A method to measure the viscosity of liquids at microscales is presented. Ituses a thin glass fiber fixed on the tip of the cantilever of an extremely lownoise Atomic Force Microscope (AFM), which accurately measures the cantilever{deflection}. When the fiber is dipped into the liquid the dissipation of thecantilever-fiber system increases. This dissipation, linked to the liquidviscosity, is computed from the power spectral density of the thermalfluctuations of the cantilever {deflection}. The {high sensitivity of the AFM}allows us to show the existence and to develop a model of the coupling betweenthe dynamics of the fiber and that of the cantilever. This model {accurately}fits the experimental data. The advantages and draw-backs of the method arediscussed
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