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Collisions and rebounds of chemically active droplets

Published online by Cambridge University Press:  14 January 2020

K. Lippera Open the ORCID record for K. Lippera [Opens in a new window] ,
M. Morozov Open the ORCID record for M. Morozov [Opens in a new window] ,
M. Benzaquen Open the ORCID record for M. Benzaquen [Opens in a new window]  and
S. Michelin Open the ORCID record for S. Michelin [Opens in a new window]
K. Lippera
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
M. Morozov
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
M. Benzaquen
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
S. Michelin*
Affiliation:
LadHyX – Département de Mécanique, CNRS – Ecole Polytechnique, Institut Polytechnique de Paris, 91128Palaiseau, France
*
†Email address for correspondence: [email protected]
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Abstract

Active droplets swim as a result of the nonlinear advective coupling of the distribution of chemical species they consume or release with the Marangoni flows created by their non-uniform surface distribution. Most existing models focus on the self-propulsion of a single droplet in an unbounded fluid, which arises when diffusion is slow enough (i.e. beyond a critical Péclet number, $Pe_{c}$). Despite its experimental relevance, the coupled dynamics of multiple droplets and/or collision with a wall remains mostly unexplored. Using a novel approach based on a moving fitted bi-spherical grid, the fully coupled nonlinear dynamics of the chemical solute and flow fields is solved here to characterise in detail the axisymmetric collision of an active droplet with a rigid wall (or with a second droplet). The dynamics is strikingly different depending on the convective-to-diffusive transport ratio, $Pe$: near the self-propulsion threshold (moderate $Pe$), the rebound dynamics is set by chemical interactions and is well captured by asymptotic analysis; in contrast, for larger $Pe$, a complex and nonlinear combination of hydrodynamic and chemical effects set the detailed dynamics, including a closer approach to the wall and a velocity plateau shortly after the rebound of the droplet. The rebound characteristics, i.e. minimum distance and duration, are finally fully characterised in terms of $Pe$.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Propulsion Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 886 , 10 March 2020 , A17
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover.Google Scholar
Acrivos, A. & Taylor, T. D. 1962 Heat and mass transfer form single spheres in Stokes flow. Phys. Fluids 5, 387–394.CrossRefGoogle Scholar
Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21 (1), 61–99.CrossRefGoogle Scholar
Bechinger, C., Leonardo, R. D., Löwen, H., Reichhardt, C., Volpe, G. & Volpe, G. 2016 Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006.CrossRefGoogle Scholar
Berg, H. C. 1993 Random Walks in Biology. Princeton University Press.Google Scholar
Brennen, C. & Winnet, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339–398.CrossRefGoogle Scholar
Crowdy, D. G. 2013 Wall effects on self-diffusiophoretic janus particles: a theoretical study. J. Fluid Mech. 735, 473–498.CrossRefGoogle Scholar
Dreyfus, R., Baudry, J., Roper, M. L., Fermigier, M., Stone, H. A. & Bibette, J. 2005 Microscopic artificial swimmers. Nature 437, 862–865.CrossRefGoogle ScholarPubMed
Duan, W., Wang, W., Das, S., Yadav, V., Mallouk, T. E. & Sen, A. 2015 Synthetic nano- and micromachines in analytical chemistry: sensing, migration, capture, delivery and separation. Annu. Rev. Anal. Chem. 8, 311–333.CrossRefGoogle ScholarPubMed
Ebbens, S. J. 2016 Active colloids: progress and challenges towards realising autonomous applications. Curr. Opin. Colloid Interface Sci. 21, 14–23.CrossRefGoogle Scholar
Fadda, F., Gonnella, G., Lamura, A. & Tiribocchi, A. 2017 Lattice Boltzmann study of chemically-driven self-propelled droplets. Eur. Phys. J. E 40 (12), 112.CrossRefGoogle ScholarPubMed
Ghosh, A. & Fischer, P. 2009 Controlled propulsion of artificial magnetic nanostructured propellers. Nano Lett. 9, 2243–2245.CrossRefGoogle ScholarPubMed
