期刊
SIAM REVIEW
卷 50, 期 2, 页码 313-322出版社
SIAM PUBLICATIONS
DOI: 10.1137/06067763X
关键词
asymptotic expansions; oscillating boundary layers; wall effects; atomic force microscopy
资金
- Intramural NIH HHS [Z01 DC000033, Z01 DC000033-12] Funding Source: Medline
High-frequency oscillations of a rigid sphere in an incompressible viscous fluid moving normal to a rigid plane are considered when the ratio of minimum clearance to sphere radius is small. Asymptotic expansions are constructed that permit an analytical estimate of the force acting on the sphere as a result of its motion. An inner expansion, valid in the neighborhood of the minimum gap, reflects the dominance of viscous effects and fluid inertia. An outer expansion, valid outside the gap, reflects the dominance of fluid inertia with a correction for an oscillating viscous boundary layer. The results are applied to the hydrodynamics of the tapping mode of an atomic force microscope and to the dynamic calibration of its cantilevers.
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