The influence of a viscous fluid on the vibration dynamics of scanning near-field optical microscopy fiber probes and atomic force microscopy cantilevers

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Abstract
The influence of a viscous fluid on the dynamic behavior of a vibrating scanning near-field optical microscopy fiber tip is investigated both theoretically and experimentally. A continuum mechanical description of a cylindric cantilever is used to calculate the resonance frequencies and the widths of the resonance bands. The linearized Naviers–Stokes equations are analytically solved and describe the interaction of the beam with the viscous fluid. The contribution of the liquid to the shift and the broadening of the resonance lines is summarized by two constants that can be derived from a master function and the kinetic Reynolds number. The theoretical values are compared with experimental data collected from an optical fiber which is used as a probe in a scanning near-field microscope. Agreement, with a relative error of less than 1%, is achieved. The theory is further developed for the application to atomic force microscopy cantilevers with a rectangular cross section. Experimental data taken from literature are in good agreement with the theory.