The effect of dimensionless numbers on the resonance frequency of a pendent drop

The study of pendent drop behavior as a nonlinear dynamical system has long been the focus of researchers. The vibrational behavior of the pendent drop at resonant frequencies contains useful information for investigating more complex dynamic systems. The oscillatory behavior of pendent drop at resonant frequencies contains useful information for investigating more complex dynamical systems. Dimensionless Bond and capillary numbers are important and effective parameters in the pendent drop behavior. In this work, the effect of dimensionless Bond and capillary numbers on the resonant frequency of the pendent drop is investigated. Two-dimensional multi-relaxation ‎time lattice Boltzmann method (MRT-LBM) was used to simulate the oscillations of the drop using a conservative model for high-density ratio. Using this model, the drop oscillatory characteristics were calculated for different values of Bond and capillary numbers. It was realized that increasing the Bo number from 0.11 to 1.96 causes an increase in natural frequency from 3.278E-4 to 1.88E-3 in an almost linear manner. Also, increasing the capillary number from ‎1.8E-5‎ to ‎7.3E-4‎ causes an increase in natural frequency from 3.278E-4 to 5.700E-4 in a non-linear logarithmic manner.