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For blending immiscible polymers, such as in the toughening modification of polylactide (PLA) via blending with rubbery materials, interfacial compatibilization is of great significance while the mechanism, especially the role of interfacial rheology, remains elusive. In this study, styrene-butadiene block copolymer elastomer (SBC) was employed to toughen PLA and a dumbbell-shaped Janus nanoparticle (JNP) consisting of polymethyl methacrylate and polystyrene spheres with equal size (∼80 nm) was used as the compatibilizer. Located at the interface, JNPs exhibited a great compatibilization efficiency in PLA/SBC blends, as demonstrated by the good morphology stabilization against droplet coalescence under static annealing and low shear flow conditions, as well as by the resistance against droplet breakup under high shear flow conditions. Moreover, as revealed from the linear viscoelasticity of JNP compatibilized blends, when JNP loading is more than 2 phr, aside from shape relaxation, an interfacial relaxation dominated by Marangoni stress was observed, indicating the possibility of particle redistribution on droplet surfaces. However, when loading is more than 4 phr, relaxations in the terminal zone no longer exist, implying the possible formation of a particle network on the droplet surface. This is consistent with the mechanical properties. The blend shows the greatest toughness at JNP loading around 3 phr, while the toughness is very poor when JNP loading is either too low or too high. This suggests interfacial relaxation to be crucial to guarantee a good toughening effect of SBC in PLA. [ABSTRACT FROM AUTHOR]

Linear temporal instability analysis of a liquid jet emerging into a stationary gas environment under a radial thermal field is carried out in this work. The basic temperature profiles are obtained by solving the heat conduction problem between the liquid jet and the surrounding gas. The normal mode method is utilized to solve the temporal evolution of small disturbance, and an analytical dispersion relation on the growth of disturbance is derived. The inviscid asymptotic solution for the liquid jet is further obtained, which shows the explicit form of disturbance growth rate and also decouples the contribution of surface tension and Marangoni stress on the jet instability. The effects of various controlling parameters on the growth of disturbance for an inviscid liquid jet are investigated through a parametric study. Theoretical results show that the jet instability can be suppressed by increasing the temperature ratio between the liquid jet and the surrounding gas, enhancing the Marangoni stress on the surface, weakening the thermal conduction and decreasing the surface tension. The physical mechanisms of Rayleigh-Plateau instability and Marangoni instability which are responsible for the growth of disturbance are distinguished. Through comparing the inviscid asymptotic solution to the disturbance growth of the viscous jet, the applicable situation for the inviscid asymptotic solution is identified, which gives the Reynolds number ranges of Re ≥ O(102). [ABSTRACT FROM AUTHOR]

Droplets of alcohol-based formulations are common in applications from sanitizing sprays to printing inks. However, our understanding of the drying dynamics of these droplets on surfaces and the influence of ambient humidity is still very limited. Here, we report the drying dynamics of picoliter droplets of isopropyl alcohol deposited on a surface under controlled humidity. Condensation of water vapor in the ambient environment onto alcohol droplets leads to unexpectedly complex drying behavior. As relative humidity (RH) increases, we observed a variety of phenomena including enhanced spreading, nonmonotonic changes in the drying time, the formation of pancake-like shapes that suppress the coffee-ring effect, and the formation of waterrich films around an alcohol-rich drop. We developed a lubrication model that accounts for the coupling between the flow field within the drop, the shape of the drop, and the vapor concentration field. The model reproduces many of the experimentally observed morphological and dynamic features, revealing the presence of unusually large spatial compositional gradients within the evaporating droplet and surface-tension-gradientdriven flows arising from water condensation/evaporation at the surface of the droplet. One unexpected feature from the simulation is that water can evaporate and condense concurrently in different parts of the drop, providing fundamental insights that simpler models based on average fluxes lack. We further observed rim instabilities at higher RH that are well-described by a model based on the Rayleigh-Plateau instability. Our findings have implications for the testing and use of alcohol-based disinfectant sprays and printing inks. [ABSTRACT FROM AUTHOR]

The stability analysis of a gravity-driven thin liquid film over a uniformly heated substrate is carried out, and the effect of an insoluble surfactant is studied. The heating induces a temperature variation at the liquid–gas interface that generates a gradient in surface tension and creates a thermocapillary flow at the liquid–gas interface. When the film is perturbed the thermocapillary stress leads to the growth of the perturbation. The governing equations for the evolution of the film thickness and surfactant concentration are simplified within the lubrication approximation. Four non-dimensional groups appear in the model that affect the film dynamics and stability, namely, Marangoni numbers, M and Σ , the surface Peclet number, P e s , and Biot number, B i. The critical conditions are explored in terms of these non-dimensional parameters for the film to become temporally unstable. Further, spatiotemporal stability analysis is performed to characterise the instability as absolute and convective instability. A critical Marangoni number is found beyond which the system is absolutely unstable independent of the inclination angle. This critical Marangoni number seems to increase with the increase in solutocapillary effect. • Temporal stability of thin film in the presence of thermocapillary stress. • Stabilisation of the film due to presence of solutal Marangoni effect. • Spatiotemporal stability of the film in presence of thermal and solutal effect. • Critical condition to obtain absolutely unstable film. • Nonlinear simulations to corroborate linear theory results. [ABSTRACT FROM AUTHOR]

Recent experimental and computational investigations have shown that trace amounts of surfactants, unavoidable in practice, can critically impair the drag reduction of superhydrophobic surfaces (SHSs), by inducing Marangoni stresses at the air--liquid interface. However, predictive models for realistic SHS geometries do not yet exist, which has limited the understanding and mitigation of these adverse surfactant effects. To address this issue, we derive a model for laminar, three-dimensional flow over SHS gratings as a function of geometry and soluble surfactant properties, which together encompass 10 dimensionless groups. We establish that the grating length g is the key geometric parameter and predict that the ratio between actual and surfactant-free slip increases with g². Guided by our model, we perform synergistic numerical simulations and microfluidic experiments, finding good agreement with the theory as we vary surfactant type and SHS geometry. Our model also enables the estimation, based on velocity measurements, of a priori unknown properties of surfactants inherently present in microfluidic systems. For SHSs, we show that surfactant effects can be predicted by a single parameter, representing the ratio between the grating length and the interface length scale beyond which the flow mobilizes the air--water interface. This mobilization length is more sensitive to the surfactant chemistry than to its concentration, such that even trace-level contaminants may significantly increase drag if they are highly surface active. These findings advance the fundamental understanding of realistic interfacial flows and provide practical strategies to maximize superhydrophobic drag reduction. [ABSTRACT FROM AUTHOR]

