Shear viscosity of langmuir monolayers in the low-density limit

Stability and thinning of liquid jets in the presence of soluble surfactants

The dynamics of many multiphase fluid systems involve the thinning and eventual break up of a slender fluid filament or a liquid jet. The interfacial instability that controls the rate of jet thinning depends on the relative magnitudes of capillary, viscous, and inertial stresses. Surfactants add an additional layer of physicochemical dynamics by reducing the surface tension of the interface and introducing reverse Marangoni flows in response to surface concentration gradients. Surfactants may also introduce an intrinsic surface rheology that affects jet thinning. Quantifying these effects has been a significant problem in chemical physics and a topic of key research interest. Recent studies have shown that insoluble surfactants delay thread thinning and suppress instabilities in Newtonian jets. However, the role of surfactant solubility in liquid jet stability is still unknown. In this work, we use linear stability analysis to quantitatively show the stabilizing effects of Marangoni stresses, surfactant adsorption and desorption time, and intermolecular forces upon adsorption. We highlight the seemingly indistinguishable way in which various surfactant properties result in the same outcome. We also identify a surface dissipative contribution that arises from the interplay of Marangoni flows with finite adsorption and desorption, which acts as an "apparent" surface viscosity. We verify predictions of our linear stability results against numerical simulations and conclude by noting that tuning surface activity and kinetics of adsorbed surfactants or particles can potentially suppress droplet formation, which is of significant impact in the printing industry and in the control of the spread of aerosols.

Motion of micro- and nano- particles interacting with a fluid interface

In this article, we review both theoretical models and experimental results on the motion of micro- and nano- particles that are close to a fluid interface or move in between two fluids. Viscous drags together with dissipations due to fluctuations of the fluid interface and its physicochemical properties affect strongly the translational and rotational drags of colloidal particles, which are subjected to Brownian motion in thermal equilibrium. Even if many theoretical and experimental investigations have been carried out, additional scientific efforts in hydrodynamics, statistical physics, wetting and colloid science are still needed to explain unexpected experimental results and to measure particle motion in time and space scales, which are not accessible so far.

Surfactant dynamics: hidden variables controlling fluid flows

Surfactants - molecules and particles that preferentially adsorb to fluid interfaces - play a ubiquitous role in the fluids of industry, of nature, and of life. Since most surfactants cannot be seen directly, their behavior must be inferred from their impact on observed flows, like the buoyant rise of a bubble, or the thickness of a coating film. In so doing, however, a difficulty arises: physically distinct surfactant processes can affect measurable flows in qualitatively identical ways, raising the specter of confusion or even misinterpretation. This Perspective describes, in one coherent piece, both the equilibrium properties and dynamic processes of surfactants, to better enable the fluid mechanics community to understand, interpret, and design surfactant/fluid systems. Specifically, §2 treats the equilibrium thermodynamics of surfactants at interfaces, including surface pressure, isotherms of soluble and insoluble surfactants, and surface dilatational moduli (Gibbs and Marangoni). §3 describes surfactant dynamics in fluid systems, including surfactant transport and interfacial stress boundary conditions, the competition between surface diffusion, advection, and adsorption/desorption, Marangoni stresses and flows, and surface excess rheology. §4 discusses paradigmatic problems from fluid mechanics that are impacted by surfactants, including translating drops and bubbles, surfactant adsorption to clean and oscillating interfaces; capillary wave damping, thin film dynamics, foam drainage, and the dynamics of particles and probes at surfactant-laden interfaces. Finally, §5 discusses the additional richness and complexity that frequently arise in 'real' surfactants, including phase transitions, phase coexistence, and polycrystalline phases within surfactant monolayers, and their impact on non-Newtonian surface rheology.

Hopanoids Like Sterols Form Compact but Fluid Films

Hopanoids are pentacyclic molecules present in membranes from some bacteria, recently proposed as sterol surrogates in these organisms. Diplopterol is an abundant hopanoid that, similar to sterols, does not self-aggregate in lamellar structures when pure, but forms monolayers at the air-water interface. Here, we analyze the interfacial behavior of pure diplopterol and compare it with sterols from different organisms: cholesterol from mammals, ergosterol from fungi, and stigmasterol from plants. We prepared Langmuir monolayers of the compounds and studied their surface properties using different experimental approaches and molecular dynamics simulations. Our results indicate that the films formed by diplopterol, despite being compact with low mean molecular areas, high surface potentials, and high refractive index, depict shear viscosity values similar to that for fluid films. Altogether, our results reveal that hopanoids have similar interfacial behavior than that of sterols, and thus they may have the capacity of modulating bacterial membrane properties in a similar way sterols do in eukaryotes.

