Surfactant-laden Droplets Research Articles

Morphology of clean and surfactant-laden droplets in homogeneous isotropic turbulence

We perform direct numerical simulations of surfactant-laden droplets in homogeneous isotropic turbulence with Taylor Reynolds number $Re_\lambda \approx 180$ . The droplets are modelled using the volume-of-fluid method, and the soluble surfactant is transported using an advection–diffusion equation. Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, thus allowing us to extend the framework developed by Hinze (AIChE J., vol. 1, no. 3, 1955, pp. 289–295) and Kolmogorov (Dokl. Akad. Navk. SSSR, vol. 66, 1949, pp. 825–828) for surfactant-free bubbles to surfactant-laden droplets. We find that surfactant-induced tangential stresses play a minor role in this set-up, thus allowing us to extend the Kolmogorov–Hinze framework to surfactant-laden droplets. The Kolmogorov–Hinze scale $d_H$ is indeed found to be a pivotal length scale in the droplets’ dynamics, separating the coalescence-dominated (droplets smaller than $d_H$ ) and the breakage-dominated (droplets larger than $d_H$ ) regimes in the droplet size distribution. We find that droplets smaller than $d_H$ have a rather compact, regular, spheroid-like shape, whereas droplets larger than $d_H$ have long, convoluted, filamentous shapes with a diameter equal to $d_H$ . This results in very different scaling laws for the interfacial area of the droplet. The normalized area, $A/d_H^2$ , of droplets smaller than $d_H$ is proportional to $(d/d_H)^2$ , while the area of droplets larger than $d_H$ is proportional to $(d/d_H)^3$ , where $d$ is the droplet characteristic size. We further characterize the large filamentous droplets by computing the number of handles (loops of the dispersed phase extending into the carrier phase) and voids (regions of the carrier fluid completely enclosed by the dispersed phase) for each droplet. The number of handles per unit length of filament scales inversely with surface tension. The number of voids is proportional to the droplet size and independent of surface tension. Handles are indeed an unstable feature of the interface and are destroyed by the restoring effect of surface tension, whereas voids can move freely in the interior of the droplets, unaffected by surface tension.

Characterizing the Microparticles Deposition Structure and its Photonic Nature in Surfactant-Laden Evaporating Colloidal Sessile Droplets.

This work presents a simple method to create photonic microstructures via the natural evaporation of surfactant-laden colloidal sessile droplets on a flat substrate. In the absence of dissolved surfactant, the evaporating colloidal droplet forms a well-known coffee ring deposition. In contrast, the presence of surfactant leads to the formation of multiple ring structures due to the repetitive pinning-depinning behavior of the droplet contact line (CL). It is found that the multiring structure shows vibrant iridescent structural colors while the coffee ring lacks a photonic nature. This difference in the structural color for the presence and absence of the surfactant is found to be dependent on the arrangement of the particles in the deposition structure. The particle arrangement in the multirings is monolayered and well-ordered. The ordering of the particles is strongly influenced by the particle dynamics, contact angle (CA), and CL dynamics of the evaporating colloidal solution droplet. Furthermore, the iridescent nature of the multiring deposition is demonstrated and explained. The dependence of the multiring deposition structure on the concentration of the dissolved surfactant and the suspended particles is also studied. The findings demonstrate that an intermediate surfactant concentration is desirable for the formation of a multiring structure. Further, the pinning-depinning CL dynamics that causes the formation of the multiring deposition structure is discussed. Finally, we demonstrate the applicability of the approach to smaller droplet volumes.

Effect of Surfactants on the Splashing Dynamics of Drops Impacting Smooth Substrates.

We present the results of a systematic study elucidating the role that dynamic surface tension has on the spreading and splashing dynamics of surfactant-laden droplets during the impact on hydrophobic substrates. Using four different surfactants at various concentrations, we generated a range of solutions whose dynamic surface tension were characterized to submillisecond timescales using maximum bubble-pressure tensiometry. Impact dynamics of these solutions were observed by high-speed imaging with subsequent quantitative image processing to determine the impact parameters (droplet size and speed) and dynamic wetting properties (dynamic contact angle). Droplets were slowly formed by dripping to allow the surfactants to achieve equilibrium at the free surface prior to impact. Our results indicate that while only the fastest surfactants appreciably affect the maximum spreading diameter, the droplet morphology during the initial stages of spreading is different to water for all surfactant solutions studied. Moreover, we show that surfactant-laden droplets splash more easily than pure liquid (water). Based on the association of the splashing ratio to our tensiometry measurements, we are able to predict the effective surface tension acting during splashing. These results suggest that droplet splashing characteristics are primarily defined by the stretching of the equilibrated droplet free surface.

