Diffusiophoretic Transport of Charged Colloids in Ionic Surfactant Gradients Entirely below versus Entirely above the Critical Micelle Concentration.

When placed in an ionic surfactant gradient, charged colloids will undergo diffusiophoresis at a velocity, uDP = MDP∇ ln S, where MDP is the diffusiophoretic mobility and S is the surfactant concentration. The diffusiophoretic mobility depends in part on the charges and diffusivities of the surfactants and their counterions. Since micellization decreases surfactant diffusivity and alters charge distributions in a surfactant solution, MDP of charged colloids in ionic surfactant gradients may differ significantly when surfactant concentrations are above or below the critical micelle concentration (CMC). The role of micelles in driving diffusiophoresis is unclear, and a previously published model that accounts for micellization suggests the possibility of a change in the sign of MDP above the CMC [Warren, P. B.; . Soft Matter 2019, 15, 278-288]. In the current study, microfluidic channels were used to measure the transport of negatively charged polystyrene colloids in sodium dodecyl sulfate (SDS) surfactant gradients established at SDS concentrations that are either fully above or fully below the CMC. Interpretation of diffusiophoresis was aided by measurements of the colloid electrophoretic mobility as a function of SDS concentration. A numerical transport model incorporating the prior diffusiophoretic mobility model for ionic surfactant gradients was implemented to elucidate signatures of positive and negative diffusiophoretic mobilities and compare with experiments. The theoretically predicted sign of the diffusiophoretic mobility below the CMC was determined to be particularly sensitive to uncertainty in colloid and surfactant properties, while above the CMC, the mobility was consistently predicted to be positive in the SDS concentration range considered in the experiments conducted here. In contrast, experiments only showed signatures of a negative diffusiophoretic mobility for these negatively charged colloids with no change of sign. Colloid diffusiophoretic transport measured in micellar solutions was more extensive than that below the CMC with the same ∇ ln S.

Effect of polymer/surfactant complexation on diffusiophoresis of colloids in surfactant concentration gradients.

HYPOTHESIS: A concentration gradient of surfactants in the presence of polymers that non-covalently associate with surfactants will exhibit a continually varying distribution of complexes with different composition, charge, and size. Since diffusiophoresis of colloids suspended in a solute concentration gradient depends on the relaxation of the gradient and on the interactions between solutes and particles, polymer/surfactant complexation will alter the rate of diffusiophoresis driven by surfactant gradients relative to that observed in the same concentration gradient in the absence of polymers. EXPERIMENTS: A microfluidic device was used to measure diffusiophoresis of colloids suspended in solutions containing a gradient of sodium dodecylsulfate (SDS) in the presence or absence of a uniform concentration of Pluronic P123 poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) nonionic triblock copolymers. To interpret the effect of P123 on the rate of colloid diffusiophoresis, electrophoretic mobility and dynamic light scattering measurements of the colloid/solute systems were performed, and a numerical model was constructed to account for the effects of complexation on diffusiophoresis. FINDINGS: Polymer/surfactant complexation in solute gradients significantly enhanced diffusiophoretic transport of colloids. Large P123/SDS complexes formed at low SDS concentrations yielded low collective solute diffusion coefficients that prolonged the existence of strong concentration gradients relative to those without P123 to drive diffusiophoresis.

Marangoni spreading time evolution and synergism in binary surfactant mixtures.

HYPOTHESIS: Marangoni spreading driven by localized surfactant solution deposition previously has been studied only for single surfactant systems. For binary surfactant mixtures, interactions that generate surface tension synergism, a thermodynamic effect, may also synergistically enhance Marangoni spreading dynamics, introducing the concept of Marangoni synergism. Spreading dynamics and possible Marangoni synergism should depend not only on thermodynamic properties but also kinetic properties of the binary system. EXPERIMENTS AND MODELING: Tracer experiments that capture post-deposition surfactant front motion were performed in parallel with computational modeling, using binary surfactant pairs with varying interaction strengths. The model coupled the Navier-Stokes and advective diffusion equations with a Frumkin-type binary adsorption model. FINDINGS: We confirm the existence of Marangoni synergism. Stronger binary surfactant attraction favors synergism in both surface tension reduction and Marangoni spreading. Binary composition ranges over which surface tension synergism occurs differ from those for Marangoni synergism, indicating that the origins of the two synergistic effects are not identical. Analysis of model spreading velocities show that the thermodynamic spreading parameter is the controlling factor at early times for both single and binary surfactant systems, while the intrinsic adsorption and desorption kinetics influence spreading velocities and thus the occurrence of Marangoni synergism at later times.

