A short review on analytical methods for the capillary oscillator in a nanoscale deformable tube

Abstract

The capillary effect has been widely applied to micro/nano devices for heat and mass transfer; however, its vibration property has been rarely studied. Its low frequency was recently revealed. This paper reviews some effective methods to solve analytically the frequency-amplitude relation of the capillary oscillator, including the variational principle, the variational iteration method, the homotopy perturbation method, He's frequency formulation, and Taylor series method.