Bulk Surfactant Concentration Research Articles

Determining interfacial tension and critical micelle concentrations of surfactants from atomistic molecular simulations

HypothesisAtomistically-detailed models of surfactants provide quantitative information on the molecular interactions and spatial distributions at fluid interfaces. Hence, it should be possible to extract from this information, macroscopical thermophysical properties such as interfacial tension, critical micelle concentrations and the relationship between these properties and the bulk fluid surfactant concentrations.Simulations and ExperimentsMolecular-scale interfacial of systems containing n-dodecyl β-glucoside (APG12) are simulated using classical molecular dynamics. The bulk phases and the corresponding interfacial regions are all explicitly detailed using an all-atom force field (PCFF+). During the simulation, the behaviour of the interface is analyzed geometrically to obtain an approximated value of the critical micelle concentration (CMC) in terms of the surfactant area number density and the interfacial tension is assessed through the analysis of the forces amongst molecules.New experimental determinations are reported for the surface tension of APG12 at the water/air and at the water/n-decane interfaces.FindingsWe showcase the application of a thermodynamic framework that inter-relates interfacial tensions, surface densities, CMCs and bulk surfactant concentrations, which allows the in silico quantitative prediction of interfacial tension isotherms.

Near Equilibration Times in the Diffusion-Controlled Adsorption.

A model of the Frumkin isotherm following adsorption on the surface of the rotating disk is developed with the purpose to calculate the time that is needed for the establishment of the near equilibrium state between the amount of adsorbate and the bulk concentration of surfactant. The "near" is quantified as 99% of the proper equilibrium surface coverage. The near equilibration time depends on the bulk concentration and on the coefficient of molecular attraction in the adsorbed layer. In the vicinity of the inflection point of the isotherm, this time exhibits sharp spike. It is caused by the diminished flux that increases surface coverage very slowly but continues for a long time. Eventually, both the flux and the surface coverage increase with time drastically under the influence of the exponential part of the Frumkin isotherm.

A second-order phase field-lattice Boltzmann model with equation of state inputting for two-phase flow containing soluble surfactants

In this paper, we propose a phase field-lattice Boltzmann (LB) model with an equation of state (EOS) inputting for two-phase flow containing soluble surfactants. In this model, both the order parameter for the phase field and the surfactant concentration are described by second-order partial differential equations, along with Navier–Stokes equations for the flow field. Changes in surfactant concentration do not affect the order parameter distribution; hence, an unwanted sharpening effect cannot arise. Most importantly, in the existing models, the EOS of surface tension is determined by posterior simulation tests instead of being directly set as an input parameter before the simulations. Hence, it is difficult to determine the model parameters in practical applications. To address this issue, we systematically develop a fully analytical EOS for surface tension based on the Gibbs–Duhem equation. Subsequently, an approximate explicit form for EOS is provided by utilizing the Jacobi–Gauss quadrature rule. Furthermore, a multiple-relaxation-time LB scheme is utilized to numerically solve the governing equations of three physical fields. Two benchmark examples are simulated to validate the accuracy of the present model. The consistency between the numerical results and the analytical EOS is verified. Moreover, the dynamics of droplets with surfactant in simple shear flow is investigated, unveiling the profound impact of various factors, such as surfactant bulk concentration, capillary number, and viscosity ratio, on single droplet deformation and two equal-sized droplets interaction. A detailed exploration of the fluid mechanism involved in two-phase flow with soluble surfactants is presented.

Numerical study of the steady core-annular flow in a focusing geometry in the presence of soluble surfactants

