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Collision between chemically driven self-propelled drops

Published online by Cambridge University Press:  30 September 2016

Shunsuke Yabunaka  and
Natsuhiko Yoshinaga Open the ORCID record for Natsuhiko Yoshinaga [Opens in a new window]
Shunsuke Yabunaka
Affiliation:
Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-Cho, Kyoto, 606-8502, Japan
Natsuhiko Yoshinaga*
Affiliation:
WPI – Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan MathAM-OIL, AIST, Sendai 980-8577, Japan
*
†Email address for correspondence: yoshinaga@wpi-aimr.tohoku.ac.jp
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Abstract

We use analytical and numerical approaches to investigate head-on collisions between two self-propelled drops described as a phase separated binary mixture. Each drop is driven by chemical reactions that isotropically produce or consume the concentration of a third chemical component, which affects the surface tension of the drop. The isotropic distribution of the concentration field is destabilized by motion of the drop, which is created by the Marangoni flow from the concentration-dependent surface tension. This symmetry-breaking self-propulsion is distinct from other self-propulsion mechanisms due to its intrinsic polarity of squirmers and self-phoretic motion; there is a bifurcation point below which the drop is stationary and above which it moves spontaneously. When two drops are moving in the opposite direction along the same axis, their interactions arise from hydrodynamics and concentration overlap. We found that two drops exhibit either an elastic collision or fusion, depending on the distance from their bifurcation point, which may be controlled, for example, by viscosity. An elastic collision occurs when there is a balance between dissipation and the injection of energy by chemical reactions. We derive the reduced equations for the collision between two drops and analyse the contributions from the two interactions. The concentration-mediated interaction is found to dominate the hydrodynamic interaction for a head-on collision.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Propulsion
Type
Papers
Information
Journal of Fluid Mechanics , Volume 806 , 10 November 2016 , pp. 205 - 233
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Copyright
© 2016 Cambridge University Press 