A bubble coalescence model for a solution with a nonionic surfactant and with a low bubble approach velocity was developed, in which the mechanism of how coalescence is hindered by Marangoni stress was quantitatively analyzed. The bubble coalescence time calculated for ethanol–water and MIBC–water systems were in good agreement with experimental data. At low surfactant concentrations, the Marangoni stress and bubble coalescence time increased with bulk concentration increase. Conversely, in the high concentration range, the Marangoni stress and coalescence time decreased with bulk concentration. Numerical results showed that the nonlinear relationship between coalescence time and surfactant concentration is determined by the mass transport flux between the film and its interface, which tends to diminish the spatial concentration variation of the interface, that is, it acts as a "damper." This damping effect increases with increased surfactant concentration, therefore decreasing the coalescence time at high concentrations. [ABSTRACT FROM AUTHOR]

Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible by creating adverse Marangoni stresses. However, testing this hypothesis is challenging. Careful experiments with purified water already show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. To test the surfactant hypothesis while controlling surfactant concentrations with precision higher than can be achieved experimentally, we perform simulations inclusive of surfactant kinetics. These reveal that surfactant-induced stresses are significant at extremely low concentrations, potentially yielding a no-slip boundary condition on the air-water interface (the "plastron") for surfactant concentrations below typical environmental values. These stresses decrease as the stream-wise distance between plastron stagnation points increases. We perform microchannel experiments with SHSs consisting of stream-wise parallel gratings, which confirm this numerical prediction, while showing near-plastron velocities significantly slower than standard surfactant-free predictions. In addition, we introduce an unsteady test of surfactant effects. When we rapidly remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients formed in the loading phase. This demonstrates the significance of surfactants in deteriorating drag reduction and thus the importance of including surfactant stresses in SHS models. Our time-dependent protocol can assess the impact of surfactants in SHS testing and guide future mitigating designs.

When a droplet comes in contact with a completely wetting surface, the liquid typically spreads until it covers the entire substrate. However, nonuniform evaporation of a multicomponent droplet can generate surface tension gradients that alter this behavior. Here, we explore the rich dynamics of fully miscible, three-component droplets composed of water, ethanol, and propylene glycol on completely wetting glass substrates. These droplets initially spread rapidly but then stop and contract. We experimentally and theoretically investigate this behavior throughout the ternary parameter space at different relative humidities. Evaporation changes the composition of the droplet over space and time, resulting in a reversal of Marangoni flows that ultimately determines the dynamic droplet shape. We illustrate the utility of such dynamics by collecting, aggregating, and removing contaminants from a 4-cm² area using a single μL-scale droplet. [ABSTRACT FROM AUTHOR]

Manipulating 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. Here, 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. It 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. [ABSTRACT FROM AUTHOR]

The present work is an experimental and theoretical study on surfactant‐laden liquid drop impact on a liquid pool. When the drop breaks into a secondary droplet after impinging, then it is called partial coalescence. If this happens successively in self‐similar manner then it is called coalescence cascade. Three different types of surfactants, cationic, anionic, and non‐ionic, are used as drop fluid and water as the liquid pool. Here we report how the surfactant types and concentrations affect the number of stages in coalescence cascade. The experimental outcome revealed that the number of stages in cascade decreases with increasing surfactant concentration. Also, we determine that drop viscosity, density, and size play a crucial role while comparing the stages of cascade among three types of surfactants. We also perform scaling analysis to determine the contribution of inertial and surface forces in the cascade. A theoretical analysis using lubrication approximation has also been carried out to justify the experimental observations. The coalescence process is actually triggered by the drainage of entrapped air between the drop and pool. The theoretical analysis reveals that the faster air drainage rate and acceleration induces a strong Marangoni stress for necking and quick pinch off. Finally, it is shown that Marangoni flow, originated due to the surface tension difference between the drop and pool, is responsible for partial coalescence and a number of coalescence stages in cascade. Complete and partial coalescence. [ABSTRACT FROM AUTHOR]

Background: Secondary lung infections are the primary cause of morbidity associated with cystic fibrosis lung disease. Aerosolized antibiotic inhalation is potentially advantageous but has limited effectiveness due to altered airway aerodynamics and deposition patterns that limit drug access to infected regions. One potential strategy to better reach infected areas is to formulate aerosols with surfactants that induce surface tension gradients and drive postdeposition drug dispersal via Marangoni transport along the airway surface liquid (ASL). Since this relies on surfactant-induced surface tension reduction, the presence of endogenous lipid monolayers may hinder drug dispersal performance. Methods: Tobramycin solutions were formulated with dipalmitoylphosphatidylcholine (DPPC), a major component of endogenous pulmonary surfactant, to drive postdeposition aerosol dispersal across a model ASL based on a liquid layer or “subphase” of aqueous porcine gastric mucin (PGM) solution with predeposited DPPC monolayers to mimic the endogenous surfactant. In vitro subphase samples were collected from regions outside the aerosol deposition zone and assayed for tobramycin concentration using a closed enzyme donor immunoassay. The motion of a tracking bead across the subphase surface and the corresponding decrease in surface tension on aerosol deposition were tracked both with and without a predeposited DPPC monolayer. The surface tension/area isotherm for DPPC on PGM solution subphase was measured to aid in the interpretation of the tobramycin dispersal behavior. Results and Conclusions: Transport of tobramycin away from the deposition region occurs in aerosols formulated with DPPC whether or not predeposited lipid is present, and tobramycin concentrations are similar in both cases across biologically relevant length scales (∼8 cm). When DPPC is deposited from an aerosol, it induces ultralow surface tensions (<5 mN/m), which drive Marangoni flows, even in the presence of a dense background layer of DPPC. Therefore, aerosolized phospholipids, such as DPPC, will likely be effective spreading agents in the human lung. [ABSTRACT FROM AUTHOR]