The steady state core annular flow of two immiscible fluids in the presence of soluble surfactants is investigated numerically in an axisymmetric tubular or flow focusing geometry. The two immiscible fluids form an interface onto which surfactants can be adsorbed/desorbed from the annular fluid where they are dissolved. The finite element method is employed to discretize the governing equations using the spine method to create the computational mesh, follow the shape of the interface and the axisymmetric wall and capture the flow domain. An unknown pressure distribution is imposed along the interface that quantifies the pressure discontinuity, while allowing the bulk pressure to remain continuous in each phase. GMRES is employed to accommodate the nearly singular nature of the jacobian matrix. The bulk surfactant concentration varies only inside a thin boundary layer of thickness δ∼Pe−1, which justifies omission of the advection-diffusion equation in the annulus bulk. Simulations reveal that the onset of Marangoni stresses tends to decelerate the velocity at the interface which is seen to translate towards the wall/axis of symmetry when the more viscous fluid is the inner/outer fluid, respectively. Finally, simulations in flow-focusing nozzles capture the development of spatially growing instabilities in the downstream region of the interface, with wavelength on the order of the nozzle radius, especially when the outer fluid is more viscous or when the surfactant concentration increases. Raising the volumetric flow rate in the annular region suppresses growth of waves due to interfacial friction. Spatial stability analysis verifies downstream growth of waves and recovers the relevant wavelength. Possible repercussions on the onset of jetting instabilities in devices with liquid focusing are discussed.

Simulation of adsorption at rotating disk

Abstract Diffusion-controlled adsorption at the rotating disk is calculated for Frumkin isotherm. The near equilibrium isotherms are simulated and their time components are analysed. The purpose of the work is to investigate the physical meanings of S-shaped isotherms that appear for strong attractions in the adsorbed layer. It is demonstrated that the surface coverage that is created gradually, by the diffusion process, consumes the concentration gradient of the dissolved surfactant in the diffusion layer. Once the equilibrium with the bulk of the solution is established, the driving force of diffusion-controlled adsorption vanishes and no additional adsorption is possible. The diffusion layer thickness on the rotating disk tends to the constant value and the flux depends only on the concentration of dissolved adsorbent at the disk surface. Hence, the equilibrium with the bulk of solution is established faster than at the stationary disk. This equilibrium takes an infinite amount of time to reach, but the system can approach close to the equilibrium within a definite period of time. The near equilibration time depends on the bulk concentration of surfactant. These relationships exhibit sharp maxima under the influence of attractions in the adsorbed layer.

The role of surface tension on the growth of bubbles by rectified diffusion

Rectified diffusion has wide and important applications in sonochemistry, ultrasonic cleaning and medical ultrasound. Recent experimental results have demonstrated that the addition of surfactant substantially enhances bubble growth rate. As a hypothesis, this was widely attributed to the acoustic microstreaming and mass transfer resistance caused by surfactants. In this research, the effects of the surfactant of sodium dodecyl sulphate on the rectification have been simulated by considering only the variation of the surface tension coefficient due to the surfactant. The computations are carried out using a newly developed tractable model based on the multi-scale method and the method of matched asymptotic expansions, which allows the prediction of bubble growth taking place over millions of oscillation cycles. The rate of bubble growth observed in the experiments is accurately predicted by our computations, for a range for bulk surfactant SDS concentrations less than or equal to 2.4 mM. Contrary to the widely held hypothesis in the published literature, this has demonstrated that the dominant physical mechanisms remain the shell and area effects in this range of bulk surfactant concentrations. The further enhancement of bubble growth rate provided by either acoustic microstreaming or the resistance to mass transfer is only evident at higher bulk surfactant concentrations. Therefore, the role of surface tension in rectified diffusion for aqueous surfactant solutions is more significant than previously understood. The new results also show that the bubble growth rate is sensitive to small changes in the bubble radius which may account for its unpredictability in applications of sonochemistry.

