The effect of alkane tail length of CiE8 surfactants on transport to the silicone oil–water interface

Curvature and shape relaxation in surface-viscous domains

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Review of the role of surfactant dynamics in drop microfluidics

Surfactants are employed in microfluidic systems not just for drop stabilisation, but also to study local phenomena in industrial processes. On the scale of a single drop, these include foaming, emulsification and stability of foams and emulsions using statistically significant ensembles of bubbles or drops respectively. In addition, surfactants are often a part of a formulation in microfluidic drop reactors. In all these applications, surfactant dynamics play a crucial role and need to be accounted for. In this review, the effect of surfactant dynamics is considered on the level of standard microfluidic operations: drop formation, movement in channels and coalescence, but also on a more general level, considering the mechanisms controlling surfactant adsorption on time- and length-scales characteristic of microfluidics. Some examples of relevant calculations are provided. The advantages and challenges of the use of microfluidics to measure dynamic interfacial tension at short time-scales are discussed.

Surface tensions at elevated pressure depend strongly on bulk phase saturation

HYPOTHESIS

Understanding interfacial phenomena at elevated pressure is crucial to the design of a variety of processes, modeling important systems, and interpreting interfacial thermodynamics. While many previous studies have offered insight into these areas, current techniques have inherent drawbacks that limit equilibrium measurements.

EXPERIMENTS

In this work, we adapt the ambient microtensiometer of Alvarez and co-workers into a high pressure microtensiometer (HPMT) capable of experimentally quantifying a wide range of interfacial phenomena at elevated pressures. Particularly, the HPMT uses a microscale spherical interface pinned to the tip of a capillary to directly measure surface tension via the Laplace equation. The stream of microscale bubbles used to pressurize the system ensures quick saturation of the bulk phases prior to conducting measurements. The HPMT is validated by measuring the surface tension of air-water as a function of pressure. We then measure the surface tension of CO₂ vapor and water as a function of pressure, finding lower equilibrium surface tension values than originally reported in the literature.

FINDINGS

This work both introduces further development of a useful experimental technique for probing interfacial phenomena at elevated pressures and demonstrates the importance of establishing bulk equilibrium to measure surface tension. The true equilibrium state of the CO₂-water surface has a lower tension than previously reported. We hypothesize that this discrepancy is likely due to the long diffusion timescales required to ensure saturation of the bulk fluids using traditional tensiometry. Thus we argue that previously reported elevated pressure measurements were performed at non-equilibrium conditions, putting to rest a long standing discrepancy in the literature. Our measurements establish an equilibrium pressure isotherm for the pure CO₂-water surface that will be essential in analyzing surfactant transport at elevated pressures.

Dilatational rheology of water-in-diesel fuel interfaces: effect of surfactant concentration and bulk-to-interface exchange

Micrometer-sized water droplets dispersed in diesel fuel are stabilized by the fuel's surface-active additives, such as mono-olein and poly(isobutylene)succinimide (PIBSI), making the droplets challenging for coalescing filters to separate. Dynamic material properties found from interfacial rheology are known to influence the behavior of microscale droplets in coalescing filters. In this work, we study the interfacial dilatational properties of water-in-fuel interfaces laden with mono-olein and PIBSI, with a fuel phase of clay-treated ultra-low sulphur diesel (CT ULSD). First, the dynamic interfacial tension (IFT) is measured using pendant drop tensiometry, and a curvature-dependent form of the Ward and Tordai diffusion equation is applied for extracting the diffusivity of the surfactants. Additionally, Langmuir kinetics are applied to the dynamic IFT results to obtain the maximum surface concentration (Γ∞) and ratio of adsorption to desorption rate constants (κ). We then use a capillary pressure microtensiometer to measure the interfacial dilatational modulus, and further extract the characteristic frequency of surfactant exchange (ω0) by fitting a model assuming diffusive exchange between the interface and bulk. In this measurement, 50-100 μm diameter water droplets are pinned at the tip of a glass capillary in contact with the surfactant-containing fuel phase, and small amplitude capillary pressure oscillations over a range of frequencies from 0.45-20 rad s-1 are applied to the interface, inducing changes in interfacial tension and area to yield the dilatational modulus, E*(ω). Over the range of concentrations studied, the dilatational modulus of CT ULSD with either mono-olein or PIBSI increases with a decrease in bulk concentration and plateaus at the lowest concentrations of mono-olein. Characteristic frequency (ω0) values extracted from the fit are compared with those calculated using equilibrium surfactant parameters (κ and Γ∞) derived from pendant drop tensiometry, and good agreement is found between these values. Importantly, the results imply that diffusive exchange models based on the equilibrium relationships between surfactant concentration and interfacial tension can be used to infer the dynamic dilatational behavior of complex surfactant systems, such as the water-in-diesel fuel interfaces in this study.

