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Collision between chemically driven self-propelled drops

  • Shunsuke Yabunaka (a1) and Natsuhiko Yoshinaga (a2) (a3)

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.

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Corresponding author

Email address for correspondence: yoshinaga@wpi-aimr.tohoku.ac.jp

References

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Anderson, D. M., Mcfadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139165.
Arfken, G. B., Weber, H. J. & Weber, H. J. 1968 Mathematical Methods for Physicists. Academic.
Bhagavatula, R., Jasnow, D. & Ohta, T. 1997 Nonequilibrium interface equations: an application to thermocapillary motion in binary systems. J. Stat. Phys. 88 (5), 10131031.
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), 255264.
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), 4566.
Cates, M. E. & Tailleur, J. 2015 Motility-induced phase separation. Annu. Rev. Condens. Matter Phys. 6 (1), 219244.
Ei, S. I., Mimura, M. & Nagayama, M. 2006 Interacting spots in reaction diffusion systems. J. Discrete Continuous Dyn. Syst. 14 (1), 3162.
Fedosov, A. I. 1956 Thermocapillary motion (translated by V. Berejnov & K. Morozov). Zh. Fiz. Khim. 30 (2), 366373 (see also arXiv:1303:024).
Golovin, A. A., Nir, A. & Pismen, L. M. 1995 Spontaneous motion of two droplets caused by mass transfer. Ind. Engng Chem. Res. 34 (10), 32783288.
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), 488496.
Hohenberg, P. C. & Halperin, B. I. 1977 Theory of dynamic critical phenomena. Rev. Mod. Phys. 49 (3), 435479.
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.
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.
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119160.
Ishimoto, K. & Gaffney, E. A. 2013 Squirmer dynamics near a boundary. Phys. Rev. E 88, 062702.
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.
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, 261290.
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.
Kawasaki, K. & Ohta, T. 1983 Kinetics of fluctuations for systems undergoing phase transitions – interfacial approach. Physica A 118 (1–3), 175190.
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.
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.
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), 17681780.
Levan, M. D. 1981 Motion of a droplet with a newtonian interface. J. Colloid Interface Sci. 83 (1), 1117.
Li, G.-J. & Ardekani, A. M. 2014 Hydrodynamic interaction of microswimmers near a wall. Phys. Rev. E 90, 013010.
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), 109118.
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.
Michelin, S., Lauga, E. & Bartolo, D. 2013 Spontaneous autophoretic motion of isotropic particles. Phys. Fluids 25 (6), 061701.
Nishiura, Y., Teramoto, T. & Ueda, K.-I. 2003 Scattering and separators in dissipative systems. Phys. Rev. E 67, 056210.
Ohta, T. 2001 Pulse dynamics in a reaction-diffusion system. Physica D 151 (1), 6172.
Ohta, T., Kiyose, J. & Mimura, M. 1997 Collision of propagating pulses in a reaction-diffusion system. J. Phys. Soc. Japan 66 (5), 15511558.
Pak, O. S. & Lauga, E. 2014 Generalized squirming motion of a sphere. J. Eng. Math. 88 (1), 128.
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), 1342413431.
Ryazantsev, Y. S. 1985 Thermocapillary motion of a reacting droplet in a chemically active medium. Fluid Dyn. 20, 491495; translated from Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza No. 3, 180–183.
Scriven, L. E. 1960 Dynamics of a fluid interface equation of motion for Newtonian surface fluids. Chem. Engng Sci. 12 (2), 98108.
Shao, D., Rappel, W.-J. & Levine, H. 2010 Computational model for cell morphodynamics. Phys. Rev. Lett. 105 (10), 108104.
Shklyaev, S., Brady, J. F. & Crdova-Figueroa, U. M. 2014 Non-spherical osmotic motor: chemical sailing. J. Fluid Mech. 748, 488520.
Spagnolie, S. E. & Lauga, E. 2012 Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations. J. Fluid Mech. 700, 105147.
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77 (19), 41024104.
Thutupalli, S., Seemann, R. & Herminghaus, S. 2011 Swarming behavior of simple model squirmers. New J. Phys. 13 (7), 073021.
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), 1238112386.
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), 50125013.
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), 13371367.
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, 434438.
Watson, G. N. 1922 A Treatise on the Theory of Bessel Functions. Cambridge University Press.
Yabunaka, S., Ohta, T. & Yoshinaga, N. 2012 Self-propelled motion of a fluid droplet under chemical reaction. J. Chem. Phys. 136 (7), 074904.
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), 12071221.
Yoshinaga, N. 2014 Spontaneous motion and deformation of a self-propelled droplet. Phys. Rev. E 89, 012913.
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.
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6 (03), 350356.
Ziebert, F., Swaminathan, S. & Aranson, I. S. 2012 Model for self-polarization and motility of keratocyte fragments. J. R. Soc. Interface 9 (70), 10841092.
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Collision between chemically driven self-propelled drops

  • Shunsuke Yabunaka (a1) and Natsuhiko Yoshinaga (a2) (a3)

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