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References

Anderson, D. M., Mcfadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139–165.Google Scholar
Arfken, G. B., Weber, H. J. & Weber, H. J. 1968 Mathematical Methods for Physicists. Academic.Google Scholar
Bhagavatula, R., Jasnow, D. & Ohta, T. 1997 Nonequilibrium interface equations: an application to thermocapillary motion in binary systems. J. Stat. Phys. 88 (5), 1013–1031.Google Scholar
Blake, J. R. 1971 Self propulsion due to oscillations on the surface of a cylinder at low reynolds number. Bull. Austral. Math. Soc. 5 (02), 255–264.Google Scholar
Bode, M., Liehr, A. W., Schenk, C. P. & Purwins, H.-G. 2002 Interaction of dissipative solitons: particle-like behaviour of localized structures in a three-component reaction-diffusion system. Physica D 161 (1–2), 45–66.Google Scholar
Cates, M. E. & Tailleur, J. 2015 Motility-induced phase separation. Annu. Rev. Condens. Matter Phys. 6 (1), 219–244.Google Scholar
Ei, S. I., Mimura, M. & Nagayama, M. 2006 Interacting spots in reaction diffusion systems. J. Discrete Continuous Dyn. Syst. 14 (1), 31–62.Google Scholar
Fedosov, A. I. 1956 Thermocapillary motion (translated by V. Berejnov & K. Morozov). Zh. Fiz. Khim. 30 (2), 366–373 (see also arXiv:1303:024).Google Scholar
Golovin, A. A., Nir, A. & Pismen, L. M. 1995 Spontaneous motion of two droplets caused by mass transfer. Ind. Engng Chem. Res. 34 (10), 3278–3288.Google Scholar
Hetsroni, G. & Haber, S. 1970 The flow in and around a droplet or bubble submerged in an unbound arbitrary velocity field. Rheol. Acta 9 (4), 488–496.Google Scholar
Hohenberg, P. C. & Halperin, B. I. 1977 Theory of dynamic critical phenomena. Rev. Mod. Phys. 49 (3), 435–479.Google Scholar
Howse, J. R., Jones, R. A. L., Ryan, A. J., Gough, T., Vafabakhsh, R. & Golestanian, R. 2007 Self-motile colloidal particles: from directed propulsion to random walk. Phys. Rev. Lett. 99 (4), 048102.CrossRefGoogle ScholarPubMed
Ikura, Y. S., Heisler, E., Awazu, A., Nishimori, H. & Nakata, S. 2013 Collective motion of symmetric camphor papers in an annular water channel. Phys. Rev. E 88, 012911.Google Scholar
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.Google Scholar
Ishimoto, K. & Gaffney, E. A. 2013 Squirmer dynamics near a boundary. Phys. Rev. E 88, 062702.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. Lett. 113, 248302.CrossRefGoogle ScholarPubMed
Jeffrey, D. J. & Onishi, Y. 1984 Calculation of the resistance and mobility functions for two unequal rigid spheres in low-reynolds-number flow. J. Fluid Mech. 139, 261–290.Google Scholar
Jiang, H.-R., Yoshinaga, N. & Sano, M. 2010 Active motion of janus particle by self-thermophoresis in defocused laser beam. Phys. Rev. Lett. 105, 268302.CrossRefGoogle ScholarPubMed
Kawasaki, K. & Ohta, T. 1983 Kinetics of fluctuations for systems undergoing phase transitions – interfacial approach. Physica A 118 (1–3), 175–190.Google Scholar
Kitahata, H., Yoshinaga, N., Nagai, K. H. & Sumino, Y. 2011 Spontaneous motion of a droplet coupled with a chemical wave. Phys. Rev. E 84 (1), 015101.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.Google Scholar
Lavrenteva, O. M., Leshansky, A. M. & Nir, A. 1999 Spontaneous thermocapillary interaction of drops, bubbles and particles: unsteady convective effects at low Peclet numbers. Phys. Fluids 11 (7), 1768–1780.CrossRefGoogle Scholar
Levan, M. D. 1981 Motion of a droplet with a newtonian interface. J. Colloid Interface Sci. 83 (1), 11–17.Google Scholar
Li, G.-J. & Ardekani, A. M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90, 013010.Google Scholar
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.Google Scholar
Matas-Navarro, R., Golestanian, R., Liverpool, T. B. & Fielding, S. M. 2014 Hydrodynamic suppression of phase separation in active suspensions. Phys. Rev. E 90, 032304.Google Scholar
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25 (6), 061701.Google Scholar
Nishiura, Y., Teramoto, T. & Ueda, K.-I. 2003 Scattering and separators in dissipative systems. Phys. Rev. E 67, 056210.Google Scholar
Ohta, T. 2001 Pulse dynamics in a reaction-diffusion system. Physica D 151 (1), 61–72.Google Scholar
Ohta, T., Kiyose, J. & Mimura, M. 1997 Collision of propagating pulses in a reaction-diffusion system. J. Phys. Soc. Japan 66 (5), 1551–1558.Google Scholar
Pak, O. S. & Lauga, E. 2014 Generalized squirming motion of a sphere. J. Eng. Math. 88 (1), 1–28.Google Scholar
Paxton, W. F., Kistler, K. C., Olmeda, C. C., Sen, A., St.Angelo, S. K., Cao, Y., Mallouk, T. E., Lammert, P. E. & Crespi, V. H. 2004 Catalytic nanomotors: autonomous movement of striped nanorods. J. Am. Chem. Soc. 126 (41), 13424–13431.Google Scholar
Ryazantsev, Y. S. 1985 Thermocapillary motion of a reacting droplet in a chemically active medium. Fluid Dyn. 20, 491–495; translated from Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza No. 3, 180–183.CrossRefGoogle Scholar
Scriven, L. E. 1960 Dynamics of a fluid interface equation of motion for Newtonian surface fluids. Chem. Engng Sci. 12 (2), 98–108.Google Scholar
Shao, D., Rappel, W.-J. & Levine, H. 2010 Computational model for cell morphodynamics. Phys. Rev. Lett. 105 (10), 108104.Google Scholar
Shklyaev, S., Brady, J. F. & Crdova-Figueroa, U. M. 2014 Non-spherical osmotic motor: chemical sailing. J. Fluid Mech. 748, 488–520.CrossRefGoogle Scholar
Spagnolie, S. E. & Lauga, E. 2012 Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations. J. Fluid Mech. 700, 105–147.Google Scholar
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77 (19), 4102–4104.CrossRefGoogle ScholarPubMed
Thutupalli, S., Seemann, R. & Herminghaus, S. 2011 Swarming behavior of simple model squirmers. New J. Phys. 13 (7), 073021.Google Scholar
Tjhung, E., Marenduzzo, D. & Cates, M. E. 2012 Spontaneous symmetry breaking in active droplets provides a generic route to motility. Proc. Natl Acad. Sci. USA 109 (31), 12381–12386.CrossRefGoogle ScholarPubMed
Toyota, T., Maru, N., Hanczyc, M. M., Ikegami, T. & Sugawara, T. 2009 Self-propelled oil droplets consuming ‘fuel’ surfactant. J. Am. Chem. Soc. 131 (14), 5012–5013.Google Scholar
Tsemakh, D., Lavrenteva, O. M. & Nir, A. 2004 On the locomotion of a drop, induced by the internal secretion of surfactant. Intl J. Multiphase Flow 30 (11), 1337–1367.Google 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, 434–438.Google Scholar
Watson, G. N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.Google Scholar
Yabunaka, S., Ohta, T. & Yoshinaga, N. 2012 Self-propelled motion of a fluid droplet under chemical reaction. J. Chem. Phys. 136 (7), 074904.Google Scholar
Yam, P. T., Wilson, C. A., Ji, L., Hebert, B., Barnhart, E. L., Dye, N. A., Wiseman, P. W., Danuser, G. & Theriot, J. A. 2007 Actin myosin network reorganization breaks symmetry at the cell rear to spontaneously initiate polarized cell motility. J. Cell Biol. 178 (7), 1207–1221.Google Scholar
Yoshinaga, N. 2014 Spontaneous motion and deformation of a self-propelled droplet. Phys. Rev. E 89, 012913.Google 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, 016108.Google Scholar
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6 (03), 350–356.Google Scholar
Ziebert, F., Swaminathan, S. & Aranson, I. S. 2012 Model for self-polarization and motility of keratocyte fragments. J. R. Soc. Interface 9 (70), 1084–1092.Google Scholar