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Electric-field-controlled diffusion of anisotropic particles: theory and experiment

Published online by Cambridge University Press:  17 August 2021

Tianyu Yuan ,
Wuhan Yuan ,
Liping Liu  and
Jerry W. Shan
Tianyu Yuan
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA
Wuhan Yuan*
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA
Liping Liu
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA
Jerry W. Shan
Affiliation:
Department of Mechanical and Aerospace Engineering, Rutgers University, Piscataway, NJ 08854, USA
*
†Email address for correspondence: [email protected]
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Abstract

We report on a theoretical and experimental study on the anisotropic diffusion of isolated prolate spheroidal particles in the presence of an aligning potential field. By analysing the microscopic stochastic equations of motion, we obtained the coarse-grained Fokker–Planck equations that govern the evolution of the probability distributions of particle orientation in various configurational spaces. In particular, we found explicit formulae for the diffusion coefficients parallel ($D_x$) and perpendicular ($D_y$) to the field direction in the long-time limit. The predicted results were experimentally validated by measuring the Brownian motions of fluid-suspended carbon nanotubes in an electric field. Good agreement was observed between theoretical and experimental results, both of which showed increasing $D_x$ and decreasing $D_y$ with increasing field strength up to a critical field strength beyond which both curves start to flatten. Our theory and experimental results provide a framework for understanding the coupling between rotation and translation in a diffusion process, and for controlling the diffusion of particles with aligning potential fields.

JFM classification

Complex Fluids: Suspensions Mathematical Foundations: General fluid mechanics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 924 , 10 October 2021 , A42
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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