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 nonspherical elongated particles that are abundant in natural environment.

Mobility of nanofiber, nanorod, and straight-chain nanoparticles in gases

“…From Brownian diffusion point of view, Tian et al (2016) examined the isotropic and anisotropic diffusion property of a nanofiber in relation to its coupled rotational behavior. Based on this study, all fibers with a time scale greater than its relaxation to isotropy time exhibits isotropic macroscopic diffusion.…”

“…Based on this study, all fibers with a time scale greater than its relaxation to isotropy time exhibits isotropic macroscopic diffusion. Orientationaveraged diffusion coefficient was then developed, and the corresponding diffusion equivalent sphere diameter was given as (Tian et al 2016) …”

“…In analogy to that of the spheres, modeling transition regime of non-spherical particle resistance predominantly followed the Cunningham (1910) approach by establishing a smooth transition from the free molecular to the continuum regimes. Such examples include the work of Dahneke (1973b), Asgharian et al (1988), Cheng (1991), Fan and Ahmadi (2000), Zhang et al (2012), Tian and Ahmadi (2016a,b), Tian et al (2016), and Gopalakrishnan et al (2015a). It should be noted that, due to the ambiguity of equivalent mobility definition, the non-spherical slip correction has appeared in a number of forms.…”

“…Their results were well supported by simulations using a combination of collision limited reaction rate theory and bipolar diffusion charging analysis. Recently, Tian et al (2016) investigated the diffusion of fibers in a quiescent air and developed a diffusion-equivalent sphere diameter for characterizing fiber mobility driven by Brownian motion. A comparison of the predicted diffusion-equivalent spheres to the measured mobility equivalent diameters for a series of nanorods (Gopalakrishnan et al 2015b) showed excellent agreement (Tian et al 2016).…”

“…Recently, Tian et al (2016) investigated the diffusion of fibers in a quiescent air and developed a diffusion-equivalent sphere diameter for characterizing fiber mobility driven by Brownian motion. A comparison of the predicted diffusion-equivalent spheres to the measured mobility equivalent diameters for a series of nanorods (Gopalakrishnan et al 2015b) showed excellent agreement (Tian et al 2016). Melas et al (2014Melas et al ( , 2015 investigated the friction coefficient and mobility radius of the fractal-like aggregates in the transition regime, and the application to straight chain agglomerates.…”