Distribution Of Surfactant Concentration Research Articles

Laboratory Study of Surfactant Film Compression and Boundary Transformation under the Action of Surface Waves

In this paper we present the results of a laboratory experiment simulating the mechanisms of a surfactant film localization under the action of periodic surface waves. It is shown that the film compressed by a surface wave, can be conditionally divided into three sections — the dense film region as the most distant from the wave source, the area of a diluted film and the region of relatively clean water. The paper is focused on the processes occurring in the diluted film region characterized by the transition from clean water to the dense film, where horizontal circulation currents are registered. The character of currents is varying depending on the wave amplitude so that the divergent circulation cells occur at small and large wave amplitudes, but at medium amplitudes the roller currents forming a convergence zone on the basin axis are observed. The experimentally obtained stationary distribution of surfactant concentration is compared with the previously developed model of film compression due to surface tension induced by waves. The comparison shows good agreement between the theory and the experimental results at small and large wave amplitudes. Their discrepancy at medium wave amplitudes in the diluted film region is presumably related to the presence of convergent cells which are not considered in the model.

A micro-kinetic model of enhanced foam stability under artificial seismic wave

Abstract To get a deeper understanding on the synergistic enhancement effect of low frequency artificial seismic wave on foam stability, a micro-kinetic model of enhanced foam stability under low frequency artificial seismic wave is established based on a vertical liquid film drainage model and elastic wave theory. The model is solved by non-dimensional transformation of the high order partial differential equations and a compound solution of implicit and explicit differences and is verified to be accurate. The foam film thickness, surfactant concentration distribution and drainage velocity under the action of low frequency artificial seismic wave are quantitatively analyzed. The research shows that low-frequency vibration can reduce the difference between the maximum and minimum concentrations of surfactant in the foam liquid film at the later stage of drainage, enhance the effect of Marangoni effect, and improve the stability of the foam liquid film. When the vibration frequency is close to the natural frequency of the foam liquid film, the vibration effect is the best, and the best vibration frequency is about 50 Hz. The higher the vibration acceleration, the faster the recovery rate of surfactant concentration in the foam liquid film is. The higher the vibration acceleration, the stronger the ability of Marangoni effect to delay the drainage of foam liquid film and the better the foam stability is. It is not the higher the vibration acceleration, the better. The best vibration acceleration is about 0.5 times of gravity acceleration. Reasonable vibration parameters would greatly enhance the effect of Marangoni effect. The smaller the initial concentration of surfactant, the better the vibration works in enhancing Marangoni effect.

Switching the Roles of Wettability-based Patterns Through Solutal Marangoni Effect

Controlling the dynamics of thin liquid films on solid surfaces is illustrated by a combination of substrate patterning and solutal Marangoni effect. A solid surface, patterned based on wettability differences, can trigger film instability due to wettability gradient-driven flows. Additionally, if insoluble surfactants are introduced at the liquid film surface, the surfactant transport can cause surface-tension gradients across the film, and a solutal Marangoni flow results. By using suitable non-uniform initial surfactant concentration distributions, the rate and direction of Marangoni flow can be manipulated to compete with the wettability gradient-driven flows. It is found that film dewetting can be reversed in selected problem parameter space. Dewetting can be engendered on more wettable patches of the bounding solid, with a consequent accumulation of the liquid on less wettable regions. The importance of length scales of the less and more wettable patches on switching the roles of wetting behaviour is also investigated.

Numerical modeling of drop coalescence in the presence of soluble surfactants

The paper presents a numerical method for simulation of the effect of a soluble surfactant on the last stage of the drop coalescence (film formation, drainage and rupture). An axisymmetric interaction between drops is studied at small capillary and Reynolds numbers and small surfactant concentrations. The hydrodynamic part of the mathematical model includes the Stokes equations in the drop phase and their lubrication approximation in the gap between the drops (film phase), coupled with velocity and stress boundary conditions at the interfaces. The surfactant is considered soluble in both (drop and film) phases and the distribution of the surfactant concentration is governed by a convection–diffusion equation. A convection–diffusion equation is also used to model the distribution of the surfactant on the interfaces. The concentration in both phases is coupled with that on the interfaces via the adsorption isotherm and the fluxes between the interface and the bulk phases. The hydrodynamic and concentration parts of the mathematical model are related via the advection of the surfactant in the fluid phases and on the interfaces. On the other hand, a non-uniform surfactant concentration on the interfaces leads to a gradient of the interfacial tension which in turn leads to an additional tangential stress on the interfaces (Marangoni effects). For the flow in the drops a simplified version of Boundary integral method is used. Finite difference method is used for the flow in the gap, the position of the interfaces and the distribution of surfactant concentration on the interfaces, as well as in the fluid phases. Different approaches are used for an optimization of the numerical algorithm: Non-uniform meshes for space discretization in both (r and z) directions; Explicit and implicit first and second order time integration schemes with automatically adaptive time steps; A multiple time step integration scheme that can decrease significantly the computational time without loss of accuracy. Tests and comparisons are performed in order to investigate the accuracy and stability of the different numerical schemes.

