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The unsteady hydrodynamic drag exerted on an oscillating sphere near a planarwall is addressed experimentally, theoretically, and numerically. Theexperiments are performed by using colloidal-probe Atomic Force Microscopy(AFM) in thermal noise mode. The natural resonance frequencies and qualityfactors are extracted from the measurement of the power spectrum density of theprobe oscillation for a broad range of gap distances and Womersley numbers. Theshift in the natural resonance frequency of the colloidal probe as the probegoes close to a solid wall infers the wall-induced variations of the effectivemass of the probe. Interestingly, a crossover from a positive to a negativeshift is observed as the Womersley number increases. In order to rationalizethe results, the confined unsteady Stokes equation is solved numerically usinga finite-element method, as well as asymptotic calculations.The in-phase andout-of-phase terms of the hydrodynamic drag acting on the sphere are obtainedand agree well to the experimental results. All together, the experimental,theoretical, and numerical results show that the hydrodynamic force felt by animmersed sphere oscillating near a wall is highly dependent on the Womersleynumber.

Unsteady drag force on an immersed sphere oscillating near a wall