between the translational and rotational brownian motions of rigid particles of arbitrary shape

Abstract

General phenomenological relations describing the diffusive and convective transport of small, rigid, anisotropic particles of any shape in physical-orientation space are developed. By employing a macroscopic hydrodynamic model, the 6 × 6 diffusion matrix arising in the theory is related to the quasi-static hydrodynamic resistance matrix of the particle, thereby furnishing the ultimate generalization of the Stokes-Einstein equations. The general properties of the diffusion matrix are systematically studied, especially as regards its positivity, symmetry, and dependence upon the choice of origin. The conceptual and computational advantages of partitioning this matrix are pointed out. The existence of coupling between the translational and rotational Brownian motions is shown to devolve upon the value of the “coupling diffusivity” submatrix at the “center of diffusion” of the particle. For particles devoid of screwlike geometric asymmetry, no coupling occurs.