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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.

We quantify the macrotransport of chemotactic and diffusiophoretic colloids, demonstrating how hydrodynamic flows could tune the colloid spreading.

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.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.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.

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.

We conduct an asymptotic analysis to derive a macrotransport equation for the long-time transport of a chemotactic/diffusiophoretic colloidal species in a uniform circular tube under a steady, laminar, pressure-driven flow and transient solute gradient. The solute gradient drives a ‘log-sensing’ advective flux of the colloidal species, which competes with Taylor dispersion due to the hydrodynamic flow. We demonstrate excellent agreement between the macrotransport equation and direct numerical solution of the full advection–diffusion equation for the colloidal species transport. In addition to its accuracy, the macrotransport equation requires times less computational runtime than direct numerical solution of the advection–diffusion equation. Via scaling arguments, we identify three regimes of the colloidal species macrotransport, which span from chemotactic/diffusiophoretic-dominated macrotransport to the familiar Taylor dispersion regime, where macrotransport is dominated by the hydrodynamic flow. Finally, we discuss generalization of the macrotransport equation to channels of arbitrary (but constant) cross-section and to incorporate more sophisticated models of chemotactic fluxes. The macrotransport framework developed here will broaden the scope of designing chemotactic/diffusiophoretic transport systems by elucidating the interplay of macrotransport due to chemotaxis/diffusiophoresis and hydrodynamic flow.

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.

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.

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 (

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.

In this study, the spontaneous rise of a Newtonian liquid in a square capillary with completely or partially wetted walls is investigated using numerical simulations. The flow is modelled using volume-of-fluid method with adaptive mesh refinement to resolve the interface for high accuracy. The computations show that for contact angles smaller than 45°, rivulets appear in the corners of the capillary. At large times the length of the capillary growth approaches the one-third power function of time. The same asymptotic behavior has been identified in the existing experimental observations for corners of different geometries. The computations predict the dependence of the rate of the rivulet growth on the liquid viscosity, gravity, width of the capillary and the contact angle. The flow in the rivulet is described using a long-wave approximation which considers three regions of the rivulet flow: the flow near the rivulet tip which is described by a similarity solution, an intermediate region approaching a static rivulet shape, and the bulk meniscus. Finally, a scaling analysis is proposed which predicts rivulet growth rates for the given parameters.

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 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 and 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.

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.

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.

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.

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.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.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.

When a drop of aqueous surfactant solution is placed on a deep subphase of water, multiple phenomena occur. The contact line of the drop spreads until the drop merges with the subphase. A capillary wave train is initiated by the disturbance caused by the drop touching the subphase surface. Marangoni stresses cause the formation and propagation of a localized distortion of the subphase surface (subsequently called the Marangoni ridge). And particles pre-deposited on the subphase surface are propelled by the flow induced by Marangoni stresses. We examine all these phenomena simultaneously at early times (

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.

Cystic fibrosis (CF) is associated with the accumulation of dehydrated mucus in the pulmonary airways. This alters ventilation and aerosol deposition patterns in ways that limit drug delivery to peripheral lung regions. We investigated the use of surfactant-based, self-dispersing aerosol carriers that produce surface tension gradients to drive two-dimensional transport of aerosolized medications via Marangoni flows after deposition on the airway surface liquid (ASL). We considered the post-deposition spreading of individual aerosol droplets and two-dimensional expansion of a field of aerosol droplets, when deposited at low fluxes that are representative of aerosol deposition in the small airways.We used physically entangled aqueous solutions of poly(acrylamide) or porcine gastric mucin as simple ASL mimics that adequately capture the full miscibility but slow penetration of entangled macromolecular chains of the ASL into the deposited drop. Surfactant formulations were prepared with aqueous solutions of nonionic tyloxapol or FS-3100 fluorosurfactant. Fluorescein dye served as a model "drug" tracer and to visualize the extent of post-deposition spreading.The surfactants not only enhanced post-deposition spreading of individual aerosol droplets due to localized Marangoni stresses, as previously observed with macroscopic drops, but they also produced large-scale Marangoni stresses that caused the deposited aerosol fields to expand into initially unexposed regions of the subphase. We show that the latter is the main mechanism for spreading drug over large distances when aerosol is deposited at low fluxes representative of the small airways. The large scale convective expansion of the aerosol field drives the tracer (drug mimic) over areas that would cover an entire airway generation or more, in peripheral airways, where sub-monolayer droplet deposition is expected during aerosol inhalation.The results suggest that aerosolized surfactant formulations may provide the means to maximize deposited drug uniformity in and access to small airways.