Surfactant spreading on a deep subphase: Coupling of Marangoni flow and capillary waves.

HYPOTHESIS: Surfactant-driven Marangoni spreading generates a fluid flow characterized by an outwardly moving "Marangoni ridge". Spreading on thin and/or high viscosity subphases, as most of the prior literature emphasizes, does not allow the formation of capillary waves. On deep, low viscosity subphases, Marangoni stresses may launch capillary waves coupled with the Marangoni ridge, and new dependencies emerge for key spreading characteristics on surfactant thermodynamic and kinetic properties. EXPERIMENTS AND MODELING: Computational and physical experiments were performed using a broad range of surfactants to report the post-deposition motion of the surfactant front and the deformation of the subphase surface. Modeling coupled the Navier-Stokes and advective diffusion equations with an adsorption model. Separate experiments employed tracer particles or an optical density method to track surfactant front motion or surface deformation, respectively. FINDINGS: Marangoni stresses on thick subphases induce capillary waves, the slowest of which is co-mingled with the Marangoni ridge. Changing Marangoni stresses by varying the surfactant system alters the surfactant front velocity and the amplitude - but not the velocity - of the slowest capillary wave. As spreading progresses, the surfactant front and its associated surface deformation separate from the slowest moving capillary wave.

Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows.

The transport of microorganisms by chemotaxis is described by the same "log-sensing" response as colloids undergoing diffusiophoresis, despite their different mechanistic origins. We employ a recently-developed macrotransport theory to analyze the advective-diffusive transport of a chemotactic or diffusiophoretic colloidal species (both referred to as "colloids") in a circular tube under a steady pressure-driven flow (referred to as hydrodynamic flow) and transient solute gradient. First, we derive an exact solution to the log-sensing chemotactic/diffusiophoretic macrotransport equation. We demonstrate that a strong hydrodynamic flow can reduce spreading of solute-repelled colloids, by eliminating super-diffusion which occurs in an otherwise quiescent system. In contrast, hydrodynamic flows always enhance spreading of solute-attracted colloids. Second, we generalize the exact solution to show that the above tunable spreading phenomena by hydrodynamic flows persist quantitatively for decaying colloids, as may occur with cell death, for example. Third, we examine the spreading of chemotactic colloids by employing a more general model that captures a hallmark of chemotaxis, that log-sensing occurs only over a finite range of solute concentration. Apart from demonstrating for the first time the generality of the macrotransport theory to incorporate an arbitrary chemotactic flow model, we reveal via numerical solutions new regimes of anomalous spreading, which match qualitatively with experiments and are tunable by hydrodynamic flows. The results presented here could be employed to tailor chemotactic/diffusiophoretic colloid transport using hydrodynamic flows, which are central to applications such as oil recovery and bioremediation of aquifers.

Effect of a Surfactant Additive on Drug Transport and Distribution Uniformity After Aerosol Delivery to Ex Vivo Lungs.

Background: Inhaled drug delivery can be limited by heterogeneous dose distribution. An additive that would disperse drug over the internal surfaces of the lung after aerosol deposition could improve dosing uniformity and increase the treated area. Our previous studies demonstrated that surfactant additives can produce surface tension-driven (Marangoni) flows that effectively dispersed aerosol-delivered drugs over mucus surfaces. Here we sought to determine whether the addition of a surfactant would increase transport of an aerosol between lung regions and also improve dosing uniformity in human lungs. Methods: We compared the deposition and postdeposition dispersion of surfactant (10 mg/mL dipalmitoylphosphatidylcholine; DPPC) and saline-based liquid aerosols, admixed with Technetium 99m (Tc99m) diethylenetriaminepentaacetic acid, using gamma scintigraphy. Deposition images were obtained ex vivo in eight pairs of ventilated human lungs. The trachea was intubated and the mainstem bronchi were alternately clamped so that saline was delivered to one lung and then DPPC to the other (sides alternated). The lungs were continually imaged for 15 minutes during delivery. We assessed transport of the deposited aerosol by quantifying the percentage of Tc99m in each of four lung quadrants over time. We quantified dose uniformity within each lung quadrant by measuring the coefficient of variation (CV = standard deviation of the pixel associated radioactive counts/mean of the counts within each quadrant). Results: There was no change in the percentage of Tc99m in each quadrant over time, indicating no improvement in transport with the addition of the surfactant. The addition of surfactant was associated with a statistically significant decrease in CV in the lower inner lung quadrant at each of the three time points, indicating an improvement in dosing uniformity. Conclusion: These preliminary results indicate the possible utility of adding surfactant to aerosols to improve drug distribution uniformity to lower inner lung regions.