Oil produced from secondary and tertiary processes is mostly in the form of oil in water emulsions, which is an inherent characteristic of the extraction process itself. An attempt to optimize the factors contributing to the cost of transporting such mixtures from the fields to the processing facilities, seems to be very useful and cost effective. In this work, a thorough investigation of the factors influencing the rheology and transportation of emulsions in circular ducts such as temperature, volume fraction, flow driving pressure and surfactants concentration, is performed using a special Lattice Boltzmann model. A dimensionless power number ratio is presented and used for the assessment of the best practices leading to a more efficient emulsions transportation system. [ABSTRACT FROM AUTHOR]

Many important industrial processes, such as additive manufacturing, involve rapid mass, flow and heat transport between gas, liquid and solid phases. Various associated challenges, such as the large density ratio between gas and condensed phases, make accurate, robust thermal multi-phase flow simulations of these processes very difficult. In order to address some of the associated challenges, a computational framework for thermal multi-phase flows is developed based on the finite element method (FEM). A unified model for thermal multi-phase flows similar to the models widely used in the manufacturing community is adopted. The combination of the level-set method and residual-based variational multi-scale formulation (RBVMS) is used to solve the governing equations of thermal multi-phase flows. Phase transitions between solid and liquid phases, i.e., melting and solidification, are considered. Interfacial forces, including surface tension and Marangoni stress, are taken into account and handled by a density-scaled continuum surface force model. A robust fully coupled solution strategy is adopted to handle various numerical difficulties associated with thermal multi-phase flow simulations, and implemented by means of a matrix-free technique using Flexible GMRES. The mathematical formulation and its algorithmic implementation are described in detail. Four numerical test cases are presented to demonstrate the capability of the proposed formulation. The first case is a benchmark example of solidification of aluminum in a graphite mold, the second case is a thermo-capillary droplet migration problem, the third case is a spot laser melting problem, and the fourth case is the melting of metal with an interior gas bubble. The computational results are compared with analytical, experimental and simulation data from other researchers, with good agreement in cases where such data is available. [ABSTRACT FROM AUTHOR]

In this work, particle image velocimetry has been used to visualize and quantify plasma-induced flow fields in liquid water. Experiments were performed in a rod-plane plasma reactor with a thin wire electrode suspended above the surface of the liquid in argon gas and a grounded plate immersed in the liquid. The velocity field has been quantified for two types of solutions: (1) aqueous NaCl solutions of varying solution conductivities and discharge frequencies and (2) aqueous NaCl solutions containing varying concentrations of the following four organic compounds: rhodamine B dye, caffeine, fluoxetine, and perfluorooctanoic acid. Results show that in neat water and aqueous caffeine solutions, the liquid is “pulled” along by the interaction of the gas molecules with the liquid molecules at the free surface and thus the direction of the liquid flow is in the direction of the gas phase flow (i.e., away from the discharge location). However, the flow was reversed (i.e., towards the discharge) for those solutions with strong surfactants such as perfluorooctanoic acid. The magnitude of the reversal depended on the initial concentration of the compound and for some compounds as time progressed the reversed flow pattern weakened and then reverted to a normal flow pattern. To determine the most likely cause of these flow reversals, a simple numerical model of the velocity field was developed to estimate relative contributions of various flow inducing mechanisms. The model indicates that in the presence of surfactants, Marangoni stresses are responsible for inducing the flow in the liquid. [ABSTRACT FROM AUTHOR]

Marangoni hydrodynamic motion and its potential technological application in reverse osmosis (RO) process for seawater desalination is discussed. The fundamental core idea in this note is the possibility to take advantage of the inherent concentration gradient in a RO process. It is well known that to run a RO process, it is necessary to apply a hydrodynamic pressure to overcome the osmotic pressure, however, by inducing a free-surface, e.g., a Leidenfrost surface, on the membrane wall, an additional hydrodynamic Marangoni stress could be generated, which, likewise than the osmotic pressure is driven by the concentration gradient but acting in the opposite direction, i.e., reducing the external hydraulic pressure to be applied. Utilizing a simplified geometrical and physical model, an analytical expression for the pressure reduction was derived. One important preliminary result in this work, is that the Marangoni stress can provide pressure against the osmotic pressure for membrane porous that are less than micrometric size. [ABSTRACT FROM AUTHOR]

The process of drop detachment from a capillary tip and formation of satellite droplets is studied for solutions of trisiloxane surfactants above the critical aggregation concentration. Two of the studied surfactants self-assemble in bilayer based phases, whereas the third forms micelles. The difference in the aggregates formed results in an essential difference in the rate of equilibration between the surface and the bulk solution and in a different behaviour near the pinch-off point. The difference in behaviour becomes pronounced when the viscosity of solutions increases 2–6 times (and therefore diffusion coefficients decrease correspondingly). In particular, when surfactant solutions are prepared in a water/glycerol mixture with a viscosity six times larger than water, the size of satellite droplets formed by the micellar solutions increases more than twice, whereas the size of droplets formed by the bilayer-forming solutions remains almost constant over a range of concentration covering two orders of magnitude. The bilayers forming solutions demonstrate a decrease in the effective surface tension near to pinch-off which can be related to the Marangoni stresses generated by surface flow during the thinning of the capillary bridge connecting the main drop with the liquid in the capillary. [ABSTRACT FROM AUTHOR]

We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical size l = a2/e0, where e0 is the mean thickness of the soap film and a = √ γ b/ρg is the capillary length ( γb stands for vapor--liquid surface tension, and ρ stands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures. [ABSTRACT FROM AUTHOR]

