Interfacial Surfactant Concentration Research Articles

A front-tracking method for computation of interfacial flows with soluble surfactants

A finite-difference/front-tracking method is developed for computations of interfacial flows with soluble surfactants. The method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations together with the incompressible Navier–Stokes equations using a non-linear equation of state that relates interfacial surface tension to surfactant concentration at the interface. The method is validated for simple test cases and the computational results are found to be in a good agreement with the analytical solutions. The method is then applied to study the cleavage of drop by surfactant—a problem proposed as a model for cytokinesis [H.P. Greenspan, On the dynamics of cell cleavage, J. Theor. Biol. 65(1) (1977) 79; H.P. Greenspan, On fluid-mechanical simulations of cell division and movement, J. Theor. Biol., 70(1) (1978) 125]. Finally the method is used to model the effects of soluble surfactants on the motion of buoyancy-driven bubbles in a circular tube and the results are found to be in a good agreement with available experimental data.

The steady propagation of a surfactant-laden liquid plug in a two-dimensional channel

In this study, we investigate the steady propagation of a liquid plug in a two-dimensional channel lined by a uniform, thin liquid film. The liquid contains soluble surfactant that can exist both in the bulk fluid and on the air-liquid interface. The Navier-Stokes equations with free-surface boundary conditions and the surfactant transport equations are solved using a finite volume numerical scheme. The adsorption/desorption process of the surfactant is modeled based on pulmonary surfactant properties. As the plug propagates, the front meniscus sweeps preexisting interfacial surfactant from the precursor film, and the surfactant accumulates on the front meniscus interface. As the front meniscus converges on the precursor film from the region where the interfacial surfactant concentration is maximized, the Marangoni stress opposes the flow. In this region, the Marangoni stress results in nearly zero surface velocity, which causes the precursor film thickness near the meniscus to be thicker than the leading film thickness. Since the peaks of wall pressure and wall shear stress occur due to narrowing of the film thickness, the observed increase of the minimum film thickness weakens these stresses. In the thicker film region, however, the drag forces increase due to an increase in the surfactant concentration. This causes the overall pressure drop across the plug to increase as a result of the increasing surfactant concentration. A recirculation flow forms inside the plug core and is skewed toward the rear meniscus as the Reynolds number increases. When no surfactant exists, the recirculation flow is in contact with both the front and the rear interfaces. As the surfactant concentration increases, the Marangoni stress begins to rigidify the front interface and forces the recirculation flow away from the front interface. Subsequently, the recirculation flow is directed away from the rear interface in a manner similar to that for the front interface. When the plug length is shorter, this change in recirculation pattern occurs at a smaller surfactant concentration.

Linear stability of a surfactant-laden annular film in a time-periodic pressure-driven flow through a capillary

This paper analyzes the effect of surfactant on the linear stability of an annular film in a capillary undergoing a time-periodic pressure gradient force. The annular film is thin compared to the radius of the tube. An asymptotic analysis yields a coupled set of equations with time-periodic coefficients for the perturbed fluid–fluid interface and the interfacial surfactant concentration. Wei and Rumschitzki (submitted for publication) previously showed that the interaction between a surfactant and a steady base flow could induce a more severe instability than a stationary base state. The present work demonstrates that time-periodic base flows can modify the features of the steady-flow-based instability, depending on surface tension, surfactant activity, and oscillatory frequency. For an oscillatory base flow (with zero mean), the growth rate decreases monotonically as the frequency increases. In the low-frequency limit, the growth rate approaches a maximum corresponding to the growth rate of a steady base flow having the same amplitude. In the high-frequency limit, the growth rate reaches a minimum corresponding to the growth rate in the limit of a stationary base state. The underlying mechanisms are explained in detail, and extension to other time-periodic forms is further exploited.

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.

