Optimal free-surface pumping by an undulating carpet

Anupam Pandey (), Zih-Yin Chen, Jisoo Yuk, Yuming Sun, Chris Roh, Daisuke Takagi, Sungyon Lee and Sunghwan Jung ()
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Anupam Pandey: Syracuse University
Zih-Yin Chen: University of Minnesota
Jisoo Yuk: Cornell University
Yuming Sun: Cornell University
Chris Roh: Cornell University
Daisuke Takagi: University of Hawaii at Manoa
Sungyon Lee: University of Minnesota
Sunghwan Jung: Cornell University

Nature Communications, 2023, vol. 14, issue 1, 1-8

Abstract: Abstract Examples of fluid flows driven by undulating boundaries are found in nature across many different length scales. Even though different driving mechanisms have evolved in distinct environments, they perform essentially the same function: directional transport of liquid. Nature-inspired strategies have been adopted in engineered devices to manipulate and direct flow. Here, we demonstrate how an undulating boundary generates large-scale pumping of a thin liquid near the liquid-air interface. Two dimensional traveling waves on the undulator, a canonical strategy to transport fluid at low Reynolds numbers, surprisingly lead to flow rates that depend non-monotonically on the wave speed. Through an asymptotic analysis of the thin-film equations that account for gravity and surface tension, we predict the observed optimal speed that maximizes pumping. Our findings reveal how proximity to free surfaces, which ensure lower energy dissipation, can be leveraged to achieve directional transport of liquids.

Date: 2023
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DOI: 10.1038/s41467-023-43059-8

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