Orientation control by flow: Exact results and Langevin simulations

TL;DR

This paper derives exact and numerical results for the orientation distribution of rod-shaped particles in flowing liquids, with applications to optical properties like dichroism and birefringence across a wide range of flow conditions.

Contribution

It provides analytical solutions and Langevin simulation methods for the orientation PDF of rods in flow, covering a broad Peclet number range, and links these to experimental optical measurements.

Findings

Accurate PDF calculations for $10^{-4} \\le \\alpha \\le 10^{8}$

Analytical and numerical methods agree across flow regimes

Application to optical property measurements like dichroism and birefringence

Abstract

Rod shaped objects suspended in a flowing liquid might be orientated by the velocity, nature of the liquid, the flow and the geometry of the channel containing the flow. Orientation settings might enhance or inhibit certain chemical reactions between the objects, other chemicals or with the walls of vessels holding the flowing suspension. The probability density function (PDF) describing the orientations of rod shaped objects in a flowing liquid satisfies a Fokker-Planck equation whose solution is obtained analytically as well as numerically from Langevin simulations for different flow parameters. The analytical and numerical methods developed in the present work enable us to calculate accurately the PDF for a range of the Peclet number $\alpha$ covering several orders of magnitude, $10^{-4} \le \alpha \le 10^{8}$. We apply these results to the experimental determination of dichroism and birefringence of the suspension as a function of $\alpha$.