Effect of soluble surfactant on the interface dynamics of a rising droplet

In this study, we present numerical simulations examining the impact of soluble surfactant on the interface dynamics of a rising droplet. To achieve this, the droplet interface is tracked using an arbitrary Lagrangian–Eulerian approach, and the bulk and interfacial surfactant concentration evolution equations fully coupled with the incompressible Navier–Stokes equations are solved. We systematically evaluate the boundary of interfacial dynamics evolution by varying certain dimensionless parameters. Specifically, we study the effects of changes in parameters such as the Langmuir number, the Biot number, the Damkohler number, the bulk Peclet number, and the elastic number on interfacial tangential velocity, interfacial concentration and its gradient, interfacial viscous shear stress, and droplet rising velocity. Our findings confirm the validity of the stagnant-cap model for describing the interfacial fluidity of a surfactant-laden rising droplet. Increasing the Langmuir number and decreasing the Damkohler number can inhibit interface fluidity, but there is a threshold for the Damkohler number. Additionally, the overall increase in interface tension may mask the hindering effect of the locally increased concentration gradient on the interfacial fluidity. The Biot number has no impact on the steady state of the interface, but a slow adsorption rate may result in a bimodal retardation before the interface reaches a steady state. A clear threshold exists for the Peclet number to hinder the interface velocity, and a too high Peclet number leads to strong nonlinearity in the interface physical quantities. Variations in the elastic number significantly affect the evolution of the interface, causing the interface velocity to pass through several states, ranging from almost no retardation, uniform retardation, stagnant-cap retardation to complete retardation.

Effect of surfactants and interfacial rheology on equilibrium drop size in turbulent liquid-liquid dispersions

Surfactants are often required to stabilize liquid-liquid dispersions produced by high shear mixers. Due to the high power input, drops are deformed rapidly in the dispersion zone so the dynamic interfacial properties governed by the surfactant adsorption rate can have a significant impact on the resulting drop size. The objective of this work is to develop a fundamental link between surfactant adsorption dynamics, interfacial properties, and turbulent emulsification processes. To ensure constant bulk surfactant concentration during dispersion, equilibrium drop size for dilute dispersions produced by a batch rotor-stator mixer were studied. Silicone oils of various viscosity were dispersed in aqueous nonionic surfactant solutions. Drop size distributions (DSD) were measured via a video microscopy/automated image analysis technique. Equilibrium interfacial tension was measured via a pendant drop technique, as a function of surfactant concentration. The dynamic surface tension was similarly measured. The data were fit to the Langmuir adsorption isotherm and the long-times approximation to the Ward – Tordai equation and the adsorption parameters and surfactant diffusivities so obtained were employed, with an estimate of the drop deformation timescale, to estimate the surface dilational modulus (Esd) or Marangoni stress acting on the drop’ surface due to interfacial tension gradients. Trends observed in the measured equilibrium mean drop size and DSD are explained in terms of the interfacial and rheological properties. Below the CMC, Esd peaks and the drop size increases with bulk surfactant concentration, despite a decrease in equilibrium interfacial tension. Above the CMC, Marangoni stresses are small but the presence of the surfactant still modifies the rheology of the interface, increasing the effective viscosity of the drops. A comprehensive set of mechanistic models for drop size in turbulent flows, based on Kolmogorov-Hinze theory, was developed and modified to partially account for the effect of surfactants via an appropriately defined effective viscosity. The approach allows integration of surfactant phenomena into widely accepted correlations for drop size in surfactant free systems.

Interface Adsorption versus Bulk Micellization of Surfactants: Insights from Molecular Simulations.

Surfactants play essential roles in many commonplace applications and industrial processes. Although significant progress has been made over the past decades with regard to model-based predictions of the behavior of surfactants, important challenges have remained. Notably, the characteristic time scales of surfactant exchange among micelles, interfaces, and the bulk solution typically exceed the time scales currently accessible with atomistic molecular dynamics (MD) simulations. Here, we circumvent this problem by introducing a framework that combines the general thermodynamic principles of self-assembly and interfacial adsorption with atomistic MD simulations. This approach provides a full thermodynamic description based on equal chemical potentials and connects the surfactant bulk concentration, the experimental control parameter, with the surfactant surface density, the suitable control parameter in MD simulations. Self-consistency is demonstrated for the nonionic surfactant C12EO6 (hexaethylene glycol monododecyl ether) at an alkane/water interface, for which the adsorption and pressure isotherms are computed. The agreement between the simulation results and experiments is semiquantitative. A detailed analysis reveals that the used atomistic model captures well the interactions between surfactants at the interface but less so their adsorption affinities to the interface and incorporation into micelles. Based on a comparison with other recent studies that pursued similar modeling challenges, we conclude that the current atomistic models systematically overestimate the surfactant affinities to aggregates, which calls for improved models in the future.

