A note on the coating of an inclined plane in the presence of soluble surfactant

We consider the flow of a thin liquid film coating an inclined plane in the presence of a soluble surfactant. A two-dimensional three-equation model is derived using lubrication theory in the rapid diffusion limit and then used to investigate the stability of the fluid height and the surfactant surface and bulk concentrations. We present solutions for an insoluble surfactant system, which are then contrasted with those obtained for a system containing a soluble surfactant; both transient growth and fully nonlinear two-dimensional simulation results are discussed. Our results indicate that the characteristics of the fingering phenomena which accompany the flow are altered by the effects of solubility. In particular, we find that these effects de-stabilise the system further over an intermediate range of surfactant solubility.     

Role of desorption kinetics in determining marangoni flows generated by using electrochemical methods and redox-active surfactants

We report quantitative measurements of Marangoni flows generated at the surfaces of aqueous solutions by using water-soluble redox-active surfactants in combination with electrochemical methods. These measurements are interpreted within the framework of a simple model that is based on lubrication theory and the proposition that the kinetics of the desorption of redox-active surfactants from the surfaces of aqueous solutions plays a central role in determining the strength of the Marangoni flow. The model predicts that the leading edge velocity of the Marangoni flow will decay exponentially with time and that the rate constant for the decay of the velocity can yield an estimate of the surfactant desorption rate constant. Good agreement between theory and experiments was found. By interpreting experimental measurements of electrochemically generated Marangoni flows within the framework of the model, we conclude that the desorption rate constant of the redox-active surfactant Fc(CH(2))(11)-N(+)(CH(3))(3)Br(-), where Fc is ferrocene, is 0.07 s(-)(1). We also conclude that the ionic strength of the aqueous solution has little effect on the desorption rate constant of the ferrocenyl surfactant.     

Chemical oscillation with periodic adsorption and desorption of surfactant ions at a water/nitrobenzene interface.

Chemical oscillations with periodic adsorption and desorption of surfactant ions, alkyl sulfate ions, at a water/nitrobenzene interface have been investigated. The interfacial tension was measured with a quasi elastic laser scattering (QELS) method and the interfacial electrical potential was obtained. We found that this oscillation consists of a series of abrupt adsorptions of ions, followed by a gradual desorption. In addition, we observed that each abrupt adsorption was always accompanied by a small waving motion of the liquid interface. From the analysis of the video images of the liquid interface or bulk phase, we could conclude that each abrupt adsorption is caused by nonlinear amplification of mass transfer of ions from the bulk phase to the liquid interface by a Marangoni convection, which was generated due to local adsorption of the surfactant ions at the liquid interface that resulted in the heterogeneity of the interfacial tension. In the present paper, we describe the mechanism of the chemical oscillation in terms of the hydrodynamic effect on the ion adsorption processes, and we also show the interfacial chemical reaction with ion exchange during the ion desorption process.     

Marangoni stresses and surface compression rheology of surfactant solutions. Achievements and problems

In the presence of soluble surfactants, the motion of liquid surfaces involves Marangoni effects. As a consequence, the surfaces exhibit elastic responses, even frequently behaving as rigid surfaces, especially at low surfactant concentration. The Marangoni effects can be conveniently quantified introducing surface viscoelastic compression parameters that characterize the mechanical response of the surface near equilibrium. Many experimental techniques allow measuring the viscoelastic parameters. However, many difficulties are encountered during the interpretation of the surface response in the various types of hydrodynamic velocity fields involved in the different techniques. The role of adsorption and desorption energy barriers appears crucial, despite the fact that little is known yet about their values. In this short review, we will present examples illustrating the different problems.     

Dewetting behavior of aqueous cationic surfactant solutions on liquid films

Previous experimental work has shown that the spreading of a drop of aqueous anionic surfactant solution on a liquid film supported by a negatively charged solid substrate may give rise to a fingering instability (Afsar-Siddiqui, A. B.; Luckham P, F.; Matar, O. K. Langmuir 2003, 19, 703-708). However, upon deposition of a cationic surfactant on a similarly charged support, the surfactant will adsorb onto the solid-liquid interface rendering it hydrophobic. Water is then expelled from the hydrophobic regions, causing film rupture and dewetting. In this paper, experimental results are presented showing how the surfactant concentration and film thickness affect the dewetting behavior of aqueous dodecyltrimethylammonium bromide solutions. At low surfactant concentrations and large film thicknesses, the film ruptures at a point from which dewetting proceeds. At higher concentrations and smaller film thicknesses, the ruptured region is annular in shape and fluid moves away from this region. At still higher concentrations and smaller film thicknesses, the deposited surfactant forms a cap at the point of deposition that neither spreads nor retracts. This variation in dewetting mode is explained by considering the relative Marangoni and bulk diffusion time scales as well as the mode of assembly of the surfactant adsorbed on the solid surface.     