Understanding the formation of particle bands and fingering patterns during evaporation of a sessile droplet containing colloids

Sessile droplets containing dispersed colloids evaporate on substrates leaving distinct deposition patterns. Applications using the droplets technique require a critical understanding of the complex particle dynamics that affect the deposition pattern. The fingering-like pattern formed when surfactant-laden droplets containing dispersed colloids evaporate is not yet well understood. The lateral imbalanced capillary meniscus forces (CMFs) between particles moving along the Marangoni vortex (MV) cluster particles into bands that deposit to form the fingering-like pattern. This work investigates the effect of particle shape, particle, and surfactant concentration on the phenomenon. Further, the importance of the contact angle and contact line (CL) dynamics of the droplet is also discussed. The results demonstrate that manipulating these parameters can control the band formation and the resulting deposition pattern. The findings of this work would be pivotal for a critical understanding of particle self-assembly and pattern morphologies of evaporating surfactant-laden droplets.

High-efficiency mechanism of enhancement of spreading performance of oil involving surfactant-laden oil droplet spreading over water surface

This study clarified the high-efficiency mechanism of enhancement of the spreading performance of oil by allowing a droplet of an organic solvent to spread over the surface of water with the addition of oil-soluble surfactants. Firstly, the effect of Span 85, Span 80, Span 20, octylphenol polyoxyethylene (4) ether (OP-4), and sodium dioctyl sulfosuccinate (AOT) on the interfacial parameters of an n-decane droplet was evaluated by measuring the surface tension and interfacial tension. Then the spreading coefficient was calculated to determine whether the surfactant-laden oil droplets could spread at the air–water interface. Moreover, the law governing the spreading of the surfactant-laden oil droplets over water was systematically studied. Furthermore, the characteristics of the dynamic behavior of the surfactants were investigated by molecular dynamics simulations to elucidate the spreading mechanism. The results of the experiments and simulations explained how the oil-soluble surfactants Span 85, Span 80, Span 20, OP-4, and AOT significantly improved the spreading performance of oil droplets over the water surface.

Coalescence of surfactant-laden droplets

Droplet coalescence is an important process in nature and various technologies (e.g., inkjet printing). Here, we unveil the surfactant mass transport mechanism and report on several major differences in the coalescence of surfactant-laden droplets as compared to pure water droplets by means of molecular dynamics simulation of a coarse-grained model. Large-scale changes to bridge growth dynamics are identified, such as the lack of multiple thermally excited precursors, attenuated collective excitations after contact, slowing down in the inertial regime due to aggregate-induced rigidity and reduced water flow, and a slowing down in the coalescence rate (deceleration) when surfactant concentration increases, while at the same time, we also confirm the existence of an initial thermal, and a power-law, inertial, regime of the bridge growth dynamics in both the pure and the surfactant-laden droplets. Thus, we unveil the key mechanisms in one of the fundamental topological processes of liquid droplets containing surfactant, which is crucial in relevant technologies.

Molecular dynamics simulation of the coalescence of surfactant-laden droplets.

We investigate the coalescence of surfactant-laden water droplets by using several different surfactant types and a wide range of concentrations by means of a coarse-grained model obtained by the statistical associating fluid theory. Our results demonstrate in detail a universal mass transport mechanism of surfactant across many concentrations and several surfactant types during the process. Coalescence initiation is seen to occur via a single pinch due to aggregation of surface surfactant, and its remnants tend to become engulfed in part inside the forming bridge. Across the board we confirm the existence of an initial thermal regime with constant bridge width followed by a later inertial regime with bridge width scaling roughly as the square root of time, but see no evidence of an intermediate viscous regime. Coalescence becomes slower as surfactant concentration grows, and we see evidence of the appearance of a further slowdown of a different nature for several times the critical concentration. We anticipate that our results provide further insights in the mechanisms of coalescence of surfactant-laden droplets.