Role of Surfactants Based on Fatty Acids in the Wetting Behavior of Solid-Oil-Aqueous Solution Systems

Surfactants based on fatty acids have attracted extensive attention thanks to their eco-friendly and pH-responsive features. Here, we studied two fatty acid-based surfactants that were paired with the same organic counterion but distinguished by their aliphatic chain lengths (monoethanolamine-oleic acid (MEA-OA) and monoethanolamine-lauric acid (MEA-LA)). Both surfactants exhibited the ability to lower the oil-water interfacial tension but lost their interfacial activity in a low-pH environment. We experimentally investigated their influence on the receding and spreading of oil droplets on solid surfaces. It was found that the interfacial tension reduction could decrease the static contact angle of the aqueous phase and hindered displacement dynamics during the oil droplet receding. Meanwhile, the interfacial activity was more likely to suppress the initiation of the oil droplet spreading due to the more stable thin-film forming prior to the spreading process. Nevertheless, the experimental results also exhibited that MEA-OA was more effective than MEA-LA in suppressing the receding dynamics and the spreading initiation even when they were characterized by similar interfacial tension values. Such an interesting observation could be attributed to the more considerable Marangoni flow in the solution of MEA-OA whose molecules have longer aliphatic chains. The insight from this study is expected to improve the knowledge on the molecular design for more efficient applications of fatty acid-based surfactants.

Phase-Dependent Surfactant Transport on the Microscale: Interfacial Tension and Droplet Coalescence

Liquid-liquid emulsion systems are usually stabilized by additives, known as surfactants, which can be observed in various environments and applications such as oily bilgewater, water-entrained diesel fuel, oil production, food processing, cosmetics, and pharmaceuticals. One important factor that stabilizes emulsions is the lowered interfacial tension (IFT) between the fluid phases due to surfactants, inhibiting the coalescence. Many studies have investigated the surfactant transport behavior that leads to corresponding time-dependent lowering of the IFT. For example, the rate of IFT decay depends on the phase in which the surfactant is added (dispersed vs continuous) due in part to differences in the near-surface depletion depth. Other key factors, such as the viscosity ratio between the dispersed and continuous phases and Marangoni stress, will also have an impact on surfactant transport and therefore the coalescence and emulsion stability. In this feature article, the measurement techniques for dynamic IFT are first reviewed due to their importance in characterizing surfactant transport, with a specific focus on macroscale versus microscale techniques. Next, equilibrium isotherm models as well as dynamic diffusion and kinetic equations are discussed to characterize the surfactant and the time scale of the surfactant transport. Furthermore, recent studies are highlighted showing the different IFT decay rates and its long-time equilibrium value depending on the phase into which the surfactant is added, particularly on the microscale. Finally, recent experiments using a hydrodynamic Stokes trap to investigate the impact of interfacial surfactant transport, or "mobility", and the phase containing the surfactant on film drainage and droplet coalescence will be presented.

Size dependent droplet interfacial tension and surfactant transport in liquid-liquid systems, with applications in shipboard oily bilgewater emulsions

Many liquid-liquid emulsions, including shipboard oily bilgewater (oil-in-water) and water entrained in diesel fuels (water-in-oil), are chemically stabilized by surfactants and additives and require treatment to destabilize and separate. The interfacial tension (IFT) of surfactant-laden interfaces between the continuous and dispersed phase, as well as the size of the dispersed droplets, are significant factors in determining emulsion stability. In particular, the timescale associated with a dynamic change in IFT due to surfactant transport is indicative of how fast the emulsion will stabilize. In the present work, the dynamic IFT of droplets at micro-scale (∼80 μm) and milli-scale (∼2 mm) is measured with simulated bilgewater with soluble surfactant systems. It is found that the IFT of micro-scale droplets decays faster than that of the milli-scale droplets due to smaller diffusion boundary layer thickness. The change in IFT was also studied for water-soluble surfactants added into the dispersed phase and continuous phase for both milli- and micro-scaled droplets. The results show that the IFT of micro-scale droplets decreases to the equilibrium value faster when the surfactant is in outer phase than in the inner phase, while the IFT does not change significantly for the milli-scale droplets. The observations are explained by the change in diffusion limited to kinetic limited surfactant transport. Finally, the surfactant diffusivities, adsorption and desorption rate constants are calculated using Langmuir's equation. The results presented here provide insight into the fundamental mechanism of the surfactant transport and helps improve mitigation strategies of oil-water emulsions.