Role of surfactants on the approaching velocity of two small emulsion drops

Here we present the exact solution of two approaching spherical droplets problem, at small Reynolds and Peclet numbers, taking into account surface shear and dilatational viscosities, Gibbs elasticity, surface and bulk diffusivities due to the presence of surfactant in both disperse and continuous phases. For large interparticle distances, the drag force coefficient, f, increases only about 50% from fully mobile to tangentially immobile interfaces, while at small distances, f can differ several orders of magnitude. There is significant influence of the degree of surface coverage, θ, on hydrodynamic resistance β for insoluble surfactant monolayers. When the surfactant is soluble only in the continuous phase the bulk diffusion suppresses the Marangoni effect only for very low values of θ, while in reverse situation, the bulk diffusion from the drop phase is more efficient and the hydrodynamic resistance is lower. Surfactants with low value of the critical micelle concentration (CMC) make the interfaces tangentially immobile, while large CMC surfactants cannot suppress interfacial mobility, which lowers the hydrodynamic resistance between drops. For micron-sized droplets the interfacial viscosities practically block the surface mobility and they approach each other as solid spheres with high values of the drag coefficient.     

An Insoluble Surfactant Model for a Vertical Draining Free Film

A mathematical model is constructed to study the evolution of a vertically oriented thin liquid film draining under gravity when there is an insoluble surfactant with finite surface viscosity on its free surface. Lubrication theory for this free film results in three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity, and the surfactant transport at leading order. We will show that in the limit of large surface viscosity, the evolution of the free surface is that obtained for the tangentially immobile case. For mobile films with small surface viscosity, transition from a mobile to an essentially immobile film is observed for large Marangoni effects. It is verified that increasing surface viscosity and the Marangoni effect retard drainage, thereby enhancing film stability. The theoretical results are compared with experiment; the purpose of both is to act as a model problem to evaluate the effectiveness of surfactants for potential use in foam-fabrication processes. Copyright 2000 Academic Press.     

Marangoni flow of Ag nanoparticles from the fluid-fluid interface

Fluid flow is observed when a volume of passivated Ag nanoparticles suspended in chloroform is mixed with a water/ethanol (v/v) mixture containing acidified 11-mercaptoundecanoic acid. Following mechanical agitation, Ag nanoparticles embedded in a film are driven from the organic-aqueous interface. A reddish-brown colored film, verified by transmission electron microscopy to contain uniformly dispersed Ag nanoparticles, is observed to spontaneously climb the interior surface of an ordinary, laboratory glass vial. This phenomenon is recorded by a digital video recorder, and a measurement of the distance traveled by the film front versus time is extracted. Surface (interfacial) tension gradients due to surfactant concentration, temperature, and electrostatic potential across immiscible fluids are known to drive interface motion; this well-known phenomenon is termed Marangoni flow or the Marangoni effect. Experimental results are presented that show the observed mass transfer is dependent on an acid surfactant concentration and on the volume fraction of water in the aqueous phase, consistent with fluid flow induced by interfacial tension gradients. In addition, an effective desorption rate constant for the Marangoni flow is measured in the range of approximately 0.01 to approximately 1 s(-1) from a fit to the relative film front distance traveled versus time data. The fit is based on a time-dependent expression for the surface (interface) excess for desorption kinetics. Such flow suggests that purposeful creation of interfacial tension gradients may aid in the transfer of 2- and 3-dimensional assemblies, made with nanostructures at the liquid-liquid interface, to solid surfaces.     

