With the recent developments in fluid dynamics, it is now possible to analyse complex background flows such as those observed in marine turbulence, saturated soils, as well as in microfluidic devices.

Growing interest in microfluidic devices and microrobots, coupled with the ubiquitous presence of self-propelled biological microswimmers such as bacteria, algae, and planktons, calls for further understanding of microswimmer dynamics in a flow current.

A useful theoretical foundation on this front is provided by Jeffery’s equations. These are a simple set of ordinary differential equations that describe how the orientation of a spheroidal body evolves over time in a viscous fluid. The non-uniform periodic rotational motion of a body immersed in a simple shear flow traces a closed orbit, known as Jeffery’s orbit.

In a recently published review, researcher Kenta Ishimoto from Kyoto University, Japan has summarized the latest progress in our understanding of microswimmer hydrodynamics through the lens of Jeffery’s orbits.

The article provides a theoretical introduction on Jeffery’s equations for simple microswimmers and considers how the equations can be used to study microswimmers with more complex shapes. The review then details the concept of “hydrodynamic shapes,” and how it relates to symmetries in the governing equations.

While summation of flow fields helps in determining the background flow for individual swimmers, scaling up these interactions can help us understand their collective behavior.

Additionally, the review suggests a potential application of Jeffery’s equations in understanding the adaptive behaviors of smart swimmers in complex environments.

In summary, the concepts presented in this review provide a comprehensive theoretical foundation of Jeffery’s orbits and their relation to microswimmers in a variety of flows, and can help advance our understanding of fluid dynamics in active and artificial fluid systems.