Orientation control by flow: Exact results and Langevin simulations

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 $\alpha$.