Aerosol drug delivery is a viable option for treating diseased airways, but airway obstructions associated with diseases such as cystic fibrosis cause non-uniform drug distribution and limit efficacy. Marangoni stresses produced by surfactant addition to aerosol formulations may enhance delivery uniformity by post-deposition spreading of medications over the airway surface, improving access to poorly ventilated regions. We examine the roles of different variables affecting the maximum post-deposition spreading of a dye (drug mimic).Entangled aqueous solutions of either poly(acrylamide) (PA) or porcine gastric mucin (PGM) serve as airway surface liquid (ASL) mimicking subphases for in vitro models of aerosol deposition. Measured aerosol deposition fluxes indicate that the experimental delivery conditions are representative of aerosol delivery to the conducting airways. Post-deposition spreading beyond the locale of direct aerosol deposition is tracked by fluorescence microscopy. Aqueous aerosols formulated with either nonionic surfactant (tyloxapol) or fluorosurfactant (FS-3100) are compared with surfactant-free control aerosols.Significant enhancement of post-deposition spreading is observed with surfactant solutions relative to surfactant-free control solutions, provided the surfactant solution surface tension is less than that of the subphase. Amongst the variables considered--surfactant concentration, aerosol flow-rate, total deposited volume, time of delivery, and total deposited surfactant mass--surfactant mass is the primary predictor of maximum spread distance. This dependence is also observed for solutions deposited as a single, microliter-scale drop with a volume comparable to the total volume of deposited aerosol.Marangoni stress-assisted spreading after surfactant-laden aerosol deposition at high fluxes on a complex fluid subphase is capable of driving aerosol contents over significantly greater distances compared to surfactant-free controls. Total delivered surfactant mass is the primary determinant of the extent of spreading, suggesting a great potential to extend the reach of aerosolized medication in partially obstructed airways via a purely physical mechanism.

A multiple-scale perturbation theory is developed to analyze the advection-diffusion transport of a passive solute through a parallel-plate channel. The fluid velocity comprises a steady and a time-oscillatory component, which may vary spatially in the transverse and streamwise directions, and temporally on the fast transverse diffusion timescale. A long-time asymptotic equation governing the evolution of the transverse averaged solute concentration is derived, complemented with Taylor dispersion coefficients and advection speed corrections that are functions of the streamwise coordinate. We demonstrate the theory with a two-dimensional flow in a channel comprising alternating shear-free and no-slip regions. For a steady flow, the dispersion coefficient changes from zero to a finite value when the flow transitions from plug-like in the shear-free section to parabolic in the no-slip region. For an oscillatory flow, the dispersion coefficient due to an oscillatory flow can be negative and two orders of magnitude larger than that due to a steady flow of the same amplitude. This motivates us to quantify the relative magnitude of the steady and oscillatory flow such that there is an overall positive dispersion coefficient necessary for an averaged (macrotransport) equation. We further substitute the transport coefficients into the averaged equation to compute the evolution of the concentration profile, which agrees well with that obtained by solving the full two-dimensional advection-diffusion equation. In a steady flow, we find that while the shear-free section suppresses band broadening, the following no-slip section may lead to a wider band compared with the dispersion driven by the same pressure gradient in an otherwise homogeneously no-slip channel. In an unsteady flow, we demonstrate that a naive implementation of the macrotransport theory with a (localized) negative dispersion coefficient will result in an aphysical finite time singularity (or “blow-up solution”), in contrast to the well-behaved solution of the full advection-diffusion equation.

