This study investigates the interaction between a freely rising, deformable bubble and a freely settling particle of the same size due to gravity. Initially, an in-line configuration is considered while varying the Bond, Galilei and Archimedes numbers. The study shows that as the bubble and particle approach each other, a liquid film forms between them that undergoes drainage. The formation of the liquid film leads to dissipation of kinetic energy, and for sufficiently large bubble velocities, particle flotation takes place. Increasing the Bond number causes the bubble to deform more severely, which may allow the particle to pass through the bubble as it ruptures. This work also considers an offset configuration, which shows that the bubble slides away from the particle, affecting its settling trajectory.

The effect of surfactants on the flow characteristics during rapid drop formation in a microchannel is investigated using high-speed imaging, micro-particle image velocimetry and numerical simulations; the latter are performed using a three- dimensional multiphase solver that accounts for the transport of soluble surfactants in the bulk and at the interface. Drops are generated in a flow-focusing microchannel, using silicone oil ($4.6$ mPa s) as the continuous phase and a 52 % w/w glycerol solution as the dispersed phase. A non-ionic surfactant (Triton X-100) is dissolved in the dispersed phase at concentrations below and above the critical micelle concentration. Good agreement is found between experimental and numerical data for the drop size, drop formation time and circulation patterns. The results reveal strong circulation patterns in the forming drop in the absence of surfactants, whose intensity decreases with increasing surfactant concentration. The surfactant concentration profiles in the bulk and at the interface are shown for all stages of drop formation. The surfactant interfacial concentration is large at the front and the back of the forming drop, while the neck region is almost surfactant free. Marangoni stresses develop away from the neck, contributing to changes in the velocity profile inside the drop.

We study the effect of insoluble surfactants on the impact of surfactant-free droplets onto surfactant-laden thin liquid films via a fully three-dimensional direct numerical simulation approach that employs a hybrid interface-tracking/level-set method, and by taking into account surfactant-induced Marangoni stresses due to gradients in interfacial surfactant concentration. Our numerical predictions for the temporal evolution of the surfactant-free crown are validated against the experimental work by Che & Matar (Langmuir, vol. 33, 2017, pp. 12140–12148). We focus on the ‘crown-splash regime’, and we observe that the crown dynamics evolves through various stages: from the growth of linear modes (through a Rayleigh–Plateau instability) to the development of nonlinearities leading to primary and secondary breakup events (through droplet shedding modulated by an end-pinching mechanism). We show that the addition of surfactants does not affect the wave selection via the Rayleigh–Plateau instability. However, the presence of surfactants plays a key role in the late stages of the dynamics as soon as the ligaments are driven out from the rim. Surfactant-induced Marangoni stresses delay the end-pinching mechanisms to result in longer ligaments prior to their capillary singularity. Our results indicate that Marangoni stresses bridge the gap between adjacent protrusions promoting the adjacent protrusions' collision and the merging of ligaments. Finally, we demonstrate that the addition of surfactants leads to surface rigidification and consequently to the retardation of the flow dynamics.

We study the effect of insoluble surfactants on the spatio-temporal evolution of turbulent jets. We use three-dimensional numerical simulations and employ an interface-tracking/level-set method that accounts for surfactant-induced Marangoni stresses. The present study builds on our previous work (Constante-Amores et al., J. Fluid Mech., vol. 922, 2021, A6) in which we examined in detail the vortex–surface interaction in the absence of surfactants. Numerical solutions are obtained for a wide range of Weber and elasticity numbers in which vorticity production is generated by surface deformation and surfactant-induced Marangoni stresses. The present work demonstrates, for the first time, the crucial role of Marangoni stresses, brought about by surfactant concentration gradients, in the formation of coherent, hairpin-like vortex structures. These structures have a profound influence on the development of the three-dimensional interfacial dynamics. We also present theoretical expressions for the mechanisms that influence the rate of production of circulation in the presence of surfactants for a general, three-dimensional, two-phase flow, and highlight the dominant contribution of surfactant-induced Marangoni stresses.

We study the effect of surfactants on the dynamics of a drop-interface coalescence using full three-dimensional direct numerical simulations. We employ a hybrid interface-tracking/level-set method, which takes into account Marangoni stresses that arise from surface-tension gradients, interfacial and bulk diffusion and sorption kinetic effects. We validate our predictions against the experimental data of Blanchette and Bigioni (Nat. Phys., vol. 2, issue 4, 2006, pp. 254–257) and perform a parametric study that demonstrates the delicate interplay between the flow fields and those associated with the surfactant bulk and interfacial concentrations. The results of this work unravel the crucial role of the Marangoni stresses in the flow physics of coalescence, with particular attention paid to their influence on the neck reopening dynamics in terms of stagnation-point inhibition, and near-neck vorticity generation. We demonstrate that surfactant-laden cases feature a rigidifying effect on the interface compared with the surfactant-free case, a mechanism that underpins the observed surfactant-induced phenomena.

The breakup of an interface into a cascade of droplets and their subsequent coalescence is a generic problem of central importance to a large number of industrial settings such as mixing, separations and combustion. We study the breakup of a liquid jet introduced through a cylindrical nozzle into a stagnant viscous phase via a hybrid interface-tracking/level-set method to account for the surface tension forces in a three-dimensional Cartesian domain. Numerical solutions are obtained for a range of Reynolds ($Re$) and Weber ($We$) numbers. We find that the interplay between the azimuthal and streamwise vorticity components leads to different interfacial features and flow regimes in $Re$–$We$ space. We show that the streamwise vorticity plays a critical role in the development of the three-dimensional instabilities on the jet surface. In the inertia-controlled regime at high $Re$ and $We$, we expose the details of the spatio-temporal development of the vortical structures affecting the interfacial dynamics. A mushroom-like structure is formed at the leading edge of the jet inducing the generation of a liquid sheet in its interior that undergoes rupture to form droplets. These droplets rotate inside the mushroom structure due to their interaction with the prevailing vortical structures. Additionally, Kelvin–Helmholtz vortices that form near the injection point deform in the streamwise direction to form hairpin vortices, which, in turn, trigger the formation of interfacial lobes in the jet core. The thinning of the lobes induces the creation of holes which expand to form liquid threads that undergo capillary breakup to form droplets.

We study the effect of surfactant on the dynamics of a bubble bursting through an interface. We perform fully three-dimensional direct numerical simulations using a hybrid interface-tracking/level-set method accounting for surfactant-induced Marangoni stresses, sorption kinetics and diffusive effects. We select an initial bubble shape corresponding to a large Laplace number and a vanishingly small Bond number in order to neglect gravity, and isolate the effects of surfactant on the flow. Our results demonstrate that the presence of surfactant affects the dynamics of the system through Marangoni-induced flow, driving motion from high to low concentration regions, which is responsible for the onset of a recirculation zone close to the free surface. These Marangoni stresses rigidify the interface, delay the cavity collapse and influence the jet breakup process.

We report the first simulations of the Faraday instability using the full three-dimensional Navier–Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid front-tracking/level-set algorithm for Lagrangian tracking of arbitrarily deformable phase interfaces. Simulations performed in square and cylindrical domains yield complex patterns. In particular, a superlattice-like pattern similar to those of Douady & Fauve (Europhys. Lett., vol. 6, 1988, pp. 221–226) and Douady (J. Fluid Mech., vol. 221, 1990, pp. 383–409) is observed. The pattern consists of the superposition of two square superlattices. We conjecture that such patterns are widespread if the square container is large compared with the critical wavelength. In the cylinder, pentagonal cells near the outer wall allow a square-wave pattern to be accommodated in the centre.