Continuous-flow production of polymeric micelles in microreactors: experimental and computational analysis

The dynamics and stability of a thin, viscous film of volatile liquid flowing under the influence of gravity over a non-uniformly heated substrate are investigated using lubrication theory. Attention is focused on the regime in which evaporation balances the flow due to gravity. The film terminates above the heater at an apparent contact line, with a microscopically thin precursor film adsorbed due to the disjoining pressure. The film develops a weak thermocapillary ridge due to the Marangoni stress at the upstream edge of the heated region. As for spreading films, a more significant ridge is formed near the apparent contact line. For weak Marangoni effects, the film evolves to a steady profile. For stronger Marangoni effects, the film evolves to a time-periodic state. Results of a linear stability analysis reveal that the steady film is unstable to transverse perturbations above a critical value of the Marangoni parameter, leading to finger formation at the contact line. The streamwise extent of the fingers is limited by evaporation. The time-periodic profiles are always unstable, leading to the formation of periodically-oscillating fingers. For rectangular heaters, the film profiles after instability onset are consistent with images from published experimental studies.     

Spontaneous oscillations due to solutal Marangoni instability: air/water interface

Systems far from equilibrium are able to self-organize and often demonstrate the formation of a large variety of dissipative structures. In systems with free liquid interfaces, self-organization is frequently associated with Marangoni instability. The development of solutal Marangoni instability can have specific features depending on the properties of adsorbed surfactant monolayer. Here we discuss a general approach to describe solutal Marangoni instability and review in details the recent experimental and theoretical results for a system where the specific properties of adsorbed layers are crucial for the observed dynamic regimes. In this system, Marangoni instability is a result of surfactant transfer from a small droplet located in the bulk of water to air/water interface. Various dynamic regimes, such as quasi-steady convection with a monotonous decrease of surface tension, spontaneous oscillations of surface tension, or their combination, are predicted by numerical simulations and observed experimentally. The particular dynamic regime and oscillation characteristics depend on the surfactant properties and the system aspect ratio.      

Adsorption behavior and dilational rheology of the cationic alkyl trimethylammonium bromides at the water/air interface

The dynamic and equilibrium surface tensions of C(n)TAB solutions for n = 12, 14, and 16 are studied using ring and bubble pressure tensiometry. Together with respective literature values, including neutron reflectivity and dilational surface rheology measurements, the experimental data are analyzed on the basis of two theoretical models, the Frumkin model and a modified reorientation model that takes into account an intrinsic compressibility of adsorbed surfactant molecules. It turns out that this new reorientation model, earlier applied to nonionic surfactant adsorption layers, is also applicable to ionic surfactants and superior to the Frumkin isotherm. All adsorption properties of one particular surfactant can be described by a single set of model parameters.     

A simple adsorption model for ionic surfactants

In the past, few theoretical attempts have been made to describe quantitatively the adsorption of ionic surfactants at liquid interfaces. Well-known adsorption isotherms due to Frumkin or Hill–de Boer cannot respond to the specific electrostatic and geometric properties of the surfactant molecules. Our approach is based on a combination of the Gouy–Chapman theory with a modified Frumkin isotherm. The modification implies that the system is free to choose an optimal head group area and an optimal arrangement of the surfactant molecules in the interface as a function of bulk concentration. Interaction energies between neighbouring adsorbed surfactant molecules and between surfactant and water molecules are taken into consideration. The minimum of the Gibbs free energy of the system is equivalent to a minimal interfacial tension. Thus, the thermodynamically stable isotherm can be obtained as the lower envelope of the family of σ versus ln c isotherms resulting from different choices of the model parameters, including the area per molecule. According to the Gibbs equation, the Γ versus ln c adsorption isotherm is obtained as the derivative of this envelope. By variation of the model parameters, the envelope of the calculated adsorption isotherms can be fitted to experimental data of the interfacial tension versus bulk concentration. A computer program is used to calculate the σ versus c and the Γ versus ln c curves as well as to fit the parameters. Received: 28 October 1999/Accepted: 8 February 2000     

Surfactant-assisted spreading of a liquid drop on a smooth solid surface

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

Immiscible surfactant droplets on thin liquid films: spreading dynamics, subphase expulsion and oscillatory instabilities

After deposition of immiscible, surface-active liquids on thin liquid films of higher surface tension, Marangoni stresses thin the liquid film around the surfactant droplet and induce a radially outward flow. We observed an oscillatory instability, caused by temporary trapping and subsequent release of subphase liquid from underneath the surfactant droplet. Height profiles of the thin liquid films were monitored using optical interferometry and fluorescence microscopy, both in the vicinity of the deposited surfactant droplet and at larger distances. Numerical calculations based on the lubrication approximation are compared to the experimental results. Good agreement between the experimental and calculated far-field dynamics and values of the spreading exponents was found.     