Motivated by the possibility of enhancing aerosol drug delivery to mucus-obstructed lungs, the spreading of a drop of aqueous surfactant solution on a physically entangled aqueous poly(acrylamide) solution subphase that mimics lung airway surface liquid was investigated. Sodium dodecyl sulfate was used as the surfactant. To visualize spreading of the drop and mimic the inclusion of a drug substance, fluorescein, a hydrophilic and non-surface active dye, was added to the surfactant solution. The spreading progresses through a series of events. Marangoni stresses initiate the convective spreading of the drop. Simultaneously, surfactant escapes across the drop’s contact line within a second of deposition and causes a change in subphase surface tension outside the drop on the order of 1 mN/m. Convective spreading of the drop ends within 2–3 seconds of drop deposition, when a new interfacial tension balance is achieved. Surfactant escape depletes the drop of surfactant and the residual drop takes the form of a static lens of non-zero contact angle. On longer time scales, the surfactant dissolves into the subphase. The lens formed by the water in the deposited drop persists for as long as 3 minutes after the convective spreading process ends due to the long diffusional timescales associated with the underlying entangled polymer solution. The persistence of the lens suggests that the drop phase behaves as if it were immiscible with the subphase during this time period. Whereas surfactant escapes the spreading drop and advances on the subphase/vapor interface, hydrophilic dye molecules in the drop do not escape, but remain with the drop throughout the convective spreading. The quasi-immiscible nature of the spreading event suggests that the chemical properties of the surfactant and subphase are much less important than their physical properties, consistent with prior qualitative studies of spreading of different types of surfactants on entangled polymer subphases: the selection of surfactant for pulmonary delivery applications may be limited only by physical and toxicological considerations. Further, the escape of surfactant from individual drops may provide an additional spreading mechanism in the lung as hydrodynamic and/or surface pressure repulsions may drive individual droplets apart after deposition.

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 1 mN/m on water. In addition, aerosolized lipid deposition also drives Marangoni flow on entangled polymer solution subphases with low initial surface tensions (~ 34 mN/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.

International audience; 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.

We investigated the phenomenon of incomplete wetting of a high-energy liquid subphase by drops of pure amphiphilic molecules as well as drops of amphiphile solutions that are immiscible with the subphase. We show that amphiphiles escape across the contact line of the drop, move on the subphase/vapor interface, and form a submonolayer or full monolayer external to the drop. If this monolayer is sufficiently dense, then it can reduce the surface tension of the subphase, raise the contact angle of the drop, and prevent the drop from fully wetting the subphase. This phenomenon is called autophobing and has been extensively studied on solid substrates. For the liquid subphase studied here, we measure the surface tensions of the three relevant interfaces before and after the drop is deposited. The measured surface tension external to the drop shows that amphiphiles can move across the contact line and form a monolayer outside of the drop. In some cases, at equilibrium, the monolayer is in a sufficiently packed state to create the nonwetting condition. In other cases, at equilibrium the monolayer density is insufficient to lower the surface tension enough to achieve the nonwetting condition. Unlike on solid substrates where the formation of the monolayer external to the drop is kinetically hindered, the amphiphiles can move rapidly across the liquid subphase by Marangoni-driven surface transport, and local equilibrium is achieved. However, because the amphiphile inventory and subphase area are limited, the achievement of autophobing on a liquid subphase depends not only on the instrinsic subphase/amphiphile interaction but also on the total amphiphile inventory and area of the liquid subphase.

Aerodynamic forces provide the primary means of distributing aerosol medications within the lungs. Partial airway obstructions can limit both air flow and aerosol penetration into diseased zones. We hypothesize that low surface tension additives may help to disperse aerosol medications after deposition in the airways, improving dose uniformity and drug delivery to underventilated regions. To test this, we performed a pilot scintigraphy study of surfactant and saline deposition and postdeposition dispersion.Because inhaled antibiotics for cystic fibrosis provide an example of where self-dispersing medications may be useful, we administered calfactant and saline aerosols with added Technetium 99m sulfur colloid (Tc-SC; 100 nm filtered) on different days in randomized order to eight cystic fibrosis (CF) subjects (average FEV(1)%, p=85 ± 12%). Nebulized delivery was matched (similar aerosol sizes and volume delivery rates, fixed breathing patterns). Tc-SC distribution in the lungs was imaged continuously for 30 min after delivery.Both aerosols were well tolerated. Aerosol distribution was mostly peripheral (58/42%) and initially similar for saline and surfactant. Changes in whole lung counts after 30 min were also similar. Peripheral lung activity decreased more rapidly on average with calfactant though the difference versus saline was not statistically significant. Central to peripheral count ratio decreased with saline and increased with calfactant and c/p changes approached significance (-0.05 ± 0.16 vs. 0.10 ± 0.10; p=0.07 Wilcoxon).Our results lack statistical significance, but suggest that inhaled calfactant increased peripheral clearance, due to either surfactant-based dispersion or mucociliary effects. Further studies are needed to define the potential for low surface tension carriers to improve drug delivery.

