Wave evolution in thin-film flows is highly relevant for heat and mass transfer applications, such as CO2 capture in falling film absorbers. To develop a detailed understanding of potential enhancement mechanisms associated with the evolution of three-dimensional (3D) waveforms, we perform 3D direct numerical simulations of passive scalar transport in laminar-wavy film flows, using a hybrid front-tracking/level-set method to accurately resolve interfacial features. CO2 absorption is greatly enhanced in the presence of interfacial waves with the liquid-side mass transfer coefficient increasing tenfold relative to that of a flat film for the highest film Reynolds numbers (Re) studied. This is primarily due to changes in interfacial and internal flow dynamics rather than an increase in the gas-liquid interfacial area. The recirculation region present in the leading and trailing fronts of the 3D waves intensifies mass transfer, and their effectiveness increases with Re. At low Re, there is a film region beneath the wavy interface, which remains relatively undisturbed where mass transfer is dominated by diffusion. The introduction of structured substrates to promote mass transfer under these conditions is recommended. The visco-capillary ripple region, which precedes the leading and trailing fronts for sufficiently high Re, provides a relatively high degree of spanwise advection, with the mean spanwise velocity magnitude reaching around one-quarter that in the streamwise direction. This underscores the importance of solving the fully-3D problem as these effects do not have a two-dimensional analogue.

We study the pinch-off dynamics of a fluid surrounded by a significantly more viscous one during fluid-fluid displacement in straight, cylindrical capillary tubes, where the interface evolves under the influence of a moving contact line. We investigate the influence of insoluble surfactants on the dynamics of both the contact line and pinch-off. We focus on a visco-capillary displacement regime where the imposed flow rate exceeds a critical threshold, beyond which the contact-line velocity is governed by the partial wettability of the confined geometry, becoming independent of the flow rate. Under these conditions, the fluid-fluid meniscus forms an advancing axial finger, leaving behind a thin film of the defending fluid. This unstable film retracts along the partially wetting walls, forming a dewetting rim that grows with the steady contact-line motion. Eventually, a surface-tension-driven Rayleigh-Plateau instability dominates, triggering pinch-off at the rim neck. For a surfactant-free interface, our results show that the early-stage evolution of the neck diameter follows a power law $ au <^>\alpha$ , where $ au$ is the time to the pinch-off singularity and the scaling exponent $\alpha$ depends on the contact-line velocity determined by the wettability. Over the range resolved in the present simulations, $\alpha$ decreases from values near $1/2$ at large contact-line velocity towards values close to $1/5$ as the contact-line velocity is reduced. We demonstrate that, in the presence of insoluble surfactants, the contact-line velocity, at a given wettability, scales linearly with surfactant elasticity due to Marangoni stresses along the dewetting rim interface, which affect the timing and location of the pinch-off. Despite these effects, at the early-time regime, the pinch-off dynamics exhibits the same self-similar scaling behaviour as in the surfactant-free case.

Direct numerical simulations of interfacial flows with surfactant-induced complexities involving surface viscous stresses are performed within the framework of the Level Contour Reconstruction Method (LCRM). This hybrid front-tracking/level-set approach leverages the advantages of both methods. In addition to interface-confined surfactant transport that results in surface diffusion and Marangoni stresses, the interface is endowed with shear and dilatational surface viscosities. The additional surface effects act to resist deformation arising from velocity gradients in the plane of the two-dimensional manifold of the interface, and interfacial compressibility effects. By adopting the Boussinesq-Scriven constitutive model, we provide a mathematical formulation of these effects that accurately captures the interfacial mechanics, which is then implemented within the LCRM-based code by exploiting the benefits inherent to the underlying front-tracking/level-set hybrid approach. We validate our numerical predictions against a number of benchmark cases that involve drops undergoing deformation when subjected to a flow field and when rising under the action of buoyancy. The results of these validation studies highlight the importance of adopting a rigorous approach in modelling the interfacial dynamics. We also present results that demonstrate the effects of surface viscous stresses on interfacial deformation in unsteady parametric surface waves and atomisation events.

