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The influence of fluid flows over Brownian motion is a topic of much theoretical and practical interest which has received wide attention. However, most of the textbooks on statistical physics are limited to Brownian motion in fluids at rest. Here, we deal with the simple example of the Brownian motion of a single particle under a steady homogeneous shear flow by starting from the Langevin equation. We explicitly solve the equation and show how the presence of the shear drastically changes the time evolution of the second moments of the position of the particle, and we discuss the form of the time-dependent effective diffusion coefficient.
Katayama et al. (Wed,) studied this question.
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