MASS TRANSPORT EFFECTS ON THE STABILITY OF EMULSION: EMULSION FILMS WITH ACETIC ACID AND ACETONE DIFFUSING ACROSS THE INTERFACE

The stability of emulsions is studied using, as a model of two interacting drops, an aqueous film of a surfactant immersed in an oil phase. It is shown that the mass transfer of a solute across the film changes its life-time. This change depends on several parameters as the nature and concentration of the solute. the direction of mass transfer, the time elapsed after the formation of the film. The destabilizing effect, of the transfer is found to be much less pronounced when the solute is in the continuous water phase. The instability is ascribed to the Marangoni effect and/or to liquid flow from the film drawn by diffusion of the solute.     

Hydrodynamic instability of a thin viscous film between two drops

Linear stability analysis is employed to derive analytical expressions for the growth rate of disturbances applied to a thin plane-parallel film trapped between two drops. From these expressions, the band of unstable wavenumbers and the "most dangerous" wavenumber are identified for systems in the absence and presence of insoluble surfactant. Marangoni effects are shown to exert a stabilizing influence and reasonably good agreement with experimental observations is found. Subsequent nonlinear analysis indicated amplification of the disturbance growth rate beyond that suggested by linear theory as the film proceeded toward rupture.     

The use of isothermal titration calorimetry to assess the solubility enhancement of simvastatin by a range of surfactants

Surfactants are commonly used to increase the solubility of poorly water soluble drugs but the interactions between drug and surfactant can be complex and quantitative relationships can be hard to derive. One approach is to quantify the thermodynamics of interaction and relate these parameters to known solubility or dissolution rate enhancement data. Isothermal titration calorimetry (ITC) was used to measure the enthalpy and free energy of transfer of a model drug (simvastatin) to a number of surfactant (SDS, HTAB, SDCH and Brij 35) micelles. These data were then compared with the solubility enhancements determined for each surfactant using HPLC assays. As expected, there was correlation between the free energy of transfer for the drug to each surfactant and the solubility enhancement of that surfactant. Although the data set is limited, the results suggest that ITC screening of a range of surfactants against a poorly water soluble drug may allow the selection of the best potential solubilising surfactants.     

Analysis of tear film rupture: effect of non-Newtonian rheology

We investigate the rupture mechanism of a precorneal thin mucus coating sandwiched between the aqueous tear film and the corneal epithelial surface with a monolayer of surfactant overlying the aqueous layer. The Ostwald constitutive relation is employed to model mucus and a linear equation of state describing the relationship between surface tension and surfactant concentration is adopted. Three nonlinear coupled evolution equations governing the transport of surfactant, mucus, and total liquid layer thicknesses, based on lubrication theory and a perturbation expansion technique, have been derived. The resulting equations are solved numerically in order to explore the influence of the rheological properties of mucus, aqueous-mucus thickness ratio, aqueous-mucus interfacial tension, Marangoni number, and surfactant concentration on both the onset of instability and tear film evolution in the presence of van der Waals interactions, which could rupture the tear film. Our results reveal that the influence of rheological properties, aqueous-mucus thickness ratio, and interfacial tension on the time required for film rupture can be significant and varies considerably, depending on the magnitude of the Hamaker constants governing the strength of the van der Waals forces.     

Aqueous foam films stabilized by sodium naphthenates

Stratification of a foam liquid film drawn from aqueous solutions of sodium naphthenate at relatively high concentration is likely due to a lamellar liquid crystal-like structure within the film. Film stratification, resulting in stepwise thinning, has been observed in foam films formed from systems containing either moderate to high concentrations of surfactant or in films formed from solutions containing solid particles. At moderate surfactant concentrations, film stratification is likely due to layers of ordered spherical micelles as postulated in Wasan and Nikolov's model of film stratification. At high surfactant concentrations, stepwise thinning of the films and occurrence of domains of uniform color within the film suggest a lamellar liquid crystal-like structure within the film, potentially up to hundred or more oriented layers. The LLC-like structure inside the film can occur at concentrations below the lower limit of the LLC existence as a bulk phase.