[Display omitted] • Wetting behaviour of pure and binary mixtures of tetrahydrofuran (THF) on complete wetting glass surface has been studied. • Pure THF shows continuous spreading followed by contact line retraction owing to evaporation. • Stearic acid and myristic acid demonstrated concentration dependent THF drop motion. • High concentration of fatty acids causes drop pinning and coffee ring stains. • Mechanism evaluated by studying the wetting behaviour of THF-surfactant mixtures. In this work, we have studied the drop dynamics of binary tetrahydrofuran (THF) solutions containing fatty acids (stearic acid and myristic acid) or surfactants (N -Cetyl-N, N, N trimethyl ammonium bromide, and sodium dodecyl sulfate). Highly volatile non-aqueous pure THF drop shows dynamic wetting behaviour i.e., droplet expansion and contraction behaviour·THF spreads continuously on fabricated total wetting surface without pinning, however addition of fatty acids causes formation of drops (instead of thin films). Such drops show autonomous motility which can be tuned by maintaining the concentration of fatty acids. The addition of fatty acids provides evaporation driven surface tension gradient (Marangoni stress) which initialize the autonomous drop motion and reduces the innate contact line pinning. It is found that addition of fatty acids showed drop dynamics which was concentration dependent. At low concentrations drop moves, while contact line pinning and subsequent evaporation was noticed at higher concentrations. The study of drop area with respect to time conveyed about the slowdown of evaporation timing of THF. This work proclaims the novel combination of highly evaporating THF with solutes (fatty acids/surfactants) showing its potential applications in self-propelled motion of non-aqueous drops. [ABSTRACT FROM AUTHOR]

In this paper we extend the conservative interface-interaction method of Hu et al. (2006) [34] , adapted for weakly-compressible flows by Luo et al. (2015) [37] , to include the effects of viscous, capillary, and Marangoni stresses consistently as momentum-exchange terms at the sharp interface. The interface-interaction method is coupled with insoluble surfactant transport which employs the underlying sharp-interface representation. Unlike previous methods, we thus achieve discrete global conservation in terms of interface interactions and a consistently sharp interface representation. The interface is reconstructed locally, and a sub-cell correction of the interface curvature improves the evaluation of capillary stresses and surfactant diffusion in particular for marginal mesh resolutions. For a range of numerical test cases we demonstrate accuracy and robustness of the method. In particular, we show that the method is at least as accurate as previous diffuse-interface models while exhibiting throughout the considered test cases improved computational efficiency. We believe that the method is attractive for high-resolution level-set interface-tracking simulations as it straightforwardly incorporates the effects of variable surface tension into the underlying conservative interface-interaction approach. [ABSTRACT FROM AUTHOR]

We present results of our numerical study of the effect of surfactants on buoyancy-driven motion of drops in a tube at intermediate Reynolds numbers. The drop and bulk phases are treated as incompressible Newtonian fluids and simulated using a front-tracking method. The steady shapes and velocity–volume curves for drops ranging in drop size from 0.2 to 1.3 of tube radius are determined numerically. At small Bond numbers, the velocity–volume curve shows a maximum before the velocity plateaus for large drops. As the Bond number increases, the maximum in the velocity–volume curve disappears with elongated, more streamlined drop shapes consistent with previous experimental studies. For increasing Weber numbers, the rear of the drop shows a flattening followed by the development of a negative curvature. Surfactants are modeled using a Langmuir equation of state in the adsorption–desorption limit and the effect of surfactant mass transfer, fractional coverage of surfactants, and the interfacial Peclet number on the velocity–volume curve is determined. Marangoni stress generated due to the non-uniform distribution of surfactants at the interface reduces drop mobility. Reduced drop mobility is more prominent for drop sizes that are comparable to the tube diameter and is maximum when mass transfer to and from the interface is inhibited. As the fractional coverage of soluble surfactants, or the interfacial Peclet number increases, larger Marangoni stresses are generated along the interface that lead to greater retardation of the drop motion. [ABSTRACT FROM AUTHOR]

• A temperature gradient can induce surface flow on a falling drop. • Surface flow can act against the buoyancy flow, reducing the settling velocity. • Water drop can get elongated due to the thermally driven surface flows. • Surface flow can retard the film drainage beneath the water drop and a solid surface. • Retarded film drainage slows down the wetting dynamics and convective heat transfer. The influence of the thermally-induced Marangoni stresses on the falling and spreading dynamics of a droplet surrounded by another liquid phase is numerically studied. A water droplet is released in a three-dimensional (3D) domain filled with oil. The droplet descends, comes at an apparent resting position above an oil film close to the bottom surface, and eventually wets the solid surface when the underneath film ruptures. A linear vertical temperature gradient is applied in the solution domain (with the bottom surface as the cold side) which imposes a surface tension gradient across the oil-water interface. The Marangoni source term is added to the momentum equation coupling the momentum and the energy equations. It is assumed that the dynamic contact angle changes according to the Kistler relation during the spreading. The Volume of Fluid (VOF) method is used to capture the interface between the phases. The solver is validated for both the falling and spreading phases. During the buoyancy-driven falling regime, the droplet retains its spherical shape at the low Reynolds number O (1) and finite Bond number O (0.001). It is revealed that the spreading rate of the droplet is a decreasing function of Marangoni number (M a). Unlike the isothermal systems, where the bottom side of the droplet becomes slightly flattened at the resting stage, the Marangoni stress imposes an upward force on the droplet which elongates the shape of droplet in the temperature gradient direction. Consequently, the ultimate spreading radius at the equilibrium state is smaller at larger M a. The slow rate of spreading and also the small wetted area at large temperature gradients adversely affect the heat transfer rate from the liquid to the cold plate where the local convective heat transfer coefficient and the average Nusselt number (N u) are decreasing functions of the Marangoni stress. [ABSTRACT FROM AUTHOR]

