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Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux

  • Paul E. Lammert (a1), Vincent H. Crespi (a1) (a2) (a3) and Amir Nourhani (a1)

Abstract

A standard approach to propulsion velocities of autophoretic colloids with thin interaction layers uses a reciprocity relation applied to the slip velocity although the surface flux (chemical, electrical, thermal, etc.), which is the source of the field driving the slip, is often more accessible. We show how, under conditions of low Reynolds number and a field obeying the Laplace equation in the outer region, the slip velocity can be bypassed in velocity calculations. In a sense, the actual slip velocity and a normal field proportional to the flux density are equivalent for this type of calculation. Using known results for surface traction induced by rotating or translating an inert particle in a quiescent fluid, we derive simple and explicit integral formulas for translational and rotational velocities of arbitrary spheroidal and slender-body autophoretic colloids.

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Email addresses for correspondence: lammert@psu.edu, nourhani@psu.edu

References

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Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 21, 6199.
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419440.
Brenner, H. 1964a The Stokes resistance of a slightly deformed sphere. Chem. Engng Sci. 19 (8), 519539.
Brenner, H. 1964b The Stokes resistance of an arbitrary particle. 4. Arbitrary fields of flow. Chem. Engng Sci. 19 (10), 703727.
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44, 791810.
Ebbens, S. J. & Howse, J. R. 2010 In pursuit of propulsion at the nanoscale. Soft Matt. 6 (4), 726738.
Fair, M. C. & Anderson, J. L. 1989 Electrophoresis of nonuniformly charged ellipsoidal particles. J. Colloid Interface Sci. 127 (2), 388400.
Gibbs, J. G. & Zhao, Y.-P. 2009 Autonomously motile catalytic nanomotors by bubble propulsion. Appl. Phys. Lett. 94 (16), 163104.
Golestanian, R., Liverpool, T. B. & Ajdari, A. 2007 Designing phoretic micro- and nano-swimmers. New J. Phys. 9, 126.
Happel, J. & Brenner, H. 1983 Low Reynolds Number Hydrodynamics. Springer.
Jiang, H.-R., Yoshinaga, N. & Sano, M. 2010 Active motion of a janus particle by self-thermophoresis in a defocused laser beam. Phys. Rev. Lett. 105, 268302.
Keller, J. B. & Rubinow, S. I. 1976 Slender-body theory for slow viscous flow. J. Fluid Mech. 75, 705714.
Kim, S. & Karrila, S. J. 2005 Microhydrodynamics: Principles and Selected Applications. Dover.
Lamb, H. 1945 Hydrodynamics, 6th edn. Dover.
Nourhani, A., Crespi, V. H. & Lammert, P. E. 2015a Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics. Phys. Rev. E 91, 062303.
Nourhani, A. & Lammert, P. E. 2016 Geometrical performance of self-phoretic colloids and microswimmers. Phys. Rev. Lett. 116, 178302.
Nourhani, A., Lammert, P. E., Crespi, V. H. & Borhan, A. 2015b A general flux-based analysis for spherical electrocatalytic nanomotors. Phys. Fluids 27, 012001.
Nourhani, A., Lammert, P. E., Crespi, V. H. & Borhan, A. 2015c Self-electrophoresis of spheroidal electrocatalytic swimmers. Phys. Fluids 27 (9), 092002.
Paxton, W. F., Kistler, K. C., Olmeda, C. C., Sen, A., St. Angelo, S. K., Cao, Y. 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.
Popescu, M. N., Dietrich, S., Tasinkevych, M. & Ralston, J. 2010 Phoretic motion of spheroidal particles due to self-generated solute gradients. Eur. Phys. J. E 31 (4), 351367.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Sabass, B. & Seifert, U. 2012 Nonlinear, electrocatalytic swimming in the presence of salt. J. Chem. Phys. 136, 214507.
Schnitzer, O. & Yariv, E. 2015 Osmotic self-propulsion of slender particles. Phys. Fluids 27 (3), 031701.
Wang, W., Duan, W., Ahmed, S., Mallouk, T. E. & Sen, A. 2013 Small power: autonomous nano- and micromotors propelled by self-generated gradients. Nano Today 8 (5), 531554.
Yariv, E. 2011 Electrokinetic self-propulsion by inhomogeneous surface kinetics. Proc. R. Soc. Lond. A 467 (2130), 16451664.
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Bypassing slip velocity: rotational and translational velocities of autophoretic colloids in terms of surface flux

  • Paul E. Lammert (a1), Vincent H. Crespi (a1) (a2) (a3) and Amir Nourhani (a1)

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