Surfactant effect on path instability of a rising bubble

AbstractWe report results from the first systematic experiments for investigating surfactant effects on path instability of an air bubble rising in quiescent water. The addition of surfactant to a gas–water system causes a non-uniform distribution of surfactant concentration along the bubble surface, resulting in variations in the gas–water boundary condition from zero shear stress to non-zero shear stress due to the Marangoni effect. This leads to retarded surface velocity and ends up with immobilization of the bubble surface with increasing surfactant concentration, where the drag corresponds to that of a solid sphere of the same size. Using two high-speed cameras and vertical traverse systems, we measure three-dimensional trajectories, velocities and aspect ratios of a millimetre-sized bubble simultaneously for ${\sim }1~\mathrm{m} $. Experimental parameters are the diameter of the bubble and the surfactant concentration of 1-Pentanol or Triton X-100. We explore the surfactant effect on the drag and lift forces acting on the bubble in helical motion. While the drag force monotonically increases with the surfactant concentration as expected, the lift force shows a non-monotonic behaviour. Nevertheless, the direction of the lift force in a reference frame that rotates with the bubble along its trajectory is kept almost constant. We also observe the transient trajectory starting from helical motion to zigzag, which has never been reported in the case of purified water. The instantaneous amplitude and frequency of the transient motion agree with those of the motion regarded as steady. Finally the bubble motions are categorized as straight/helical/zigzag and experimentally examined in the field of two dimensionless numbers: Reynolds number $\mathit{Re}\in $ [300 900] and the normalized drag coefficient ${ C}_{D}^{\ast } $ which represents the slip condition. Remarkably it is found that the motions of a bubble with the intermediate slip conditions between free-slip and no-slip are helical for a broad range of $\mathit{Re}$.

Linear instability of two-fluid Taylor–Couette flow in the presence of surfactant

The effect of an insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor–Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis. The interface is assumed to be concentric with the cylinders. The gravitational effects are ignored. Influences of density and viscosity stratification, surface tension, surfactant concentration distribution and Taylor–Couette shearing are considered comprehensively. The instability characteristics due to competition and interaction between various physical instability mechanisms are of principal concern. Neutral curves with upper and lower branches in the Reynolds number (Re1)/axial wavenumber (k) plane are obtained. A window of parameters is identified in which the flow is linearly stable. The Marangoni traction force caused by the gradient of surfactant concentration stabilizes the axisymmetric perturbations but initiates an instability corresponding to non-axisymmetric modes in the presence of basic Couette shearing flow. Co-rotation of the outer cylinder has a stabilizing effect in expanding the stable region, which dwindles in the counter-rotation situation.

Modifications of Surfactant Distributions and Surface Morphologies in Latex Films Due to Moisture Exposure

Migration of surfactants in water-based, pressure-sensitive adhesive (PSA) films exposed to static and cyclic relative humidity conditions was investigated using confocal Raman microscopy (CRM) and atomic force microscopy (AFM). Studied PSA films contain monomers n-butyl acrylate, vinyl acetate, and methacrylic acid and an equal mass mixture of anionic and nonionic nonylphenol ethoxylate emulsifiers. A leveling of surfactant concentration distributions is observed via CRM after films stored at 50% relative humidity (RH) are exposed to a 100% RH for an extended time period, while relatively small increases in surface enrichment occur when films are stored at 0% RH. Use of CRM for binary mixtures containing anionic or nonionic surfactant and latex that has undergone dialysis to remove nonpolymeric components indicates that surfactant-polymer compatibility governs to a great extent surface enrichment, but not changes observed with humidity variations. AFM images show that upon drying latex coatings, surfactant and other additives collect in large aggregation regions, which protrude from film surfaces. These structures are absent at high humidity, which appears to result from lateral spreading across the polymer surface. When humidity is reduced, aggregation regions reform but appear to be smaller and more evenly dispersed, and by cycling humidity between 0 and 100% RH, interfacial enrichment can be seen to diminish. Presented results provide greater insights into the distribution behavior of surfactants in latex films and potential mechanisms for observed issues arising for these systems.

