Fluid-induced resonances in vibrational and Brownian dynamics of a shear oscillator

• We generally solve the dynamic responses of a shear oscillator interacting with a confined Newtonian fluid.
• The oscillator shows harmonic and anharmonic motions, controlled by confining height and oscillator-fluid coupling strength.
• We find fluid-induced resonances in vibrational and Brownian dynamics for the originally over-damped oscillator.
• These dynamic features could be exploited for investigating fluid properties, using shear-mode atomic force microscope.

We generally describe vibrational and Brownian dynamics of a shear oscillator interacting with a confined Newtonian fluid. We show that the shear oscillator exhibits three characteristic dynamics in viscous, weak inertial, and strong inertial regimes, and the dynamics are controlled by two system parameters, effective confining height and oscillator-fluid coupling strength. While resonances of oscillators are usually deteriorated in fluids, we interestingly find the resonances arisen in originally overdamped oscillators, originated from hydrodynamic memory effects in strong inertial regime. The present theory could be exploited for improving designs and performances of shear oscillators in fluids, and reciprocally for investigating fluid properties by using shear oscillatory probes such as atomic force microscope in shear-mode.