A temperature rise on the order of tenths of a degree is observed as one fluid spreads over a hygroscopic fluid. While this behavior is only exhibited with hygroscopic fluids, it is independent of the properties of the spreading fluid. The spreading induces a ‘rolling’ motion in the subphase which brings ‘fresh’ fluid to the surface, exposing it to the water vapor in the air. As water is absorbed into the hygroscopic liquid, heat is released. The same behavior is observed whether the spreading fluid has a spreading monolayer that drives a convection front or is a spreading lens with a moving three-phase contact line.

Soluble surfactants are often deposited from volatile solvents through moving contact lines. In this study, we demonstrate that altering the flow field near such a contact line fundamentally changes the deposited surfactant structure. At slow contact line speeds, the substrate emerges dry. A densely packed, tilted monolayer of surfactant is deposited along the solid-vapor interface from the rolling fluid motion at the contact line. At faster speeds, the substrate emerges with an evaporating thin film entrained on its surface. Surfactant is confined in the film in a constantly increasing concentration environment. Monodisperse crystalline islands nucleate and grow on the surface with sizes and shapes controlled by varying the deposition conditions. These results contrast with disordered deposits that result from evaporation at a pinned contact line. Our results suggest that dip-coating with control of dipping speed and evaporation rate may provide better control of deposition through contact lines of evaporating solvents.

The impact of fluid elasticity on the dynamic wetting of polymer solutions is important because many polymer solutions in technological use exhibit non-Newtonian behaviors in the high shear environment of the wedge-like flow near a moving contact line. Our former study [G.K. Seevaratnam, Y. Suo, E. Rame, L.M. Walker, Phys. Fluids 19 (2007) Art. No. 012103] showed that shear thinning induced by a semi-flexible high molecular weight polymer reduces the viscous bending near a moving contact line as compared to a Newtonian fluid having the same zero-shear viscosity. This results in a dramatic reduction of the dependence of the effective dynamic contact angle on contact line speed. In this paper, we discuss dynamic wetting of Boger fluids which exhibit elasticity-dominated rheology with minimal shear thinning. These fluids are prepared by dissolving a dilute concentration of high molecular weight polymer in a “solvent” of the oligomer of the polymer. We demonstrate that elasticity in these fluids increases curvature near the contact line but that the enhancement arises mostly from the weakly non-Newtonian behavior already present in the oligomeric solvent. We present evidence of instabilities on the liquid/vapor interface near the moving contact line.

Coalescence of liquid drops is critical in many phenomena such as emulsion stability, inkjet printing, and coating applications. For sessile drops on a solid surface, the coalescence process is more complicated than the coalescence of drops suspended in a fluid medium as a result of the coupling of the contact line motions to the fluid flow. In this paper, we use video microscopy to track the evolution of the interfaces and contact lines as well as the internal fluid motion within a merged sessile droplet. In this study, the fluids in the coalescing drops are miscible and have similar surface tensions and drop volumes but different viscosities and densities. Coalescence occurs in three stages. During the first stage, rapid healing of the bridge between the drops occurs just after they touch. In the second stage, slower rearrangement of the liquids occurs. We show that these intermediate rearrangements are driven by gravity even for density differences of the two fluids as small as 1%. For the systems examined, little to no mixing occurs during these first two stages. Finally, in the third stage, diffusion leads to mixing of the fluids. Dimensional analysis reveals the scaling of the intermediate flow behavior as a function of density difference and geometric dimensions of the merged drop; however, the scaling with viscosity is more complicated, motivating development of a lubrication analysis of the coalescence problem. Numerical calculations based on the lubrication analysis capture aspects of the experimental observations and reveal the governing forces and time scales of the coalescence process. The results reveal that internal fluid motions persist over much longer time scales than imaging of the external interface alone would reveal. Furthermore, nearly imperceptible motions of the external composite drop interface can lead to important deviations from the predominant gravity current scaling, where viscous resistance of the lighter fluid layer plays a significant role in the internal fluid motion.