Direct Resolution of the Interactions of a Hydrocarbon Gas with Adsorbed Surfactant Monolayers at the Water/Air Interface Using Neutron Reflectometry

We have directly resolved in the present work the interfacial composition during and after the interactions of a saturated atmosphere of oil vapor with soluble surfactant solutions at a planar water/air interface for the first time. Experiments were conducted on interactions of hexane vapor with solutions of alkyltrimethylammonium bromides and sodium dodecyl sulfate to observe the balance between cooperativity and competition of the components at the interface. In all cases, hexane adsorption was strongly enhanced by the presence of the surfactant, even at bulk surfactant concentrations four orders of magnitude below the critical micelle concentration. Cooperativity of the surfactant adsorption was observed only for sodium dodecyl sulfate at intermediate bulk concentrations, yet for all four systems, competition set in at higher concentrations, as hexane adsorption reduced the surfactant surface excess. The data fully supported the complete removal of hexane from the interface following venting of the system to remove the saturated atmosphere of oil vapor. These results help to identify future experiments that would elaborate and could explain the cooperativity of surfactant adsorption, such as on cationic surfactants with short alkyl chains and a broader series of anionic surfactants. This work holds relevance for oil recovery applications with foam, where there is a gas phase saturated with oil vapor.

Microtensiometer for Confocal Microscopy Visualization of Dynamic Interfaces.

Adsorption of surface-active molecules to fluid-fluid interfaces is ubiquitous in nature. Characterizing these interfaces requires measuring surfactant adsorption rates, evaluating equilibrium surface tensions as a function of bulk surfactant concentration, and relating how surface tension changes with changes in the interfacial area following equilibration. Simultaneous visualization of the interface using fluorescence imaging with a high-speed confocal microscope allows the direct evaluation of structure-function relationships. In the capillary pressure microtensiometer (CPM), a hemispherical air bubble is pinned at the end of the capillary in a 1 mL volume liquid reservoir. The capillary pressure across the bubble interface is controlled via a commercial microfluidic flow controller that allows for model-based pressure, bubble curvature, or bubble area control based on the Laplace equation. Compared to previous techniques such as the Langmuir trough and pendant drop, the measurement and control precision and response time are greatly enhanced; capillary pressure variations can be applied and controlled in milliseconds. The dynamic response of the bubble interface is visualized via a second optical lens as the bubble expands and contracts. The bubble contour is fit to a circular profile to determine the bubble curvature radius, R, as well as any deviations from circularity that would invalidate the results. The Laplace equation is used to determine the dynamic surface tension of the interface. Following equilibration, small pressure oscillations can be imposed by the computer-controlled microfluidic pump to oscillate the bubble radius (frequencies of 0.001-100 cycles/min) to determine the dilatational modulus The overall dimensions of the system are sufficiently small that the microtensiometer fits under the lens of a high-speed confocal microscope allowing fluorescently tagged chemical species to be quantitatively tracked with submicron lateral resolution.

The effect of the molecular structure of alkyl ether carboxylate surfactants on the oil–water interfacial tension

• OPLS-AA is not applicable to study surfactants at the alkane-water interface. • Trappe-UA and OPLS-AA underestimate the effect of surfactants on the IFT. • The adsorption limit decreases with the increase in the surfactant headgroup length. • Doubling the tailgroup length leads to a small decrease in the adsorption limit. • The effect of a surfactant molecule size on the adsorption limit is asymptotical. Alkyl ether carboxylate surfactants at the alkane–water interface are explored experimentally through interfacial tension measurements with the spinning drop method and molecular dynamics simulations. The experimental interfacial tension dependence on bulk surfactant concentration is interpreted with the Redlich-Peterson adsorption model, which fits the experiments well. The critical micelle concentrations obtained from the experimental isotherms agree reasonably with published data on other surfactants of the same class. The length of the ethylene oxide hydrophilic segment significantly influences the dependence of the CMC and the interfacial tension at CMC on temperature. The excess surface density of the surfactant at the decane-water interface is calculated with the Redlich-Peterson model and compared with the molecular dynamics simulations, which are performed with two different forcefields. The simulations showed only semiquantitative agreement with the experiments: surfactants interfacial concentrations corresponding to a particular value of tension are systematically higher than the values derived from the experiments, for both forcefields by a certain factor that appears constant. Simulations of surfactants with different lengths of the alkyl tail and ethylene oxide head segments revealed general tendencies related to the surfactants interactions in the layer. Initially, the ethylene oxide segment elongation decreases the monolayer density and increases the effective elasticity. However, as the number of ethylene oxide monomers exceeds approximately eight, the density and compressibility become invariant of the length, which is likely explained by the dominance of electrostatic forces between the charged carboxylate groups that decay with the distance slower than the steric repulsion between the ethylene oxide chains.

