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Unsteady drag force on an immersed sphere oscillating near a wall

Published online by Cambridge University Press:  14 December 2023

Zaicheng Zhang Open the ORCID record for Zaicheng Zhang [Opens in a new window] ,
Vincent Bertin Open the ORCID record for Vincent Bertin [Opens in a new window] ,
Martin H. Essink Open the ORCID record for Martin H. Essink [Opens in a new window] ,
Hao Zhang ,
Nicolas Fares Open the ORCID record for Nicolas Fares [Opens in a new window] ,
Zaiyi Shen ,
Thomas Bickel Open the ORCID record for Thomas Bickel [Opens in a new window] ,
Thomas Salez Open the ORCID record for Thomas Salez [Opens in a new window]  and
Abdelhamid Maali Open the ORCID record for Abdelhamid Maali [Opens in a new window]
Zaicheng Zhang
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
Vincent Bertin
Affiliation:
Physics of Fluids Group and Max Planck Center for Complex Fluid Dynamics, Department of Science and Technology, and J.M. Burgers Center for Fluid Dynamics, University of Twente, 7500, Enschede, The Netherlands
Martin H. Essink
Affiliation:
Physics of Fluids Group and Max Planck Center for Complex Fluid Dynamics, Department of Science and Technology, and J.M. Burgers Center for Fluid Dynamics, University of Twente, 7500, Enschede, The Netherlands
Hao Zhang
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
Nicolas Fares
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
Zaiyi Shen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China
Thomas Bickel
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
Thomas Salez*
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
Abdelhamid Maali*
Affiliation:
Univ. Bordeaux, CNRS, LOMA, UMR 5798, 33405 Talence, France
*
†Email addresses for correspondence: thomas.salez@cnrs.fr, abdelhamid.maali@u-bordeaux.fr
†Email addresses for correspondence: thomas.salez@cnrs.fr, abdelhamid.maali@u-bordeaux.fr
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Abstract

The unsteady hydrodynamic drag exerted on an oscillating sphere near a planar wall is addressed experimentally, theoretically and numerically. The experiments are performed by using colloidal-probe atomic force microscopy in thermal noise mode. The resonance frequencies and quality factors are extracted from the measurement of the power spectrum density of the probe oscillation for a broad range of gap distances and Womersley numbers. The shift in the resonance frequency of the colloidal probe as the probe goes close to a solid wall infers the wall-induced variations of the effective mass of the probe. Interestingly, a crossover from a positive to a negative shift is observed as the Womersley number increases. In order to rationalize the results, the confined unsteady Stokes equation is solved numerically using a finite-element method, as well as asymptotic calculations. The in-phase and out-of-phase terms of the hydrodynamic drag acting on the sphere are obtained and agree well with the experimental results. All together, the experimental, theoretical and numerical results show that the hydrodynamic force felt by an immersed sphere oscillating near a wall is highly dependent on the Womersley number.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 977 , 25 December 2023 , A21
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© The Author(s), 2023. Published by Cambridge University Press

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