Experimental and theoretical investigation of large-amplitude oscillations of liquid droplets

Abstract

Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.

Determination of dynamic surface tension and viscosity of non-Newtonian fluids from drop oscillations

“…The initial oscillation amplitude, a 2 (0), is less than 10% of the drop radius for which a linear theory is expected to hold. 15,16 The surface tension and viscosity of the fluid were derived from Eqs. (2)- (4), respectively, on the assumption that they were invariant over the measured time interval.…”

“…The initial amplitude of oscillation in the fundamental mode is approximately 25% of the drop radius, where non-linear effects are expected to be negligible. 16 The surface tensions and viscosities derived from Eqs. (2)- (4) …”

“…This result also agrees with the conclusion of Becker et al that nonlinear effects were most evident for higher oscillation modes (l > 2). 16 The neglect of vorticity in Lamb's analysis was investigated by Prosperetti,4 who showed that the irrotational approximation only held at low Ohnesorge numbers, Oh < 0.1. For Oh = 0.2, Lamb's formula overestimates the viscosity by about 30%.…”

“…They found that nonlinear effects were most evident for higher oscillation modes (l > 2) while the fundamental mode conformed to the linear theory even for initial amplitudes exceeding 50% of the drop radius. 16 Matsumoto et al…”

Drop formation in a one-dimensional approximation of the Navier–Stokes equation

“…Therefore boundary conditions become irrelevant and the flow is determined by γ/ρ alone. If ∆t = t s − t represents the time distance from the singularity, the only available length scale is the combination (γ∆t 2 /ρ) 1 3 . Hence, introducing…”