Solute effects on the dynamics and deformation of emulsion droplets during freezing.

Soft or rigid particles, suspended in a liquid melt, interact with an advancing solidification front in various industrial and natural processes, such as fabrication of particle-reinforced-composites, growth of crystals, cryopreservation, frost heave, and growth of sea ice. The particle dynamics relative to the front determine the microstructure as well as the functional properties of the solidified material. Previous studies have extensively investigated the interaction of foreign objects with a moving solid-liquid interface in pure melts while in most real-life systems, solutes or surface active impurities are almost always present. Here we study experimentally the interaction of spherical oil droplets with a moving planar ice-water interface, while systematically increasing the surfactant concentration in the bulk liquid, using in situ cryo-confocal microscopy. We demonstrate that a small amount of surfactant in the bulk liquid can instigate long-range droplet repulsion, extending over a length scale of 40 to 100 μm, in contrast to the short-range predicted previously (<1 μm). We report on the droplet deformation, while they are in contact with the ice-water interface, as a function of the bulk surfactant concentration, the droplet size, and the crystal growth rate. We also depict the dynamic evolution of solute-enriched premelted films (≈5 μm). Our results demonstrate how an increasing concentration of surfactant in the bulk and its subsequent segregation during solidification can dramatically alter the solidification microstructures. We anticipate that our experimental study can aid in the development of theoretical models incorporating solute effects.

Polymer drag reduction in surfactant-contaminated turbulent bubbly channel flows

Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is accomplished by a non-linear equation of state that relates the surface tension to the surfactant concentration. For Newtonian turbulent bubbly flows, the effects of Triton X-100 and 1-Pentanol surfactant are examined. It is observed that the sorption kinetics highly affect the dynamics of bubbly flow. A minute amount of Triton X-100 is found to be sufficient to prevent the formation of bubble clusters restoring the single-phase behavior while even two orders of magnitude more 1-Pentanol surfactant is not adequate to prevent the formation of layers. For viscoelastic turbulent flows, it is found that the viscoelasticity promotes formation of the bubble-wall layers and thus the polymer drag reduction is completely lost for the surfactant-free bubbly flows, while the addition of small amount of surfactant (Triton X-100) in this system restores the polymer drag reduction resulting in $25\%$ drag reduction for the $Wi=4$ case.

Effect of surfactant lengths on gas-liquid oxygen mass transfer from a single rising bubble

This work is an experimental investigation of the effect of the nature of surfactants on oxygen mass transfer. The study focuses on three cationic surfactants with different hydrophobic chain lengths, and four nonionic surfactants with different hydrophilic chain lengths. Equilibrium adsorption isotherms are calculated for each surfactant from experimental values of surface tension in static conditions. Surfactant solutions at concentrations between 2.5 × 10-8 and 5 × 10-3 mol/L were prepared and oxygen transfer from millimetric air bubbles (between 0.82 and 1.08 mm) was measured by Planar Laser Induced Fluorescence with Inhibition (PLIF-I). When the bulk concentration of surfactant was increased, results showed a sharp decrease of bubble velocity, in the range of 283–75 mm/s, and of liquid-side mass transfer coefficient, in the range of 5.6 × 10-4–0.4 × 10-4 m/s. This effect was observed for all surfactants studied. However, the length of the hydrophilic chain did not appear to affect the hydrodynamics of the rising bubble or the oxygen transfer at the same bulk concentration. Furthermore, for the same bulk concentration, increasing the hydrophobic chain length had an impact on the velocity and the mass transfer coefficient of oxygen. Finally, the Sherwood number was calculated in each medium and compared with classical correlations for gas–liquid mass transfer prediction. Those correlations seemed to reach a limit for a very concentrated medium.

