Surfactant Mass Transfer Research Articles

Model of the quasi-monodisperse micelles with application to the kinetics of micellization, adsorption and diffusion in surfactant solutions and thin liquid films

The micelles in a water surfactant solution are considered as quasi-monodisperse aggregates of two kinds: large and small. They give rise to two micellization processes, fast and slow, in response to any external perturbation. During the fast process the bigger micelles release a certain number of monomers to transfer into the smaller ones, while the total micelle concentration remains constant. During the slow process both types of micelle decrease in number until the effect of perturbation is compensated. Using an asymptotic mathematical procedure, we derive analytical expressions for the concentrations of species and the characteristic time constants of relaxation. The time constants obtained are consistent with the experimental data for the micellization kinetics and also with their counterparts known from the polydisperse micelle model. The advantage of the quasi-monodisperse model dealing with only two micelle fractions is further exploited to solve a more complicated diffusion problem for the kinetics of adsorption. It turns out that the micellization process is important for surfactant mass transfer; because the time constant of this process is commensurable with the characteristic time of diffusion. The set of coupled equations derived for the diffusion of free monomers and micelles contains source terms accounting for the exchange of material among the species. The equations are solved for a semi-infinite micellar solution and the analytical expression for the dynamic surface tension is compared with experimental data for different surfactants, measured by various methods. In all cases the slow micellization process predetermines the adsorption kinetics, i.e. the micelles have to be destroyed in order to fill the adsorption layer with monomers. In contrast to this observation, the fast relaxation process affects the adsorption on the two opposite surfaces of a thin liquid film, because the diffusion in the film is much faster than in a semi-infinite medium. For this reason the micelles can compensate the surface tension gradients created in the course of film thinning by simply releasing monomers. The calculated velocity of thinning is effectively increasing above the critical micelle concentration, which is in accord with existing experimental data. The thin film hydrodynamics turns out to be affected by the bulk diffusion of monomers enhanced by the micellization kinetics. This is opposite to the mechanism accepted for films without micelles, whose hydrodynamics is governed by the surface diffusion in the adsorbed layer.

An Adsorption–Desorption-Controlled Surfactant on a Deforming Droplet

The effects of a sorption-controlled, monolayer-forming surfactant on a drop deforming in an extensional flow are studied numerically. Scaling arguments are presented for drops of 1 cm and 1 μm, indicating the applicability of these results. For all simulations, when mass transfer is slow compared to surface convection, the insoluble limit is recovered; when mass transfer is rapid, the drop behavior is the same as that for a surfactant-free drop. For a surfactant which forms a monolayer, there is an upper bound to the surface concentration, Γ∞. The surface tension reduction diverges as the surface concentration Γ approaches this limit, strongly altering the hydrodynamics.The drop deformation is studied relative to a surfactant-free drop in terms of the capillary number, Ca, the ratio of characteristic viscous stresses to surface tension. In the insoluble limit, for Γ ⪡ Γ∞, droplets deform more than in the absence of surfactants at a given Ca and break-up at lower Ca. When stable drop shapes are attained, stagnant caps form at the drop tips. Finite surfactant mass transfer rates eliminate these caps and diminish the deformation.For Γ approaching Γ∞in the insoluble limit, interfaces are strongly stressed for perturbative surface concentration gradients; Γ remains nearly uniform throughout the deformation process. Deformations are reduced at a given Ca. When stable drop shapes are attained, the surface is completely stagnated. Marangoni stresses force the surface velocity to zero to keep Γ below its upper bound. For soluble surfactants, as mass transfer rates increase, the magnitude of these stresses diminishes. Deformations change nonmonotonically with mass transfer rates and are not bounded by the limiting clean interface and insoluble limits.The drop contribution to the volume averaged stress tensor Σ is also calculated. The axial component Σzzincreases with the drop length; the radial component Σrrincreases with the drop breadth. Since the deformation is strongly influenced by the surfactant concentration and the mass transfer rates, so too is Σ.

Hydrodynamic Theory for Spontaneously Growing Dimple in Emulsion Films with Surfactant Mass Transfer

In this paper we propose a theory for the recently discovered phenomenon of spontaneous cycling dimpling. The latter is responsible for the high stability of non-equilibrium aqueous emulsion films when surfactant is transferred across the interfaces toward the surrounding oil phases. Our treatment is based on the lubrication approximation for the thin film hydrodynamics, with account for the surfactant fluxes due to convection and diffusion. A fourth-order differential equation is derived for the time evolution of the surface shape. This equation is solved numerically, and the results are compared with experimental profiles (determined by means of interferometry). Very good agreement is observed. It is proved that the surface viscosity and the surface diffusion are insignificant for the dimple growth. Quite essential is the Marangoni effect: the exhaustion of surfactant from the region around the film center gives rise to gradients of the interfacial tension which set the interface into motion, and consequently, liquid is dragged into the film, feeding the dimple.