• Self-propulsion on glass is observed for a binary droplet containing short-chain carboxylic acid and Silwet. • Directed motion of the self-propelled droplet can be achieved on a linear runway constructed by coating polysilazane on glass. • The existence of the precursor film associated with the self-propelled droplet is verified by the two proposed methods. • Noncontact interactions between a self-propelled droplet and a static droplet are observed by optical microscopy. • The originally static droplet can be induced to move by its interaction with the self-propelled droplet. Acetic and propionic acids on glass show a total wetting behavior with a large exponent beyond Tanner's law. However, incorporating the Silwet L-77 surfactant into the droplet of acids causes the wetting behavior to change from spreading to random motion. The directed motion of the self-propelled droplet can be achieved on a linear runway constructed by coating polysilazane on glass. The absence of contact line pinning can be attributed to a thin film extending from the edge of the bulk droplet. Two simple methods are proposed to observe the precursor film associated with the spreading droplet and the self-running Silwet-laden droplet: (i) the color change of nearby water droplets containing a pH indicator, and (ii) the noncontact interaction observed using an optical microscope. Because of the precursor film, the self-running droplet can induce the motion of a static droplet without direct contact between their contact lines. This interesting finding may be explained using the interfacial tension gradient associated with the Marangoni stress due to the contact between the precursor film and the static droplet. [ABSTRACT FROM AUTHOR]

We address the dynamics of a surfactant-laden droplet on a solid surface in simple shear flow numerically. Our analysis uses the front-tracking method to take surfactant transport into account. The interfacial tension and the slip coefficient, both of which depend heavily on the surfactant concentration, are fully integrated into the generalized Navier boundary condition to model the moving contact lines. Accurate prediction of droplet motion indicates that the surfactant can change droplet behavior drastically. Surfactant-induced effects, such as interfacial tension reduction, the Marangoni stress, and wettability alternation, are investigated for various capillary numbers, surface wettabilities, elasticity numbers, and surface Péclet numbers. Deformation and motion of a sliding droplet are enhanced by the Marangoni effect, which is associated with an interfacial tension gradient. When the capillary number reaches a critical value, the sliding-to-detachment and detachment-to-pinch-off transitions occur. Both transitions can be triggered and accelerated by a surfactant, especially when convection is dominant. As a result, the critical capillary number decreases, but exhibits a non-monotonic relationship with the elasticity number and Péclet number. The mechanisms that underlie the effect of Marangoni stress are discussed by analyzing the distributions of the surfactant concentration and the hydrodynamic forces exerted on the droplet. Accumulation of surfactants near the receding contact line reverses the local concentration gradient, attempts to change its direction along the interface, and delays droplet detachment. Furthermore, the strong surfactant dilution reduces both the surfactant concentration and the interfacial tension gradient, and thereby increasing the critical value for droplet pinch-off. [Display omitted] [ABSTRACT FROM AUTHOR]

The paper presents a numerical method for simulation of the effect of a soluble surfactant on the last stage of the drop coalescence (film formation, drainage and rupture). An axisymmetric interaction between drops is studied at small capillary and Reynolds numbers and small surfactant concentrations. The hydrodynamic part of the mathematical model includes the Stokes equations in the drop phase and their lubrication approximation in the gap between the drops (film phase), coupled with velocity and stress boundary conditions at the interfaces. The surfactant is considered soluble in both (drop and film) phases and the distribution of the surfactant concentration is governed by a convection–diffusion equation. A convection–diffusion equation is also used to model the distribution of the surfactant on the interfaces. The concentration in both phases is coupled with that on the interfaces via the adsorption isotherm and the fluxes between the interface and the bulk phases. The hydrodynamic and concentration parts of the mathematical model are related via the advection of the surfactant in the fluid phases and on the interfaces. On the other hand, a non-uniform surfactant concentration on the interfaces leads to a gradient of the interfacial tension which in turn leads to an additional tangential stress on the interfaces (Marangoni effects). For the flow in the drops a simplified version of Boundary integral method is used. Finite difference method is used for the flow in the gap, the position of the interfaces and the distribution of surfactant concentration on the interfaces, as well as in the fluid phases. Different approaches are used for an optimization of the numerical algorithm: Non-uniform meshes for space discretization in both ( r and z ) directions; Explicit and implicit first and second order time integration schemes with automatically adaptive time steps; A multiple time step integration scheme that can decrease significantly the computational time without loss of accuracy. Tests and comparisons are performed in order to investigate the accuracy and stability of the different numerical schemes. [ABSTRACT FROM AUTHOR]

Hypothesis Interfacial tension gradients at a liquid/liquid interface drive Marangoni flows. When colloidal particles are adsorbed to an interface in systems with spatial and temporal gradients of surfactant concentration, these interfacial flows can be potentially significant contributors to the direction and rate of particle transport. Experiments In this work, we use optical microscopy to measure the interfacial velocities of 5 μm diameter polystyrene latex particles adsorbed at an oil/water interface, using olive oil to represent polar oils often encountered in cleaning applications. Findings On surfactant adsorption the maximum interfacial velocity scales linearly with bulk surfactant concentration, even for concentrations exceeding the critical micelle concentration (CMC). The maximum interfacial velocity weakly decreases with increasing flow rate, but it varies non-monotonically with the radial distance from the inlet. Upon surfactant desorption into a rinse solution, the maximum velocity increases with increasing concentration of the original surfactant solution, but only up to a plateau near the CMC. These experimental trends are well-described by a convective-diffusion model for surfactant transport to or from the liquid/liquid interface coupled with Langmuir-type adsorption, using a constitutive relation between the interfacial tension gradient and interfacial velocity based on the interfacial tangential stress jump. [ABSTRACT FROM AUTHOR]