Evaporative Deposition of Surfactant-Laden Nanofluid Droplets over a Silicon Surface.

Morphologies of evaporative deposition, which has been widely applied in potential fields, were induced by the competition between internal flows inside evaporating droplets. Controlling the pattern of deposition and suppressing the coffee-ring effect are essential issues of intense interest in the aspects of industrial technologies and scientific applications. Here, evaporative deposition of surfactant-laden nanofluid droplets over silicon was experimentally investigated. A ring-like deposition was formed after complete evaporation of sodium dodecyl sulfate (SDS)-laden nanofluid droplets with an initial SDS concentration ranging from 0 to 1.5 CMC. In the case of initial SDS concentrations above 1.3 CMC, no cracks were observed in the ring-like deposition, indicating that the deposition patterns of nanofluid droplets could be completely changed and cracks could be eliminated by sufficient addition of SDS. With the increase of the initial concentration of hexadecyl trimethylammonium bromide (CTAB), the width of the deposition ring gradually decreased until no ring-like structure was formed. On the contrary, with the increase of the initial Triton X-100 (TX-100) concentration, the width of the deposition ring gradually increased until a uniform deposition was generated. Moreover, when the initial TX-100 concentration was high, a "tree-ring-like" pattern was discovered. Besides, morphologies of evaporative pattern due to the addition of surfacants were qualitatively analyzed.

A Lagrangian particle-based numerical model for surfactant-laden droplets at macroscales

Atmospheric aerosols can consist of inorganic and organic substances, including surfactants at a significant concentration. Importantly, the latter can reduce the surface tension at the liquid–vapor surfaces, where they preferentially adsorb due to their amphiphilic structure. As a result, processes such as droplet coalescence, development of precipitation, and ultimately cloud lifetime may depend on the presence of surfactants in the aerosols. Here, we present a numerical model for cloud droplet formation, which is based on the Lagrangian particle-based microphysics-scheme superdroplet method and takes into account the presence of the surfactant in the droplets. Our results show that surfactant facilitates cloud formation by increasing the number and size of activated droplets, which concentrate at the bottom of the cloud, while the largest droplets are concentrated at the top of the cloud. This indicates a circulation of droplets that involves activation and growth processes from the bottom of the cloud toward the top. Moreover, our conclusions are independent of the particular approach used for modeling the diffusion of Eulerian variables due to the subgrid-scale turbulence. We anticipate that our results will enrich our understanding of the role of surfactants in the behavior of atmospheric aerosols and, importantly, will pave the way for further developments in the numerical modeling of systems with surfactants at macroscopic scales.

Enhancing Boiling Heat Transfer on a Superheated Surface by Surfactant-Laden Droplets.

Boiling, one of the most common phase-change heat transfer methods, is widely used in nuclear power plants, spacecraft, integrated circuits, and other situations, where rapid and efficient heat transfer is crucial. However, boiling heat transfer is efficient only in a specific surface temperature range when a droplet impacts a superheated surface. Here, we enhance the boiling heat transfer and extend this temperature range by adding a tiny amount of surfactant. We find that surfactants can weaken the Kelvin effect of boiling bubbles, and thus reduce the onset of boiling driven temperature and significantly enhance the maximum vaporization rate of the droplet effectively. In particular, different from previous studies, we find that the surfactants at lower concentrations can increase the Leidenfrost temperature of the droplets. All the above effects jointly expand the temperature range of effective boiling heat transfer. This study sheds new light on the role of surfactants in the boiling process and offers a new medium to promote heat-transfer applications.

On the droplet impact dynamics of nonionic surfactant solutions on non-wettable coatings

