Unsteady drag force on an immersed sphere oscillating near a wall
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 extra...
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| Veröffentlicht in: | Journal of fluid mechanics 2023-12, Vol.977, Article A21 |
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| container_title | Journal of fluid mechanics |
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| creator | Zhang, Zaicheng Bertin, Vincent Essink, Martin H. Zhang, Hao Fares, Nicolas Shen, Zaiyi Bickel, Thomas Salez, Thomas Maali, Abdelhamid |
| description | 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. |
| doi_str_mv | 10.1017/jfm.2023.987 |
| format | Article |
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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.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2023.987</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Asymptotic methods ; Atomic force microscopy ; Condensed Matter ; Drag ; Experiments ; Finite element method ; Fluid Dynamics ; Fluid mechanics ; Hydrodynamics ; JFM Papers ; Mathematical analysis ; Mechanics ; Microscopy ; Physics ; Resonance ; Reynolds number ; Soft Condensed Matter ; Thermal noise ; Viscosity</subject><ispartof>Journal of fluid mechanics, 2023-12, Vol.977, Article A21</ispartof><rights>The Author(s), 2023. Published by Cambridge University Press</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c374t-d94c84bf37ecce901884b851a9375d16eddeffe74d9a37c24f8d6f53819f62d93</citedby><cites>FETCH-LOGICAL-c374t-d94c84bf37ecce901884b851a9375d16eddeffe74d9a37c24f8d6f53819f62d93</cites><orcidid>0000-0002-8351-6824 ; 0000-0001-6111-8721 ; 0000-0001-7472-1597 ; 0000-0002-9459-6081 ; 0000-0002-3139-8846 ; 0000-0003-0493-5164 ; 0000-0003-0987-7629</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0022112023009874/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,230,314,776,780,881,27903,27904,55606</link.rule.ids><backlink>$$Uhttps://hal.science/hal-04158163$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Zhang, Zaicheng</creatorcontrib><creatorcontrib>Bertin, Vincent</creatorcontrib><creatorcontrib>Essink, Martin H.</creatorcontrib><creatorcontrib>Zhang, Hao</creatorcontrib><creatorcontrib>Fares, Nicolas</creatorcontrib><creatorcontrib>Shen, Zaiyi</creatorcontrib><creatorcontrib>Bickel, Thomas</creatorcontrib><creatorcontrib>Salez, Thomas</creatorcontrib><creatorcontrib>Maali, Abdelhamid</creatorcontrib><title>Unsteady drag force on an immersed sphere oscillating near a wall</title><title>Journal of fluid mechanics</title><addtitle>J. Fluid Mech</addtitle><description>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.</description><subject>Asymptotic methods</subject><subject>Atomic force microscopy</subject><subject>Condensed Matter</subject><subject>Drag</subject><subject>Experiments</subject><subject>Finite element method</subject><subject>Fluid Dynamics</subject><subject>Fluid mechanics</subject><subject>Hydrodynamics</subject><subject>JFM Papers</subject><subject>Mathematical analysis</subject><subject>Mechanics</subject><subject>Microscopy</subject><subject>Physics</subject><subject>Resonance</subject><subject>Reynolds number</subject><subject>Soft Condensed Matter</subject><subject>Thermal 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drag force on an immersed sphere oscillating near a wall</title><author>Zhang, Zaicheng ; Bertin, Vincent ; Essink, Martin H. ; Zhang, Hao ; Fares, Nicolas ; Shen, Zaiyi ; Bickel, Thomas ; Salez, Thomas ; Maali, Abdelhamid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c374t-d94c84bf37ecce901884b851a9375d16eddeffe74d9a37c24f8d6f53819f62d93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Asymptotic methods</topic><topic>Atomic force microscopy</topic><topic>Condensed Matter</topic><topic>Drag</topic><topic>Experiments</topic><topic>Finite element method</topic><topic>Fluid Dynamics</topic><topic>Fluid mechanics</topic><topic>Hydrodynamics</topic><topic>JFM Papers</topic><topic>Mathematical analysis</topic><topic>Mechanics</topic><topic>Microscopy</topic><topic>Physics</topic><topic>Resonance</topic><topic>Reynolds number</topic><topic>Soft Condensed 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Abdelhamid</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unsteady drag force on an immersed sphere oscillating near a wall</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2023-12-14</date><risdate>2023</risdate><volume>977</volume><artnum>A21</artnum><issn>0022-1120</issn><eissn>1469-7645</eissn><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.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2023.987</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0002-8351-6824</orcidid><orcidid>https://orcid.org/0000-0001-6111-8721</orcidid><orcidid>https://orcid.org/0000-0001-7472-1597</orcidid><orcidid>https://orcid.org/0000-0002-9459-6081</orcidid><orcidid>https://orcid.org/0000-0002-3139-8846</orcidid><orcidid>https://orcid.org/0000-0003-0493-5164</orcidid><orcidid>https://orcid.org/0000-0003-0987-7629</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Asymptotic methods Atomic force microscopy Condensed Matter Drag Experiments Finite element method Fluid Dynamics Fluid mechanics Hydrodynamics JFM Papers Mathematical analysis Mechanics Microscopy Physics Resonance Reynolds number Soft Condensed Matter Thermal noise Viscosity |
| title | Unsteady drag force on an immersed sphere oscillating near a wall |
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