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.

Dramatic Slowing Down of Oil/Water/Silica Contact Line Dynamics Driven by Cationic Surfactant Adsorption on the Solid.

We report on the contact line dynamics of a triple-phase system silica/oil/water. When oil advances onto silica within a water film squeezed between oil and silica, a rim forms in water and recedes at constant velocity. We evidence a sharp (three orders of magnitude) decrease of the contact line velocity upon the addition of cationic surfactants above a threshold concentration, which is slightly smaller than the critical micellar concentration. We show that, with or without surfactant, and within the range of small capillary numbers investigated, the contact line dynamics can be described by a friction term that does not reduce to pure hydrodynamical effects. In addition, we derive a model that successfully accounts for the selected contact line velocity of the rim. We further demonstrate the strong increase of the friction coefficient with surfactant bulk concentration results from the strongly nonlinear adsorption isotherm of surfactants on silica. From the variations of the friction coefficient and spreading parameter with surface concentration, we suggest a picture in which the part of the adsorbed surfactants that are strongly bound to the silica interface is trapped under the oil droplet and is responsible for the large increase in line friction.

Ionic Surfactants at Air/Water and Oil/Water Interfaces: A Comparison Based on Molecular Dynamics Simulations.

Ionic surfactants are known to build up higher interfacial pressures at oil/water interfaces than at air/water interfaces for the same surfactant bulk concentration. Here, we systematically investigate this effect through atomistic molecular dynamics (MD) simulations of surfactant-loaded air/water and oil/water interfaces. Two prototypical ionic surfactants, C12TAB and sodium dodecyl sulfate (SDS), are studied and found to give consistent results, which are also robust with respect to variations in the simulation force field. The simulations reproduce the experimental interfacial pressure data on a semiquantitative level and reveal that the influence of oil on the surfactants' in-plane distribution is a major contribution to the observed effect, albeit insufficient to be the sole reason. The simulations are further analyzed with regard to surfactant/oil cooperative/competitive effects that have been invoked recently as an explanation. However, the interfacial orientation of oil molecules, a presumable indicator for such behavior, is found to display changes only for high levels of surfactant coverage.

Modeling Gas-Liquid Interfaces by Dissipative Particle Dynamics: Adsorption and Surface Tension of Cetyl Trimethyl Ammonium Bromide at the Air-Water Interface.

Adsorption of surfactants at gas-liquid interfaces that causes reduction in the surface tension is a classical problem in colloid and interface science with multiple practical applications in oil and gas recovery, separations, cosmetics, personal care, and biomedicine. Here, we develop an original coarse-grained model of the liquid-gas interface within the conventional dissipative particle dynamics (DPD) framework with the goal of quantitatively predicting the surface tension in the presence of surfactants. As a practical case-study example, we explore the adsorption of the cationic surfactant cetyl trimethyl ammonium bromide (CTAB) on the air-water interface. The gas phase is modeled as a DPD fluid composed of fictitious hard-core "gas" beads with exponentially decaying repulsive potentials to prevent penetration of the liquid phase components. A rigorous parametrization scheme is proposed based on matching the bulk and interfacial properties of water and octane taken as the reference compounds. Quantitative agreement between the simulated and experimental surface tension of CTAB solutions is found for a wide range of bulk surfactant concentrations (∼10-3 to ∼1 mmol/L) with the reduction of the surface tension from ∼72 mN/m (pure water) to the limiting value of ∼37.5 mN/m at the critical micelle concentration. The gas phase DPD model with the proposed parametrization scheme can be extended and applied to modeling various gas-liquid interfaces with surfactant and lipid monolayers, such as bubble suspensions, foams, froths, etc.

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 [25], 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.