We perform three-dimensional simulations of miscible and immiscible displacements in a cylindrical pipe. For the miscible case, both laminar and turbulent displacement regimes are considered, and our numerical framework uses direct numerical simulation (DNS) and a Large Eddy Simulation (LES) approach based on a Lilly-Smagorinsky model. The dynamics of the flow are governed by the Navier-Stokes equations, coupled with a convective-diffusion equation for the concentration of the more viscous fluid when considering the miscible cases. For the immiscible laminar cases, we perform two-phase DNS considering both pinned and moving contact lines to capture the full range of immiscible dynamic behaviours. The pinned contact line reflects stationary interfaces constrained by surface heterogeneity, while the moving contact line accounts for dynamic interfacial motion influenced by viscous and capillary forces. This study shows that the viscosity contrasts between the two fluids play a significant role in determining the efficiency of 'cleaning' of a pipe containing an initially highly viscous resident fluid. When the viscosity of the displaced fluid is low, the laminar displacement flow is efficient in cleaning the pipe; however, when the viscosity increases, the laminar displacement becomes inadequate. Our numerical predictions in the turbulent regime showed that more efficient cleaning is achieved when the viscosity contrast between the two fluids is large. Lastly, our results reveal that the dynamics of a moving contact line can impact both the efficiency and the pattern of cleaning within the pipe.

Dilatational and shear surface viscosities are highly correlated parameters, making their individual contributions difficult to disentangle in Stokes flow, linearised flow models, or two-dimensional flows. We therefore investigate the three-dimensional interfacial standing waves as a means to decouple the influence of dilatational and shear surface viscosities. Two dimensionless controlling parameters are introduced: $Bq$, the total Boussinesq number, which quantifies the the relative importance of surface viscous stresses compared with bulk viscous stresses, and $\tan χ$, which quantifies the ratio of surface dilatational viscosity to surface shear viscosity. The growth rates and threshold accelerations are independent of $χ$, consistent with previous theoretical predictions. Nonlinear analyses of square and hexagonal patterns reveal that Fourier decomposition of wave-patterns can effectively decouple the intricate dynamics into axial modes, where the waves are weakly dependent on $χ$, and oblique modes, where additional damping occurs in the shear surface viscous dominant interface. These results demonstrate that Faraday wave-patterns provide a route for identifying and quantifying the distinct roles of dilatational and shear surface viscosities.

The formation of a superlattice pattern in two-frequency-driven Faraday waves discovered and named SSS-I by Arbell Fineberg (1998, 2002) is investigated by means of Direct Numerical Simulations (DNS) of the full three-dimensional Navier–Stokes equations with a free surface. Two simulations with distinct quasi-hexagonal initial conditions run at a forcing amplitude 25% above the Faraday-wave onset followed quite different routes, but both led eventually to the same superlattice pattern after around 250 forcing periods. This regime is inaccessible to the approximations of weak nonlinearity or viscosity. The standing-wave pattern contain rows of patches, alternating in time between hills and lakes that are connected by a long skeleton resembing the backbone of DNA strands. The patches and skeleton of the pattern can be related to its spatial Fourier decomposition, which combines hexagonal modes with a spatially and temporally subharmonic mode. One of the transition routes passes through several fairly long-lived transients including different hexagonal patterns and another superlattice pattern; the other passes only through erratic and disordered states. After another 100 periods, the pattern became unstable and was succeeded by a dynamic version of SSS-I in which the superlattice is modulated and drifts in the direction of the backbone, while preserving its basic shape. Convergence to SSS-I states both experimentally in a large geometry and numerically from two different initial conditions and in a minimal geometry demonstrates the robustness of the SSS-I pattern.

Parametric oscillations of an interface separating two fluid phases create nonlinear surface waves, called Faraday waves, which organise into simple patterns, such as squares and hexagons, as well as complex structures, such as double hexagonal and superlattice patterns. In this work, we study the influence of surfactant-induced Marangoni stresses on the formation and transition of Faraday-wave patterns. We use a control parameter, $B$ , that assesses the relative importance of Marangoni stresses as compared with the surface-wave dynamics. Our results show that the threshold acceleration required to destabilise a surfactant-covered interface through vibration increases with increasing $B$ . For a surfactant-free interface, a square-wave pattern is observed. As $B$ is incremented, we report transitions from squares to asymmetric squares, weakly wavy stripes and ultimately to ridges and hills. These hills are a consequence of the bidirectional Marangoni stresses at the neck of the ridges. The mechanisms underlying the pattern transitions and the formation of exotic ridges and hills are discussed.