pH-Dependent Interfacial Tension and Dilatational Modulus Synergism of Oil-Soluble Fatty Acid and Water-Soluble Cationic Surfactants at the Oil/Water Interface.

While the concept of interfacial tension synergism in surfactant mixtures is well established, little attention has been paid to the possibility of synergistic effects on the interfacial rheology of mixed surfactant systems. Furthermore, interfacial tension synergism is most often investigated for mixtures of surfactants residing in a single phase. Here, we define dilatational modulus synergism and report a study of interfacial tension isotherms and complex dilatational moduli for a binary surfactant system with the two surfactants accessing the oil/water interface from opposite sides. Using an oil-soluble fatty acid surfactant (palmitic acid, PA) that may be ionized at the oil/water interface and a quaternary ammonium water-soluble cationic surfactant (tetradecyltrimethylammonium bromide, TTAB), the binary interfacial interaction was tuned by the aqueous phase pH. Interfacial tensions and dilatational moduli were measured by the pendant drop method for the binary surfactant system as well as the corresponding single-surfactant systems to identify synergistic effects. The possible occurrence of dilatational modulus synergism was probed from two perspectives: one for a fixed total surfactant concentration and the other for a fixed interfacial tension. The aqueous pH was found to have a controlling effect on both interfacial tension synergism and the dilatational modulus synergism. The conditions for interfacial tension synergism coincided with those for the storage modulus synergism: both tension and storage modulus synergisms were observed under all conditions tested at pH 7 where PA was mostly deprotonated, for both perspectives examined, but not for any conditions tested at pH 3 where PA is mostly protonated. The loss modulus synergism exhibited more complex behaviors, such as frequency and interfacial tension dependences, but again was only observed at pH 7. The tension and modulus synergism at pH 7 were attributed to the increased attraction between ionized PA and cationic TTAB and the formation of catanionic complexes at the oil/water interface.

Surfactant Driven Marangoni Spreading in the Presence of Predeposited Insoluble Surfactant Monolayers.

When an insoluble surfactant is deposited on the surface of a thin fluid film, stresses induced by surface tension gradients drive Marangoni spreading across the subphase surface. The presence of a predeposited layer of an insoluble surfactant alters that spreading. In this study, the fluid film was aqueous, the predeposited insoluble surfactant was dipalmitoylphosphatidylcholine (DPPC), and the deposited insoluble surfactant was oleic acid. An optical density-based method was used to measure subphase surface distortion, called the Marangoni ridge, associated with propagation of the spreading front. The movement of the Marangoni ridge was correlated with movement of surface tracer particles that indicated both the boundary between the two surfactant layers and the surface fluid velocities. As the deposited oleic acid monolayer spread, it compressed the predeposited DPPC monolayer. During spreading, the surface tension gradient extended into the predeposited monolayer, which was compressed nonuniformly, from the deposited monolayer. The spreading was so rapid that the compressed predeposited surfactant could not have been in quasi-equilibrium states during the spreading. As the initial concentrations of the predeposited surfactant were increased, the shape of the Marangoni ridge deformed. When the initial concentration of the predeposited surfactant reached about 70 A2/molecule, there was no longer a Marangoni ridge but rather a broadly distributed excess of fluid above the initial fluid height. The nonuniform compression of the annulus of the predeposited monolayer also caused tangential motion ahead of both the Marangoni ridge and the boundary between the two monolayers. Spreading ceased when the two monolayers reached the same final surface tension. The final area per molecule of the DPPC monolayer matched that expected from the equilibrium DPPC isotherm at the same final surface tension. Thus, at the end of spreading, there was a simple surface tension balance between the two distinct monolayers.

Interfacial dilatational rheology as a bridge to connect amphiphilic heterografted bottlebrush copolymer architecture to emulsifying efficiency.