HypothesisThe impact dynamics of droplets containing nonionic surfactants are dependent on their molecular weight and concentration. This study investigates the role of these key parameters on the droplet dynamic behavior of nonionic surfactant solutions on non-wettable alkyl ketene dimer surfaces. ExperimentsAqueous solutions of 3 nonionic surfactants, MEGA-10, Brij C10 and Brij O20, with molecular weights of ∼ 350, 683 and 1150 g/mol, were prepared at various concentrations. The droplet impact dynamics of these solutions were observed using a high-speed camera. FindingsThe results show that neither the concentration nor the molecular weight can noticeably change the spreading of the surfactant-laden droplets. A strong correlation was established between droplets’ maximum spreading factor (βmax) and Weber number (βmax = 0.76We0.29). In addition, with a slight modification, we adopted two existing analytical models to predict βmax. While the model of Pasandideh-Fard et al. overpredicts βmax, especially at We < 40, the statistical analyses showed the reasonable accuracy of the model of Ukiwe and Kwok. Furthermore, as the molecular weight decreases, the surfactants more noticeably weaken the vertical oscillation of the droplets in the retraction phase. Surfactant solutions can act similar to dampers and limit the complete/partial rebound of the droplets with no effect on their splashing behavior.

An efficiently linear and totally decoupled variant of SAV approach for the binary phase-field surfactant fluid model

In this work, an efficiently linear, totally decoupled, and unconditionally energy-stable time-marching scheme is developed for solving the Cahn–Hilliard (CH) type phase-field incompressible surfactant fluid model. The proposed scheme is based on a variant of scalar auxiliary variable (SAV) approach. By defining several time-dependent auxiliary variables, the original governing equations are reformulated into equivalent forms which provide the foundation to construct the time-discretized numerical method. Different from the original SAV approach, the proposed method achieves totally decoupled computations of all variables. In each time step, the surfactant is explicitly calculated, then the phase-field function is updated by solving linear elliptic type equations. The velocity and pressure fields are calculated by the projection method. The time-discretized energy dissipation law is estimated in detail. The numerical validations indicate that the proposed method not only has desired energy stability but also works well for surfactant-laden droplets dynamics.

Surfactant-laden droplet size prediction in a flow-focusing microchannel: a data-driven approach.

The control of droplet formation and size using microfluidic devices is a critical operation for both laboratory and industrial applications, e.g. in micro-dosage. Surfactants can be added to improve the stability and control the size of the droplets by modifying their interfacial properties. In this study, a large-scale data set of droplet size was obtained from high-speed imaging experiments conducted on a flow-focusing microchannel where aqueous surfactant-laden droplets were generated in silicone oil. Three types of surfactants were used including anionic, cationic and non-ionic at concentrations below and above the critical micelle concentration (CMC). To predict the final droplet size as a function of flow rates, surfactant type and concentration of surfactant, two data-driven models were built. Using a Bayesian regularised artificial neural network and XGBoost, these models were initially based on four inputs (flow rates of the two phases, interfacial tension at equilibrium and the normalised surfactant concentration). The mean absolute percentage errors (MAPE) show that data-driven models are more accurate (MAPE = 3.9%) compared to semi-empirical models (MAPE = 11.4%). To overcome experimental difficulties in acquiring accurate interfacial tension values under some conditions, both models were also trained with reduced inputs by removing the interfacial tension. The results show again a very good prediction of the droplet diameter. Finally, over 10 000 synthetic data were generated, based on the initial data set, with a Variational Autoencoder (VAE). The high-fidelity of the extended synthetic data set highlights that this method can be a quick and low-cost alternative to study microdroplet formation in future lab on a chip applications, where experimental data may not be readily available.

Evaporation Dynamics of Surfactant-Laden Droplets on a Superhydrophobic Surface: Influence of Surfactant Concentration.

Surfactant-laden sessile droplet evaporation plays a crucial role in a variety of omnipresent natural and technological applications, such as drying, coating, spray, and inkjet printing. Surfactant molecules can adsorb easily on interfaces and, hence, destructively ruin the useful gas-trapping wetting state (i.e., Cassie-Baxter, CB) of a drop on superhydrophobic (SH) surfaces. However, the influence of surfactant adsorption or concentration on evaporation modes has been rarely investigated so far. Here, we investigate the evaporation dynamics of aqueous didodecyldimethylammonium bromide (DDAB) sessile droplet on SH surfaces made of regular hydrophobic micropillars, with various dimensionless surfactant concentrations (CS), primarily using experiments. We find that all drops initially form a CB state with a pinned base radius and evaporate in a mode of constant contact radius (CCR). Water and low-CS (=0.02) drop subsequently evaporate with a constant contact angle (CCA) mode, followed by a CCR mode and, eventually, a mixed-mode. By contrast, high-CS (of 0.25-1) droplets undergo a complex mixed mode, with rapidly increasing base radius, and finally a mixed mode, with slowly decreasing base radius and contact angle. The experimental data reveal that contact-angle-dependent evaporative mass flux, ṁ, collapses onto a nearly universal curve depending on CS. For the low-CS (of 0-0.25) drops, ṁ is lower and consistent with an evaporative cooling model, whereas high-CS (of 0.5-1) droplets are consistent with a pure vapor-diffusive model. We further show that the critical CS delineating these two evaporative models correlates with saturated surfactant adsorption on both liquid-solid and liquid-vapor interfaces.

