Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-30T20:35:19.696Z Has data issue: false hasContentIssue false
  • English
  • Français

Swimming dynamics of a self-propelled droplet

Published online by Cambridge University Press:  14 January 2022

Gaojin Li Open the ORCID record for Gaojin Li [Opens in a new window]
Gaojin Li*
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai 200240, PR China School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Chemically active droplets often show intriguing self-propulsion behaviour in a surfactant solution. The drop motion is controlled by the nonlinear coupling among chemical transport in the bulk fluid, consumption of surfactant at the drop surface, and the fluid flow driven by the self-generated Marangoni stress. To quantify the underlying hydrodynamics, this work investigates the swimming motion of a two-dimensional drop that is determined by two dimensionless parameters, the Péclet number ($Pe$) and Damköhler number ($Da$). The weakly nonlinear analysis shows that near the instability threshold, the drop undergoes a supercritical bifurcation with velocity $U\sim \sqrt {Pe-Pe_c}$, where $Pe_c$ is the critical Péclet number for the onset of dipole mode. In the highly nonlinear regime, the drop transits from steady translation of pusher swimming to unsteady motion of mixed pusher–puller swimming along zigzaging trajectories of quadrangle and/or triangle waves. Mode decomposition shows that the zigzag motion is directly related to the interaction between the secondary wake of low surfactant concentration and the primary wake.