Electric fields enable tunable surfactant transport to microscale fluid interfaces

The transport dynamics of oil-soluble surfactants to oil-water interfaces are quantified using a custom-built electrified capillary microtensiometer platform. Dynamic interfacial tension measurements reveal that surfactant transport is enhanced under a dc electric field, due to electro-migration of charge carriers in the oil toward the interface. Notably, this enhancement can be precisely tuned by altering the field strength and temporal scheduling. We demonstrate electric fields as a new parameter to manipulate surfactant transport to microscale fluid-fluid interfaces.

Search for the Source of an Apparent Interfacial Resistance To Mass Transfer of CnEm Surfactants To the Water/Oil Interface

Experiments have shown that relaxation of oil/water interfacial tension by adsorption of alkyl ethoxylate surfactants from water onto an oil droplet is delayed relative to diffusion-controlled adsorption. We examine possible causes of this delay, and we show that several are implausible. We find that redissolution of the surfactant in the oil droplet cannot explain the apparent interfacial resistance at short times because the interface will preferentially fill before any such redissolution occurs. We also perform umbrella sampling with molecular dynamics simulation and do not find any evidence of a free-energy barrier or low-diffusivity zone near the interface. Nor do we find evidence from the simulation that premicellar aggregation slows diffusion enough to cause the observed resistance to interfacial adsorption. We are therefore unable to pinpoint the cause of the resistance, but we suggest that "dead time" associated with the experimental method could be responsible-specifically a local depletion of surfactant by the ejected droplet when creating the fresh interface between the oil and water.

Colloidal stability dictates drop breakup under electric fields

Electric fields can deform drops of fluid from their equilibrium shape, and induce breakup at sufficiently large field strengths. In this work, the electric field induced breakup of a squalane drop containing a colloidal suspension of carbon black particles with polyisobutylene succinimide (OLOA 11000) surfactant is studied. The drop is suspended in silicone oil. The breakup mode of a drop containing carbon black depends strongly on the suspension stability. It is observed that a drop of a stable suspension of carbon black has the same breakup mode as a drop with surfactant alone, i.e., without added carbon black. At lower electric fields, these drops break by the formation of lobes at the two ends of the drop; and at higher fields the homogeneous lobes break in a non-axisymmetric manner. However, a drop of an unstable suspension shows a drastically different breakup mode, and undergoes breakup much faster compared to a drop with surfactant alone. These drops elongate and form asymmetric lobes that develop into fingers and eventually disintegrate in an inhomogeneous, three-dimensional fashion. As a basis for comparison, the breakup of a pure squalane drop, and a squalane drop with equivalent surfactant concentrations but no carbon black particles is examined. Axisymmetric boundary integral computations are used to elucidate the mechanism of breakup. Our work demonstrates the impact of colloidal stability on the breakup of drops under an electric field. Colloidal stability on the time scale of drop deformation leads to rich and unexplored breakup phenomena.

Nanoparticle adsorption dynamics at fluid interfaces

Understanding the dynamic adsorption of nanoparticles (NPs) at fluid interfaces is important for stabilizing emulsions and for the preparation of 2D NP-based materials. Here we show that the Ward-Tordai equations commonly employed to describe the dynamics of surfactant adsorption at a fluid interface combined with a Frumkin adsorption isotherm can be employed to model the diffusion-limited adsorption of NPs onto a fluid interface. In contrast to surfactants, an additional wetting equation of state (EOS) must be incorporated to characterize the dynamic interfacial tension during the adsorption of NPs to the oil-water interface. Our results show agreement between the model and experiments with NP area fractions <0.3. Slower dynamics are observed at larger area fractions, which are speculated to arise from polydispersity or re-organization at the interface. We show the model can be extended to the competitive adsorption between the NPs and a surface active species.

Using bulk convection in a microtensiometer to approach kinetic-limited surfactant dynamics at fluid-fluid interfaces

The impact of transport of surfactants to fluid-fluid interfaces is complex to assess and model, as many processes are in the regime where kinetics, diffusion and convection are comparable. Using the principle that the timescale for diffusion decreases with increasing curvature, we previously developed a microtensiometer to accurately measure fundamental transport coefficients via dynamic surface tension at spherical microscale liquid-fluid interfaces. In the present study, we use a low Reynolds number flow in the bulk solution to further increase the rate of diffusion. Dynamic surface tension is measured as a function of Peclet number and the results are compared with a simplified convection-diffusion model. Although a transition from diffusion to kinetic-limited transport is not observed experimentally for the surfactants considered, lower bounds on the adsorption and desorption rate constants are determined that are much larger than previously reported rate constants. The results show that the details of the flow field do not need to be controlled as long as the local Reynolds number is low. Aside from other pragmatic advantages, this experimental tool and analysis allows the governing mechanisms of surfactant transport at liquid-fluid interfaces to be quantified using flow near the interface to decrease the length scale for diffusion, separating the relevant timescales.