In this work, we present a hierarchy of mathematical models for extraction in microchannels with two-phase stratified flow. A flat stable inter-fluid interface is considered. We present three models for rectangular channels, of varying degrees of complexity: 2D, 1D Laminar and 1D Plug models. The predictions of these models are compared with each other and with experiments reported in the literature. Conditions under which a simpler 1D model can replace the complex 2D model are identified. Next, a detailed model for channels with a circular cross-section is developed using bipolar cylindrical coordinates. We also show how a much simpler description can be obtained by applying the 1D rectangular channel models to a circular channel. The relative performance of co-current and counter-current flow configurations is analysed next, using the 1D Plug flow model. Finally, the model is extended to account for Marangoni stresses that result from the variation of interfacial tension with solute concentration. The effect of Marangoni stresses on extraction in stable stratified flow is found to be insignificant. This is because the flow induced by Marangoni stresses is too weak to control the pressure-driven primary flow. [ABSTRACT FROM AUTHOR]

Self-propelled droplets are a class of active matter systems composed of one fluid dispersed in another immiscible fluid. Despite the inherent spherical symmetry in the initial droplet shape and composition, self-propulsion in these systems is achieved by a spontaneous symmetry-breaking bifurcation. Either a chemical reaction, micelle-induced solubilization, or a phase transition may induce gradients in the interfacial tension, generating a Marangoni convection and thereby resulting in self-propulsion. The simplicity associated with these self-propelled droplet systems makes them excellent candidates for investigating the solitary and collective behaviour of several biological swimmers, ranging from single-celled bacteria to school of fishes. Additionally, due to their tunable mobility characteristics, these swimmers have immense potential as smart materials designed to execute intricate tasks in microscopic domains. In this review, we present state-of-the-art experimental and theoretical research relevant to self-propelled swimming droplets. [Display omitted] [ABSTRACT FROM AUTHOR]

Abstract: Numerical methods for imposing body forces in two-phase flow simulations are discussed. Numerical schemes are presented to avoid the inaccurate solutions that result from inconsistent implementation of forces. First, the momentum equations are discretized so that they accurately accommodate the discontinuity in fluid properties at an interface. Consistent numerical estimations for different body forces such as interfacial (including Marangoni), gravity and electromagnetic forces are discussed. Then, it is shown that the standard pressure–velocity coupling scheme for collocated algorithms is not sufficient for multiphase flows, and therefore a new pressure–velocity coupling is devised and tested for both single and two-phase flows. Finally, to advect the level set function, a cost effective fifth-order WENO method is developed. These formulations are accurate and efficient both for uniform and non-uniform meshes. Several test cases are presented and compared with a standard implementation of body forces to demonstrate the efficiency of the proposed algorithm. [Copyright &y& Elsevier]

[•] Temperature applied to a regular, periodic two-dimensional foam. [•] Simulations show that, due to a Marangoni effect, vertices migrate. [•] Changes in foam structure mean changes in shear properties. [•] Temperature variations on the order of tens of degrees are significant. [Copyright &y& Elsevier]

Abstract: The evolution of an advancing fluid front formed by a gravity-driven thin film flowing down a planar substrate is considered, with particular reference to the presence of Marangoni stresses and/or surface topography. The system is modelled using lubrication theory and solved via an efficient, adaptive multigrid method that incorporates automatic, error-controlled grid refinement/derefinement and time stepping. The detailed three dimensional numerical results obtained reveal that, for the problems investigated, while both of the above features affect the merger of rivulets by either delaying or promoting the same, topography influences the direction of growth. [Copyright &y& Elsevier]

Abstract: We conduct a numerical study to investigate the effect of surfactants on the drop formation process in a co-flowing system using a hybrid volume-of-fluid (VOF) method combined with a front-tracking scheme. The drop and bulk phases are treated as incompressible Newtonian fluids, and the surfactants are modeled using a Langmuir adsorption framework. We consider the effect of soluble surfactants in the adsorption–desorption limit on the drop formation process. A drop in the co-flowing geometry typically breaks up at the primary neck, close to the primary drop, in the absence of surfactants. When surfactants are present, they accumulate in the neck region resulting in Marangoni stresses that slow down the neck thinning rate. This results in longer breakup times with larger drop volumes. At high surfactant coverages, the primary neck formation slows down enough and breakup occurs at the secondary neck, close to the remnant drop. Increasing the outer co-flowing flow weakens the retarding effect of the high surfactant coverage leading to breakup again at the primary neck. The adsorption–desorption kinetics also affects the neck breakup position, and the primary drop volume and breakup time depend non-linearly on the Biot number. For any given Biot number, a critical fractional coverage exists beyond which the drop fails to neck. The presence of a confining wall may lower the value of the critical equilibrium fractional coverage required for the drop to enter the no-necking regime. [Copyright &y& Elsevier]

Abstract: During our investigations of two-phase flow in long hydrophobic minitubes and capillaries, we have observed transformation of the main rivulet into different new hydrodynamic modes with the use of different kinds of surfactants. The destabilization of rivulet flow at air velocities <80m/s occurs primarily due to the strong branching off of sub-rivulets from the main rivulet during the downstream flow in the tube. The addition of some surfactants of not-so-high surface activity was found to increase the frequency of sub-rivulet formation and to suppress the Rayleigh and sinuous instabilities of the formed sub-rivulets. Such instabilities result in subsequent fragmentation of the sub-rivulets and in the formation of linear or sinuous arrays of sub-rivulet fragments (SRFs), which later transform into random arrays of SRFs. In the downstream flow, SRFs further transform into large sliding cornered droplets and linear droplet arrays (LDAs), a phenomenon which agrees with recent theories. At higher surface activity, suppression of the Rayleigh instability of sub-rivulets with surfactants becomes significant, which prevents sub-rivulet fragmentation, and only the rivulet and sub-rivulets can be visualized in the tube. At the highest surface activity, the bottom rivulet transforms rapidly into an annular liquid film. The surfactant influence on the behavior of the rivulets in minitubes is incomparably stronger than the classic example of the known surfactant stabilizing influence on a free jet. The evolution of a rivulet in the downstream flow inside a long minitube includes the following sequence of hydrodynamic modes/patterns: i) single rivulet; ii) rivulet and sub-rivulets; and iii) rivulet, sub-rivulets, sub-rivulet fragments, cornered droplets, linear droplet arrays, linear arrays of sub-rivulet fragments and annular film. The formation of these many different hydrodynamic patterns downstream is in drastic contrast with the known characteristics of two-phase flow, which demonstrates one mode for the entire tube length. Recent achievements in fluid mechanics regarding the stability of sliding thin films and in wetting dynamics have allowed us to interpret many of our findings. However, the most important phenomenon of the surfactant influence on sub-rivulet formation remains poorly understood. To achieve further progress in this new area, an interdisciplinary approach based on the use of methods of two-phase flow, wetting dynamics and interfacial rheology will be necessary. [Copyright &y& Elsevier]