We characterize the movement of carbon black particles in inhomogeneous, two-dimensional dc electric fields. Motivated by display applications, the particles are suspended in a nonpolar solvent doped with a charge control agent. The two-dimensional fields are generated between strip electrodes on a glass slide spaced 120 microm apart with field strengths up to 10(4) V/m. Such fields are insufficient to drive either electrohydrodynamic instabilities or natural convection due to ohmic heating, but they move the particles between the electrodes in about 30 s. In the center region between the strip electrodes, the particles move by electrophoresis; that is, the particle velocity is proportional to the electric field. However, when imposing a constant-potential or constant-current boundary condition at the electrodes to derive the electrical field, the electrophoretic mobility calculated from the measured particle velocities is outside the range of mobilities predicted from the theory of O'Brien and White. Near the electrodes the particles either speed up or slow down, depending on the polarity of the electrode, and these changes in velocity cannot be explained simply by electrophoresis in a spatially varying electric field. We suggest that this anomalous motion arises from electrohydrodynamic flows originating from the interaction between the space charge of the polarized layers above the electrodes and the electric field. Approximate calculations indicate such flows could be sufficiently strong to explain the anomalous trajectories near the edges of the electrodes.

Re-self-assembly of surfactant molecules must occur at moving contact lines of soluble surfactant solutions. Molecules are transported into and out of the contact line region from four sources: the three interfaces meeting at the contact line and the fluid confined between the solid-liquid and liquid-vapor interfaces. As molecules move among these sources at the contact line, they must rearrange. The dynamics of this re-self-assembly has been shown to have a dominating effect on the structure of advancing contact lines, causing unsteady motion and complex structure of the contact line. It might be assumed that the re-self-assembly for receding contact lines leads to more steady contact line movement. However, in this article we show that for a wide variety of systems this is not true. Quasi-static distortions of the contact line occur as it retreats because of the inability of the surfactant to completely re-self-assemble at localized positions along the contact line.

Electrical current versus potential relationships were measured for solutions of dodecane containing the charge control agent poly(isobutylene succinimide) (PIBS) at various concentrations. Both one-dimensional (parallel planar electrodes) and two-dimensional (strip electrodes) fields were studied. The initial current was proportional to the applied voltage for both electrode configurations. Using the initial decay rate of the current (t < 0.5 s) in the planar electrode cell and the Gouy−Chapman model for electrode polarization, we determined the diffusion coefficient of the charge carriers (micelles) in the solution, from which we calculated their effective radius to be 10 nm. The constancy of the carrier radius over a 7-fold change in PIBS concentration, along with the proportionality between conductivity and concentration, supports the hypothesis that the charged species result from the interactions between two micelles. The experimentally determined geometric factor (cell constant) relating current to...

Slip–stick vibration driven by friction is important in many applications, and to model it well enough to make reliable predictions requires detailed information about the underlying physical mechanisms of friction. To characterize the frictional behavior of an interface in the stick–slip regime requires measurements that themselves operate in the stick–slip regime. A novel methodology for measurements of this kind is presented, based on the excitation of a stretched string “bowed” with a rod that is coated with the friction material to be investigated. Measurements of the motion of the string allow the friction force and the velocity waveform at the contact point to be determined by inverse calculation. These friction results can be correlated with microscopic analysis of the wear track left in the coated surface. Results are presented using rosin as a friction material. These show that “sticking” involves some temperature-dependent shear flow in the friction material, and that the exact definit...

The hydrodynamics near moving contact lines of two room-temperature polymer melts, polyisobutylene (PIB) and polystyrene (PS), are different from those of a third polymer melt, polydimethylsiloxane (PDMS). While all three fluids exhibit Newtonian behavior in rotational rheological measurements, a model of the hydrodynamics near moving contact lines which assumes Newtonian behavior of the fluid accurately describes the interface shape of a variety of PDMS fluids but fails to describe the interface deformation by viscous forces in PIB and PS. The magnitude of the deviations from the model and the distance along the liquid-vapor interface over which they are seen increase with increasing capillary number. We conclude that the wetting behaviors of PIB and PS are influenced by weak elasticity in these low molecular weight melts and that dynamic wetting is more sensitive to this elasticity than standard rheometric techniques.

Wetting states are quantitatively described by the number of inflection points on the liquid-vapor interface and by the macroscopic contact angle. The number of inflection points required for complete, partial, and pseudopartial wetting is determined for geometries with positive, zero, and negative capillary pressures. The wetting state of a material system is not always independent of the magnitude of the capillary pressure; for example, the wetting state of a fluid inside a capillary tube may depend on the capillary radius. In particular, a fluid that pseudopartially wets the inside of a tube exhibits a transition to partial wetting (or complete wetting) as the capillary radius is decreased.

