Classical work of Jeffery from 1922 established how at low Reynolds number, ellipsoids in steady shear flow undergo periodic motion with non-uniform rotation rate, termed 'Jeffery orbits'. I will present two problems where Jeffery orbits play a critical role in understanding the transport and aggregation of rod-shaped organisms. I will discuss the trapping of motile chemotactic bacteria in high shear, and the sedimentation rate of negatively buoyant plankton.
Bearon, R. N., & Hazel, A. L. (2015). The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel. JOURNAL OF FLUID MECHANICS, 771. doi:10.1017/jfm.2015.198
Clifton, W., Bearon, R. N., & Bees, M. A. (2018). Enhanced sedimentation of elongated plankton in simple flows. IMA JOURNAL OF APPLIED MATHEMATICS, 83(4), 743-766. doi:10.1093/imamat/hxy024