Abstract: The viscous froth model is a rheological model for dry, “two-dimensional” foams, such as a monolayer of bubbles confined between two glass plates. The model is typically out of mechanical equilibrium due to viscous dissipation by drag along the confining plates. By introducing variable local surfactant coverages and variable local surface tensions, we modify the model such that, in addition to being out of mechanical equilibrium, foam structures can also be out of physicochemical equilibrium. We include effects accounting for spatially and temporally varying Marangoni forces and surfactant transport, and we investigate the effects on a simple, periodic honeycomb lattice under shear. It is found that surfactant coverage can vary substantially between and within films, with surfactant becoming highly depleted on film edges that are subjected to rapid direct shear. Moreover substantial deviations from Plateau''s laws occur at flowing three-fold vertices an effect previously noted in experiments but without any definitive explanation in theory or models. For large enough values of the governing dimensionless groups (capillary, Deborah, and Marangoni numbers), angles may locally vary from 120° by 10° or more. Correspondingly, the change in surface tensions at a three-fold vertex leads to a change in the time required to induce a topological rearrangement (T1) in a sheared foam sample. In this sense, variable surfactant coverage effects help to preserve the structure of a flowing foam, but also lead to an increase in energy storage within the foam. [Copyright &y& Elsevier]

Abstract: Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence. [ABSTRACT FROM AUTHOR]

Abstract: The effect of surfactant monolayer concentration on the measurement of interfacial surface tension using transient drop deformation methods is studied using the Boundary Integral Method. Emulsion droplets with a surfactant monolayer modeled with the Langmuir equation of state initially in equilibrium are suddenly subjected to axisymmetric extensional flows until a steady state deformation is reached. The external flow is then removed and the retraction of the drops to a spherical equilibrium shape in a quiescent state is simulated. The transient response of the drop to the imposed flow is analyzed to obtain a characteristic response time, . Neglecting the initial and final stages, the retraction process can be closely approximated by an exponential decay with a characteristic time, . The strength of the external flow on each model drop is increased in order to investigate the coupled effect of deformation and surfactant distribution on the characteristic relaxation time. Different model drops are considered by varying the internal viscosity and the equilibrium surfactant concentrations from a surfactant free state (clean) to high concentrations approaching the maximum packing limit. The characteristic times obtained from the simulated drop dynamics both in extension and retraction are used to determine an apparent surface tension employing linear theory. In extension the apparent surface tension under predicts the prescribed equilibrium surface tension. The error increases monotonically with the equilibrium surfactant concentration and diverges as the maximum packing limit is approached. In retraction the apparent surface tension under predicts the prescribed equilibrium surface tension depends non-monotonically on the equilibrium surfactant concentration. The error is highest for moderate surfactant concentrations and decreases as the maximum packing limit is approached. It was found that the difference between the prescribed surface tension and the apparent surface tension increased as the viscosity ratio decreased. Differences as large as 40% were seen between the prescribed surface tension and the apparent surface tension predicted by the linear theory. [Copyright &y& Elsevier]

Abstract: Thermocapillary convection within a differentially-heated open rectangular cavity containing two immiscible liquid layers is considered in the absence of gravitational effects. The temperature and flow fields in the two layers are computed using domain mapping in conjunction with a finite-difference scheme on a staggered grid. The melt–encapsulant and air–encapsulant interfaces are allowed to deform, with the contact lines pinned on the solid boundaries. The presence of a free surface at the top leads to increased convection in the encapsulant phase while retarding thermocapillary flow in the melt. The intensity of thermocapillary convection in the encapsulated layer is reduced as the viscosity of the encapsulant is increased or the thickness of the encapsulant layer is decreased. Choosing an encapsulant with a greater sensitivity of interfacial tension to temperature (as compared to that of the melt phase) can almost completely suppress thermocapillary convection in the melt. Deformations of the melt–encapsulant interface in an open cavity are found to be larger than those in a closed cavity with a rigid top surface, due to higher pressure gradients realized in the encapsulant phase. In contrast to interface deformation behavior reported earlier for a double-layer system in a closed cavity, the shape of the melt–encapsulant interface is qualitatively similar for all values of the viscosity ratio, with the interface dipping into the melt near the cold wall, and into the encapsulant near the hot wall. For the double-layers considered in this study, a free surface at the top of the encapsulant layer was found to be more effective than a rigid top in reducing the intensity of thermocapillary convection in the melt. [Copyright &y& Elsevier]

Abstract: Axisymmetric spreading of a liquid drop containing a soluble surfactant on a smooth solid substrate is numerically investigated for the case in which surfactant mass transfer between the interface and the bulk liquid is sorption/kinetic controlled. The fastest spreading rate is achieved by drops with values of Biot number for which the rate of surface convection is comparable to the sorption rate, and the surfactant molecules transferred to the interface are effectively convected to the contact line region. [Copyright &y& Elsevier]