Swimming sheet near a plane surfactant-laden interface

In this work we analyze the velocity of a swimming sheet near a plane surfactant-laden interface by assuming the Reynolds number and the sheet's deformation to be small. We observe a nonmonotonic dependence of the sheet's velocity on the Marangoni number (Ma) and the surface Péclet number (Pe_{s}). For a sheet passing only transverse waves, the swimming velocity increases with an increase in Ma for any fixed Pe_{s}. When Pe_{s} is increasing, on the other hand, the swimming velocity of the same sheet either increases (at large Ma) or it initially increases and then decreases (at small Ma). This dependence of the swimming velocity on Ma and Pe_{s} is altered if the sheet is passing longitudinal waves in addition to the transverse waves along its surface.

FCS Analysis of Protein Mobility on Lipid Monolayers

In vitro membrane model systems are used to dissect complex biological phenomena under controlled unadulterated conditions. In this context, lipid monolayers are a powerful tool to particularly study the influence of lipid packing on the behavior of membrane proteins. Here, monolayers deposited in miniaturized fixed area-chambers, which require only minute amounts of protein, were used and shown to faithfully reproduce the characteristics of Langmuir monolayers. This assay is ideally suited to be combined with single-molecule sensitive fluorescence correlation spectroscopy (FCS) to characterize diffusion dynamics. Our results confirm the influence of lipid packing on lipid mobility and validate the use of FCS as an alternative to conventional surface pressure measurements for characterizing the monolayer. Furthermore, we demonstrate the effect of lipid density on the diffusional behavior of membrane-bound components. We exploit the sensitivity of FCS to characterize protein interactions with the lipid monolayer in a regime in which the monolayer physical properties are not altered. To demonstrate the potential of our approach, we analyzed the diffusion behavior of objects of different nature, ranging from a small peptide to a large DNA-based nanostructure. Moreover, in this work we quantify the surface viscosity of lipid monolayers. We present a detailed strategy for the conduction of point FCS experiments on lipid monolayers, which is the first step toward extensive studies of protein-monolayer interactions.

Kinetic control of the coverage of oil droplets by DNA-functionalized colloids

We report a study of reversible adsorption of DNA-coated colloids on complementary functionalized oil droplets. We show that it is possible to control the surface coverage of oil droplets using colloidal particles by exploiting the fact that, during slow adsorption, compositional arrest takes place well before structural arrest occurs. As a consequence, we can prepare colloid-coated oil droplets with a "frozen" degree of loading but with fully ergodic colloidal dynamics on the droplets. We illustrate the equilibrium nature of the adsorbed colloidal phase by exploring the quasi-two-dimensional phase behavior of the adsorbed colloids under the influence of depletion interactions and present simulations of a simple model that illustrates the nature of the compositional arrest and the structural ergodicity.

Diffusional motion as a gauge of fluidity and interfacial adhesion. Supported alkylphosphonate monolayers

We report on the use of diffusion measurements to gauge the fluidity and surface binding properties of a molecular monolayer. The monolayer film consists of octadecyl-1-phosphonic acid (ODPA) and controlled amounts of a lyso-phosphatidic acid tagged with the fluorescent probe BODIPY (BLPA). The monolayer films were formed using a Langmuir-Blodgett (LB) trough and deposited onto a glass slide. Monolayer morphology was characterized during film formation using Brewster angle microscopy (BAM). Fluorescence Recovery After Photobleaching (FRAP) microscopy was used to measure translational diffusion of BLPA and Fluorescence Anisotropy Decay Imaging (FADI) was used to measure rotational diffusion of the BLPA chromophore. These results provide information on the motional freedom of the probe and, importantly, on the strength of interaction between the probe and the support. Compositional variations in the monolayer give rise to changes in constituent dynamics that reflect intermolecular interactions.

