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.     

Film drainage between two surfactant-coated drops colliding at constant approach velocity

The drainage of the intervening continuous phase film between two drops approaching each other at constant velocity under the influence of insoluble surfactant is investigated. The mathematical model to be solved is a coupled pair of fourth-order nonlinear partial differential equations which arise from the relationships governing the evolution of the film thickness and the surfactant interfacial concentration in the lubrication approximation. We adopt a simplified approach which uses lubrication theory to describe the flow within the drop, marking a departure from the conventional framework in which Stokes flow is assumed. When the model is solved numerically together with the relevant initial and boundary conditions, the results obtained are compared with those found in the literature using the "boundary integral" method to solve for the flow in the drop phase. The close agreement between the results inspires confidence in the predictions of the simplified approach adopted. The analysis on the effect of insoluble surfactant indicates that its presence retards the drainage of the film: The fully immobile interface limit is recovered even in the presence of a small amount of surfactant above a critical concentration; film rupture is either prolonged or prevented. The retardation of the film was attributed to gradients of interfacial tension which gave rise to the Marangoni effect. A study of the influence of various system parameters on the drainage dynamics was conducted and three regimes of drainage and possible rupture were identified depending on the relative magnitudes of the drop approach velocity and the van der Waals interaction force: Nose rupture, rim rupture, and film immobilization and flattening. Finally, the possibility of forming secondary droplets by encapsulating the continuous phase film into the coalesced drop at rupture was examined and quantified in light of these regimes.     

Effect of interparticle interactions on the rate of injection of charge carriers into electroactive polymer films

A phenomenological approach is used for deriving a difference equation for the density of reduced sites in films of electroactive polymers with conspicuous interparticle interactions. The approach involves simultaneous application of the lattice methods and Broensted’s rule. This leads to generalization of equations for the surface layer that are known in theory of surface tension for nonelectrolytic solutions. Together with the Poisson equation for electric potential, the derived relationships make a complicated system of differential equations. Nevertheless, it can be solved by iterative methods. In the framework of this approach, expressions for the rates of injection of charge carriers into polymer films are obtained. Within a first approximation with regard to allowance for the forces of short-range interactions, their influence on the rates of injection of electrons and protons into a film is discussed.     

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.     

The Dynamics of Marangoni-Driven Local Film Drainage between Two Drops

A study of Marangoni-driven local continuous film drainage between two drops induced by an initially nonuniform interfacial distribution of insoluble surfactant is reported. Using the lubrication approximation, a coupled system of fourth-order nonlinear partial differential equations was derived to describe the spatio-temporal evolution of the continuous film thickness and surfactant interfacial concentration. Numerical solutions of these governing equations were obtained using the Numerical Method of Lines with appropriate initial and boundary conditions. A full parametric study was undertaken to explore the effect of the viscosity ratio, background surfactant concentration, the surface Péclet number, and van der Waals interaction forces on the dynamics of the draining film for the case where surfactant is present in trace amounts. Marangoni stresses were found to cause large deformations in the liquid film: Thickening of the film at the surfactant leading edge was accompanied by rapid and severe thinning far upstream. Under certain conditions, this severe thinning leads directly to film rupture due to the influence of van der Waals forces. Time scales for rupture, promoted by Marangoni-driven local film drainage were compared with those associated with the dimpling effect, which accompanies the approach of two drops, and implications of the results of this study on drop coalescence are discussed. Copyright 2001 Academic Press.     