Impact Dynamics and Freezing Behavior of Surfactant-Laden Droplets on Non-Wettable Coatings at Subzero Temperatures.

The present study investigates the impact and freezing behavior of the droplets of surfactant solutions on non-wettable coatings at very low temperatures of -10 to -30 °C. Our goal is to elucidate the critical role of concentration, molecular weight, and ionic nature of surfactants on these phenomena. To achieve this goal, we used sodium dodecyl sulfate (anionic), hexadecyltrimethylammonium bromide (cationic), and n-decanoyl-n-methylglucamine (nonionic) at four concentrations ranging from 0 to 2 × CMC (critical micelle concentration). We captured the impact-freezing of the droplets on superhydrophobic alkyl ketene dimer coatings using a high-speed camera at 5000 frames per second. The results show that the ability of the droplets to spread and retract on the coatings is a function of concentration, ionic nature, and molecular weight of the surfactants, as well as the temperature-dependent viscosity of the solutions. Additionally, surfactant-laden droplets generally demonstrated an accelerated freezing compared to pure water. This might be due to the fact that the presence of surfactants can promote both heterogeneous ice nucleation from within the liquid and a larger solid-liquid interfacial area by filling the air pockets of the surface, leading to enhanced heat transfer. The behavior of the cationic surfactant at certain concentrations was, however, an exception leading to a freezing delay, for which a mechanism will be proposed.

Interfacial viscosity-induced suppression of lateral migration of a surfactant laden droplet in a nonisothermal Poiseuille flow

Understanding and modulating the cross-stream motion of a surfactant-coated droplet in pressure driven flow has great implications in many practical applications. A combination of interfacial viscosity and Marangoni stress acting over a surfactant-coated droplet in pressure driven flow offers greater flexibility to modulate the cross-stream motion of it. Despite the intense theoretical and numerical research towards manipulating the surfactant-laden Newtonian droplets in Poiseuille flow, the experimental investigations are seldom explored. Herein, we report our study on understanding the influence of interfacial viscosity on the cross-stream motion of a surfactant-coated Newtonian droplet in both isothermal and non-isothermal Poiseuille flow from a theoretical as well as an experimental perspective. A theoretical model has been developed to understand the effect of interfacial viscosity on the lateral migration of a droplet under the assumptions of no shape deformation and negligible fluid inertia or thermal convection. Theoretical analysis is performed under two limiting conditions: (i) when the transport of surfactants is dominated by surface-diffusion and (ii) when the transportation of surfactants is dominated by surface-convection. Our theoretical analysis shows that both the dilatational as well as the shear surface viscosities suppress the lateral migration velocity of the droplet. Experiments have been performed to validate the theoretically predicted droplet trajectories and to understand the influence of channel confinement on the lateral migration of the droplet. It has been observed from the experiments that the droplet travels faster towards the centerline of the flow in a highly confined domain. The results presented in this study could provide new vistas in designing and analyzing various droplet-based microfluidic, biomedical and bio-microfluidic devices.

Absorption of surfactant-laden droplets into porous media: A numerical study

HypothesisDroplets can absorb into permeable substrates due to capillarity. It is hypothesized that the contact line dynamics influence this process and that an unpinned contact line results in slower absorption than a pinned contact line, since the contact area between the droplet and the substrate will decrease over time for the former. Furthermore, it is expected that surfactants can be used to accelerate the absorption. SimulationsLubrication theory is employed to model the droplet and Darcy’s law is combined with the conservation law of mass to describe the absorption dynamics. For the surfactant transport, several convection-diffusion-adsorption equations are solved. FindingsIt is found that moving contact lines result in a parabola-shaped wetted area and a slower absorption and a deeper penetration depth than pinned contact lines. The evolution of the penetration depth was quantitatively validated by comparison with two experimental studies from literature. Surfactants were shown to accelerate the absorption process, but only if their adsorption kinetics are slow compared to the absorption. Otherwise, all surfactant adsorbs onto the pore walls before reaching the wetting front, resulting in the same absorption rate as without surfactants. This behavior agrees with both experimental and analytical literature.

