Measurement of the friction coefficient of a fluctuating contact line using an AFM-based dual-mode mechanical resonator

A dual-mode mechanical resonator using an atomic force microscope (AFM) as a force sensor is developed. The resonator consists of a long vertical glass fiber with one end glued onto a rectangular cantilever beam and the other end immersed through a liquid - air interface. By measuring the resonant spectrum of the modified AFM cantilever, one is able to accurately determine the longitudinal friction coefficient ζ_v along the fiber axis associated with the vertical oscillation of the hanging fiber and the traversal friction coefficient ζ_h perpendicular to the fiber axis associated with the horizontal swing of the fiber around its joint with the cantilever. The technique is tested by measurement of the friction coefficient of a fluctuating (and slipping) contact line between the glass fiber and the liquid interface. The experiment verifies the theory and demonstrates its applications. The dual-mode mechanical resonator provides a powerful tool for the study of the contact line dynamics and the rheological property of anisotropic fluids.