Shape oscillations of an oil drop rising in water: effect of surface contamination

Abstract

International audienceInertial shape oscillations of heptane drops rising in water are investigated experimentally. Diameters from 0.59 to 3.52 mm are considered, corresponding to a regime where the rising motion should not affect shape oscillations for pure immiscible fluids. The interface, however, turns out to be contaminated. The drag coefficient is considerably increased compared to that of a clean drop due to the well-known. Marangoni effect resulting from a gradient of surfactant concentration generated by the fluid motion along the interface. Thanks to the decomposition of the shape into spherical harmonics, the eigenfrequencies and the damping rates of oscillation modes n = 2, 3, 4 and 5 have been measured. Frequencies are not affected by contamination, while damping rates are increased by a considerable amount that depends neither on drop instantaneous velocity nor on diameter. This augmentation, however, depends on the mode number: it is maximum for mode two (multiplied by 2.4) and then relaxes towards the value of a clean drop as n increases. A previous similar investigation of a drop attached to a capillary has not revealed such an increase of the damping rates, indicating that the coupling between rising motion and surface contamination is responsible for this effect

Effect of rising motion on the damped shape oscillations of drops and bubbles

“…The damping rate of the oscillations of a drop of heptane rising in water has been shown to be significantly increased because of the presence of surface-active impurities. 17 Also, contrary to what is observed in microgravity conditions, 1 bubbles rising in a uniform turbulent water flow were not observed to experience surface-tension-driven oscillations after having been deformed by an intense turbulent eddy. 18 The objective of this work is to characterize the oscillations of drops or bubbles made of pure fluids rising under the action of buoyancy.…”

“…Nevertheless, it is worth mentioning that this is only true provided surface-active contaminants are absent, since they can increase three times the damping rate through a Marangoni effect. 17 For bubbles at terminal velocity, the frequency -which is given by Meiron's theory -and the damping rate are also weakly affected by the rising velocity. However, during transient stages when the equilibrium shape of the bubble is changing at a rate comparable to the oscillating frequency, complex and sudden changes in the amplitude of the spherical harmonics can be observed.…”

“…This configuration is similar to experiments in which a drop is released from a capillary. 17 After the release, the drop or bubble accelerates and performs shape oscillations around an average flattened shape that evolves in time. It finally reaches a terminal velocity and a steady spheroidal oblate shape with its minor axis oriented in the vertical direction.…”

Numerical simulations of a rising drop with shape oscillations in the presence of surfactants

“…Finally, in the presence of both surfactants and gravity, Abi Chebel et al [28] have measured the frequency and the damping rate of several modes in contaminated cases, observing that the effect of contamination becomes negligible for higher order modes. As far as we know, there is no numerical simulations of this complete problem, although the numerical approach is well suited to study separately the independent and coupled influences of the presence of both surfactant and gravity effects, as addressed in the present paper.…”

A model for drop and bubble breakup frequency based on turbulence spectra

“…Even if expressions of Eq. have been obtained without considering the influence of gravity in the shape oscillations, they are generally still valid in the presence of a buoyancy‐induced motion, under the conditions given by Lalanne et al Moreover, more complex expressions of ω 2 and β 2 can also be computed by considering effect of surfactants adsorbed at the drop surface.…”