Further Step toward a Comprehensive Understanding of the Effect of Surfactant Additions on Altering the Impact Dynamics of Water Droplets.

The addition of surfactants to pure water for specific applications has made controlling the impact dynamics of surfactant-laden droplets a complex phenomenon. This work investigates the influence of the molecular weight (MW), concentration, and ionic nature of the surfactants as well as the substrate surface characteristics on the impact dynamics of surfactant-laden droplets using a high-speed camera at 10 000 frames per second. Sodium dodecyl sulfate, hexadecyltrimethylammonium bromide, and n-decanoyl-n-methylglucamine were used as anionic, cationic, and nonionic surfactants, respectively. We used hydrophilic glass slides, hydrophobic polytetrafluoroethylene, and superhydrophobic alkyl ketene dimer (AKD) as substrates. The results show that the efficiency of the surfactant addition in increasing the maximum spreading diameter is significantly influenced by the molecular weight and ionic nature of the solutions as well as the nonwettability of the substrate. Among all of the surfaces examined, the concentration and ionic nature of the solutions were found to be more dominant parameters in determining the energy dissipation in the retraction phase of the droplet impact on the superhydrophobic AKD surfaces. As the concentration decreases or positive charges are present in the solution, it is more likely to observe a similar retraction dynamic to pure water when the droplet hits the superhydrophobic AKD having negatively charged surface sites. Finally, in terms of the impact outcomes of the surfactant-laden droplets on the superhydrophobic AKD, it is shown that the influence of the surfactant addition is more noticeable at lower Weber numbers, where the droplet tries to rebound by overcoming the energy loss that occurred in the spreading.

Surfactant-Laden Janus Droplets with Tunable Morphologies and Enhanced Stability for Fabricating Lens-Shaped Polymeric Microparticles.

Janus droplets can function as excellent templates for fabricating physically and chemically anisotropic particles. Here, we report new surfactant-laden Janus droplets with curvature controllability and enhanced stability against coalescence, suitable for fabricating shape-anisotropic polymer microparticles. Using a microfluidic flow-focusing device on a glass chip, nanoliter-sized biphasic droplets, comprising an acrylate monomer segment and a silicone-oil (SO) segment containing a surfactant, were produced in a co-flowing aqueous polyvinyl alcohol (PVA) solution. At equilibrium, the droplets formed a Janus geometry based on the minimization of interfacial energy, and each of the two Janus segments were uniform in size with coefficient-of-variation values below 3%. By varying the concentration of the surfactant in the SO phase, the curvature of the interface between the two lobes could be shifted among concave, planar, and convex shapes. In addition, the Janus droplets exhibited significantly improved stability against coalescence compared with previously reported Janus droplets carrying no surfactant that coalesced rapidly. Finally, via off-chip photopolymerization, concave-convex, planar-convex, and biconvex lens-shaped particles were fabricated.

Directed self-propulsion of droplets on surfaces absent of gradients for cargo transport

HypothesisManipulating droplet transportation without inputting work is desired and important in microfluidic systems. Although the creation of wettability gradient on surfaces has been employed to achieve this goal, the transport distance is very limited, hindering its applications in long-term operations. ExperimentsHere, we show that programming long-ranged transport of droplets on surfaces can be achieved by the addition of trisiloxane surfactants and the creation of deep grooves. The former provides Marangoni stress to actuate the droplet motion and also reduces the inherent contact line pinning. The latter acts as a railing to guide the motion of surfactant-laden droplets to follow various layouts with geometric features of roads. FindingsIt is found that the droplets with microliters can move over 20 cm. This work-free method is applicable to a variety of substrate materials and liquids. By using self-running shuttles, a convenient platform for liquid cargos transport is developed and demonstrated. Moreover, the coalescence of cargos carried by different shuttles is accomplished in a three-branch layout, revealing new droplet microreactors.