JFM classification

Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A20
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Andres, J.T.H. & Cardoso, S.S.S. 2011 Onset of convection in a porous medium in the presence of chemical reaction. Phys. Rev. E 83 (4), 046312.CrossRefGoogle Scholar
Ban, T., Sugiyama, M., Nagatsu, Y. & Tokuyama, H. 2018 Motion-based detection of lanthanides (iii) using self-propelled droplets. J. Phys. Chem. B 122 (46), 10647–10651.CrossRefGoogle ScholarPubMed
Ban, T., Tani, K., Nakata, H. & Okano, Y. 2014 Self-propelled droplets for extracting rare-earth metal ions. Soft Matt. 10 (33), 6316–6320.CrossRefGoogle ScholarPubMed
Chen, Y., Chong, K.L., Liu, L., Verzicco, R. & Lohse, D. 2021 Instabilities driven by diffusiophoretic flow on catalytic surfaces. J. Fluid Mech. 919, A10.CrossRefGoogle Scholar
Frigo, M. & Johnson, S.G. 2005 The design and implementation of FFTW3. Proc. IEEE 93 (2), 216–231. Special issue on “Program Generation, Optimization, and Platform Adaptation”.CrossRefGoogle Scholar
Golestanian, R. 2009 Anomalous diffusion of symmetric and asymmetric active colloids. Phys. Rev. Lett. 102 (18), 188305.CrossRefGoogle ScholarPubMed
Golestanian, R., Liverpool, T.B. & Ajdari, A. 2005 Propulsion of a molecular machine by asymmetric distribution of reaction products. Phys. Rev. Lett. 94 (22), 220801.CrossRefGoogle ScholarPubMed
Herminghaus, S., Maass, C.C., Krüger, C., Thutupalli, S., Goehring, L. & Bahr, C. 2014 Interfacial mechanisms in active emulsions. Soft Matt. 10 (36), 7008–7022.CrossRefGoogle ScholarPubMed
Hokmabad, B.V., Dey, R., Jalaal, M., Mohanty, D., Almukambetova, M., Baldwin, K.A., Lohse, D. & Maass, C.C. 2021 Emergence of bimodal motility in active droplets. Phys. Rev. X 11 (1), 011043.Google Scholar
Hu, W.-F., Lin, T.-S., Rafai, S. & Misbah, C. 2019 Chaotic swimming of phoretic particles. Phys. Rev. Lett. 123 (23), 238004.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Jin, C., Krüger, C. & Maass, C.C. 2017 Chemotaxis and autochemotaxis of self-propelling droplet swimmers. Proc. Natl Acad. Sci. USA 114 (20), 5089–5094.CrossRefGoogle ScholarPubMed
Krüger, C., Klös, G., Bahr, C. & Maass, C.C. 2016 Curling liquid crystal microswimmers: a cascade of spontaneous symmetry breaking. Phys. Rev. Lett. 117 (4), 048003.CrossRefGoogle ScholarPubMed
Lighthill, M.J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Maths 5 (2), 109–118.CrossRefGoogle Scholar
Li, G., Townsend, A., Archer, L.A., Koch, D.L. 2022 Electroconvection near an ion-selective surface with Butler–Volmer kinetics. J. Fluid Mech. 930, A26.CrossRefGoogle Scholar
Michelin, S. & Lauga, E. 2014 Phoretic self-propulsion at finite Péclet numbers. J. Fluid Mech. 747, 572–604.CrossRefGoogle Scholar
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25 (6), 061701.CrossRefGoogle Scholar
Morozov, M. & Michelin, S. 2019 a Nonlinear dynamics of a chemically-active drop: from steady to chaotic self-propulsion. J. Chem. Phys. 150 (4), 044110.CrossRefGoogle ScholarPubMed
Morozov, M. & Michelin, S. 2019 b Self-propulsion near the onset of Marangoni instability of deformable active droplets. J. Fluid Mech. 860, 711–738.CrossRefGoogle Scholar
Nagai, K.H., Takabatake, F., Sumino, Y., Kitahata, H., Ichikawa, M. & Yoshinaga, N. 2013 Rotational motion of a droplet induced by interfacial tension. Phys. Rev. E 87 (1), 013009.CrossRefGoogle ScholarPubMed
Ohta, T., Ohkuma, T. & Shitara, K. 2009 Deformation of a self-propelled domain in an excitable reaction-diffusion system. Phys. Rev. E 80 (5), 056203.CrossRefGoogle Scholar
Sario, L., Nakai, M., Wang, C. & Chung, L.O. 1977 Laplace-Beltrami Operator, pp. 12–25. Springer Berlin Heidelberg.CrossRefGoogle Scholar
Schmid, P.J. & Henningson, D.S. 2002 Stability and Transition in Shear Flows. Springer.Google Scholar
Stone, H.A. & Samuel, A.D.T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77 (19), 4102.CrossRefGoogle ScholarPubMed
Suda, S., Suda, T., Ohmura, T. & Ichikawa, M. 2021 Straight-to-curvilinear motion transition of a swimming droplet caused by the susceptibility to fluctuations. Phys. Rev. Lett. 127 (8), 088005.CrossRefGoogle ScholarPubMed
Suga, M., Suda, S., Ichikawa, M. & Kimura, Y. 2018 Self-propelled motion switching in nematic liquid crystal droplets in aqueous surfactant solutions. Phys. Rev. E 97 (6), 062703.CrossRefGoogle ScholarPubMed
Thutupalli, S., Seemann, R. & Herminghaus, S. 2011 Swarming behavior of simple model squirmers. New J. Phys. 13 (7), 073021.CrossRefGoogle Scholar
Toyota, T., Sugiyama, H., Hiroi, S., Ito, H. & Kitahata, H. 2020 Chemically artificial rovers based on self-propelled droplets in micrometer-scale environment. Curr. Opin. Colloid Interface Sci. 49, 60–68.CrossRefGoogle Scholar
Tu, Y., Peng, F., André, A.A.M., Men, Y., Srinivas, M. & Wilson, D.A. 2017 Biodegradable hybrid stomatocyte nanomotors for drug delivery. ACS Nano 11 (2), 1957–1963.CrossRefGoogle ScholarPubMed
Vervisch, L. & Poinsot, T. 1998 Direct numerical simulation of non-premixed turbulent flames. Annu. Rev. Fluid Mech. 30 (1), 655–691.CrossRefGoogle Scholar
Yoshinaga, N., Nagai, K.H., Sumino, Y. & Kitahata, H. 2012 Drift instability in the motion of a fluid droplet with a chemically reactive surface driven by Marangoni flow. Phys. Rev. E 86 (1), 016108.CrossRefGoogle ScholarPubMed

Li Supplementary Movie 1

The concentration field and trajectory for a swimming drop at Pe=38 and Da=0.

Download Li Supplementary Movie 1(Video)
Video 61.2 MB

Li Supplementary Movie 2

The concentration field and trajectory for a swimming drop at Pe=40 and Da=0.

Download Li Supplementary Movie 2(Video)
Video 60.2 MB