Damped shape oscillations of a viscous compound droplet suspended in a viscous host fluid

A study of small-amplitude shape oscillations of a viscous compound droplet suspended in a viscous host fluid is performed. A generalized eigenvalue problem is formulated and is solved by using the spectral method. The effects of the relevant non-dimensional parameters are examined for three cases, i.e. a liquid shell in a vacuum and a compound droplet in a vacuum or in a host fluid. The fundamental mode $l=2$ is found to be dominant. There exist two oscillatory modes: the in phase and the out of phase. In most situations, the interfaces oscillate in phase rather than out of phase. For the in-phase mode, in the absence of the host, as the viscosity of the core or the shell increases, the damping rate increases whereas the oscillation frequency decreases; when the viscosity exceeds a critical value, the mode becomes aperiodic with the damping rate bifurcating into two branches. In addition, when the tension of the inner interface becomes smaller than some value, the in-phase mode turns aperiodic. In the presence of the unbounded host fluid, there exists a continuous spectrum. The viscosity of the host may decrease or increase the damping rate of the in-phase mode. The mechanism behind it is discussed. The density contrasts between fluids affect oscillations of the droplet in a complicated way. Particularly, sufficiently large densities of the core or the host lead to the disappearance of the out-of-phase mode. The thin shell approximation predicts well the oscillation of the compound droplet when the shell is thin.

Collision of Bubbles with Solid Surface in the Presence of Specific Surfactants

The present work is motivated by the effort to understand basic processes occurring in three-phase systems where small bubbles interact with large particles. The simplified system of a single bubble rising in a stagnant liquid and colliding with a solid surface is studied. The effect of two specific surfactants, α-Terpineol and n-Octanol, is investigated. Two independent measurements are combined: (i) bubble–solid surface collision experiments and (ii) the bubble shape oscillations induced by a movable capillary. Both experiments are based on high-speed imaging resulting in the evaluation of the restitution coefficient characterizing the collision process and the relative damping time characterizing the bubble shape oscillations in the presence of surfactants. It was observed that even for small concentrations of a surfactant, both the bubble shape oscillations and the bubble bouncing on the solid surface are significantly suppressed. Two predictions for the restitution coefficient are proposed. The equations include a term characterizing the suppression of the damping time in the presence of surfactants and a term balancing the inertia, capillary and viscous forces in the liquid film separating the bubble and the solid surface. The proposed equations successfully predict the restitution coefficient of bubble bouncing on the solid surface in liquids with the addition of specific surfactants.

Coalescence and shape oscillations of Au nanoparticles in CO2 hydrogenation for methanol reaction

Recently, there has been renewed interest in Au nanoparticle (Au NP) catalysts owing to their high selectivity for CO2 hydrogenation to methanol. However, there is still limited knowledge on the...

Active shape oscillations of giant vesicles with cyclic closure and opening of membrane necks

During each active oscillation cycle, the vesicle shape undergoes a symmetry-breaking transformation from an up-down symmetric to an up-down asymmetric dumbbell followed by the reverse symmetry-restoring transformation.

Acoustic bubble dynamics in a yield-stress fluid

Bubbles initially trapped in a yield-stress fluid can be displaced by acoustic forces and exhibit shape oscillations at higher acoustic pressure, but irreversible motion is not observed.