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

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.