Motion of foam films in diverging-converging channels

Existing theories of the motion of foam films in capillaries often assimilate the pressure drop over the foam films to the static capillary pressure obtained from the Young-Laplace equation. Hence, they ignore the contribution of dynamic effects associated with the rapid stretching and contraction of the foam films to the overall viscous dissipation. This paper reports an investigation of the motion of foam films in axisymmetric diverging-converging channels, taking into account surface viscosity and elasticity. First, a phenomenological theory for the motion of the foam films is developed using simple physical arguments. We show that the displacement of the film obeys a nonlinear second-order differential equation, which can be solved numerically for the (dimensionless) distance from the inlet and the pressure drop as a function of time. Experiments with foam film motion, conducted using glass diverging-converging channels (minimum radius = 3.00 +/- 0,01 mm, maximum diameter = 7,98 +/- 0,01 mm) and nitrogen foam stabilized with sodium dodecyl sulfate (SDS) in brine, are discussed. For a single film motion in the diverging channel, we find that (a) the static pressure drop is a concave-upward function of distance and decreases from 1.0 to about 0.3, whereas (b) the dynamic pressure drop is concave downward and increases from 1 to a maximum of 1.3 and then decreases to 0.7. In the converging channel both the static and dynamic pressure drops are concave-downward functions, but the dynamic pressure drop values are always higher than the static ones. For two films the motions were found to be rather sensitive to the initial arrangement in the channel. The experiments are found to be in excellent agreement with the theoretical predictions. These observations imply that the large flow resistance obtained during foam flow in granular porous media, where converging-diverging channels are abundant, is largely due to the surface elasticity and viscosity of the films.     

Computer Simulation on TiO2 Nanostructure Films and Experimental Study Using Sol–Gel Method

Molecular dynamics simulation with an experimental work was performed on the TiO₂ nanostructure film. The Morse potential function was used for the interatomic interactions. Then, the equations of motion for molecules and atoms are solved by Verlet algorithm. The effects of deposition rate and the number of TiO₂ molecules were studied for morphology characterization of film surface. In addition, TiO₂ nanostructure film was prepared experimentally with the sol–gel dip-coating method. The results of MD simulations provide a reasonable compatibility with Dektak surface profiler, atomic force microscopy (AFM) and scanning electron microscopy (SEM) images due to the morphology and surface structure of films.     

Theory of phase transition kinetics with growth site impingement. I. Homogeneous nucleation

The nonlinear integral equations governing phase transition kinetics with homogeneous nucleation and growth site impingement are developed and solved to the first order for the two-dimensional case. It is shown that the fractional transformed area at time t is given approximately by a(t) = Kt³/(1 + Kt³). The iteration method used to get the solution is applicable to certain other nonlinear differential and integral equations. It is shown that the theory predicts the total number of growth sites formed, and that the nucleation rate and growth constants can be deduced from this and the gross kinetic data. The extension of the method of three-dimensional growth is indicated.     

Influences of hydration force and elastic strain energy on the stability of solid film in a very thin solid-on-liquid structure

Since hydration forces become very strong at short range and are particularly important for determining the magnitude of the adhesion between two surfaces or interaction energy, the influences of the hydration force and elastic strain energy due to hydration-induced layering of liquid molecules close to a solid film surface on the stability of a solid film in a solid-on-liquid (SOL) nanostructure are studied in this paper. The liquid of this thin SOL structure is a kind of water solution. Since the surface forces play an important role in the structure, the total free energy change of SOL structures consists of the changes in the bulk elastic energy within the solid film, the surface energy at the solid-liquid interface and the solid-air interface, and highly nonlinear volumetric component associated with interfacial forces. The critical wavelength of one-dimensional undulation, the critical thickness of the solid film, and the critical thickness of the liquid layer are studied, and the stability regions of the solid film have been determined. Emphasis is placed on calculation of critical values, which are the basis of analyzing the stability of the very thin solid film.     

Thinning of drying latex films due to surfactant

Lateral non-uniformities in surfactant distribution in drying latex films induce surface tension gradients at the film surface and lead to film thinning through surfactant spreading. Here we investigate the influence of the surfactant driven to the air-water interface, during the early stages of latex film drying, on the film thinning process which could possibly lead to film rupture. A film height evolution equation is coupled with conservation equations for particles and surfactant, within the lubrication approximation, and solved numerically, to obtain the film height, particle volume fraction, and surfactant concentration profiles. Parametric analysis identifies the effect of drying rate, dispersion viscosity and initial particle volume fraction on film thinning and reveals the conditions under which films could rupture. The results from surface profilometry conform qualitatively to the model predictions.     