On liquid-liquid mass transfer in two-liquid-phase fermentations

Almost all two-liquid phase bioprocesses are characterized by the presence of surface active materials (biosurfactants), which significantly influence the interaction between the phases. In order to predict mass transfer rates during cultivations of Pseudomonas oleovorans biosurfactant was isolated from the biosuspension and added in defined amounts to n-octane/water model-dispersions. Effects of biosurfactant concentration on interfacial tension, mean Sauter-diameter, drop size distribution, dispersion stability and liquid-liquid mass transfer coefficients were studied. A comparison was made between calculated solvent transfer rates (STR) and measured solvent uptake rates (SUR) of P. oleovorans cultures. With increasing interfacial surfactant concentration interfacial tension and mean Sauter-diameter decreased until a minimum for both, interfacial tension and mean Sauter-diameter, were reached. Interfacial tension measurements indicate that these minima have to be attributed to a maximum monomolecular surfactant concentration and the formation of polymolecular adsorption layers. Drop size distributions showed that, coalescence and droplet break-up disappear because droplets are stabilized by the biosurfactant adsorption layers at the interface. Mass transfer regime shifted from forced convection and surface renewal to diffusion. Comparison of solvent uptake rates (SUR) and solvent transfer rates (STR) showed that n-octane transfer usually will not be limiting P. oleovorans cultures, however, can become dominant in cultures where solvents with very low miscibilities like n-decane are used.

The effects of slightly soluble surfactants on the flow around a spherical bubble

This paper reports the results of a numerical investigation of the transient evolution of the flow around a spherical bubble rising in a liquid contaminated by a weakly soluble surfactant. For that purpose the full Navier–Stokes equations are solved together with the bulk and interfacial surfactant concentration equations, using values of the physical-chemical constants of a typical surfactant characterized by a simple surface kinetics. The whole system is strongly coupled by nonlinear boundary conditions linking the diffusion flux and the interfacial shear stress to the interfacial surfactant concentration and its gradient. The influence of surfactant characteristics is studied by varying arbitrarily some physical-chemical parameters. In all cases, starting from the flow around a clean bubble, the results describe the temporal evolution of the relevant scalar and dynamic interfacial quantities as well as the changes in the flow structure and the increase of the drag coefficient. Since surface diffusion is extremely weak compared to advection, part of the bubble (and in certain cases all the interface) tends to become stagnant. This results in a dramatic increase of the drag which in several cases reaches the value corresponding to a rigid sphere. The present results confirm the validity of the well-known stagnant-cap model for describing the flow around a bubble contaminated by slightly soluble surfactants. They also show that a simple relation between the cap angle and the bulk concentration cannot generally be obtained because diffusion from the bulk plays a significant role.

Lattice-gas simulations of domain growth, saturation, and self-assembly in immiscible fluidsand microemulsions

We investigate the dynamical behavior of both binary fluid and ternary microemulsion systems in two dimensions using a recently introduced hydrodynamic lattice-gas model of microemulsions. We find that the presence of amphiphile in our simulations reduces the usual oil-water interfacial tension in accord with experiment and consequently affects the non-equilibrium growth of oil and water domains. As the density of surfactant is increased we observe a crossover from the usual two-dimensional binary fluid scaling laws to a growth that is {\it slow}, and we find that this slow growth can be characterized by a logarithmic time scale. With sufficient surfactant in the system we observe that the domains cease to grow beyond a certain point and we find that this final characteristic domain size is inversely proportional to the interfacial surfactant concentration in the system.

Study of Drop-Interface Coalescence Using Piezoimaging

A novel technique for monitoring drop/homophase coalescence in liquid−liquid dispersions having an opaque or turbid dispersion medium has been developed and described in this paper. This technique is based on using a piezotransducer to monitor the process of coalescence of a drop at a liquid−liquid interface. The piezotransducer signal observed when coalescence occurs has two distinct parts. This study shows that the first part of the signal is due to interfacial instability, while the second part of the signal is due to a transient jet which is ejected into the homophase during coalescence. The effects of interfacial tension, homophase viscosity, and surfactant concentration in the dispersion medium on the observed signal are studied. Several other potential applications of the technique such as measuring the rate of phase separation are also discussed.

Dynamic surface tension of surfactant TA: experiments and theory.

A bubble surfactometer was used to measure the surface tension of an aqueous suspension of surfactant TA as a function of bubble area over a range of cycling rates and surfactant bulk concentrations. Results of the surface tension-interfacial area loops exhibited a rich variety of phenomena, the character of which varied systematically with frequency and bulk concentration. A model was developed to interpret and explain these data and for use in describing the dynamics of surface layers under more general circumstances. Surfactant was modeled as a single component with surface tension taken to depend on only the interfacial surfactant concentration. Two distinct mechanisms were considered for the exchange of surfactant between the bulk phase and interface. The first is described by a simple kinetic relationship for adsorption and desorption that pertains only when the interfacial concentration is below its maximum equilibrium value. The second mechanism is "squeeze-out" by which surfactant molecules are expelled from an interface compressed past a maximum packing state. The model provided good agreement with experimental measurements for cycling rates from 1 to 100 cycles/min and for bulk concentrations between 0.0073 and 7.3 mg/ml.

