Dynamic simulation of atomic force microscope cantilevers oscillating in liquid

To simulate the behavior of an atomic force microscope (AFM) operating in liquid, a lumped-parameter model of a 40×5 μ m² thick silicon cantilever with natural frequencies ranging from 3.0 to 6.0× 10⁵ rad/s was combined with a transient Navier-Stokes solver. The equations of motion were solved simultaneously with the time-dependent flow field. The simulations successfully capture known characteristics of the AFM in liquid, including large viscous losses, reduced peak resonant frequencies, and frequency-dependent damping. From these simulations, the transfer function G (s) of the system was obtained. While the transfer function shares many of the characteristics of a second-order system at higher frequencies, the frequency-dependent damping means that a second-order model cannot be applied. The viscous damping of the system is investigated in greater depth. A phase difference between the peak velocity and peak damping force is observed. Both the phase difference and the magnitude of the damping are shown to be functions of the excitation frequency. Finally, the damping is shown to be strongly dependent on the liquid viscosity and weakly dependent on the liquid density.