Many materials-processing applications such as crystal growth from the melt involve thermocapillary flows that can affect the quality of the final product, particularly under microgravity conditions where the influence of buoyancy-driven convection is minimized. When the melt contains volatile components, as in the production of III–V semiconductor crystals, it is often encapsulated in a low-melting point amorphous molten glass phase such as boron oxide or pyrolytic boron nitride in order to prevent evaporation of the volatile components. The addition of the encapsulant layer and the melt–encapsulant interface in such cases can alter the thermocapillary flow in the melt. In this study, thermocapillary convection within a differentially heated rectangular cavity containing two immiscible liquid layers is considered in the absence of gravity. Domain mapping is used in conjunction with a finite difference scheme on a staggered grid to solve for the temperature and flow fields. The melt–encapsulant and the air–encapsulant interfaces are allowed to deform, with the contact lines pinned on the solid boundaries. The computed flow fields are compared to the corresponding results for a cavity with a rigid top surface. The presence of a free surface at the top leads to increased convection in the encapsulant phase while suppressing the thermocapillary flow in the melt phase. The flow pattern in the encapsulated layer is strongly dependent on the viscosity of the encapsulant layer. The intensity of the thermocapillary flow within the melt is significantly reduced as the viscosity of the encapsulant layer is increased. However, for a higher encapsulant viscosity, the retarding effect of the free top surface on thermocapillary convection in the melt is weakened. [ABSTRACT FROM AUTHOR]

Abstract: The effect of insoluble surfactants on drop deformation and breakup in simple shear flow is studied using a combination of a three-dimensional boundary-integral method and a finite-volume method to solve the coupled fluid dynamics and surfactant transport problem over the evolving interface. The interfacial tension depends nonlinearly on the surfactant concentration, and is described by the equation of state for the Langmuir isotherm. Results are presented over the entire range of the viscosity''s ratio λ and the surface coverage x, as well as the capillary number Ca that spans from that for small deformation to values that are beyond the critical one . The values of the elasticity number E, which reflects the sensitivity of the interfacial tension to the maximum surfactant concentration, are chosen in the interval and a convection dominated regime of surfactant transport, where the influence of the surfactant on drop deformation is the most significant, is considered. For a better understanding of the processes involved, the effect of surfactants on the drop dynamics is decoupled into three surfactant related mechanisms (dilution, Marangoni stress and stretching) and their influence is separately investigated. The dependence of the critical capillary number on the surface coverage is obtained and the boundaries between different modes of breakup (tip-streaming and drop fragmentation) in the (λ; x) plane are searched for. The numerical results indicate that at low capillary number, even with a trace amount of surfactant, the interface is immobilized, which has also been observed by previous studies. In addition, it is shown that for large Péclet numbers the use of the small deformation theory to measure the interfacial tension in the case where surfactants are present can introduce a significant error. [Copyright &y& Elsevier]

Abstract: Thermocapillary flows are of considerable technological importance in materials processing applications such as crystal growth from the melt, particularly under microgravity conditions where the influence of buoyancy-driven convection is minimized. In this study, thermally driven convection within a differentially heated rectangular cavity containing two immiscible liquid layers is considered in the absence of gravity. The introduction of a more viscous encapsulant layer leads to a significant reduction in the intensity of the thermocapillary flow within the encapsulated layer. Interface deformations are small when the contact line of the interface is pinned on the solid boundaries. The higher viscosity of the encapsulant layer gives rise to a larger pressure gradient in that layer, thereby resulting in interface deformations that are qualitatively different from those observed at the free surface in the absence of the encapsulant layer. The flow pattern in the encapsulated layer and the resulting interface deformations are strongly dependent on both the thickness and the viscosity of the encapsulant layer. It is shown that the flow within the encapsulated layer may be closely approximated by simply considering the single-layer problem with a modified stress condition at the interface. The modified tangential stress balance for the effective single-layer model is derived based on asymptotic results for small-aspect-ratio double-layer systems and the insight gained from double-layer computations for finite-aspect-ratio systems. It is shown that the single-layer model accurately predicts the flow in the double-layer system even for large aspect-ratios. [Copyright &y& Elsevier]

Abstract: Axisymmetric spreading of a liquid drop covered with an insoluble surfactant monolayer on a smooth solid substrate is numerically investigated. As the drop spreads, the adsorbed surfactant molecules are constantly redistributed along the air–liquid interface by convection and diffusion, leading to nonuniformities in surface tension along the interface. The resulting Marangoni stresses affect the spreading rate by altering the surface flow and the drop shape. In addition, surfactant accumulation in the vicinity of the moving contact line affects the spreading rate by altering the balance of line forces. Two different models for the constitutive relation at the moving contact line are used, in conjunction with a surface equation of state based on the Frumkin adsorption framework, to probe the surfactant influence. The coupled evolution equations for the drop shape and monolayer concentration profile are integrated using a pseudospectral method to determine the rate of surfactant-assisted spreading over a wide range of the dimensionless parameters governing the spreading process. The insoluble monolayer enhances spreading through two mechanisms; a reduction in the equilibrium contact angle, and an increase in the magnitude of the radial pressure gradient within the drop due to the formation of positive surface curvature near the moving contact line. Both mechanisms are driven by the accumulation of surfactant at the contact line due to surface convection. Although the Marangoni stresses induced at the air–liquid interface reduce the rate of spreading during the initial stages of spreading, their retarding effect is overwhelmed by the favorable effects of the aforementioned mechanisms to lead to an overall enhancement in the rate of spreading in most cases. The spreading rate is found to be higher for bulkier surfactants with stronger repulsive interactions. With the exception of monolayers with strong cohesive interactions which tend to retard the spreading process, the overall effect of an insoluble monolayer is to increase the rate of drop spreading. Simulation results for small Bond numbers indicate the existence of a power-law region for the time-dependence of the basal radius of the drop, consistent with experimental measurements. [Copyright &y& Elsevier]

Development and optimization of multifunctional devices for fluidic manipulation of films, drops, and bubbles require detailed understanding of interfacial phenomena and microhydrodynamic flows. Systems are distinguished by a large surface to volume ratio and flow at small Reynolds, capillary, and Bond numbers are strongly influenced by boundary effects and therefore amenable to control by a variety of surface treatments and surface forces. We review the principles underlying common techniques for actuation of droplets and films on homogeneous, chemically patterned, and topologically textured surfaces by modulation of normal or shear stresses. [ABSTRACT FROM AUTHOR]