Experimental Confirmation of the Oscillating Bubble Technique with Comparison to the Pendant Bubble Method: The Adsorption Dynamics of 1-Decanol

A new oscillating bubble method is used to measure surfactant mass transfer kinetics at liquid–gas interfaces. A spherical bubble is formed, equilibrated, and oscillated radially with a small amplitude. The radial oscillations cause the gas-phase pressure to cycle about its equilibrium because of the periodic changes in bubble curvature and surface tension. The phase angle θ between the radial and the pressure oscillations and the amplitude ratio of these two quantities are measured as a function of forcing frequency ω′ and concentrationC′(0). These data are analyzed according to a linear analysis presented in part I of this research (J. Colloid Interface Sci.168,21, 1994) to find surfactant diffusivities and adsorption/desorption coefficients. The required input data are the equilibrium adsorption isotherm and the corresponding surface equation of state. For 1-decanol at the air–aqueous interface, equilibrium surface tension data are obtained by video-enhanced pendant bubble tensiometry and fitted to the generalized Frumkin model. The oscillating bubble method is then used to determine the mass transfer kinetics of 1-decanol. For ω′ ≤ 1 rad/s, the mass transfer is diffusion-controlled. Diffusivities found from the oscillating bubble data are in agreement with those obtained from pendant bubble relaxation data. For elevatedC′(0)and ω′ ≥ 1.0 rad/s, the mass transfer is controlled by both diffusion and the kinetics of adsorption–desorption. A mixed diffusion–kinetic model applied to these data yields a value for the desorption kinetic constant of α = 2.7 s−1. These results are consistent with the shift in controlling mechanism from pure diffusion control at dilute concentrations to mixed diffusion–kinetic control at elevated concentrations.

An oscillating bubble technique to determine surfactant mass transfer kinetics

In this paper, an oscillating bubble method is introduced as a spherical analog of the longitudinal wave method. In the longitudinal wave method, amplitude ratios and phase angles between surface tension variations at two locations on the interface are related to the surfactant mass transfer kinetics. In the analogous oscillating bubble method, by forcing small-amplitude radial perturbations about an equilibrium base state, and measuring the phase angle between the bubble radius and the gas phase pressure, the surfactant diffusion and sorption kinetics can be determined. In this communication, data are presented for n-decanol at the aqueous-gas interface. The phase angle is measured as a function of bulk concentration and forcing frequency. By minimizing the error between theoretical and experimental phase angle profiles, the diffusivity and desorption coefficients of n-decanol are obtained.

Marangoni Retardation of the Terminal Velocity of a Settling Droplet: The Role of Surfactant Physico-Chemistry

Nonlinear adsorption models accounting formonolayer saturationandnonideal surfactant interactionsare used to find the terminal velocityU′ of a droplet settling through a surfactant solution. Most prior research uses a linear adsorption model which cannot capture these effects. The solution concentration[formula]is assumed to be large enough for the surfactant mass transfer to be adsorption-controlled. The Langmuir model accounts for monolayer saturation by incorporating an upper bound for the surface concentration,[formula]Two competing effects result which alterU′ from that predicted by the linear model. For slow adsorption–desorption kinetics, strong Marangoni stresses develop when the surface concentration at the rear pole approaches[formula]. These stresses favorstrong retardationinU′. The adsorption flux is proportional to the unoccupied space on the interface, so depleted regions are supplied more rapidly. This diminishes Marangoni stresses and favorsweak retardation.This effect dominates for rapid sorption kinetics. The Frumkin framework incorporates monolayer saturation and nonideal surfactant interactions which alter the amount of adsorbed surfactant, the sensitivity of the surface tension, and the dynamics of adsorptive–desorptive exchange. For a fixed mass of adsorbed surfactant,U′ retarded for no interactions is increased by intersurfactant repulsion and decreased for cohesion. At elevated[formula]U′ asymptotes to a value less than the Hadamard–Rybczynski velocity[formula]for the Langmuir case and for cohesive interactions. For repulsive interactions,U′ approaches[formula]in this limit. These asymptotes indicate the degree of surface remobilization attainable for finite adsorption–desorption kinetics and nonideal interactions.

Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory

A theoretical analysis is presented for the shape oscillations of drops suspended in air. For drops of surfactant solution, the oscillation frequency is basically determined by the surface tension; the free-damping constant depends on the surface viscoelasticities. Different types of surfactant mass transfer at the droplet surface produce different surface rheological behaviors. Analytical approximate solutions for free-oscillation frequency and damping constant are derived by a perturbation method as functions of surface compositional elasticity, surface dilatational viscosity, and surface shear viscosity. These solutions are verified with exact numerical solutions. The existence of a second oscillation mode due to surface elasticity is illustrated. The phase relationships between the external driving forces and the droplet shapes for forced oscillations are discussed. It is found that at the 90° phase shift, the driving frequency and the slope of the phase diagram are equivalent to the free-oscillation frequency and damping constant.

Effect of nonionic surfactant addition on bacterial metabolism of naphthalene: Assessment of toxicity and overflow metabolism potential

Two factors potentially accounting for the variability of bioremediation outcomes when surfactant micelles are used to increase polycyclic aromatic hydrocarbon (PAH) bioavailability were investigated: (1) surfactant toxicity and (2) the link between microbial metabolism and the intended effect of surfactant addition, enhanced solubilization and mass transfer from a solid phase. The nonionic surfactant, octaethyleneglycol mono n-dodecyl ether, did not alter the metabolism of succinate and glucose by an isolate from a creosote-contaminated soil indicating that the surfactant is nontoxic. When the culture was supplied with solid naphthalene, growth was limited by the dissolution of solid naphthalene after the aqueous-phase naphthalene was depleted. Moreover, increasing dissolution rate by increasing interfacial surface area increased the microbial growth rate. However, increasing bioavailability further by increasing interfacial surface area, introducing convective mass transfer, and adding surfactant were all found to reduce growth rate and prompt incomplete metabolism of naphthalene to a compound whose UV absorption corresponds to 1,2-naphthaquinone. Lowering the surfactant concentration diminished the metabolic overflow and permitted sustained growth. The results suggest that different mismatches between solubilization/mass transfer and metabolic capacity may be among the factors responsible for variable bioremediation outcomes.

Oscillating Bubble Tensiometry: A Method for Measuring the Surfactant Adsorptive-Desorptive Kinetics and the Surface Dilatational Viscosity

Mobilities of surfactant laden interfaces are determined by both surfactant-mass-transfer kinetics and surface viscosities. In this paper, a theoretical framework for measuring these parameters by analyzing forced radial oscillations of a spherical pendant bubble about an equilibrium, quiescent base state is developed. Because of the Gibbs-Marangoni elasticity caused by hindered surfactant mass transfer, and the surface viscosities, oscillations in the gas phase pressure and bubble radius are out of phase. Using a linear analysis of the governing fluid mechanical and mass-transfer equations, the phase lag (θ) and the amplitude ratio of these two quantities (Λ) are derived. Three cases are considered for the surfactant mass transfer: a mixed-controlled model in which diffusion and sorption kinetics play a role, along with the limiting cases of diffusion-control and sorption-control, respectively. Both θ and Λ depend upon the bulk diffusivity, the equilibrium physicochemical constants, and two unknowns: the sorption kinetic constant and the surface dilatational viscosity. In this paper, by varying these unknowns, theoretical families of curves for both θ and Λ vs forcing frequency, ω′, are generated using values for the bulk diffusivity and the equilibrium physicochemical constants for decanol at aqueous-air interfaces from Lin et al. (Langmuir 7, 1055, 1991). These curves indicate the potential of the oscillating bubble as a measurement tool, i.e., that experiments in which θ and Λ are measured vs ω′ can be used to determine the adsorption-desorption kinetic constants and the surface dilatational viscosity and to differentiate them from each other.

Modeling surfactant removal in foam fractionation: I — Theoretical development

Surfactant removal by foam fractionation was theoretically analyzed by treating surfactant mass transfer from a bulk solution onto a moving bubble as a convective diffusion process. A mathematical model expressing the removal rate as a function of pertinent parameters was developed. The parameters included superficial air velocity, bubble size, bubble rising velocity, surfactant diffusion coefficient, and concentration. The model indicated that surfactant removal can be described as a first-order process whose rate increases with the diffusion coefficient, the superficial air velocity and the surfactant concentration in the bulk solution, but decreases with bubble size and bubble rising velocity. Based on the assumption of a completely mixed reactor within a section of a foam fractionator, a simplified model for foam fractionation under batch operation conditions was also presented. This simplified model provides a theoretical basis according to which the diffusion coefficient of surfactants can be determined and the model itself can be verified with experimental data.

