Transition in swimming direction in a model self-propelled inertial swimmer


Motility is defined as the ability of an organism to move independently using metabolic energy. Motility is genetically determined, but may be affected by environmental factors. Therefore, understanding motility requires connections between fundamental physics and biology. Motility has numerous potential applications, such as in drug-delivering nanomachines and autonomous underwater vehicles. Generally, in fluid mechanics swimming regimes are classified using Reynolds number (Re). For high (Re>1) and low (Re<1, also Stokes flows) Re flow systems, much has been published, however, for intermediate Re (Re int~1-1000), little has been done. In fact, most prior studies on Reint motility have focused on the details of specific organisms hence few general models exist for motility at Reint. All factors considered, there is insufficient understanding regarding the unifying physical mechanisms that swimmers at Reint exhibit. Therefore, to develop a theoretical basis for swimming, more models with varying degrees of freedom that operate under different conditions at Reint are needed.

Recently, a team of scientists led by Dr. Daphne Klotsa of the University of North Carolina at Chapel Hill, Dr. Thomas Dombrowski, Dr. Shannon K. Jones, and Dr. Boyce E. Griffith together with Dr. Georgios Katsikis at Massachusetts Institute of Technology and Dr. Amneet Pal Singh Bhalla at San Diego State University presented a study in which they put forward a facile, reciprocal and self-propelled model swimmer, termed the spherobot, at intermediate Re. Specifically, the presented spherobot made use of steady streaming (SS), i.e. the nonzero, time-averaged flow that arises at Reint due to oscillations of a rigid body in a fluid, for propulsion. Their work is currently published in the research journal, Physical Review Fluids.

The spherebot composed of two unequal spheres with specific radii were coupled to one another by prescribing the distance between their centers, in antiphase, generating SS flows. The scientists then computationally studied the spherobot’s motility over a broad range of parameters: viscosity, sphere amplitudes, distance between the spheres, sphere radii, and sphere radii ratio.

The authors observed that at Re=0, the spherobot could not swim because of Purcell’s scallop theorem, while as its reciprocal; stoke, did not break time reversal symmetry. At low, nonzero Re, the spherobot started to swim and, interestingly, switched swimming direction from a small-sphere-leading to a large-sphere-leading regime. Additionally, the scholars found out that the point of transition collapsed to a critical value when the appropriate Reynolds number was used, which revealed a strong dependence on the SS flows of the small sphere. Further analysis of the flow fields revealed that the transition in swimming direction corresponded to the reversal of SS flows around the spherobot that occurred as the Reynolds number increased.

In summary, the study reported a new model spherebot swimmer that utilized steady streaming to propel itself. In general, the team’s main findings were: first, a transition in the swimming direction that collapsed onto a single critical Reynolds number, and secondly, the physical mechanism for the transition in swimming is the reversal of SS flows. Altogether, based on these findings, the research team proposed that SS could be an important physical mechanism present more generally in motility at Reint, both in biological organisms and also when designing artificial swimmers.


Thomas Dombrowski, Shannon K. Jones, Georgios Katsikis, Amneet Pal Singh Bhalla, Boyce E. Griffith, Daphne Klotsa. Transition in swimming direction in a model self-propelled inertial swimmer. Physical Review Fluids 4, 021101(R) (2019)

Go To Physical Review Fluids 

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