# Experimental characterization of helical swimming trajectories in circular channels

## Abstract

Trajectories of microorganisms and artificial helical swimmers in confinements are important in biology and for controlled swimming in medical applications. Numerical studies on the locomotion of model microorganisms and spherical particles are reported in the literature. Here, we report experimental results on the trajectories and velocities of artificial helical swimmers in circular channels. Trajectories are recorded by a digital camera and images are processed to obtain the radial position and the orientation of the swimmer. Tail length, channel diameter, rotation frequency and the rate of the Poiseuille flow are varied in the experiments. Experimental results demonstrate that confinement and flow affect the orientation of swimmer and the swimming performance. Swimmers follow stable helical trajectories in the forward direction when the tail pushes the swimmer. However, when the tail pulls the swimmer in the backward direction trajectories converge to a straight line in the narrow channel, whereas helical trajectories are observed for pullers as well in the wide channel.

## Keywords

Confined swimming Low-Reynolds-number swimming Swimming trajectories Image processing Refraction correction## Supplementary material

## References

- Acemoglu A, Yesilyurt S (2014) Effects of geometric parameters on swimming of micro organisms with single helical flagellum in circular channels. Biophys J 106(7):1537–1547CrossRefGoogle Scholar
- Acemoglu A, Yesilyurt S (2015) Effects of poiseuille flows on swimming of magnetic helical robots in circular channels. Microfluid Nanofluid 19(5):1109–1122CrossRefGoogle Scholar
- Berg HC, Turner L (1990) Chemotaxis of bacteria in glass capillary arrays.
*Escherichia coli*, motility, microchannel plate, and light scattering. Biophys J 58(4):919–930CrossRefGoogle Scholar - Biondi SA, Quinn JA, Goldfine H (1998) Random motility of swimming bacteria in restricted geometries. AIChE J 44(8):1923–1929CrossRefGoogle Scholar
- Chacón R (2013) Chaotic dynamics of a microswimmer in Poiseuille flow. Phys Rev E 88(5):052905CrossRefGoogle Scholar
- Ghosh A, Fischer P (2009) Controlled propulsion of artificial magnetic nanostructured propellers. Nano Lett 9(6):2243–2245CrossRefGoogle Scholar
- Ghosh A, Paria D, Singh HJ, Venugopalan PL, Ghosh A (2012) Dynamical configurations and bistability of helical nanostructures under external torque. Phys Rev E 86(3):031401CrossRefGoogle Scholar
- Hosney A, Klingner A, Misra S, Khalil ISM (2015) Propulsion and steering of helical magnetic microrobots using two synchronized rotating dipole fields in three-dimensional space. In: 2015 IEEE/RSJ international conference on intelligent robots and systems (IROS). IEEE, pp 1988–1993Google Scholar
- Lele PP, Roland T, Shrivastava A, Chen Y, Berg HC (2016) The flagellar motor of
*Caulobacter crescentus*generates more torque when a cell swims backwards. Nat Phys 12(2):175CrossRefGoogle Scholar - Man Y, Lauga E (2013) The wobbling-to-swimming transition of rotated helices. Phys Fluids 25(7):071904CrossRefGoogle Scholar
- MathWorks (2016) User’s guide (R2016a)Google Scholar
- Peyer KE, Zhang L, Kratochvil BE, Nelson BJ (2010) Non-ideal swimming of artificial bacterial flagella near a surface. In: Robotics and automation (ICRA), 2010 IEEE International Conference on. IEEE, pp 96–101Google Scholar
- Tabak AF, Yesilyurt S (2014) Computationally-validated surrogate models for optimal geometric design of bio-inspired swimming robots: helical swimmers. Comput Fluids 99:190–198MathSciNetCrossRefGoogle Scholar
- Temel FZ, Yesilyurt S (2013) Simulation-based analysis of micro-robots swimming at the center and near the wall of circular mini-channels. Microfluid Nanofluid 14(1–2):287–298CrossRefGoogle Scholar
- Tottori S, Zhang L, Qiu F, Krawczyk KK, Franco-Obregón A, Nelson BJ (2012) Magnetic helical micromachines: fabrication, controlled swimming, and cargo transport. Adv Mater 24(6):811–816CrossRefGoogle Scholar
- Zhang L, Abbott JJ, Dong L, Kratochvil BE, Bell D, Nelson BJ (2009a) Artificial bacterial flagella: fabrication and magnetic control. Appl Phys Lett 94(6):064107CrossRefGoogle Scholar
- Zhang L, Abbott JJ, Dong L, Peyer KE, Kratochvil BE, Zhang H et al (2009b) Characterizing the swimming properties of artificial bacterial flagella. Nano Lett 9(10):3663–3667CrossRefGoogle Scholar
- Zhu L, Lauga E, Brandt L (2013) Low-Reynolds-number swimming in a capillary tube. J Fluid Mech 726:285–311MathSciNetCrossRefMATHGoogle Scholar
- Zöttl A, Stark H (2012) Nonlinear dynamics of a microswimmer in Poiseuille flow. Phys Rev Lett 108(21):218104CrossRefGoogle Scholar
- Zöttl A, Stark H (2013) Periodic and quasiperiodic motion of an elongated microswimmer in Poiseuille flow. Eur Phys J E 36(4):1–10Google Scholar