Brownian diffusion of a partially wetted colloid

The dynamics of colloidal particles at interfaces between two fluids plays a central role in microrheology, encapsulation, emulsification, biofilm formation, water remediation and the interface-driven assembly of materials. Common intuition corroborated by hydrodynamic theories suggests that such dynamics is governed by a viscous force lower than that observed in the more viscous fluid. Here, we show experimentally that a particle straddling an air/water interface feels a large viscous drag that is unexpectedly larger than that measured in the bulk. We suggest that such a result arises from thermally activated fluctuations of the interface at the solid/air/liquid triple line and their coupling to the particle drag through the fluctuation-dissipation theorem. Our findings should inform approaches for improved control of the kinetically driven assembly of anisotropic particles with a large triple-line-length/particle-size ratio, and help to understand the formation and structure of such arrested materials.

Dynamic mechanical properties of a polyelectrolyte adsorbed insoluble lipid monolayer at the air-water interface

Polymers have been used to stabilize interfaces or to tune the mechanical properties of interfaces in various contexts, such as in oil emulsions or biological membranes. Although the structural properties of these systems are relatively well-studied, instrumental limitations continue to make it difficult to understand how the addition of polymer affects the dynamic mechanical properties of thin and soft films. We have solved this challenge by developing a new instrument, an optical-tweezer-based interface shear microrheometer (ISMR). With this technique, we observed that the interface shear modulus, G*, of a dioctadecyldimethylammonium chloride (DODAC) monolayer at the air-water interface significantly increased with adsorption of polystyrenesulfonate (PSS). In addition, the viscous film (DODAC monolayer) became a viscoelastic film with PSS adsorption. At a low salt concentration, 10 mM of NaCl in the subphase, the viscoelasticity of the DODAC/PSS composite was predominantly determined by a particular property of PSS, that is, it behaves as a Gaussian chain in a θ-solvent. At a high salt concentration, 316 mM of NaCl, the thin film behaved as a polymer melt excluding water molecules.

Micro and macrorheology at fluid-fluid interfaces

Interfacial transport phenomena play an important role in the dynamics of liquid interfaces found in emulsions, foams, and membranes. Both macroscopic and microscopic measurements of interfacial transport and rheology can be made, the former typically relying on the use of at least millimeter-scale probes, and the latter exploiting the motion of micrometer-scale probes. Recent publications have shown multiple orders of magnitude differences between experimentally observed diffusivities in passive microrheology, and the diffusivities expected based on macroscopic measurements of the surface rheology. In the present work, interfacial rheological measurements were made with both microrheological and macrorheological methods and the results are compared for different monolayers at an air-water interface. We have identified multiple aspects of particle-tracking microrheology that can contribute to orders-of-magnitude disagreement with macrorheological methods. In particular, unintentional tracking of particles not residing at the interface, the presence of large-scale interfacial heterogeneities, and underestimating static noise can all decrease estimates of surface viscosity from particle-tracking microrheology by orders of magnitude. After taking care to address these artifacts, we show that viscosities obtained from both methods agree well for poly(tert-butyl methacrylate) (PtBMA), and for dipalmitoylphosphatidylcholine (DPPC), but disagree by orders of magnitude for hexadecanol. In poly(tert-butyl acrylate) (PtBA), large-scale heterogeneities prevented us from obtaining representative surface viscosities. By making surface viscosity measurements in an interfacial stress rheometer (ISR) with needles of different aspect ratio, we show that compressibility or Marangoni stress related effects may be contributing to the orders of magnitude disagreement in micro and macrorheological measurements observed in the hexadecanol system.

Particle laden fluid interfaces: dynamics and interfacial rheology

We review the dynamics of particle laden interfaces, both particle monolayers and particle+surfactant monolayers. We also discuss the use of the Brownian motion of microparticles trapped at fluid interfaces for measuring the shear rheology of surfactant and polymer monolayers. We describe the basic concepts of interfacial rheology and the different experimental methods for measuring both dilational and shear surface complex moduli over a broad range of frequencies, with emphasis in the micro-rheology methods. In the case of particles trapped at interfaces the calculation of the diffusion coefficient from the Brownian trajectories of the particles is calculated as a function of particle surface concentration. We describe in detail the calculation in the case of subdiffusive particle dynamics. A comprehensive review of dilational and shear rheology of particle monolayers and particle+surfactant monolayers is presented. Finally the advantages and current open problems of the use of the Brownian motion of microparticles for calculating the shear complex modulus of monolayers are described in detail.

