Numerical analysis of non-linear oscillations of micrometre size fluid droplets

Abstract

Nonlinear oscillations of free viscous drops are investigated by solving the full Navier-Stokes equation using the finite element software COMSOL Multiphysics. Oscillations are investigated for droplets released form static initial conditions deformed in the second and third perturbation mode with a Reynolds number varying from 12 to 120 and deformation amplitude ranging from 0.001 to 0.4. Nonlinearities are identified by comparison with linear theory. Special attention is given to the mode coupling phenomenon. Moreover a qualitative investigation of the nonlinear quantities: convection, vorticity, viscosity and nonlinear curvature, is conducted by visualization of the individual effects during the oscillations.For large deformations, a decrease in frequency is observed along with significant mode coupling. The new results show that nonlinear curvature effects in the capillary force is the main contribution to the nonlinear behavior. Linear theory tends to overestimate curvature and therefore fails to predict the decrease in frequency for large amplitudes. Moreover, the linear theory is unable to resolve certain characteristics of the curvature, which in real oscillations leads to mode coupling.The parametric limits (Reynolds number and deformation amplitude) of the linear theory was determined. For small amplitudes, the parametric limit of the linear theory was determined to be between Re = 60 and Re = 30. While for low viscosity and varying initial amplitude, it was found that nonlinear effect could not be neglected for initial amplitudes above 10%.