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Rotation of a low-Reynolds-number watermill: theory and simulations
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0002-3443-0709
Princeton Univ, Dept Mech & Aerosp Engn, Princeton, NJ 08544 USA..
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 849, p. 57-75Article in journal (Refereed) Published
Abstract [en]

Recent experiments have demonstrated that small-scale rotary devices installed in a microfluidic channel can be driven passively by the underlying flow alone without resorting to conventionally applied magnetic or electric fields. In this work, we conduct a theoretical and numerical study on such a flow-driven 'watermill' at low Reynolds number, focusing on its hydrodynamic features. We model the watermill by a collection of equally spaced rigid rods. Based on the classical resistive force (RF) theory and direct numerical simulations, we compute the watermill's instantaneous rotational velocity as a function of its rod number N, position and orientation. When N >= 4, the RF theory predicts that the watermill's rotational velocity is independent of N and its orientation, implying the full rotational symmetry (of infinite order), even though the geometrical configuration exhibits a lower-fold rotational symmetry; the numerical solutions including hydrodynamic interactions show a weak dependence on N and the orientation. In addition, we adopt a dynamical system approach to identify the equilibrium positions of the watermill and analyse their stability. We further compare the theoretically and numerically derived rotational velocities, which agree with each other in general, while considerable discrepancy arises in certain configurations owing to the hydrodynamic interactions neglected by the RP theory. We confirm this conclusion by employing the RP-based asymptotic framework incorporating hydrodynamic interactions for a simpler watermill consisting of two or three rods and we show that accounting for hydrodynamic interactions can significantly enhance the accuracy of the theoretical predictions.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2018. Vol. 849, p. 57-75
Keywords [en]
low-Reynolds-number flows, MEMS/NEMS, microfluidics
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-238929DOI: 10.1017/jfm.2018.416ISI: 000448745500003Scopus ID: 2-s2.0-85048779241OAI: oai:DiVA.org:kth-238929DiVA, id: diva2:1263042
Note

QC 20181114

Available from: 2018-11-14 Created: 2018-11-14 Last updated: 2018-11-16Bibliographically approved

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Zhu, Lailai

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