Correlated diffusion of colloidal particles near a liquid-liquid interface

Optical microscopy and multi-particle tracking are used to investigate the cross-correlated diffusion of quasi two-dimensional colloidal particles near an oil-water interface. The behaviors of the correlated diffusion along longitudinal and transverse direction are asymmetric. It is shown that the characteristic length for longitudinal and transverse correlated diffusion are particle diameter and the distance from particle center to the interface, respectively, for large particle separation . The longitudinal and transverse correlated diffusion coefficient and are independent of the colloidal area fraction when , which indicates that the hydrodynamic interactions(HIs) among the particles are dominated by HIs through the surrounding fluid for small . For high area fraction , the power law exponent for the spatial decay of begins to decrease, which suggests the HIs are more contributed from the 2D particle monolayer self for large .

Solid character of membrane ceramides: a surface rheology study of their mixtures with sphingomyelin

The compression and shear viscoelasticities of egg-ceramide and its mixtures with sphingomyelin were investigated using oscillatory surface rheology performed on Langmuir monolayers. We found high values for the compression and shear moduli for ceramide, compatible with a solid-state membrane, and extremely high surface viscosities when compared to typical fluid lipids. A fluidlike rheological behavior was found for sphingomyelin. Lateral mobilities, measured from particle tracking experiments, were correlated with the monolayer viscosities through the usual hydrodynamic relationships. In conclusion, ceramide increases the solid character of sphingomyelin-based membranes and decreases their fluidity, thus drastically decreasing the lateral mobilities of embedded objects. This mechanical behavior may involve important physiological consequences in biological membranes containing ceramides.

Interface shear microrheometer with an optically driven oscillating probe particle

We report the first experimental demonstration of an active interfacial shear microrheometer (ISMR) that uses a particle trapped by oscillating optical tweezers (OT) to probe the shear modulus G(s)(*)(ω) of a gas/liquid interface. The most significant advantages of the oscillating OT in a rheology study are: (1) very high sensitivity compared to other active microrheology methods and (2) the ability to measure both the real and imaginary components of the complex shear modulus without relying on the use of Kramers-Kronig relation, which can be problematic at low frequencies for most of the passive methods. We demonstrate the utilities of our ISMR in two case studies: (1) a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine monolayer and (2) a composite of poly(styrene sulfonate) and dioctadecyldimethylammonium at the air/water interface in regimes where no other active instruments can explore.

Interfacial rheology through microfluidics

The bulk properties and structural characteristics of emulsions arise substantially from their interfacial rheology, which depends strongly on surfactant mass transfer and its coupling to flow. Typical methods used to measure such properties often employ simpler flows and larger drops than those encountered in typical processing applications. Mass transfer mechanisms are governed by droplet size; therefore experimentation at length scales typical of those encountered in applications is desired. Utilizing a microfluidic approach allows high-throughput experimentation at relevant length scales and with adjustable flow dynamics. Using a microfluidic device that facilitates the measurement of interfacial tension in two-phase droplet flows, particle tracers are also used to determine the droplet internal circulation velocity as a measure of interfacial mobility. Combining these measurements in a single device, the coupling between interfacial tension, interfacial retardation, and surfactant mass transfer is explored and mass transfer coefficients and interfacial mobility are measured for a two-phase system containing a diffusing surfactant. Such a device is also used to probe the deformability of elastic capsules and viscoelastic biological cells.

Active microrheology and simultaneous visualization of sheared phospholipid monolayers

Two-dimensional films of surface-active agents-from phospholipids and proteins to nanoparticles and colloids-stabilize fluid interfaces, which are essential to the science, technology and engineering of everyday life. The 2D nature of interfaces present unique challenges and opportunities: coupling between the 2D films and the bulk fluids complicates the measurement of surface dynamic properties, but allows the interfacial microstructure to be directly visualized during deformation. Here we present a novel technique that combines active microrheology with fluorescence microscopy to visualize fluid interfaces as they deform under applied stress, allowing structure and rheology to be correlated on the micron-scale in monolayer films. We show that even simple, single-component lipid monolayers can exhibit viscoelasticity, history dependence, a yield stress and hours-long time scales for elastic recoil and aging. Simultaneous visualization of the monolayer under stress shows that the rich dynamical response results from the cooperative dynamics and deformation of liquid-crystalline domains and their boundaries.

Nanoscale mechanical probing of supported lipid bilayers with atomic force microscopy

We present theory and experiments for the force-distance curve F(z(0)) of an atomic force microscope (AFM) tip (radius R) indenting a supported fluid bilayer (thickness 2d). For realistic conditions the force is dominated by the area compressibility modulus κ(A) of the bilayer and, to an excellent approximation, given by F=πκ(A)Rz(0)(2)/(2d-z(0))(2). The experimental AFM force curves from coexisting liquid ordered and liquid disordered domains in three-component lipid bilayers are well described by our model, which provides κ(A) in agreement with literature values. The liquid ordered phase has a yieldlike response that we model as due to the breaking of hydrogen bonds.

