Effect of interfacial mobility on rupture of thin stagnant films on a solid surface due to random mechanical perturbations

Previous analysis of Narsimhan [G. Narsimhan, J. Colloid Interface Sci. 287 (2005) 624-633] for the evaluation of rupture of a nondraining thin film on a solid support due to imposed random mechanical perturbations modeled as a Gaussian white noise has been extended for partially mobile gas-liquid interfaces. The average rupture time of film is evaluated by first passage time analysis (as the mean time for the amplitude of perturbation to become equal to film thickness). The interfacial mobility is accounted for through surface viscosity as well as Marangoni effect. The mean rupture time for partially mobile gas-liquid interface, as characterized by two dimensionless groups, dimensionless surface viscosity and Marangoni number, lies between the two extreme limits for fully mobile and immobile films. The critical wavenumber for minimum rupture time is shown to be insensitive to interfacial mobility. However, the critical dimensionless surface viscosity and critical Marangoni number at which the behavior of thin film deviates from that of fully mobile film and the behavior approaches that of fully immobile film are smaller for higher Hamaker constants, smaller film thickness and smaller surface potentials.     

Stability of draining plane-parallel films containing surfactants

The stability of partially mobile draining thin liquid films with respect to axisymmetric fluctuations was studied. The material properties of the interfaces (Gibbs elasticity, surface and bulk diffusions) were taken into account. When studying the long wave stability of films, the coupling between the drainage and perturbation flows was considered and the lubrication approximation was applied. Two types of wave modes were examined: radially-bounded and unbounded waves. The difference between the thickness of loss of stability, h(st), the transitional thickness, h(tr), at which the critical wave causing rupture becomes unstable, and the critical thickness, h(cr), when the film ruptures, is demonstrated. Both the linear and the non-linear theories give h(st) > h(tr) > h(cr). The numerical results show that the interfacial mobility does not significantly influence the thickness of the draining film rupture. The interfacial tension and the disjoining pressure are the major factors controlling the critical thickness. The available experimental data for critical thicknesses of foam and emulsion films show excellent agreement with the theoretical predictions. The important role of the electromagnetic retardation term in the van der Waals interaction is demonstrated. Other published theories of the film stability are discussed.     

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.     

Influence of interfacial rheology on foam and emulsion properties

Foams and emulsions are stabilized by surfactant monolayers that adsorb at the air-water and oil-water interfaces, respectively. As a result of monolayer adsorption, the interfaces become viscoelastic. We will describe experiments showing that foaming, emulsification, foam and emulsion stability, are strongly dependent upon the value of compression elasticity and viscosity. This will include excited surface wave devices for the measurement of surface viscoelasticity and thin film videointerferometry for the study of model films between air bubbles and emulsion drops.     

Stability of thin stagnant film on a solid surface with a viscoelastic air-liquid interface

Linear stability analysis for a film on a solid surface with a viscoelastic air-liquid interface is presented. The interfacial dilatational and shear viscoelastic properties were described by Maxwell models. Dilatational and shear interfacial elasticity and viscosity were shown to improve film stability. When the interfacial rheological properties are extremely large or small, the maximum perturbation growth coefficient is shown to reduce to those for immobile and mobile interfaces respectively. Calculated values of maximum growth coefficient for thin film stabilized by 0.5% beta-lactoglobulin approached those of mobile films for thick (>2000 nm) and those for immobile films for thin (<100 nm) films respectively with the values lying between the two limits for intermediate film thicknesses.     

Interfacial dilational rheological property and lamella stability of branched alkyl benzene sulfonates solutions

The dynamic dilational properties of branched alkyl benzene sulfonates at the air–water and decane–water interfaces were investigated by drop shape analysis, and their lamella stability was measured. The influences of time, dilational frequency, and bulk concentration on surface dilational elasticity and dilational viscosity were expounded. The results show that the molecular interaction controls the nature of adsorption film during lower concentration range and the film behaves elastic in nature. During higher concentration range, the diffusion-exchange process controls the dynamic dilational properties and the surface film shows remarkable viscoelasticity. An increase in hydrophobic chain length enhances the molecular interaction, which results in the increase of dilational parameters and lamella stability. The data correlation suggests that the ability to form a stable lamella is linked to the intrinsic surface dilational elasticity.     