The self-assembly of nonionic surfactants in bulk solution and on hydrophobic surfaces is driven by the same intermolecular interactions, yet their relationship is not clear. While there are abundant experimental and theoretical studies for self-assembly in bulk solution and at the air-water interface, there are only few systematic studies for hydrophobic solid-water interfaces. In this work, we have used optical reflectometry to measure adsorption isotherms of seven different nonionic alkyl polyethoxylate surfactants (CH3(CH2)I-1(OCH2CH2)JOH, referred to as CIEJ surfactants, with I = 10-14 and J = 3-8), on hydrophobic, chemically homogeneous self-assembled monolayers of octadecyltrichlorosilane. Systematic changes in the adsorption isotherms are observed for variations in the surfactant molecular structure. The maximum surface excess concentration decreases (and minimum area/molecule increases) with the square root of the number of ethoxylate units in the surfactant (J). The adsorption isotherms of all surfactants collapse onto the same curve when the bulk and surface excess concentrations are rescaled by the bulk critical aggregation concentration (CAC) and the maximum surface excess concentration. In an accompanying paper we compare these experimental results with the predictions of a unified model developed for self-assembly of nonionic surfactants in bulk solution and on interfaces.

Lead drops exhibit partial wetting on some substrates and pseudopartial wetting on others. In pseudopartial wetting, a film is in equilibrium with a capillary body with a nonzero contact angle. Using a free energy formulation appropriate for the experiments, we show the conditions under which minimization of the system energy is accurately achieved by minimizing the energy of the film alone. Using a set of simple surface energy isotherms, we explain the various wetting behaviors of lead. We contrast isotherms for autophobing systems and the metallic systems considered here.

We examine the effects of thick (micron scale) fluid films and thin molecular scale (10–100 A) films on the hydrodynamics near advancing contact lines by measuring the liquid–vapor interface shape of a meniscus and comparing the measurements to three models. Using flow visualization, we directly observe the fluid flow field near the moving contact line and give a qualitative description of the stagnation point and dividing streamline emanating from the contact line region. For thick films, when the capillary number satisfies Ca(a/d)3/2⩽O(1) (where d is the film thickness and a is the macroscopic length scale of the system), the liquid–vapor interface is bent only slightly by the viscous flow and the effective dynamic contact angle is close to zero. As Ca approaches O(1/ln(a/d)), a modulated wedge-like region appears at some distance from the film and expands both away from and toward the film as Ca increases. The dynamic contact angle approaches the classic power law behavior as this region expands. For m...

We explore the equilibrium wetting behavior and precursor film growth in pure and alloy metallic systems. The systems exhibit equilibrium "pseudopartial" wetting, that is, a thin film in equilibrium with a nonzero contact angle in both liquid and solid states. The film spreading kinetics clearly indicates a diffusive transport mechanism. The alloying has only a small impact on the equilibrium wetting properties but strongly affects the transport during the growth of the precursor film.

The carryover of surfactant ahead of contact lines on hydrophilic surfaces results in unusual wetting behavior of surfactant solutions, such as the autophobic effect. This carryover of surfactant ahead of the contact line is due to the strong interactions between the hydrophilic surface and the headgroup of ionic and nonionic surfactants. However, in the case of a nonionic surfactant and a hydrophobic surface, the possibility of self-assembly of surfactant ahead of the contact line has been neglected because of the absence of any obvious strong interactions and any unusual wetting behavior. In this paper, we provide evidence of carryover of a nonionic surfactant (octaethyleneoxide monododecyl ether, C12E8) ahead (i.e., on the solid−vapor, SV, side) of advancing and receding contact lines on hydrophobic self-assembled monolayers of octadecyltrichlorosilane. This system of a nonionic surfactant and hydrophobic surface was thought to be an unlikely system to show the presence of surfactant ahead of the conta...