Nonlinear surface wave instability for electrified Kelvin fluids

A weakly nonlinear approach is utilized here to discuss surface wave instability for two superposed electrified fluids of Kelvin type. The influence of a vertical electric field is discussed. The linear form for equations of motion is solved in the light of nonlinear boundary conditions. The method of multiple scales is used for the purpose of nonlinear perturbation. The surface wave response is governed by the well-known nonlinear Ginzburg-Landau equation rather than the transcendental dispersion relation in the linear scope. Although linear stability conditions are not available for arbitrary viscosity, the nonlinear analysis allowed deriving necessary and sufficient stability conditions. Moreover, at the marginal state, the nonlinear scope for stability is discussed through its dependence on the wavetrain frequency, in which short-wave disturbance is assumed to relax the linear transcendental terms. Besides the linear stability constraint, the nonlinear scope gives an additional constraint on the wavetrain frequency. Nonlinear stability criteria are derived and are performed in view of a nondimensional form. Furthermore, the nonlinear analysis is repeated for an arbitrary wave disturbance. A suitable choice for dimensionless form made it possible to relax transcendental terms included in stability conditions. Numerical calculations at the marginal state show that both the vertical electric field and the stratified fluid density play a dual role in the stability criteria. This dual role is the opposite to the dual role that the stratified viscosity plays in the stability profile. For the marginal state representation, numerical examination shows that elasticity plays a dual role in the stability criteria in a manner similar to that of the viscosity behavior.     

Refinement of the Theory of Electrodissolution of Difficultly-Soluble Compounds from Metal Surfaces: Taking into Account Nonuniform Film Thickness Along the Electrode Surface

An equation that describes the electrodissolution of a film of a difficultly-soluble compound from the surface of metallic electrode during a linear potential scan is derived and solved numerically. The model accounts for a nonuniform deposit distribution over the electrode surface and for the diffusion of the deposit particles through the film. Voltammograms for the compound electroreduction display peaks whose shape is dependent on the deposit distribution over thickness. The obtained results are analyzed.     

电毛细管中非线性PB积分方程及其数值解

依据电毛细管非线性Ｐｏｉｓｓｏｎ Ｂｏｌｔｚｍａｎｎ微分方程的物理原理,导出其积分形式的ＰＢ方程．并采用数值迭代法给出相应方程的数值解．数值计算只用到电势Ψ的离散值,不需要Ψ的导数值,从根本上解决了因电势在管壁陡然变化引起数值解法的困难．文中给出的计算实例表明该算法是正确的、有效的和高精度的（相对误差小于０．０１％）,且在ＰＣ机上容易实现．     

Instability of confined thin liquid film trilayers

The instability of a system in which three stratified thin liquid films are confined in a channel with parallel walls and the interior film is subject to van der Waals-driven breakup is examined in this work. We derive a model based on lubrication theory and consisting of a pair of nonlinear partial differential equations describing the position of the two liquid interfaces. A linear stability analysis is carried out to show that the effects of varying the boundary film thicknesses can be understood in terms of several known limits, including a supported monolayer, confined bilayer, and supported bilayer. Variation of the boundary film viscosities is shown in many cases to eliminate the supported-bilayer limit. The parameter regimes in which squeezing and bending modes dominate the initial growth are determined, and nonlinear simulations are used to show that the mode always switches to squeezing near rupture. It is also found that a multi-modal dispersion relation may be created by asymmetries in thickness ratio, but not viscosity ratio, even in the absence of asymmetric interfacial tensions. The results of this study are expected to be relevant to multiphase microfluidic systems and the lithographic printing process.     

Differential permeation and absorption of water vapor in polyacrylamide film

An investigation has been made of successive differential absorption and differential permeation of water vapor in polyacrylamide a t 30°C. The successive differential ab sorptions showed two types of non-Fickian anomalies: sigmoid type and two-stage type curves. The experimental data have been analyzed in terms of the Fick diffusion equation assuming a time-dependent approach of the surface concentration. The calculated family of absorption curves agreed with the experimental results. The permeation curves in the region of high and low pressure increments were apparently normal, but at medium pressures they showed anomalous behavior. It was found that in the differential type of permeation experiment the stress effect induced by a concentration gradient between the surfaces of the film was eliminated. By assuming the time-dependent approach of the equilibrium surface concentration, we calculated the time lag as a function of film thickness and applied the theory to the data for permeation through polyacrylamide film with different film thicknesses a t relatively small pressure intervals. The rate parameter calculated from permeation data was found to be in good agreement with that from successive differential absorption data.     