Theoretical evaluation of dispersed droplet radii in submicron oil-in-water emulsions

A theoretical model which predicts the mass mean radius for oil droplets dispersed in aqueous media is described. Using a modified equation of state for interfacially adsorbed films and the LaPlace equation, the oil droplet radii can be described as a function of several variables including the oil concentration, surfactant concentration and surfactant hydrophile/lipophile balance (HLB). All relevant parameters are measurable or readily calculated. Eighteen experimental emulsions were evaluated utilizing 10% or 20% v/v soy oil and 0.5–3.0% w/v non-ionic surfactant (Myrj 45/glycerol monostearate; HLB 9.5, 10.0 or 10.5). The emulsification technique used for the experimental emulsions utilized the Microfluidizer device, which produces uniform and highly turbulent homogenization. Using these components and processing techniques it is possible to produce submicron o/w emulsions with low interfacial surfactant concentrations. Under these conditions, there is good agreement between the measured droplet radii and the proposed theoretical mechanisms governing their production. This agreement also extends to published data where submicron emulsions have been produced at relatively low o/w interfacial surfactant loading. This non-empirical approach to emulsion droplet size analysis may have predictive value in optimizing submicron emulsion droplet size under the proposed conditions.

Contact Angle And Interfacial Tension Studies of Some Hydrocarbon-Water-Solid Systems

Abstract An apparatus was built to measure interfacial tensions and contact angles of hydrocarbon-water-solid s:rstems at variable temperatures and atmospheric pressure. Interfacial tensions were measured for benzene, n-dodecane, Klearol and nitrogen against water over a temperature range of 25 to 90 °C. For the n-dodecane-water system, a water-soluble cationic surfactant, a water-soluble nonionic surfactant and an oil-soluble carboxylic acid were added. Relationships among interfacial tension, temperature, surfactant concentration and interface age were determined. Contact angle measurements were made primarily for the n-dodecane-water system on flat quartz and calcite crystal surfaces. An oil-soluble amine, a carboxylic acid, and water-soluble anionic, cationic and nonionic surfactants were used as additives. Without the surfactants, the carefully cleaned solids were completely water-wet. Finite contact angles resulted from contamination or the addition of certain of the surface-active compounds, and were generally accompanied by hysteresis. The magnitude of the contact angles indicates the orientation and degree of packing of surface-active molecules at solid-liquid interfaces, and points out the role of surface charge and polarity in adsorption. Introduction IN CANADA AND THE UNITED STATES, approximately 90 per cent of all the oil produced through the application of enhanced recovery processes is obtained bywaterflooding. The rising cost of exploring for new oil, coupled with the higher cost of applying alternate recovery schemes, creates an incentive for waterfloods to be conducted under conditions favouring most efficient oil recovery. This requires that research be carried out into factors which might significantly improve the immiscible displacement mechanisms. Mungan(1) has shown that interfacial effects in the immiscible displacement of oil from porous media can significantly influence the recovery, and Melrose(2) has recently discussed the role which interfacial phenomena or capillary forces play in determining the extent to which a fluid can be displaced from a porous solid by another immiscible fluid. A general discussion of capillarity was given recently by Schwartz(3). Three factors affect capillary forces in porous media:the interfacial tension between the two fluids,the contact angle between the fluids and the solid surface, andthe pore size and pore size distribution of the porous media. Because of the small pore sizes and the large interfacial areas existing between oil, water and the reservoir rock, the interfacial forces become appreciable and can dominate in the displacement. Moore and Blum(4) estimated that to mobilize residual oil structures, assumed to be several grain sizes in length, through average reservoir rock openings would require a pressure gradient of something like 500 psi/ft - an impossible value to attain in operations. An alternative is to reduce the interfacial tension to low values, say 0.01 dyne/cm, which reduces the pressure requirement to move these same residuals to only 0.33 psi/ft. Chatenever, et al.(5), using microscopic examination of fluid movement in all-glass and all-lucite cells, showed that the residual oil formation and structures we.re significantly different under water-wet and oil-wet situations.