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A reciprocal theorem for Marangoni propulsion

  • Hassan Masoud (a1) (a2) and Howard A. Stone (a1)


We study the Marangoni propulsion of a spheroidal particle located at a liquid–gas interface. The particle asymmetrically releases an insoluble surface-active agent and so creates and maintains a surface tension gradient leading to the self-propulsion. Assuming that the surface tension has a linear dependence on the concentration of the released agent, we derive closed-form expressions for the translational speed of the particle in the limit of small capillary, Péclet and Reynolds numbers. Our derivations are based on the Lorentz reciprocal theorem, which eliminates the need to develop the detailed flow field.


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Acree, W. E. 1984 Empirical expression for predicting surface tension of liquid mixtures. J. Colloid Interface Sci. 101, 575576.
Adamson, A. W. 1990 Physical Chemistry of Surfaces. Wiley.
Bush, J. W. M. & Hu, D. L. 2006 Walking on water: biolocomotion at the interface. Annu. Rev. Fluid Mech. 38, 339369.
Crowdy, D. G. 2013 Wall effects on self-diffusiophoretic Janus particles: a theoretical study. J. Fluid Mech. 735, 473498.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics, with Special Applications to Particulate Media. Prentice-Hall.
Lauga, E. & Davis, A. M. J. 2012 Viscous Marangoni propulsion. J. Fluid Mech. 705, 120133.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. McGraw-Hill.
Nadim, A., Haj-Hariri, H. & Borhan, A. 1990 Thermocapillary migration of slightly deformed droplets. Part. Sci. Technol. 8, 191198.
Nakata, S., Iguchi, Y., Ose, S., Kuboyama, M., Ishii, T. & Yoshikawa, K. 1997 Self-rotation of a camphor scraping on water: new insight into the old problem. Langmuir 13, 44544458.
Rayleigh, L. 1889 Measurements of the amount of oil necessary in order to check the motions of camphor upon water. Proc. R. Soc. Lond. 47, 364367.
Stone, H. A. & Samuel, A. D. T. 1996 Propulsion of microorganisms by surface distortions. Phys. Rev. Lett. 77, 41024104.
Zhang, H., Duan, W., Liu, L. & Sen, A. 2013 Depolymerization-powered autonomous motors using biocompatible fuel. J. Am. Chem. Soc. 135, 1573415737.
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A reciprocal theorem for Marangoni propulsion

  • Hassan Masoud (a1) (a2) and Howard A. Stone (a1)


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