短链烷基对多取代烷基苯磺酸盐界面性质的影响

利用悬挂滴方法研究了2,5-二乙基-4-壬基苯磺酸钠(292)、2,5-二丙基-4-壬基苯磺酸钠(393)和2,5-二丁基-4-壬基苯磺酸钠(494)在空气-水表面和正癸烷-水界面的扩张流变性质,考察了时间、界面压、工作频率及体相浓度对扩张弹性和粘性的影响。研究发现,在低表面活性剂浓度条件下,表面吸附膜类似弹性膜,其强度由膜内分子的相互作用决定;高浓度下体相与表面间的扩散交换过程控制表面膜的性质。油分子的插入导致界面吸附分子之间相互作用的削弱,扩散交换过程主导界面膜性质;但随着短链烷基长度增加,油分子的影响变小。表面膜的强度在吸附达到平衡前已经决定,而界面膜在吸附饱和后仍然随界面分子重排而变化。     

Manifestation of Gibbs Elasticity in Thin Films

The elasticity of multicomponent closed and partially open thin films is analyzed. The elastic modulus of a completely closed film is shown to be additive with respect to contributions that are due to the Gibbs elasticity and disjoining pressure. In the case of only one closed component (e.g., a surfactant), both contributions are inseparably related to each other and may be expressed one through the other. For films of surfactant solutions, the resultant expressions make it possible to explain the marked maximum (observed in many experiments) of the foaming capacity of solutions and stability of foams in the vicinity of the critical micellization concentration.     

Scanning force microscopy as a tool to investigate the properties of polyglycerol ester foams

Foamed products are a popular class of food products. The mechanism of stabilization of the air bubbles is often only partially understood. The current study aims at better understanding the stabilization of air-water interfaces through the low molecular weight surfactant polyglycerol ester (PGE). We chose PGE films as an exemplary case for a non-equilibrium situation at an air-water interface--a situation that requires the development of new experimental techniques. Several different film preparation and transfer methods onto solid substrates have been tested. The films were then investigated by scanning force microscopy, and structural artifacts associated to the sample preparation were identified and discussed. In addition to the study of Langmuir monolayers and Gibbs adsorption layers, we have proposed a new approach to investigate the skins of foam bubbles. We thereby were able to determine that PGE indeed covers bubbles by a multilayer structure and that the pH plays a role in the structuring of the films. We show that a combination of different film preparation methods allows us to get an insight into the aggregation behavior of PGE at the air-water interface and thereby better understand the stabilization mechanism of this particular surfactant.     

Effects of interface mobility on the dynamics of colliding bubbles

At its core, the outcome of the collision between air bubbles is determined by the hydrodynamic interaction forces, which in turn are strongly dependent on the tangential mobility of the gas–liquid interfaces. A clean gas–liquid interface is tangentially mobile, whereas the presence of surfactant contaminants can immobilise the interface. Bubbles with mobile surfaces coalescence much easier because of the low hydrodynamic resistance to drainage of the thin liquid film separating the colliding bubbles. In this opinion, we highlight recent experimental and numerical simulations demonstrating that in addition to the expected faster coalescence, mobile-surface bubbles can produce a much stronger rebound from a mobile liquid interface compared to an immobile one. The stronger rebound is explained by the lower viscous dissipation during collisions involving mobile surfaces. The role of the surface mobility in controlling the stability of gas or liquid emulsion should be reassessed in the light of these new findings.     

Plate coating: influence of concentrated surfactants on the film thickness

We present a large range of experimental data concerning the influence of surfactants on the well-known Landau-Levich-Derjaguin experiment where a liquid film is generated by pulling a plate out of a bath. The thickness h of the film was measured as a function of the pulling velocity V for different kinds of surfactants (C(12)E(6), which is a nonionic surfactant, and DeTAB and DTAB, which are ionic) and at various concentrations near and above the critical micellar concentration (cmc). We report the thickening factor α = h/h(LLD), where h(LLD) is the film thickness obtained without a surfactant effect, i.e., as for a pure fluid but with the same viscosity and surface tension as the surfactant solution, over a wide range of capillary numbers (Ca = ηV/γ, with η being the surfactant solution viscosity and γ its surface tension) and identify three regimes: (i) at small Ca α is large due to confinement and surface elasticity (or Marangoni) effects, (ii) for increasing Ca there is an intermediate regime where α decreases as Ca increases, and (iii) at larger (but still small) Ca α is slightly higher than unity due to surface viscosity effects. In the case of nonionic surfactants, the second regime begins at a fixed Ca, independent of the surfactant concentration, while for ionic surfactants the transition depends on the concentration, which we suggest is probably due to the existence of an electrostatic barrier to surface adsorption. Control of the physical chemistry at the interface allowed us to elucidate the nature of the three regimes in terms of surface rheological properties.     

