Skip to main content

Rotation of a low-Reynolds-number watermill: Theory and simulations

Author(s): Zhu, L; Stone, Howard A

To refer to this page use:
Full metadata record
DC FieldValueLanguage
dc.contributor.authorZhu, L-
dc.contributor.authorStone, Howard A-
dc.identifier.citationZhu, L, Stone, HA. (2018). Rotation of a low-Reynolds-number watermill: Theory and simulations. Journal of Fluid Mechanics, 849 (57 - 75. doi:10.1017/jfm.2018.416en_US
dc.description.abstractRecent 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 , position and orientation. When , the RF theory predicts that the watermill's rotational velocity is independent of 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 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 RF theory. We confirm this conclusion by employing the RF-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.en_US
dc.format.extent57 - 75en_US
dc.relation.ispartofJournal of Fluid Mechanicsen_US
dc.rightsAuthor's manuscripten_US
dc.titleRotation of a low-Reynolds-number watermill: Theory and simulationsen_US
dc.typeJournal Articleen_US

Files in This Item:
File Description SizeFormat 
Rotation of a low-Reynolds-number watermill Theory and simulations.pdf626.83 kBAdobe PDFView/Download

Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.