Guasto, J. S., Rusconi, R. & Stocker, R. 2012 Fluid mechanics of planktonic microorganisms. Annu. Rev. Fluid Mech. 44, 373–400.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media (Mechanics of Fluids and Transport Processes). Springer.Google Scholar
Herminghaus, S., Maass, C. C., Krüger, C., Thutupalli, S., Goehring, L. & Bahr, C. 2014 Interfacial mechanisms in active emulsions. Soft Matt. 10, 7008–7022.CrossRefGoogle ScholarPubMed
Ibrahim, Y. & Liverpool, T. B. 2016 How walls affect the dynamics of self-phoretic microswimmers. Eur. Phys. J. 225 (8–9), 1843–1874.Google Scholar
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. Let. 113, 248302.CrossRefGoogle ScholarPubMed
Kanso, E. & Michelin, S. 2019 Phoretic and hydrodynamic interactions of weakly confined autophoretic particles. J. Chem. Phys. 150, 044902.Google ScholarPubMed
Kim, S. & Karrila, S. J. 2013 Microhydrodynamics: Principles and Selected Applications. Courier Corporation.Google Scholar
Kirchman, D. L. 2008 Microbial Ecology of the Oceans. Wiley.CrossRefGoogle Scholar
Krüger, C., Bahr, C., Herminghaus, S. & Maass, C. C. 2016a Dimensionality matters in the collective behaviour of active emulsions. Eur. Phys. J. E 39 (6), 64.CrossRefGoogle Scholar
Krüger, C., Klös, G., Bahr, C. & Maass, C. C. 2016b Curling liquid crystal microswimmers: a cascade of spontaneous symmetry breaking. Phys. Rev. Lett. 117, 048003.CrossRefGoogle Scholar
Lamb, H. 1945 Hydrodynamics. Dover Books on Physics.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming micro-organisms. Rep. Prog. Phys. 72, 096601.CrossRefGoogle Scholar
Leal, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.CrossRefGoogle Scholar
Liebchen, B. & Löwen, H. 2019 Which interactions dominate in active colloids? J. Chem. Phys. 150 (6), 061102.Google ScholarPubMed
Maass, C. C., Krger, C., Herminghaus, S. & Bahr, C. 2016 Swimming droplets. Annu. Rev. Condens. Matter Phys. 7, 171–193.CrossRefGoogle Scholar
Marchetti, M. C., Joanny, J. F., Ramaswamy, S., Liverpool, T. B., Prost, J., Rao, M. & Simha, R. A. 2013 Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189.CrossRefGoogle Scholar
Masoud, H. & Stone, H. A. 2019 The reciprocal theorem in fluid dynamics and transport phenomena. J. Fluid Mech. 879, P1.CrossRefGoogle Scholar
Medina-Sánchez, M., Schwarz, L., Meyer, A. K., Hebenstreit, F. & Schmidt, O. G. 2015 Cellular cargo delivery: toward assisted fertilization by sperm-carrying micromotors. Nano Lett. 16 (1), 555–561.CrossRefGoogle ScholarPubMed
Michelin, S., Gallino, G., Gallaire, F. & Lauga, E. 2019 Viscous growth and rebound or a bubble near a rigid surface. J. Fluid Mech. 860, 172–199.CrossRefGoogle Scholar
Michelin, S., Guérin, E. & Lauga, E. 2018 Collective dissolution of microbubbles. Phys. Rev. Fluids 3, 043601.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. 2015 Autophoretic locomotion from geometric asymmetry. Eur. Phys. J. E 38 (2), 7.CrossRefGoogle ScholarPubMed
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25, 061701.CrossRefGoogle Scholar
Moerman, P. G., Moyses, H. W., van der Wee, E. B., Grie, D. G., van Blaaderen, A., Kegel, W. K., Groenewold, J. & Brujic, J. 2017 Solute-mediated interactions between active droplets. Phys. Rev. E 96, 032607.Google ScholarPubMed
Moran, J. L. & Posner, J. D. 2017 Phoretic self-propulsion. Annu. Rev. Fluid Mech. 49, 511.CrossRefGoogle Scholar
Morozov, M. & Michelin, S. 2019a Nonlinear dynamics of a chemically-active drop: from steady to chaotic self-propulsion. J. Chem. Phys. 150, 044110.Google Scholar
Morozov, M. & Michelin, S. 2019b Orientational instability and spontaneous rotation of active nematic droplets. Soft Matt. 15, 7814–7822.CrossRefGoogle Scholar
Morozov, M. & Michelin, S. 2019c Self-propulsion near the onset of Marangoni instability of deformable active droplets. J. Fluid Mech. 860, 711–738.CrossRefGoogle Scholar
Pak, O. S., Feng, J. & Stone, H. A. 2014 Viscous Marangoni migration of a drop in a Poiseuille flow at low surface Péclet numbers. J. Fluid Mech. 753, 535–552.CrossRefGoogle Scholar
Palacci, J., Sacanna, S., Steinberg, A. P., Pine, D. J. & Chaikin, P. M. 2013 Living crystals of light-activated colloidal surfers. Science 339, 936–940.CrossRefGoogle ScholarPubMed
Park, B.-W., Zhuang, J., Yasa, O. & Sitti, M. 2017 Multifunctional bacteria-driven microswimmers for targeted active drug delivery. ACS Nano 11 (9), 8910–8923.CrossRefGoogle ScholarPubMed