HYPOTHESIS: Molecular architecture and composition of amphiphilic bottlebrush copolymers will dictate the dominant interfacial relaxation modes and the corresponding dilatational rheology for adsorbed layers at oil/water interfaces in a way that will correlate with the emulsifying efficiency of different bottlebrush copolymers. EXPERIMENTS: Amphiphilic, xylene-soluble poly(ethylene oxide)-poly(n-butyl acrylate) (PEO-PBA) heterografted bottlebrush copolymers with controlled differences in backbone length, hydrophilicity and arm length were synthesized by atom transfer radical polymerization. Dilatational rheology of adsorbed layers at the xylene/water interface was probed via pendant drop tensiometry by measuring the interfacial stress response to either large-amplitude strain cycling or small-amplitude strain oscillation. The rheological response was recorded as a function of interfacial pressure for adsorbed layers under different compression states. Emulsifying efficiency was determined as the lowest copolymer concentration that yielded water-in-xylene emulsions with at least one-month stability against coalescence. FINDINGS: The more hydrophilic copolymers with longer PEO arms exhibited non-hysteretic stress-strain response curves in large-amplitude strain cycling and a tendency for the modulus to increase with increasing interfacial pressure. These were more efficient emulsifiers than less hydrophilic copolymers that exhibited hysteretic interfacial rheology. Mere existence of significant moduli did not correlate with high emulsifying efficiency, while an increase in modulus with increasing interfacial pressure did so.

Advective-diffusive spreading of diffusiophoretic colloids under transient solute gradients.

We analytically calculate the one-dimensional advective-diffusive spreading of a point source of diffusiophoretic (DP) colloids, driven by the simultaneous diffusion of a Gaussian solute patch. The spreading of the DP colloids depends critically on the ratio of the DP mobility, M (which can be positive or negative), to the solute diffusivity, Ds. For instance, we demonstrate, for the first time, that solute-repelling colloids (M < 0) undergo long-time super-diffusive transport for M/Ds < -1. In contrast, the spreading of strongly solute-attracting colloids (M/Ds≫ 1) can be spatially arrested over long periods on the solute diffusion timescale, due to a balance between colloid diffusion and DP under the evolving solute gradient. Further, a patch of the translating solute acts as a "shuttle" that rapidly transports the colloids relative to their diffusive timescale. Finally, we use numerical computations to show that the above behaviors persist for three-dimensional, radially symmetric DP spreading. The results presented here could guide the use of DP colloids for microscale particle sorting, deposition, and delivery.

Flow regime transitions and effects on solute transport in surfactant-driven Marangoni flows.

HYPOTHESIS: Surfactant-driven Marangoni flow on liquid films is predicted to depend on subphase depth and initial surface tension difference between the subphase and deposited surfactant solution drop. Changes in flow behavior will impact transport of soluble species entrained in the Marangoni flow along the surface. In extreme cases, the subphase film may rupture, limiting transport. Understanding this behavior is important for applications in drug delivery, coatings, and oil spill remediation. EXPERIMENTS: A trans-illumination optical technique measured the subphase height profiles and drop content transport after drop deposition when varying initial subphase depth, surfactant concentration, and subphase viscosity. FINDINGS: Three distinct flow regimes were identified depending on the subphase depth and surfactant concentration and mapped onto an operating diagram. These are characterized as a "central depression" bounded by an outwardly traveling ridge, an "annular depression" bounded by a central dome and the traveling ridge, and an "annular dewetting" when the subphase ruptures. Well above the critical micelle concentration, transitions between regimes occur at characteristic ratios of gravitational and initial surface tension gradient stresses; transitions shift when surfactant dilution during spreading weakens the stress before the completion of the spreading event. Drop contents travel with the ridge, but dewetting hinders transport.

Evolution and Disappearance of Solvent Drops on Miscible Polymer Subphases.

Traditionally, an interface is defined as a boundary between immiscible phases. However, previous work has shown that even when two fluids are completely miscible, they maintain a detectable "effective interface" for long times. Miscible interfaces have been studied in various systems of two fluids with a single boundary between them. However, this work has not extended to the three-phase system of a fluid droplet placed on top of a miscible pool. We show that these three-phase systems obey the same wetting conditions as immiscible systems, and that their drop shapes obey the Augmented Young-Laplace Equation. Over time, the miscible interface diffuses and the shape of the drop evolves. We place 2-microliter drops of water atop miscible poly(acrylamide) solutions. The drop is completely wetted by the subphase, and then remains detectable beneath the surface for many minutes. An initial effective interfacial tension can be approximated to be on the order of 0.5 mN/m using the capillary number. Water and poly(acrylamide) are completely miscible in all concentrations, and yet, when viewed from the side, the drop maintains a capillary shape. Study of this behavior is important to the understanding of effective interfaces between miscible polymer phases, which are pervasive in nature.