Rheological properties of a two phase lipid monolayer at the air/water interface: effect of the composition of the mixture

Many biologically relevant monolayers show coexistence of discrete domains of a long-range ordered condensed phase dispersed in a continuous, disordered, liquid-expanded phase. In this work, we determined the viscous and elastic components of the compressibility modulus and the shear viscosity of monolayers exhibiting phase coexistence with the aim at elucidating the contribution of each phase to the observed monolayer mechanical properties. To this purpose, mixed monolayers with different proportions of distearoylphosphatidylcholine (DSPC) and dimyristoylphosphatidylcholine (DMPC) were prepared and their rheological properties were analyzed. The relationship between the phase diagram of the mixture at 10 mN m(-1) and the rheological properties was studied. We found that the monolayer shear viscosity is highly dependent on the presence of domains and on the domain density. In turn, the monolayer compressibility is only influenced by the presence of domains for high domain densities. For monolayers that look homogeneous on the micrometer scale (DSPC amount lower that 23 mol %), all the analyzed rheological properties remain similar to those observed for pure DMPC monolayers, indicating that in this proportion range the DSPC molecules contribute as DMPC to the surface rheology in spite of having hydrocarbon chains four carbons longer.

Interfacial microrheology as a tool to study viscoelastic transitions in nanoconfined soft matter

We present a method to perform in situ microrheological measurements on monolayers of soft materials undergoing viscoelastic transitions under compression. Using the combination of a Langmuir trough mounted on the inverted microscope stage of a laser scanning confocal microscope we track the motion of individual fluorescent quantum dots partly dispersed in monolayers spread at the air-water interface. From the calculated mean square displacement of the probe particles and extending a well established scheme of the generalized Stokes-Einstein relation in bulk to the interface we arrive at the viscoelastic modulus for the respective monolayers as a function of surface density. Measurements on monolayers of glassy as well as nonglassy polymers and a standard fatty acid clearly show sensitivity of our technique to subtle variations, in the viscoelastic properties of the highly confined materials under compression. Evidence for possible spatial variations of such viscoelastic properties at a given surface density for the fatty acid monolayer is also provided.

Combined passive and active microrheology study of protein-layer formation at an air-water interface

We investigate the mechanical properties of layers of the protein beta-lactoglobulin during their formation at the air-water interface using a combination of passive and active microrheological techniques. The passive microrheology, which employs multiple particle tracking measurements using spherical colloids, indicates that the interfacial rheology evolves over time through three stages as protein adsorbs at the interface: (i) an increase in viscosity, (ii) a period of spatial heterogeneity in which the interface contains elastic and viscous regions, and (iii) the development of a uniformly rigid elastic film. Varying solution pH between pH = 5.2, the isoelectric point of beta-lactoglobulin, and pH = 7.0 has no qualitative effect on this mechanical evolution. The active microrheology, which employs ferromagnetic nanowires rotating in response to magnetic torques, similarly shows an increasing interfacial viscosity at early times and evidence of mechanical heterogeneity at intermediate times. However, at late times, the nanowire mobility becomes strongly pH dependent. For pH = 5.2, the layer responds as a rigid elastic film to the stress imposed by the wire. For pH = 7.0, it displays a viscous response that contrasts with the passive measurements. We associate this contrast with a nonlinear response to the wire at late times that reflects a low yield stress of the film at higher pH. This ability to compare passive and active measurements demonstrates the advantage of applying multiple microrheological methods to resolve ambiguity in any single approach.

Combined macro- and microrheometer for use with Langmuir monolayers

A Langmuir monolayer trough that is equipped for simultaneous microrheology and standard rheology measurements has been constructed. The central elements are the trough itself with a full range of optical tools accessing the air-water interface from below the trough and a portable knife-edge torsion pendulum that can access the interface from above. The ability to simultaneously measure the mechanical response of Langmuir monolayers on very different length scales is an important step for our understanding of the mechanical response of two-dimensional viscoelastic networks.

Microrheology: a review of the method and applications

A set of local mechanical probes has been developed over the last ten years, allowing a kind of dynamical mechanical testing known as microrheology. This paper provides a short introductory review of these methods of performing rheology, comparing them to conventional rheometry, and highlighting the major advantages. The authors also share their outlook on some of the most promising and fastest developing areas that are being studied though microrheology, in the areas of biophysics and soft matter.

