Proximity effect on hydrodynamic interaction between a sphere and a plane measured by Force Feedback Microscopy at different frequencies

In this article, we measure the viscous damping $G'',$ and the associated stiffness $G',$ of a liquid flow in sphere-plane geometry in a large frequency range. In this regime, the lubrication approximation is expected to dominate. We first measure the static force applied to the tip. This is made possible thanks to a force feedback method. Adding a sub-nanometer oscillation of the tip, we obtain the dynamic part of the interaction with solely the knowledge of the lever properties in the experimental context using a linear transformation of the amplitude and phase change. Using a Force Feedback Microscope (FFM)we are then able to measure simultaneously the static force, the stiffness and the dissipative part of the interaction in a broad frequency range using a single AFM probe. Similar measurements have been performed by the Surface Force Apparatus with a probe radius hundred times bigger. In this context the FFM can be called nano-SFA.