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Slow motion of a sphere near a sinusoidal surface

Published online by Cambridge University Press:  16 November 2023

Gaojin Li Open the ORCID record for Gaojin Li [Opens in a new window]
Gaojin Li*
Affiliation:
State Key Laboratory of Ocean Engineering, Shanghai 200240, PR China School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, PR China
*
†Email address for correspondence: gaojinli@sjtu.edu.cn
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Abstract

Particle motion near non-plane surfaces can exhibit intricate hydrodynamics, making it an attractive tool for manipulating particles in microfluidic devices. To understand the underlying physics, this work investigates the Stokesian dynamics of a sphere near a sinusoidal surface, using a combination of perturbation analysis and boundary element simulation. The Lorentz reciprocal theorem is employed to solve the particle mobility near a small-amplitude surface. Compared with a plane wall, the curved topography induces additional translation and rotation velocity components, with the direction depending on the location of the sphere and the wavelength of the surface. At a fixed distance from the surface, the longitudinal and vertical mobilities of the sphere are strongly affected by the wavelength and amplitude of the surface, whereas its transverse mobility is only mildly influenced. When a sphere settles perpendicular to a sinusoidal surface, the far-field hydrodynamic effect drives the particle towards the local hill, while the near-field effect attracts the particle to the valley. These results provide valuable insights into the particle motion near surfaces with complex geometry.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 975 , 25 November 2023 , A31
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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