CFD evaluation of drop retraction methods for the measurement of interfacial tension of surfactant-laden drops

Drop retraction methods are popular means of measuring the interfacial tension between immiscible polymers. Experiments show that two different drop retraction methods, imbedded fiber retraction (IFR) and deformed drop retraction (DDR), give inconsistent results when a surfactant is present on the surface of the drop. These inconsistencies are deemed to be due to dilution of the surfactant and due to gradients in interfacial concentration of surfactant along the drop surface. This physical picture is quantified for the simple case of a Newtonian drop in a Newtonian matrix, with an insoluble, nondiffusive surfactant at the interface. The drop is deformed in computational fluid dynamics simulations by shearing the matrix, and then allowed to retract. Dilution and interfacial tension gradients effects are found to be especially large at the early stages of retraction, making IFR unsuitable for measuring the interfacial tension of surfactant-laden interfaces. The effects of surfactant dilution and gradients are found to persist even at late stages of retraction, causing the DDR method to underestimate the equilibrium interfacial tension significantly. The largest underestimates occur when the drop viscosity is lower than the matrix viscosity.     

Factors controlling the formation and stability of air bubbles stabilized by partially hydrophobic silica nanoparticles

Air bubbles have been formed using partially hydrophobic silica nanoparticles as the stabilizer. The particles were of primary particle size 20 nm, chemically treated to different degrees with dichlorodimethylsilane to render them partially hydrophobic. Above a certain bubble size range (typically 80-microm diameter), the bubbles seemed to be almost indefinitely stable, while for any size above 20 microm their stability against disproportionation is far better than bubbles stabilized by any protein film investigated in previous studies. A possible theoretical justification for this observation is presented. Bubbles could be formed by shaking water with the particles, but a much higher volume fraction of bubbles was obtained by pressurizing the aqueous phase to 5 atm overnight followed by suddenly releasing the pressure to nucleate bubbles within the silica dispersion. Sonicating the silica dispersion before nucleation also gave more bubbles, which were also found to be more stable. There appeared to be an optimum degree of surface hydrophobicity that gave maximum foamability and foam stability, where around 20-33% of the silanol groups on the silica surface had been converted to dimethylsilane groups. However, a sharp increase in stability occurred when between 1.8 and 2 mol dm(-3) NaCl was also included in the aqueous phase. The change in stability due to inclusion of salt can be rationalized in terms of changes occurring in the value of the particle contact angle. The effects of increasing sonication and an optimum surface chemical treatment can be explained by the need to make the particles sufficiently hydrophobic so that they adsorb strongly enough, while at the same time minimizing their tendency to aggregate in the bulk aqueous phase, which hinders their adsorption. Furthermore, confocal laser scanning microscopy of the bubble dispersions suggests that a large volume fraction of stable bubbles is only formed when the particles adsorbed to the bubbles are also part of a spanning silica particle network in the bulk aqueous solution, forming a weak gel with a finite yield stress.     

Photodissociation of ICN at the liquid/vapor interface of water

The photodissociation of ICN adsorbed at the liquid/vapor interface of water is studied using classical molecular dynamics with nonadiabatic surface hopping. The cage escape, geminate recombination to form ICN and INC and the subsequent vibrational relaxation of these two molecules (on their ground electronic states) is compared with the same process in bulk water and with previous photodissociation studies at liquid interfaces. We find that the reduced surface density and weaker solvent-solute interactions give rise to reduced rate of nonadiabatic transitions and that the probability for cage escape at the interface is significantly enhanced due to the possibility that one or both of the photodissociation fragments desorb into the gas phase. The overall desorption probability varies from 75% to 92% for ICN initially located just below the Gibbs surface (50% bulk density) to ICN located just above the Gibbs surface, respectively. The corresponding geminate recombination probabilities are 18% and 9%, respectively. The vibrational relaxation rate of the recombined ICN is slower than in the bulk by a factor of 2.3.     