Surfactant-induced Marangoni transport of lipids and therapeutics within the lung.

Understanding the fundamentals of surface transport on thin viscous films has important application in pulmonary drug delivery. The human lung contains a large-area interface between its complex fluid lining and inhaled air. Marangoni flows driven by surface tension gradients along this interface would promote enhanced distribution of inhaled therapeutics by carrying them from where they are deposited in the upper airways, along the fluid interface to deeper regions of the lung. Motivated by the potential to improve therapies for acute and chronic lung diseases, we review recent progress in modeling and experimental studies of Marangoni transport induced by the deposition of surfactant-containing microliter drops and liquid aerosols (picoliter drops) onto a fluid interface. The roles of key system variables are identified, including surfactant solubility, drop miscibility with the subphase, and the thickness, composition and surface properties of the subphase liquid. Of particular interest is the unanticipated but crucial role of aerosol processing to achieve Marangoni transport via phospholipid vesicle dispersions, which are likely candidates for a biocompatible delivery system. Progress in this field has the potential to not only improve outcomes in patients with chronic and acute lung diseases, but also to further our understanding of surface transport in complex systems.

Spontaneous rise in open rectangular channels under gravity.

Fluid movement in microfluidic devices, porous media, and textured surfaces involves coupled flows over the faces and corners of the media. Spontaneous wetting of simple grooved surfaces provides a model system to probe these flows. This numerical study investigates the spontaneous rise of a liquid in an array of open rectangular channels under gravity, using the Volume-of-Fluid method with adaptive mesh refinement. The rise is characterized by the meniscus height at the channel center, outer face and the interior and exterior corners. At lower contact angles and higher channel aspect ratios, the statics and dynamics of the rise in the channel center show little deviation with the classical model for capillarity, which ignores the existence of corners. For contact angles smaller than 45°, rivulets are formed in the interior corners and a cusp at the exterior corner. The rivulets at long times obey the one-third power law in time, with a weak dependence on the geometry. The cusp behaviour at the exterior corner transforms into a smooth meniscus when the capillary force is higher in the channel, even for contact angles smaller than 45°. The width of the outer face does not influence the capillary rise inside the channel, and the channel size does not influence the rise on the outer face.

Aerosolizing Lipid Dispersions Enables Antibiotic Transport Across Mimics of the Lung Airway Surface Even in the Presence of Pre-existing Lipid Monolayers.

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.

Transport of a partially wetted particle at the liquid/vapor interface under the influence of an externally imposed surfactant generated Marangoni stress.

Marangoni flows offer an interesting and useful means to transport particles at fluid interfaces with potential applications such as dry powder pulmonary drug delivery. In this article, we investigate the transport of partially wetted particles at a liquid/vapor interface under the influence of Marangoni flows driven by gradients in the surface excess concentration of surfactants. We deposit a microliter drop of soluble (sodium dodecyl sulfate aqueous solution) surfactant solution or pure insoluble liquid (oleic acid) surfactant on a water subphase and observe the transport of a pre-deposited particle. Following the previous observation by Wang et al. [1] that a surfactant front rapidly advances ahead of the deposited drop contact line initiates particle motion but then moves beyond the particle, we now characterize the two dominant, time- and position-dependent forces acting on the moving particle: 1) a surface tension force acting on the three-phase contact line around the particle periphery due to the surface tension gradient at the liquid/vapor interface which always accelerates the particle and 2) a viscous force acting on the immersed surface area of the particle which accelerates or decelerates the particle depending on the difference in the velocities of the liquid and particle. We find that the particle velocity evolves over time in two regimes. In the acceleration regime, the net force on the particle acts in the direction of particle motion, and the particle quickly accelerates and reaches a maximum velocity. In the deceleration regime, the net force on the particle reverses and the particle decelerates gradually and stops. We identify the parameters that affect the two forces acting on the particle, including the initial particle position relative to the surfactant drop, particle diameter, particle wettability, subphase thickness, and surfactant solubility. We systematically vary these parameters and probe the spatial and temporal evolution of the two forces acting on the particle as it moves along its trajectory in both regimes. We find that a larger particle always lags behind the smaller particle when placed at an equal initial distance from the drop. Similarly, particles more deeply engulfed in the subphase lag behind those less deeply engulfed. Further, the extent of particle transport is reduced as the subphase thickness decreases, due to the larger velocity gradients in the subphase recirculation flows.