(苄基三乙基铵)双(1,3-二硫杂环戊烯-2-硫酮-4,5-二硫基)-金的三阶非线性光学性质

合成了一种新的配位化合物(苄基三乙基铵)双(1,3-二硫杂环戊烯-2-硫酮-4,5-二硫基)-金(BTEAADT). 利用旋涂技术制备了该材料与聚甲基丙烯酸甲酯(PMMA)掺杂的复合薄膜, 该材料在复合薄膜中的质量分数为1%. 采用Z扫描方法, 分别测试了该材料的乙腈溶液和该材料与PMMA复合薄膜在波长为1064 nm, 脉宽为20 ps条件下的三阶非线性光学特性. 同时还研究了复合薄膜的线性光学性质. Z扫描的结果表明, 复合薄膜和该材料的乙腈溶液都具有自散焦效应, 非线性折射率都是负值. 在实验条件下, 两者的非线性吸收效应都是可以忽略的. 经过计算得出溶液样品的非线性折射率为-1.459×10^-18 m²·W^-1, 复合薄膜样品的非线性折射率为-3.978×10^-15 m²·W^-1. 该材料在1064 nm处的非线性光学器件方面有潜在应用价值.     

Influence of electrostatic and chemical heterogeneity on the electric-field-induced destabilization of thin liquid films

A numerical model for thin liquid film (<100 nm) drainage in the presence of an external electric field is developed. Long-wave theory is applied to approximate and simplify the governing equations. A spatiotemporal film morphology evolution equation thus obtained is then solved using a combination of finite difference to resolve the spatial dimensions and an adaptive time step ODE solver for the temporal propagation. The effect of fluid properties, namely, viscosity and surface tension, on the film drainage time is observed for a homogeneous electric field, which leads to random dewetting spots. Electrically heterogeneous fields, achieved by modeling electrodes with various periodic patterns, are explored to identify their effect on the drainage time and behavior. Finally, the chemical heterogeneity of the substrate is coupled with the periodic electric heterogeneity to understand the implications of combined heterogeneity. It is observed that the introduction of any heterogeneity results in faster drainage of the film when compared to that of the homogeneous field. In all cases, the thin film is drained, leaving submicrometer-scale structures at the interface. Well-controlled surface patterns are found on the application of periodic heterogeneity. This study effectively demonstrates the immense potential of electrically induced thin film drainage as a means for faster de-emulsification and for the creation of ordered submicrometer-scale surface patterns on soft materials.     

The selectivity of triethylene glycol modified glassy carbon electrode for charged and uncharged pieces

A triethylene glycol modified glassy carbon electrode(TEG–GCE) was fabricated by a controlledpotential electrolysis procedure. The performance of the film on the modified electrode surface was investigated by cyclic voltammetry with different probes. It was firstly found that while neutral pieces could penetrate the TEG film on the GCE surface, the ionic pieces, whatever it is anion or cation, was blocked by the film. This property was successfully used for determining dopamine(DA) in the presence of ascorbic acid(AA) with differential pulse voltammetry(DPV).     

Tribology of thin wetting films between bubble and moving solid surface

This work shows a successful example of coupling of theory and experiment to study the tribology of bubble rubbing on solid surface. Such kind of investigation is reported for the first time in the literature. A theory about wetting film intercalated between bubble and moving solid surface was developed, thus deriving the non-linear evolution differential equation which accounted for the friction slip coefficient at the solid surface. The stationary 3D film thickness profile, which appears to be a solution of the differential equation, for each particular speed of motion of the solid surface was derived by means of special procedure and unique interferometric experimental setup. This allowed us to determine the 3D map of the lift pressure within the wetting film, the friction force per unit area and the friction coefficient of rubbing at different speeds of motion of the solid surface. Thus, we observed interesting tribological details about the rubbing of the bubble on the solid surface like for example: