Skip to main content Accessibility help
×
Home

No net motion for oscillating near-spheres at low Reynolds numbers

  • K. Lippera (a1), O. Dauchot (a2), S. Michelin (a1) and M. Benzaquen (a1)

Abstract

We investigate the flow around an oscillating nearly spherical particle at low, yet non-vanishing, Reynolds numbers ( $Re$ ), and the potential resulting locomotion. We analytically demonstrate that no net motion can arise up to order one in $Re$ and order one in the asphericity parameter, regardless of the particle’s shape. Therefore, geometry-induced acoustic streaming propulsion, if any, must arise at higher order.

Copyright

Corresponding author

Email address for correspondence: michael.benzaquen@polytechnique.edu

References

Hide All
Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Courier Corporation.
Ahmed, S., Wang, W., Bai, L., Gentekos, D. T., Hoyos, M. & Mallouk, T. E. 2016 Density and shape effects in the acoustic propulsion of bimetallic nanorod motors. ACS Nano 10 (4), 47634769.
Alben, S. & Shelley, M. 2005 Coherent locomotion as an attracting state for a free flapping body. Proc. Natl Acad. Sci. USA 102 (32), 1116311166.
Bechinger, C., Di Leonardo, R., Löwen, H., Reichhardt, C., Volpe, G. & Volpe, G. 2016 Active particles in complex and crowded environments. Rev. Mod. Phys. 88 (4), 150.
Bricard, A., Caussin, J.-B., Desreumaux, N., Dauchot, O. & Bartolo, D. 2013 Emergence of macroscopic directed motion in populations of motile colloids. Nature 503 (7474), 95.
Buttinoni, I., Bialké, J., Kümmel, F., Löwen, H., Bechinger, C. & Speck, T. 2013 Dynamical clustering and phase separation in suspensions of self-propelled colloidal particles. Phys. Rev. Lett. 110 (23), 238301.
Collis, J. F., Chakraborty, D. & Sader, J. E. 2017 Autonomous propulsion of nanorods trapped in an acoustic field. J. Fluid Mech. 825, 2948.
Dreyfus, R., Baudry, J., Roper, M. L., Fermigier, M., Stone, H. A. & Bibette, J. 2005 Microscopic artificial swimmers. Nature 437 (7060), 862865.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. Prentice Hall.
Izri, Z., Van Der Linden, M. N., Michelin, S. & Dauchot, O. 2014 Self-propulsion of pure water droplets by spontaneous Marangoni-stress-driven motion. Phys. Rev. Lett. 113 (24), 248302.
Kim, S. & Karrila, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Li, J., Rozen, I. & Wang, J. 2016 Rocket science at the nanoscale. ACS Nano 10, 56195634.
Martinez-Pedrero, F. & Tierno, P. 2015 Magnetic propulsion of self-assembled colloidal carpets: efficient cargo transport via a conveyor-belt effect. Phys. Rev. Appl. 3 (5), 051003.
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25 (6), 061701.
Moran, J. L. & Posner, J. D. 2017 Phoretic self-propulsion. Annu. Rev. Fluid Mech. 49, 511540.
Nadal, F. & Lauga, E. 2014 Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies. Phys. Fluids 26 (8), 082001.
Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. 2013 Living crystals of light-activated colloidal surfers. Science 339 (6122), 936940.
Purcell, E. M. 1977 Life at low-Reynolds number. Am. J. Phys. 45, 311.
Sabrina, S., Tasinkevych, M., Ahmed, S., Brooks, A. M., Olivera de la Cruz, M., Mallouk, T. E. & Bishop, K. J. M. 2018 Shape-directed microspinners powered by ultrasound. ACS Nano 12 (3), 29392947.
Sani, R. L.1963 Convective instability. PhD thesis, University of Minnesota.
Soto, F., Wagner, G. L., Garcia-Gradilla, V., Gillespie, K. T., Lakshmipathy, D. R., Karshalev, E., Angell, C., Chen, Y. & Wang, J. 2016 Acoustically propelled nanoshells. Nanoscale 8 (41), 1778817793.
Sundararajan, S., Lammert, P. E., Zudans, A. W., Crespi, V. H. & Sen, A. 2008 Catalytic motors for transport of colloidal cargo. Nano Lett. 8 (5), 12711276.
Tiwari, D. K., Behari, J. & Sen, P. 2008 Application of nanoparticles in waste water treatment. World Appl. Sci. J. 3 (3), 417433.
Wang, S. & Wu, N. 2014 Selecting the swimming mechanisms of colloidal particles: bubble propulsion versus self-diffusiophoresis. Langmuir 30, 34773486.
Wang, W., Castro, L. A., Hoyos, M. & Mallouk, T. E. 2012 Autonomous motion of metallic microrods propelled by ultrasound. ACS Nano 6 (7), 61226132.
Wiggins, C. H. & Goldstein, R. E. 1998 Flexive and propulsive dynamics of elastica at low Reynolds number. Phys. Rev. Lett. 80 (17), 3879.
Zhang, W. & Stone, H. A. 1998 Oscillatory motions of circular disks and nearly spherical particles in viscous flows. J. Fluid Mech. 367, 329358.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed