Surface Tension Relaxation Research Articles

Adsorption Kinetics of Ionic Surfactants with Detailed Account for the Electrostatic Interactions

The problem of diffusion-controlled adsorption from a non-micellar solution of an ionic surfactant in the absence of added electrolyte is solved analytically for the case of small deviations from equilibrium. For that purpose the electro-diffusion equations of the transport of surfactant ions and counterions are combined with the Poisson–Boltzmann equation for the electrical field. The resulting set of equations is linearized and Laplace transform is applied. Analytical expression for the Laplace image of the adsorption is obtained in terms of elementary functions. Simple formulae for the short-time and long-time asymptotics of adsorption and surface tension relaxation are derived. To illustrate the effect of the electrostatic interactions we calculated the theoretical dependence of the characteristic relaxation time on the bulk surfactant concentration and surface potential for aqueous surfactant solutions in contact with various non-aqueous phases (air, heptane, decane, petroleum ether) and two surfactants: SDS and DTAB. The general trend is that the electrostatic effects decelerate the process of adsorption, as it could be expected. The derived exact analytical expressions quantifying these effects can be directly applied for the interpretation of experimental data for the kinetics of ionic surfactant adsorption. The reliability of our approach is verified through a comparison with other available theories.

Influence of elasticity and dynamic surface tension on the wave motion spectrum of a charged liquid surface

It is shown that the combined influence of the relaxation of viscosity and surface tension on the position of the boundary of the capillary wave spectrum established in a system is not a simple summation of each effect separately because of the nonlinearity of the dispersion equation in the corresponding physical parameters.

Adsorption Kinetics of C12E8 at the Air−Water Interface: Desorption from a Compressed Interface

The desorption of C 12 E 8 out of an overcrowded interface due to the sudden shrinkage of a pendant bubble in a quiescent surfactant solution is studied. A video-enhanced pendant bubble tensiometry is utilized for the measurement of the relaxation in surface tension due to the desorption of surfactant. The desorption process is found to be diffusive-kinetic mixed controlled. Rate constants of adsorption/desorption are computed by comparing these tension profiles with numerical solutions, which consider both bulk diffusion and kinetic desorption processes. The values of the kinetic rate constants of C 12 E 8 obtained from the desorption experiment are nearly the same as that obtained from the clean adsorption study (Lin, S. Y., et al., Langmuir 1996, 12, 6530). The concept that there exists a shift in controlling mechanism from diffusion control at dilute concentration to mixed diffusion-kinetic control at more elevated bulk concentration for C 12 E 8 is therefore confirmed.

Adsorption kinetics of soluble surfactants and the phase transition model 1. Theoretical simulation

Surfactants with strong cohesion can have purely diffusive adsorption and mixed re-equilibration relaxations. This idea is illustrated in this study by theoretical simulations of the relaxation in surface tension due to adsorption onto an initially clean planar interface and re-equilibration of an interface containing a monolayer which has been perturbed. A phase transition model is utilized to describe the adsorption kinetics of soluble surfactants with strong intermolecular attractions between the adsorbed molecules. The cohesion forces lead to the formation of a surface liquid phase, raise the energy barrier for desorption of the adsorbed molecule into the bulk sublayer and correspondingly lower the desorption rate. Novel regions are identified where the surface tension relaxation for adsorption onto a clean interface is diffusion controlled, and that for re-equilibration is mixed. The effects of the bulk concentration, the cohesion energy, and the compression ratio are also reported. Within these regions, adsorption experiments can be done to measure the diffusion coefficient, and re-equilibration experiments can be used to obtain the sorption rate constants.

Surface stresses and vacancies

Atomistic calculations for surface stress and the effect of vacancies on the surface stress have been carried out using a two-dimensional embedded-atom method model. Stresses due to the presence of the surface are large, localized within a few atomic planes of the surface and vary rapidly with depth with the net stress being a tension. The effect of vacancies at or near the surface is not localized within a few atomic planes of the surface, reduces the tension if in contact with the surface but increases the tension if below the surface. Vacancy configurations which provide the greatest relaxation of surface tension are generally not those with the lowest energy. None of these results should be specific to a two-dimensional model.