From inkjet printing to agricultural spraying, the impact of droplets onto complex-fluid pools plays a crucial role in various fields. To reveal the effects that surfactants play in the dynamics of splashing, we combine high-speed imaging and 3D numerical simulations allowing us to investigate crown formation and breakup when a clean droplet strikes a surfactant-laden pool. We first characterise three surfactants (Surfynol 465, SDS, and Triton X-100) by measuring their dynamic surface tension, in relation to the characteristic crown-collapse time, t. High-speed imaging reveals three distinct post-impact regimes (smooth receding, recoiling breakup, and splashing), based on the Weber number, where 'fast-acting' surfactants trigger splashing at significantly lower Weber numbers than 'slow-acting' or surfactant-free systems. To probe the smooth-receding regime in detail, we developed and experimentally-validated numerical simulations for SDS-laden pools, capturing both reduced surface tension and Marangoni stresses. Varying the Peclet number reveals that surfactant transport slows crown evolution, producing taller, narrower sheets with approximately 5% more interfacial area but lower kinetic energy than in the clean case. Our results demonstrate that the dynamic surface tension at t serves as a reliable predictor of the onset of splashing, while the Peclet number governs the crown morphology. By elucidating the interplay between surfactant kinetics and fluid inertia, this work offers critical insights for optimising droplet-based technologies, such as coatings, 3D printing, and pesticide applications where precise control over splashing and fragmentation is essential.

Spreading time, the time that an impacting droplet attains the maximum wetting area on a solid surface, plays a critical role in many engineering applications particularly where heat transfer or chemical reactions are involved. Although the impact dynamics of a droplet significantly differ across the different spreading regimes depending on various collision parameters, it still remains unclear how the spreading time changes for each spreading regime. In the present study, the spreading time during droplet impact on a large spherical target is systematically studied at the three different spreading regimes for a wide range of impact parameters (Weber number, equilibrium contact angle, and Ohnesorge number). The changes of spreading time depending on the impact parameters and underlying physical mechanisms are analyzed in detail at the level of three different spreading regimes. Our results show that the spreading time, proper time scales, dominant impact parameters and associated physical behaviors all significantly and non-linearly change across the three spreading regimes. An improved prediction model for the spreading time is also proposed for each regime, which is now based on only the controllable variables and has an explicit form. Finally, a data-driven prediction model is proposed to represent the complicated and non-linear nature of the spreading time broadly across the three spreading regimes.

This study investigates the transport of particles in density-stratified fluids, a prevalent natural phenomenon. In the ocean, particles and marine snow descend through fluids with significant density variations due to salinity and temperature gradients. Such heterogeneity in the background fluid affects the settling or rising rates of particles, often leading to accumulation at transitional density layers. Previous research has primarily focused on spherical particles, examining their isolated motion, pairwise interactions, and collective transport in stratified fluids. This work, however, extends the investigation to the interaction between two spheroidal particles settling in-line in a linearly stratified fluid. This study employs an immersed-boundary technique to perform particle-resolved numerical simulations in a three-dimensional Cartesian domain. The results showcase the effects of varying the stratification strength through the Froude number, the particles’ aspect ratios, and the initial separation distance between the particles on the interaction dynamics between the settling spheroids.

We demonstrate the application of a recurrent neural network (RNN) to perform multistep and multivariate time-series performance predictions for stirred and static mixers as exemplars of complex multiphase systems. We employ two network architectures in this study, fitted with either long short-term memory and gated recurrent unit cells, which are trained on high-fidelity, three-dimensional, computational fluid dynamics simulations of the mixer performance, in the presence and absence of surfactants, in terms of drop size distributions and interfacial areas as a function of system parameters; these include physicochemical properties, mixer geometry, and operating conditions. Our results demonstrate that while it is possible to train RNNs with a single fully connected layer more efficiently than with an encoder-decoder structure, the latter is shown to be more capable of learning long-term dynamics underlying dispersion metrics. Details of the methodology are presented, which include data preprocessing, RNN model exploration, and methods for model performance visualization; an ensemble-based procedure is also introduced to provide a measure of the model uncertainty. The workflow is designed to be generic and can be deployed to make predictions in other industrial applications with similar time-series data.

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.

We present a parametric study of the unsteady phenomena associated with the flow of elongated gas bubbles travelling through liquid-filled square capillaries under high Weber number conditions. These conditions consistently induce the formation of a re-entrant jet at the back of the bubble that commonly gives way to a deep liquid cavity. Subsequent steps include pinch-off events in the cavity to generate one or multiple encapsulated drops which may coalesce, in conjunction with the bursting of the bubble-liquid interface by either the cavity or the drops. Some of these interfacial instabilities have previously been reported experimentally (Olbricht 1996) and numerically (Izbassarov & Muradoglu 2016) for liquid-liquid flow in microchannels. We carry out three-dimensional direct numerical simulations based on a hybrid interface-tracking/level-set method capable of accounting for the presence and dynamic exchange of surfactants between the liquid bulk phase and the liquid-gas interface. Our results indicate that the delicate interplay amongst inertia, capillarity, viscosity, surfactant adsorption/desorption kinetics, and Marangoni stresses has a dramatic influence over the non-axisymmetric morphological structures of the encapsulated drops-elongated bubble. This strong coupling also influences the pinch-off time, penetration depth of the cavity, and number, size, and velocity of the encapsulated drops across the bubble. The observed phenomena are summarised in three main morphological regimes based on surfactant-related parameters and dimensionless groups. A discussion of the flow regime maps is also provided.

We present a numerical study of the main sub-stages preceding aerosol formation via bursting bubbles: capillary wave propagation along the bubble, convergence at the bubble's apex, the ascent of a Worthington jet and its break-up to release liquid drops. We focus on two crucial yet overlooked aspects of the system: the presence of surface-active agents and dynamics driven by non-negligible gravitational effects, quantified by the Bond number. Our results propose, for the first time, a mechanism explaining capillary wave retardation in the presence of surfactants, involving the transition from bi- to uni-directional Marangoni stresses, which pull the interface upwards, countering the motion of the waves. We also quantitatively elucidate the variable nature of the waves' velocity with various surfactant parameters, including surfactant solubility and elasticity, a departure from the constant behaviour well-documented in clean interfaces.

This paper is associated with a poster winner of a 2023 American Physical Society Division of Fluid Dynamics (DFD) Milton Van Dyke Award for the 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.2023.GFM.P0030.

This study aims to elucidate, for the first time, the intricate fundamental physics governing the dispersion dynamics of a surfactant-laden two-phase liquid-liquid system in the well-known SMX static mixer. Following the analysis carried out in the preceding publication to this work (Valdes et al., 2023), a comparative assessment of the most relevant and recurrent deformation and breakup mechanisms is conducted for a 3 -drop scenario and then extrapolated to a more industrially-relevant multi-drop set-up. A parametric study on relevant surfactant physico-chemical parameters (i.e., elasticity, sorption kinetics) is undertaken, isolating each property by considering insoluble and soluble surfactants. In addition, the role of Marangoni stresses on the deformation and breakage dynamics is explored. High fidelity, three-dimensional direct numerical simulations coupled with a state-of-the-art hybrid interface capturing algorithm are carried out, providing a wealth of information previously inaccessible via volume-averaged or experimental approaches.

The internal dynamics of static mixers handling liquid–liquid flows have been comprehensively explored over the past decade. Although the effect of the inlet configuration is often overlooked, a few studies have suggested a relationship between the phases’ initial set-up and the performance of the mixer in terms of the droplet size distribution (DSD). Accordingly, different dispersed phase morphologies at the inlet of a SMX static mixer have been tested and their effect on the overall dispersion performance of the mixer has been evaluated based on the DSD and growth of interfacial area. In particular, three representative scenarios are considered: (1) Isolated cases, where one and three individual droplets are injected, mimicking a controlled syringe injection; (2) Numerous variable-sized droplets, simulating a pre-mixed/dispersed inlet; and (3) Jet inlet, emulating a standard phase injection from a gear pump. In addition, this study provides novel insight into the underlying physics dictating droplet deformation and breakage in SMX mixers for industrially-relevant scenarios. This can be achieved thanks to the massively-parallel high-fidelity three-dimensional direct numerical simulations computed with a robust hybrid front-tracking/level-set algorithm, which provides a wealth of information on intricate interfacial dynamics; this information cannot be obtained via experimental or volume-averaged modelling techniques implemented in past studies.