The diffusion of Ag away from partially wetting Ag particles on Ni(1 0 0) substrates, to form so-called precursing films, has been studied by means of molecular dynamics simulations. The maximum thickness of the precursing film is one Ag monolayer at the edge of the particle. An analysis of the time dependence of the concentration gradient in the film shows that the kinetics of film growth may be described by diffusional processes, with a diffusivity that is significantly coverage dependent. No ordered surface phases, or evidence of surface alloying of the Ag with the Ni substrate have been found. It is also shown that the coverage dependence of diffusivity can be interpreted only qualitatively in terms of simple diffusive processes in the limits of high and low coverage.

The relative motion between two colloidal particles loosely deposited on an electrode passing alternating current was investigated. Parameters such as zeta potential, electrolyte composition, elect...

We examine experimentally the hydrodynamics of dip-coated, finite-length films of evaporative fluids, from the film tip through the film body all the way to the connection with the main meniscus. The characteristic film thickness has a power-law dependence on the withdrawing speed similar to that for the thickness of “infinite” films formed by nonvolatile liquids. The film length and cross-sectional area have power-law dependence on the withdrawing speed as well, but the prefactors of the power laws are controlled by the evaporation rate of the fluid. These power laws are consistent with the global mass balance over the film between mass lost by evaporation and mass input by the solid motion. We have also found that the apparent contact angle and the curvature at the film tip both have power-law dependencies on the withdrawing speed that are consistent with those found for the length and the film thickness. Film shape measurements near the film tip reach thicknesses ∼100 A from the solid; but we did not detect any influence of the inner scale hydrodynamics and van der Waals forces on this shape. We have developed a systematic method for measuring the contributions of gravity, capillary force, viscous force, and vapor recoil on the pressure and flow fields in the film. This exercise reveals detailed information about the flow in evaporative films. The combined effects of evaporation and Marangoni flow on the hydrodynamics are deduced from experimental data, independent of evaporation models.

We have examined the structures of surfactant self-assemblies left on substrates as a contact line spontaneously retreats across the surface during an autophobing event. A continuous structural gradient is formed during the spontaneous retreat: from molecules lying down on the surface with low packing densities in a region never touched by the solution, to molecules standing up with higher packing densities in a region where the contact line has moved slowly. Despite significant free volumes within the self-assemblies, there is no evidence of clustering of molecules. We have observed a clear correlation between retreating contact line speeds and deposited surfactant structures. The dynamics during at least a later period of the autophobing event is dominated by the time evolution of Young's force dictated by the self-assembly near the contact line.

The relative motion between pairs of negatively charged latex particles 9.7 μm in diameter and deposited on an electrode was measured by optical microscopy and image analysis. At an rms field of approximately 30 V cm−1, the two particles moved toward each other at frequencies below 500 Hz, but they separated at 1000 Hz. In the cases of aggregation, there are several interesting characteristics. First, when the center-to-center separation of a pair was initially 6 particle radii or more apart, a transient ‘incubation’ period of tens of seconds was observed before the particles began to move toward each other. Second, the two particles never came into contact, rather at long times the pair maintained a stationary gap between them equal to approximately one-half the particle radius. This stationary gap between particles was also observed for the aggregation of clusters of three or more particles. Finally, the rate of approach for a pair of particles decreased as the frequency increased. Larger fields are required to move particles together in ac compared to dc fields; at 30 Hz the ac field must be 130 times greater than the dc field to achieve the same rate of approach. Taking advantage of the qualitative and quantitative differences of the cooperative motion of particles in dc vs. ac fields, one should be able to re-position particles by alternating between these two modes. We demonstrated that the same pair of particles can be brought together at low frequency (100 or 200 Hz) and then separated at high frequency (1000 Hz).

We have studied the unsteady spreading of a liquid on a solid surface by observing the liquid−air meniscus shape and analyzing it with the hydrodynamic theory for Stokes' flow. The unsteady spreading process exhibits both quasi-steady and unsteady regimes. The unsteadiness in our moderately high viscosity system arises from temporal relaxation of the contact angle rather than inertial effects or momentum diffusion. The quasi-steady regime can be accurately described by a model that ascribes a steady-state flow near the contact line. “Spontaneous” spreading, i.e., spreading to final state of zero contact line speed, is recognized as a special case of the general unsteady spreading process with the commonly used power laws for spreading occurring only under special conditions.

Surfactant solutions exhibit a wide variety of wetting and dewetting behaviors on high energy surfaces. These behaviors are driven by surfactant self-assemblies at the moving contact line. To probe...