A generalized scale of free energy of excess adsorption of solute and absolute composition of the interfacial phase

Moles of a surfactant (gamma2(1)) absorbed per unit area of the solid-liquid interface estimated analytically from the difference of the solute molality in the bulk phase before and after adsorption have been quantitatively related to the absolute compositions deltan1 and deltan2 of the solvent and solute forming the inhomogeneous surface phase in contact with the bulk phase of homogeneous composition. By use of isopiestic experiments, negative values of gamma2(1) for the adsorption of inorganic salts onto a solid-liquid interface have been calculated in the same manner. From the linear plot of gamma2(1) versus the ratio of the bulk mole fractions of the solute and solvent, values of deltan1 and deltan2 have been evaluated under a limited range of concentrations. For the adsorption of the surfactant and the inorganic salt respectively onto the fluid interface, gamma2(1) values have been evaluated from the surface tension concentration data using the Gibbs adsorption equation. Gamma2(1) based on the arbitrary placement of the Gibbs dividing plane near the fluid interface is quantitatively related to the composition of the inhomogeneous surface phase. Also, the Gibbs equation for multicomponent solutions has been appropriately expressed in terms of a suitably derived coefficient m. Integrating the Gibbs adsorption equation for a multicomponent system, the standard free energy change, deltaG degrees, per unit of surface area as a result of the maximum adsorption gamma2(m) of the surfactant at fluid interfaces due to the change of the activity alpha2 of the surfactant in the bulk from zero to unity have been calculated. A similar procedure has been followed for the calculation of deltaG degrees for the surfactant adsorption at solid-liquid interfaces using thermodynamically derived equations. deltaG degrees values for surfactant adsorption for all such systems are found to be negative. General expressions of deltaG degrees for negative adsorption of the salt on fluid and solid-liquid interfaces respectively have also been derived on thermodynamic grounds. deltaG degrees for all such systems are positive due to the excess spontaneous hydration of the interfacial phase in the presence of inorganic salt. Negative and positive values of deltaG degree for excess surfactant and salt adsorption respectively have been discussed in light of a generalized scale of free energy of adsorption.     

Instability of thin liquid films between membranes

The conditions for instability of the thin liquid film between two plane-parallel membranes were derived taking into account the influence of the membrane tension, the membrane bending elasticity, the film viscosity and the disjoining pressure. It was shown that the liquid film could be unstable if the negative (attractive) disjoining pressure is predominant. The characteristic timeτ _m of growth of perturbation due to thermal or other fluctuations of the membrane shape increases with increasing the film viscosity, the membrane tension and the membrane bending elasticity, and decreasing the film thickness and the negative disjoining pressure. It is of the order of 10^?2÷10³ sec. When the membranes approach each other at certain value of the average film thicknessh _cr called critical, the fastest growing perturbations lead to formation of a liquid film with smaller (or zero) thickness. It was found that the critical thickness increases with increasing the negative disjoining pressure and the membrane area and decreasing the membrane tension and the bending elasticity having typical values of the order of 10^?6÷10^?5 cm. The case of a membrane approaching a solid plane was also considered. Excluding the small differences in numerical coefficients the results are similar to the case of two identical membranes.     

Interfacial dilational properties of tri-substituted alkyl benzene sulfonates at air/water and decane/water interfaces

The dilational rheological properties of absorbed film of three pairs of structural isomers, tri-substituted alkyl benzene sulfonates, at the air-water and decane-water interfaces have been investigated by drop shape analysis method. The influences of bulk concentration on dilational elasticity and viscosity were expounded. Interfacial tension relaxation method was employed to obtain dilational parameters in a reasonably broad frequency range. The experimental results showed that the meta-alkyl to sulfonate group plays a crucial role in the interfacial dilational properties: the longer meta-alkyl will lead to higher dilational parameters for air-water interface and lower ones for decane-water interface when the total alkyl carbon numbers are equal. For alkyl benzene sulfonates with shorter meta-alkyl, the surface dilational properties are similar to interfacial dilational properties, whereas the surface dilational parameters are obviously higher than the interfacial dilational parameters for alkyl benzene sulfonates with longer meta-alkyl in general. The possible mechanism has been proposed and ensured by Cole-Cole plots.     

聚氧乙烯醚类表面活性剂表面扩张粘弹性质研究

研究了非离子表面活性剂壬基苯酚聚氧乙烯醚NP-8, NP-10和NP-12水溶液的表面扩张粘弹性质, 考察了氧乙烯数的变化对表面吸附膜特性的影响. 研究结果表明, 三种表面活性剂的扩张弹性随着工作频率的增大而增大, 扩张粘性则在0.1~0.01 Hz范围内通过不明显的极大值; 扩张弹性和粘性随着浓度的增加在同一浓度处通过一个极大值; 氧乙烯数从8增加到12, 表面扩张弹性、粘性和相角的变化不大. 从发生在表面上和表面附近的微观弛豫过程的角度对实验结果进行了讨论.     

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.