The effect of bulk concentration on surfactant adsorption processes: The shift from diffusion-control to mixed kinetic-diffusion control with bulk concentration.

The surface tension relaxation at interfaces between surfactant solutions and immiscible fluids is calculated by the rate that surfactant adsorbs in a two-step process: surfactant in the sublayer adsorbs, which, in turn, establishes a diffusive flux from the bulk. Therefore, both the adsorption and diffusion rates determine the behavior. These rates are commonly determined by minimizing the difference between experimental surface tension vs. time profiles and mass transfer model predictions. Usually, only a limited range of bulk concentrations Co is studied, and the profiles are found to be in agreement with a diffusion-control model. It is argued here that such apparent agreement is insufficient evidence to disregard the role of the adsorption/desorption kinetics in the adsorption process. In this paper, the concept of a shift in controlling mechanism from diffusion control at dilute concentration to mixed diffusion-kinetic control at more elevated bulk concentration is explored. This idea is illustrated theoretically for clean interface adsorption on a pendant bubble or drop using the Langmuir adsorption model in dimensionless form. It is further developed using the model constants for C12E8.

Capillary waves in a relaxing conducting viscous fluid with a surface charge

The influence of weak viscosity and dynamical surface tension relaxation effect on the structure of the wave motion spectrum in a conducting viscous fluid with a surface charge is investigated. Taking these phenomena into account leads to the appearance of additional branches of both wave and aperiodic motions associated with fluid elasticity effects and the finite time taken by the fluid surface layer to respond to fast external excitation.

Modeling and computation of the onset of failure in polymeric liquid filaments

In this paper we study a one-dimensional (1-D) quasilinear hyperbolic model for the elongation and onset of failure of polymeric liquid filaments. Our model is derived from the full 3-D free surface boundary value problem, assuming a Maxwell constitutive law for the polymeric liquid, by (a) positing a dominant balance of inertia, surface tension, gravity, viscosity and elastic relaxation, and (b) applying the slender axisymmetric perturbation methods of Bechtel et al., J. Stability Appl. Anal. Continua, 2 (1992) 1. The transient 1-D approximate equations in Lagrangian form consist of a coupled system of five, first-order quasilinear partial differential equations which admit explicit characteristic analysis and classification. The system may be genuinely hyperbolic or mixed elliptic-hyperbolic type. Importantly, a simulation which begins hyperbolic may evolve into the ill-posed mixed type regime at a particular time and location. Such a transition corresponds to a departure from slender behavior and breakdown of the 1-D theory, which we equate with onset of filament failure. The detailed nature of this transition from slender behavior is given particular scrutiny here. Our 1-D model is applied with appropriate initial and boundary data to simulate the experimental conditions in which one end of a filament is attached to a ceiling and the other to a falling drop which pulls a slender filament behind it. We show a representative sample of extensive parameter studies in which the model for the filament is initially a well-posed hyperbolic system, and numerical predictions are made on the filament behavior as it stretches. A remarkable variety of filament behavior is predicted within this 1-D Maxwell model. As we vary the competing physical effects, we predict qualitatively different locations, timescales and modes of onset of failure.

Surface tension anisotropy and relaxation in uniaxially compressed Langmuir monolayers

Surface tension anisotropy and relaxation in uniaxially compressed Langmuir monolayers

Diffusion-limited interpretation of the induction period in the relaxation in surface tension due to the adsorption of straight chain, small polar group surfactants: theory and experiment

The relaxation in surface tension due to the adsorption of bulk-soluble, unbranched, long chain surfactants with small polar groups at the air-water interface is often characterized by an initial induction period in which the surface tension relaxes very slowly. In this study, the origin of this induction in the surface tension relaxation is attributed to intermolecular cohesive forces among the adsorbed surfactant molecules which develop as the surface coverage increases.

