The effect of shear flow on the rotational diffusion of a single axisymmetric particle

Journal Article · Tue Apr 28 04:00:00 EDT 2015 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2015.186· OSTI ID:1418542

Leahy, Brian D. ^[1]; Koch, Donald L. ^[2]; Cohen, Itai ^[3]

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1. Cornell Univ., Ithaca, NY (United States). Dept. of Physics; Cornell University
2. Cornell Univ., Ithaca, NY (United States). Dept. of Chemical Engineering and Biomolecular Engineering
3. Cornell Univ., Ithaca, NY (United States)

Understanding the orientation dynamics of anisotropic colloidal particles is important for suspension rheology and particle self-assembly. However, even for the simplest case of dilute suspensions in shear flow, the orientation dynamics of non-spherical Brownian particles are poorly understood. Here we analytically calculate the time-dependent orientation distributions for non-spherical axisymmetric particles confined to rotate in the flow–gradient plane, in the limit of small but non-zero Brownian diffusivity. For continuous shear, despite the complicated dynamics arising from the particle rotations, we find a coordinate change that maps the orientation dynamics to a diffusion equation with a remarkably simple ratio of the enhanced rotary diffusivity to the zero shear diffusion: $$D_{eff}^{r}/D_{0}^{r}=(3/8)(p-1/p)^{2}+1$$ , where $$p$$ is the particle aspect ratio. For oscillatory shear, the enhanced diffusion becomes orientation dependent and drastically alters the long-time orientation distributions. We describe a general method for solving the time-dependent oscillatory shear distributions and finding the effective diffusion constant. As an illustration, we use this method to solve for the diffusion and distributions in the case of triangle-wave oscillatory shear and find that they depend strongly on the strain amplitude and particle aspect ratio. These results provide new insight into the time-dependent rheology of suspensions of anisotropic particles. For continuous shear, we find two distinct diffusive time scales in the rheology that scale separately with aspect ratio $$p$$, as $$1/D_{0}^{r}p^{4}$$ and as $$1/D_{0}^{r}p^{2}$$ for $$p\gg$$ 1. For oscillatory shear flows, the intrinsic viscosity oscillates with the strain amplitude. Finally, we show the relevance of our results to real suspensions in which particles can rotate freely. Collectively, the interplay between shear-induced rotations and diffusion has rich structure and strong effects: for a particle with aspect ratio 10, the oscillatory shear intrinsic viscosity varies by a factor of $${\approx}2$$ and the rotational diffusion by a factor of $${\approx}40$$.

• Research Organization: Cornell Univ., Ithaca, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Science Foundation (NSF)
• DOE Contract Number: FG02-08ER46517
• OSTI ID: 1418542
• Journal Information: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 772; ISSN 0022-1120
• Publisher: Cambridge University Press
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
colloids
rheology
suspensions