Enabling Marangoni flow at air-liquid interfaces through deposition of aerosolized lipid dispersions.

It has long been known that deposited drops of surfactant solution induce Marangoni flows at air-liquid interfaces. These surfactant drops create a surface tension gradient, which causes an outward flow at the fluid interface. We show that aqueous phospholipid dispersions may be used for this same purpose. In aqueous dispersions, phospholipids aggregate into vesicles that are not surface-active; therefore, drops of these dispersions do not initiate Marangoni flow. However, aerosolization of these dispersions disrupts the vesicles, allowing access to the surface-active monomers within. These lipid monomers do have the ability to induce Marangoni flow. We hypothesize that monomers released from broken vesicles adsorb on the surfaces of individual aerosol droplets and then create localized surface tension reduction upon droplet deposition. Deposition of lipid monomers via aerosolization produces surface tensions as low as 1mN/m on water. In addition, aerosolized lipid deposition also drives Marangoni flow on entangled polymer solution subphases with low initial surface tensions (∼34mN/m). The fact that aerosolization of phospholipids naturally found within pulmonary surfactant can drive Marangoni flows on low surface tension liquids suggests that aerosolized lipids may be used to promote uniform pulmonary drug delivery without the need for exogenous spreading agents.

Effect of polyelectrolyte-surfactant complexation on Marangoni transport at a liquid-liquid interface.

Complexation of surfactants and oppositely charged polyelectrolytes is expected to alter Marangoni transport at a fluid interface compared to either single component system due to altered interfacial tension isotherms and mass transfer rates as well as adsorption irreversibility effects. We investigate Marangoni transport at the oil/water interface by passing mixtures of the anionic surfactant sodium dodecyl sulfate (SDS) and cationic polyelectrolyte poly(3-(2-methylpropionamide)propyl) trimethylammonium chloride-acrylamide (poly[AM-MAPTAC]), or rinsing solutions, over an oil/water interface in a radial, stagnation point flow. The displacements of adsorbed tracer particles are recorded through optical microscopy. The net displacement, defined as the sum of the displacements occurring during the adsorption and desorption stages of one application and rinsing cycle, is up to 10 times greater for complexing surfactant/polymer mixtures compared to either single component system. The enhanced net displacement is largely determined by the enhanced transport upon adsorption, while the reverse displacement that would normally occur upon rinsing is partially suppressed by partially irreversible polymer adsorption at the oil/water interface. In addition to effects of complexation on interfacial tension gradient induced flow, complexation effects on the bulk, and possibly interfacial, viscosity also influence the interfacial transport.

Stability of a compound sessile drop at the axisymmetric configuration.

The equilibrium configuration of compound sessile drops has been calculated previously in the absence of gravity. Using the Laplace equations, we establish seven dimensionless parameters describing the axisymmetric configuration in the presence of gravity. The equilibrium axisymmetric configuration can be either stable or unstable depending on the fluid properties. A stability criterion is established by calculating forces on a perturbed Laplacian shape. In the zero Bond number limit, the stability criterion depends on the density ratio, two ratios of interfacial tensions, the volume ratio of the two drops, and the contact angle. We use Surface Evolver to examine the stability of compound sessile drops at small and large Bond numbers and compare with the zero Bond number approximation. Experimentally, we realize a stable axisymmetric compound sessile drop in air, where the buoyancy force exerted by the air is negligible. Finally, using a pair of fluids in which the density ratio can be tuned nearly independently of the interfacial tensions, the stability transition is verified for the axisymmetric configuration. Even though the perturbations are different for the theory, simulations and experiments, both simulations and experiments agree closely with the zero Bond number approximation, exhibiting a small discrepancy at large Bond number.

Transient Marangoni transport of colloidal particles at the liquid/liquid interface caused by surfactant convective-diffusion under radial flow.

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 5µm 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.