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Fluid ratcheting by oscillating channel walls with sawteeth

  • Jie Yu (a1) (a2)


A laboratory experiment shows that fluid can be pumped from one end to another in a narrow channel whose sawtooth walls vibrate transversely opposite to each other. The phenomenon is referred to as ratcheting fluid. Inspired by this, we put forward here a theory describing the rectified steady flow, and the net directional pumping. In a conformally transformed plane, the induced steady streaming in the Stokes boundary layer of the oscillatory flow is analysed, elucidating the driving mechanism that is due to the nonlinearity and viscosity. The solution of the stream function is given, showing the complex spatial structure of the induced steady flow and its spatial average that is related to the directional pumping. Whereas the wall sawtooth shape is the primary source of asymmetry, the difference in entrance and exit flow conditions due to the geometries at channel ends is found to be a secondary source to break the left–right symmetry of the system. This latter can affect the net directional transport of fluid, in particular in short channels with a small number of sawteeth. Various influences on the net pumping rate are analysed.


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Auerbach, D., Moehring, W. & Moser, M. 2004 An analytic approach to the Liebau problem of valveless pumping. Cardiovascular Engng 4, 201207.
Dupeux, G., Le Merrer, M., Lagubeau, G., Clanet, C., Hardt, S. & Quéré, D. 2011 Viscous mechanism for Leidenfrost propulsion on a ratchet. Europhys. Lett. 96, 58001. doi:10.1209/0295-5075/96/58001.
Hara, T. & Mei, C. C. 1990 Oscillatory flows over periodic ripples. J. Fluid Mech. 211, 183209.
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535581.
Longuet-Higgins, M. S. 1983 Peristaltic pumping in water waves. J. Fluid Mech. 137, 393407.
Mahadevan, L., Daniel, S. & Chaudhury, M. K. 2004 Biomimetic ratcheting motion of a soft, slender, sessile gel. Proc. Natl Acad. Sci. USA 101 (1), 2326.
Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. World Scientific.
Mei, C. C. & Yu, J. 1997 The instability of sand ripples under partially standing surface waves. Phys. Fluids 9 (6), 16061620.
Rayleigh, L. 1883 On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems. Phil. Trans. R. Soc. Lond. 175, 121.
Rinderknecht, D., Hickerson, A. I. & Gharib, M. 2005 A valveless micro impedance pump driven by electromagnetic actuation. J. Micromech. Microengng 15, 861866.
Shapiro, A. H., Jaffrin, M. Y. & Weinberg, S. L. 1969 Peristaltic pumping with long wavelengths at low Reynolds number. J. Fluid Mech. 37, 799825.
Spagnolie, S. E. & Shelley, M. J. 2009 Shape-changing bodies in fluid: hovering, ratcheting, and bursting. Phys. Fluids 21, 013103.
Takagi, D. & Balmforth, N. J. 2011 Peristaltic pumping of viscous fluid in an elastic tube. J. Fluid Mech. 672, 196218.
Thiria, B. & Zhang, J.2010 Ratcheting fluid using geometric anisotropy, Bulletin of the American Physical Society (APS), Program of the 63rd Annual Meeting of the Division of Fluid Dynamics, Long Beach, California, 2010,
van Oeveren, R. M. & Houghton, G. 1971 Levitation and counter-gravity motion of spheres by non-uniform hydrodynamic oscillations. Chem. Engng Sci. 26, 19581961.
Yin, F. C. P. & Fung, Y. C. 1971 Comparison of theory and experiment in peristaltic transport. J. Fluid Mech. 47, 93112.
Yu, J. & Howard, L. N. 2012 Exact Floquet theory for waves over arbitrary periodic topographies. J. Fluid Mech. 712, 451470.
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Fluid ratcheting by oscillating channel walls with sawteeth

  • Jie Yu (a1) (a2)


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