Role of surfactant-induced Marangoni stresses in retracting liquid sheets

In this work, we study the effect of insoluble surfactants on the three-dimensional rim-driven retraction dynamics of thin water sheets in air. We employ an interface-tracking/level-set method to ensure the full coupling between the surfactant-induced Marangoni stresses, interfacial diffusion and inertia. Our findings are contrasted with the (Newtonian) dynamics of a liquid sheet edge, finding that the surfactant concentration can delay, or effectively prevent, the breakup of the rim. Our simulations use the fastest growing Rayleigh–Plateau instability to drive droplet detachment from the fluid sheet (rim). The results of this work unravel the significant role of Marangoni stresses in the retracting sheet dynamics at large elasticity numbers. We study the sensitivity of the dynamics to the elasticity number and the rigidification of the interface

Dynamics of a surfactant-laden bubble bursting through an interface

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

Rico and the jets: Direct numerical simulations of turbulent liquid jets

This paper is associated with a poster winner of a 2019 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2019.GFM.P0020

Direct numerical simulations of transient turbulent jets: vortex-interface interactions

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

Dynamics of retracting surfactant-laden ligaments at intermediate Ohnesorge number

The dynamics of ligaments retracting under the action of surface tension occurs in a multitude of natural and industrial applications; these include inkjet printing and atomization. We perform direct, fully three-dimensional, two-phase numerical simulations of the retracting process over a range of system parameters that account for surfactant solubility, sorption kinetics, and Marangoni stresses. Our results indicate that the presence of surfactant inhibits the “end-pinching” mechanism and promotes neck reopening through Marangoni-flow; this is induced by the formation of surfactant concentration gradients that drive flow-reversal toward the neck. The vortical structures associated with this flow are also analyzed in detail. We also show that these Marangoni stresses lead to interfacial rigidification, observed through a reduction of the retraction velocity and ligament kinetic energy

Role of surfactant-induced Marangoni stresses in retracting liquid sheets

In this work, we study the effect of insoluble surfactants on the three-dimensional rim-driven retraction dynamics of thin water sheets in air. We employ an interface-tracking/level-set method to ensure the full coupling between the surfactant-induced Marangoni stresses, interfacial diffusion and inertia. Our findings are contrasted with the (Newtonian) dynamics of a liquid sheet edge, finding that the surfactant concentration can delay, or effectively prevent, the breakup of the rim. Our simulations use the fastest growing Rayleigh–Plateau instability to drive droplet detachment from the fluid sheet (rim). The results of this work unravel the significant role of Marangoni stresses in the retracting sheet dynamics at large elasticity numbers. We study the sensitivity of the dynamics to the elasticity number and the rigidification of the interface

Role of surfactant-induced Marangoni stresses in drop-interface coalescence

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

Direct numerical simulations of turbulent jets: vortex-interface-surfactant interactions

We study the effect of insoluble surfactants on the spatio-temporal evolution of turbulent jets. We use three-dimensional numerical simulations and employ an interfacetracking/level-set method that accounts for surfactant-induced Marangoni stresses. The present study builds on our previous work (Constante-Amores et al., 2021, J. Fluid Mech., 922, 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 surfactantinduced 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 surfactant-induced Marangoni stresses

Effect of surfactant on elongated bubbles in capillary tubes at high Reynolds number

The effect of surfactants on the tail and film dynamics of elongated gas bubbles propagating through circular capillary tubes is investigated by means of an extensive three-dimensional numerical study using a hybrid front-tracking/level-set method. The focus is on the visco-inertial regime, which occurs when the Reynolds number of the flow is much larger than unity. Under these conditions, “clean” bubbles exhibit interface undulations in the proximity of the tail, with an amplitude that increases with the Reynolds number. We perform a systematic analysis of the impact of a wide range of surfactant properties, including elasticity, bulk surfactant concentration, solubility, and diffusivity, on the bubble and flow dynamics in the presence of inertial effects. The results show that the introduction of surfactants is effective in suppressing the tail undulations as they tend to accumulate near the bubble tail. Here large Marangoni stresses are generated, which lead to a local “rigidification” of the bubble. This effect becomes more pronounced for larger surfactant elasticities and adsorption depths. At reduced surfactant solubility, a thicker rigid film region forms at the bubble rear, where a Couette film flow is established, while undulations still appear at the trailing edge of the downstream “clean” film region. In such conditions, the bubble length becomes an influential parameter, with short bubbles becoming completely rigid

Role of kidney stones in renal pelvis flow

We examine the time-dependent flow dynamics inside an idealised renal pelvis in the context of a surgical procedure for kidney stone removal, extending previous work by [1,2], who showed how vortical flow structures can hinder mass transport in a canonical two-dimensional domain. Here, we examine the time-dependent evolution of these vortical flow structures in three-dimensions, and incorporate the presence of rigid kidney stones. We perform direct numerical simulations, solving the transient Navier-Stokes equations in a spherical domain. Our numerical predictions for the flow dynamics in the absence of stones are validated with experimental and 2D numerical data from [1], and the governing parameters and flow regimes are chosen carefully in order to satisfy several clinical constraints. The results shed light on the crucial role of flow circulation in the renal cavity and its effect on the trajectories of rigid stones. We demonstrate that stones can either be washed out of the cavity along with the fluid, or be trapped in the cavity via their interaction with vortical flow structures. Additionally, we study the effect of multiple stones in the flow field within the cavity in terms of the kinetic energy, entrapped fluid volume, and the clearance rate of a passive tracer modelled via an advection-diffusion equation. We demonstrate that the flow in the presence of stones features a higher vorticity production within the cavity compared with the stone-free cases