Pohl, O. & Stark, H. 2014 Dynamic clustering and chemotactic collapse of self-phoretic active particles. Phys. Rev. Lett. 112 (23), 238303.CrossRefGoogle ScholarPubMed
Popescu, M. N., Tasinkevych, M. & Dietrich, S. 2011 Pulling and pushing a cargo with a catalytically active carrier. Eur. Phys. Lett. 95, 28004.CrossRefGoogle Scholar
Rednikov, A. Y., Kurdyumov, V. N., Ryazantsev, Y. S. & Velarde, M. G. 1995 The role of time-varying gravity on the motion of a drop induced by Marangoni instability. Phys. Fluids 7 (11), 2670–2678.CrossRefGoogle Scholar
Rednikov, A. Y., Ryazantsev, Y. S. & Velarde, M. G. 1994 Drop motion with surfactant transfer in a homogeneous surrounding. Phys. Fluids 6, 451.CrossRefGoogle Scholar
Reigh, S. Y. & Kapral, R. 2015 Catalytic dimer nanomotors: continuum theory and microscopic dynamics. Soft Matt. 11, 3149–3158.CrossRefGoogle ScholarPubMed
Ryazantsev, Y. S., Velarde, M. G., Rubio, R. G., Guzman, E., Ortega, F. & Lopez, P. 2017 Thermo-and soluto-capillarity: passive and active drops. Adv. Colloid Interface Sci. 247, 52–80.CrossRefGoogle ScholarPubMed
Saha, S., Golestanian, R. & Ramaswamy, S. 2014 Clusters, asters, and collective oscillations in chemotactic colloids. Phys. Rev. E 89 (6), 062316.Google ScholarPubMed
Schmitt, M. & Stark, H. 2013 Swimming active droplet: a theoretical analysis. Eur. Phys. Lett. 101 (4), 44008.CrossRefGoogle Scholar
Singh, A. V., Hosseinidoust, Z., Park, B.-W., Yasa, O. & Sitti, M. 2017 Microemulsion-based soft bacteria-driven microswimmers for active cargo delivery. ACS Nano 11 (10), 9759–9769.CrossRefGoogle ScholarPubMed
Soto, R. & Golestanian, R. 2014 Self-assembly of catalytically active colloidal molecules: tailoring activity through surface chemistry. Phys. Rev. Lett. 112, 068301.CrossRefGoogle ScholarPubMed
Soto, R. & Golestanian, R. 2015 Self-assembly of active colloidal molecules with dynamic function. Phys. Rev. E 91 (5), 052304.Google ScholarPubMed
Stimson, M. & Jeffery, G. B. 1926 The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. 111 (757), 110–116.CrossRefGoogle Scholar
Suarez, S. S. & Pacey, A. A. 2006 Sperm transport in the female reproductive tract. Human Reprod. Update 12, 23–37.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, 062703.Google ScholarPubMed
Theurkauff, I., Cottin-Bizonne, C., Palacci, J., Ybert, C. & Bocquet, L. 2012 Dynamic clustering in active colloidal suspensions with chemical signaling. Phys. Rev. Lett. 108, 268303.CrossRefGoogle ScholarPubMed
Thutupalli, S., Geyer, D., Singh, R., Adhikari, R. & Stone, H. A. 2018 Flow-induced phase separation of active particles is controlled by boundary conditions. Proc. Natl Acad. Sci. USA 115 (21), 5403–5408.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., Tsuha, H., Yamada, K., Takakura, K., Ikegami, T. & Sugawara, T. 2006 Listeria-like motion of oil droplets. Chem. Lett. 35 (7), 708–709.CrossRefGoogle Scholar
Uspal, W. E., Popescu, M. N., Dietrich, S. & Tasinkevych, M. 2015 Self-propulsion of a catalytically active particle near a planar wall: from reflection to sliding and hovering. Soft Matt. 11 (3), 434–438.CrossRefGoogle Scholar
Varma, A. & Michelin, S. 2019 Modeling chemo-hydrodynamic interactions of phoretic particles: a unified framework. Phys. Rev. Fluids 4, 124204.CrossRefGoogle Scholar
Varma, A., Montenegro-Johnson, T. D. & Michelin, S. 2018 Clustering-induced self-propulsion of isotropic autophoretic particles. Soft Matt. 14 (35), 7155–7173.CrossRefGoogle ScholarPubMed
Yabunaka, S. & Yoshinaga, N. 2016 Collision between chemically driven self-propelled drops. J. Fluid Mech. 806, 205–233.CrossRefGoogle Scholar
Yariv, E. 2016 Wall-induced self-diffusiophoresis of active isotropic colloids. Phys. Rev. Fluids 1 (3), 032101.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.Google ScholarPubMed

Lippera et al. supplementary movie 1

Collision dynamics of a droplet with a rigid wall with Pe=6. The evolution of the concentration field is also shown (colours)

Download Lippera et al. supplementary movie 1(Video)
Video 4.2 MB

Lippera et al. supplementary movie 2

Collision dynamics of a droplet with a rigid wall with Pe=20. The evolution of the concentration field is also shown (colours)

Download Lippera et al. supplementary movie 2(Video)
Video 3.1 MB