Spontaneous Cyclic Dimpling in Emulsion Films Due to Surfactant Mass Transfer between the Phases

A fascinating spontaneous cyclic phenomenon was encountered during observations of aqueous emulsion films between oil phases, Nonionic surfactants (Tweens) initially dissolved in the water phase were used as stabilizers. The films (with typical diameter of 300 μm) were formed in a capillary and were illuminated in reflected monochromatic light. After the films thin down to their equilibrium thickness, a dimple (lens-shaped thicker formation) spontaneously forms and starts to grow around their center. Upon reaching a certain size the dimple forms a channel to the periphery and flows out, leaving a plane-parallel film behind. Immediately afterward a new dimple starts to grow, and so on. This cyclic process could go on for hours. We have proved that the driving force of the process is the surfactant redistribution between the phases. We presume that similar phenomena, resulting from the coupling of the processes of surfactant redistribution and interfacial and hydrodynamic motion inside the films, could be important for the stability of newly formed emulsions.

Mass transfer of surfactants and hydrodynamic interaction at small separations in emulsion systems 2. Potential theory

Scaling parameters are applied in order to propose a physically adequate asymptotic model for the coupling of the mass transfer of soluble surfactants and the fluid flows in emulsion systems. The hydrodynamic interaction at small gap widths is studied when thin liquid layers are formed. The classical potential theory is used for the numerical calculations. Expressions are obtained for the tangential mobility of the fluid flow interfaces and the drag force in the cases of low and high viscosities of the disperse phase.

Mass transfer of surfactants and hydrodynamic interaction at small separations in emulsion systems 1. Scaling concepts

A model investigation of the coupling of the mass transfer of surfactants and the fluid flows in emulsion systems is presented. The case of close approach of two emulsion droplets, when a thin liquid layer is formed in the narrowest parts between the fluid interfaces, is analysed. New scaling parameters are proposed, based on the introduction of the surface Peclet number Pe s. The increase in this surface analogue of the bulk Peclet number results in an increased mobility of the interfaces and in a reduced influence of the surfactant. The validity of the lubrication theory model for the drainage of the thin layers is outlined in terms of the tangential mobility and the Gibbs elasticity of the interfaces. The influence of surfactants on the tangential mobility and the velocity of coalescence is discussed.

Stability of a spherical drop with surfactant mass transfer

Interphase convection and Marangoni instability have recently become the subject of active study [1–5]. The description of a number of phenomena associated with the interaction between surfactant mass transfer and capillary effects are examined at the kinetic and hydrodynamic levels, using an experimentally realizable physical model. For this model the boundary-value problem of the stability of diffusion transfer of surfactant across an initially spherical interface between two immiscible liquids in the diffusion and adsorption kinetics regimes is solved analytically. The critical values of the dimensionless parameters of the problem at which convectionless mass transfer becomes unstable with respect to monotonic disturbances are found. The drop drift effect is examined. The change in the shape of the drop and the influence of surface viscosity and diffusion effects are taken into account. The possible practical applications of the problems solved include: modeling spontaneous emulsification, cytokinesis and chemotaxis, and estimating the effect of interphase turbulence on the rate of mass transfer across media interfaces in various industrial processes.

Hydrochemical stability of a drop in the mass transfer of surfactants

Hydrochemical stability of a drop in the mass transfer of surfactants

The influence of surfactants on the hydrodynamical interaction in emulsion systems

A system of two emulsion droplets is examined as they mutually approach at small separations. The mass transfer of diffusion-controlled surfactants towards the interface is regarded. The cases of a surfactant soluble in only one of the phases as well as in all of them are analysed. Quantitative estimates are presented for the tangential mobility of the droplet/thin layer interface. Different regimes of mass transfer and flow in the drops and a creeping flow and various regimes of mass transfer in the thin layer between them are considered.

Membrane ultrafiltration of a nonionic surfactant

AbstractAqueous solutions 1.65 × 10−4 to 1.10 × 10−2 molar in the nonionic surfactant Triton X‐100 are subjected to membrane ultrafiltration over the temperature range of 22 to 50°C in a continuous flow, thin channel cell, with channel Reynolds numbers from 50 to 1175. Data for the ultrafiltrate flux through the optimum polyelectrolyte complex membrane (of the three tested) are correlated by an equation involving the in‐series resistances of the membrane and of the polarized boundary layer of the sufactant rejected by the membrane, with the latter resistance varied over a wide range. The correlations are used to estimate the required membrane area and resultant ultrafiltrate concentration of surfactant to achieve any specified water recovery using cells‐in‐series and cells‐in‐parallel operation. The gelation concentration and surfactant mass transfer coefficient are used to estimate water flux in the gel‐polarization region.