Brownian diffusion of fibers

Abstract

Motion of nanoparticles suspended in fluids are dominated by Brownian diffusion - a physical property well understood following the work by Einstein in 1905. While theoretical derivation and experimental measurement of the diffusion coefficients for spherical particles are well developed, such information is lacking for non-spherical particles as the coupled rotational and translational motion hinders a clear description of the overall diffusive outcome. In this study, the Brownian diffusion of elongated nano-fibers is investigated numerically. Motion of the nano-fiber is resolved by solving the system of equations governing its coupled translational and rotational motion. To isolate the Brownian diffusion from other diffusive forces, test fibers are immersed in an unbounded quiescent fluid where only the hydrodynamic drag and Brownian forces are present. The study allows a close look at the Brownian diffusion of nano-fibers with respect to the translation, rotation, coupling, and how the rotation affects the particle's macroscopic diffusion properties. In this study, the Brownian diffusion of ellipsoidal particles are studied. The translational and the rotational Brownian motions and their coupling are included in the analysis. Particular attention was given to the rotational relaxation time in determining the non-spherical particle's isotropic and anisotropic diffusive properties. Theoretical and semi-empirical equations are developed to quantify the diffusion coefficients of nano-fibers. The predications are compared with available experimental data. The comparison to the analytic solution in the limiting case of a sphere is with excellent accuracy. The study opens up new approaches for studying fundamental diffusive processes of non-spherical elongated particles that are abundant in natural environment.