Apparent microrheology of oil-water interfaces by single-particle tracking

We investigate the dynamics of charged microparticles at polydimethylsiloxane (oil)-water interfaces using Pickering emulsions as an experimental template. The mobility of the charged particles depends largely on the viscoelastic properties of the oil phase and the wettability of the solid particles. In addition, we have explored the potential of developing microrheology at liquid-liquid interfaces from the single-particle tracking technique. The apparent loss modulus, storage modulus, and relaxation time of the oil-water interfaces obtained from singe-particle microrheology depend strongly on the surface nature of the tracer particles, especially when the oil phase is viscoelastic.

Two-particle microrheology of quasi-2D viscous systems

We study the spatially correlated motions of colloidal particles in a quasi-2D system (human serum albumin protein molecules at an air-water interface) for different surface viscosities eta s. We observe a transition in the behavior of the correlated motion, from 2D interface dominated at high eta s to bulk fluid dependent at low eta s. The correlated motions can be scaled onto a master curve which captures the features of this transition. This master curve also characterizes the spatial dependence of the flow field of a viscous interface in response to a force. The scale factors used for the master curve allow for the calculation of the surface viscosity eta s that can be compared to one-particle measurements.

Dynamics of charged microparticles at oil-water interfaces

Solid-stabilized emulsions have been used as a model system to investigate the dynamics of charged microparticles with diameters of 1.1 microm at oil-water interfaces. Using confocal microscopy, we investigated the influences of interfacial curvature, cluster size, and temperature on the diffusion of solid particles. Our work suggests that a highly curved emulsion interface slows the motion of solid particles. This qualitatively supports the theoretical work by Danov et al. (Danov, K. D.; Dimova, R.; Pouligny, B. Phys. Fluids 2000, 12, 2711); however, the interfacial curvature effect decreases with increasing oil-phase viscosity. The diffusion of multiparticle clusters at oil-water interfaces is a strong function of cluster size and oil-phase viscosity and can be quantitatively related to fractal dimension. Finally, we report the influence of temperature and quantify the diffusion activation energy and friction factor of the particles at the investigated oil-water interfaces.

Autonomously moving nanorods at a viscous interface

We study the autonomous motion of catalytic nanorods in Gibbs monolayers. The catalytic activity of the rods on a hydrogen peroxide aqueous subphase gives rise to anomalous translational and rotational diffusion. The rods perform a Levy-walk superdiffusive motion that can be decomposed into thermal orientation fluctuations and an active motion of the rods with a constant velocity along their long axis. Since interfacial dissipation increases relative to bulk phase dissipation when miniaturizing the size of objects moving in the interface, the autonomous nanorods allow for precise measurements of surface shear viscosities as low as a few nN s/m. The cross over from active motion toward passive diffusion when increasing the surfactant concentration is explained by a loss of friction asymmetry of the rods.

Compactification of a Myelin Mimetic Langmuir Monolayer upon Adsorption and Unfolding of Myelin Basic Protein

The surface shear viscosity of a myelin mimetic Langmuir monolayer is investigated upon adsorption of myelin basic protein (MBP). We measure an increase of the surface shear viscosity at picomolar concentrations of the protein, suggesting that the globular conformation of MBP changes upon adsorption at the monolayer. The conformational change enables hydrodynamic interactions of the proteins, with a typical separation of hundreds of nanometers. This unfolding is essential for the compactification of the myelin sheath, serving an enhanced saltatory signal transduction in vertebrates. The viscometry used extends the sensitivity of standard surface viscometers toward lower viscosities.

Linear dependence of surface drag on surface viscosity

Flow at an air-water interface is limited by drag from both the two-dimensional surface and three-dimensional subphase. Separating these contributions to the interfacial drag is necessary to measure surface viscosity as well as to understand the influence of the interface on flow. In these experiments, a magnetic needle floating on a monolayer-covered air-water interface is put in motion by applying a constant magnetic force, F(m). The needle velocity varies exponentially with time, reaching a terminal velocity F(m)/C, in which C is the drag coefficient. C is shown to be linearly proportional to the monolayer surface viscosity, eta(s), for dipalmitoylphosphatidylcholine monolayers in the condensed phase by comparison to surface viscosity measured by channel viscometry.