Spinodal Decomposition of the Interface in a Nonlinear Growth Model with Noise

ABSTRACTWe consider a non-linear version of Edwards-Wilkinson interface model for the growth in the presence of a collimated partjcie flux. We include both surface tension and surface diffusion relaxation. In a range of positive small values of the surface tension, the interface develops a state which fulfills standard criteria for spinodal decomposition. This suggests the existence of a phase transition from the ordinary state with the interface perpendicular to the incoming flux to a novel, noue.induced state with the interface apontaneously tilted with respect to the direction of the flux.

Diffusion‐controlled surfactant adsorption studied by pendant drop digitization

AbstractPendant drop tensiometry enhanced by video‐image digitization is shown to be a useful tool for the experimental measurement of the relaxation in interfacial tension due to the adsorption of surfactant at a fluid interface. Using this method, profiles of the relaxation in surface tension of a diffusion‐controlled, nonionic polyethoxy surfactant were measured. A diffusion coefficient was computed by comparing these profiles with numerical solutions of the bulk surfactant diffusion equation and a Frumkin equilibrium adsorption isotherm. This comparison was made for the entire relaxation period. This method establishes a more reproducible diffusion coefficient than current techniques that utilize only the short‐ or long‐time parts of the relaxation spectrum. In addition, lower bounds on the kinetic constants for the sorption process are inferred for the polyethoxy surfactant used by comparing numerical solutions of mixed diffusion and surface kinetic transfer with the diffusion‐limited result.

Geometric fluctuations of a micellar particle

When organic molecules containing hydrophobic and hydrophilic parts are dispersed in aqueous solutions micellar structures (micelles) are formed. These are spherical particles with hydrophilic “heads” at the surface and hydrophobic “tails” on the inside. They range from 20 to 1000 A in size. To within a certain approximation the micelle is a liquid drop with surface tension whose magnitude is determined by the interaction between the molecules forming the micelle. This holds true as long as the variation of the external influences with time remains sufficiently slow. In the presence of high-frequency external forces the micelle may be regarded as a solid spherical particle with a certain thickness and elasticity containing liquid on the inside. In this article a rigorous theoretical description of the fluctuations of the shape of the micellar particle is given over a broad interval of particle sizes and it is shown that the abovementioned models of a micellar particle are equally possible, since the corresponding vibration spectra are similar in form. The decisive influence of viscosity and surface tension relaxation processes on the vibration spectra of small micelles is also demonstrated.

Surface Compressional Modulus of Surfactant Solutions. A Time Domain Method of Measurement

AbstractA method is presented for determining the surface compressional modulus, as a function of frequency, by the Fourier transformation of the surface tension relaxation function. Data are reported for submicellar aqueous solutions of the surfactants: dimethyldodecylphosphine oxide, sodium dioctylsulfosuccinate and heptaethylene glycol nonylphenyl ether. The method appears to be advantageous for rapidity of measurement and for the possibility to obtain data in the low frequency range for very dilute solutions.

Surface tension relaxation in a surface containing surfactant particles

At the surface of aqueous systems containing slightly soluble surfactants, slow relaxation processes occur that are accompanied by high values of the surface dilational modulus. A detailed investigation into these phenomena was carried out in systems containing dodecanol, tetradecanol and hexadecanol, using longitudinal surface waves and stress-relaxation experiments. The state of the surfaces involved resembles a monolayer after collapse: particles are present which do not consist of the thermodynamically stable bulk phase of the surfactant. A quantitative interpretation of the surface tension relaxation is given in terms of two processes: surfactant exchange in the surface between the monolayer and the particles, and diffusional exchange of surfactant between monolayer and bulk solution. The parameters characterizing these processes were measured; the values obtained are in satisfactory agreement with the results of other experiments.

Aureole profile in bursting soap films. Surface tension and surface relaxation in rapidly compressed monolayers

Aureole profile in bursting soap films. Surface tension and surface relaxation in rapidly compressed monolayers