Oscillatory marangoni convection around bubbles and drops in heterogenous solutions of surfactants

Experimental investigation was performed to study the concentration convection around stationary gas bubbles and insoluble drops in a thin liquid layer placed in a vertical Hele-Shaw cell. The bubbles or drops, squeezed between the two parallel cell walls, took the shape of short cylinders with free lateral surfaces. The cell was filled in with an aqueous solution of a surface-tension active fluid (surfactant) with vertically stratified concentration. A special wire frame prevented bubbles from rising up under the buoyancy force, thus modelling the microgravity conditions. A convective motion in the mixture develops at the bubble or drop interface, due to the solutocapillary Marangoni forces. Owing to a small thickness of the liquid layer (∼1mm), the arising flows and surfactant concentration distributions are nearly two-dimensional so that it is possible to investigate their structure and evolution by interferometric technique. The experiments revealed the development of oscillatory convection around the drop interface, which was similar to that observed in bubble tests. The period and duration of oscillations were determined in relation to time, surfactant concentration gradient and concentration Marangoni number. The analysis of bubble and drop behavior showed that the existence of self-oscillatory modes is related to the specific interaction between the solutocapillary and soluto-gravitational mechanisms of motion.

Modeling of the Adsorption Kinetics of Surfactants at the Liquid−Fluid Interface of a Pendant Drop

This paper presents a theoretical model for simulating the adsorption kinetics of a surfactant at the liquid-fluid interface of a pendant drop. The diffusion equation is solved numerically by applying the semidiscrete Galerkin finite element method to obtain the time-dependent surfactant concentration distributions inside the pendant drop and inside the syringe needle that is used to form the pendant drop. With the obtained bulk surfactant concentration distributions, the adsorption at the interface is determined by using the conservation law of mass. It should be noted that the theoretical model developed in this study considers the actual geometry of the pendant drop, the depletion process of the surfactant inside the pendant drop, and the mass transfer of the surfactant from the syringe needle to the pendant drop. The present pendant-drop model is applied to study the adsorption kinetics of surfactant C10E8 (octaethylene glycol mono n-decyl ether) at the water-air interface of a pendant drop. The numerical results show that the Ward and Tordai equation, which was derived for adsorption from a semi-infinite surfactant solution to a planar interface, is unsuitable for interpreting the dynamic surface or interfacial tension data measured by using the pendant-drop-shape techniques, especially at low initial surfactant concentrations. The spherical-drop model, which assumes the pendant drop to be a perfectly spherical drop with the same drop volume, can be used to interpret the dynamic surface or interfacial tension data for pendant drops either with high initial surfactant concentrations or with low initial surfactant concentrations in short adsorption durations only. For pendant drops with low initial surfactant concentrations in long adsorption durations, the theoretical model developed in this study is strongly recommended.

Concentration measurements downstream of an insoluble monolayer front

The surfactant concentration distribution on a planar uniform flow with a surface-piercing barrier was measured via the nonlinear optical technique of second-harmonic generation. The measurements were performed for an insoluble surfactant monolayer on the air/water interface. A theoretical model balancing surface elasticity and bulk shear at the interface was developed to predict the concentration profile for any insoluble monolayer. Measured equations of state, relating the surface tension to the surfactant concentration, were used in the model along with velocity data obtained using boundary-fitted digital particle image velocimetry. Theoretical concentration profiles were in agreement with experimental results. Additionally, global predictions from the model for four different insoluble surfactant systems also showed agreement with experimental measurements.

Role of pulmonary surfactant in airway closure: a computational study.

A numerical model that simulates airway closure by liquid bridging during expiration has been developed. The effects of both surfactant and time-varying geometry have been included; the model determines the liquid layer flow resulting from a surface tension (Rayleigh) instability, and the computation traces the film's development to closure, yielding pressure, velocity, surface shape, and surfactant concentration distributions. It is found that surfactant is effective in retarding or eliminating liquid bridging through the reduction of the mean surface tension and the action of surface tension gradients. The former effect is also critical in minimizing the magnitude of the negative pressure in the liquid layer and thus presumably in reducing the tendency for airway compliant collapse.

Thermocapillary migration of a droplet with insoluble surfactant: I. Surfactant cap

The steady thermocapillary migration of a drop, in the presence of a stagnant cap of an insoluble nondiffusing surfactant, is treated theoretically. Gravitational effects are included for completeness, and analytical solutions are obtained under conditions of negligible convective transport of momentum and energy in the bulk phases. The migration velocity of the drop is calculated, and is found to reduce to the proper asymptotes in limiting cases. Typical streamline plots as well as interfacial velocity distributions are displayed. The distribution of surfactant concentration in the cap region is obtained using an ideal film model, and the conditions for the existence of the cap are discussed.

A micromechanical derivation of Fick's law for interfacial diffusion of surfactant molecules

A theory is presented for the diffusion of surfactant molecules, modeled as noninteracting Brownian spheres in proximity to, or straddling, the interface between two immiscible fluids. The spheres are assumed to be physicochemically inert except for the existence of short-range forces, which may be attractive and/or repulsive with respect to the interface. The number density of such particles is assumed small. Two alternative views of the diffusion process are presented; one, termed microscopic, in which variations in concentration are resolvable down to the scale l imposed by the short-range attractive or repulsive forces between the particles and the interface, and the other, termed macroscopic, in which variations are only discernible at the much larger scale, L, of gradients in the bulk surfactant concentration distribution, which are assumed to exist parallel to the interface. It is demonstrated that a rigorous theory can be developed, at the microscale, for prediction of the concentration profiles and diffusive flux of surfactant molecules parallel to the interface using only the well-established Stokes-Einstein theory of bulk-phase Brownian diffusion, and low Reynolds number hydrodynamics for the motion of a torque-free particle in close proximity, or straddling, a fluid-fluid interface. On the other hand, a macroscopic description of the same phenomena requires the introduction of new concepts, such as “adsorption” and “surface diffusion,” which are specifically associated with the interface, as seen from the macroscale of O( L). In the present paper, constitutive relationships for these macrosurface processes are derived in a rigorous manner from the more fundamental and complete microscopic description of the system. It is shown that Fick's law is applicable to surface diffusion, with the driving gradient based on a surface-excess concentration for surfactant particles. Furthermore, the surface diffusion coefficient is found to depend upon the Stokesian hydrodynamic resistance of a torque-free sphere translating parallel to the interface, as a function of the distance of its center from the interface, and upon the “adsorptive-potential” energy function which tends to cause the particles to accumulate there. Numerical values await the solution of the low Reynolds number hydrodynamics problem thereby posed, as well as the acquisition of knowledge relating to the potential energy function. Two examples of such potential energy functions are discussed for Brownian particles, one based upon a difference in area-specific, surface-free energies (i.e., solid/liquid interfacial tensions) for the two fluids, and the other on a simple density differential between the particle and the two fluids. Simple geometric models of surfactant molecules are also discussed in the context of potential energy functions for interaction between the molecules and the interface. The possibility of using such models in the analysis of other equilibrium and surface transport phenomena is pointed out.

An Improved Method for Simulating Ideal Low-Tension Flooding Processes

Introduction Most reservoir simulators employ finite-difference methods to solve the appropriate set of equations. Variables that influence the accuracy of the results are the time-step size and the cell dimensions. While the effects of these variables on the results of conventional simulators can be significant, they can be even more important with chemical-flooding models. This is because of the presence of an additional phase, such as a surfactant slug that is moving with time and that can occupy part of, or all of, a cell. Within this slug, fluid saturations and relative permeability relations are different than those ahead or behind it. This causes a mathematical problem that is the subject of this work. problem that is the subject of this work. DESCRIPTION OF THE PROBLEM Simulation of the low-tension flooding process involves calculating the three unknown variables, pressure, saturation, and surfactant concentration, pressure, saturation, and surfactant concentration, as a function of time and space. The pressure and saturation distributions can be calculated using the usual finite-difference methods of solution of the equations for immiscible flow. The surfactant concentration distribution can be determined by tracking the surfactant slug boundaries analogous to the scheme proposed by Vela et al. for polymerflood simulation. However, the surfactant slug polymerflood simulation. However, the surfactant slug maintains a fairly sharp boundary as it moves through the reservoir. Therefore, in some finite-difference cells, two distinct parts may exist, one with and one without surfactant. Each part is different from the other in fluid saturations and relative permeability relations. However, the finite-difference method of solution requires that the two parts be represented by one average saturation and by one relative permeability value. Thus, the problem is how to average the two parts and to determine how sensitive the results of simulation are to the averaging scheme, to the cell size, and to the time step. METHOD OF ATTACK Ideally, one wants an averaging scheme that (1) gives answers that are not sensitive to the time step or to the cell size, and (2) gives correct answers. The second criterion is the most difficult to check since no exact solution to the surfactant flood is reported in the literature. The work was started by developing an analytic solution (Buckley-Leverett type) to a one-dimensional surfactant flood. The solution is analogous to solutions for other tertiary recovery projects. It combines the relationship for the normalized motion of a point of constant saturation, with expressions for the dimensionless velocity of each phase, and vw = (1-fo)/(1-So). (fo is fractional flow of oil; So is oil saturation.) Saturations throughout the one-dimensional reservoir are thereby obtained. Several solution regimes result. (1) For oil-water viscosity ratios greater than unity, oil moves exclusively in front of the surfactant, forming a bank, and all the oil is produced. (2) For slightly unfavorable viscosity ratios, an oil bank is still formed, but the oil gradually invades the surfactant and may result in reduced production. (3) Highly unfavorable viscosity ratios cause all the oil to move through the surfactant, and no bank is formed. The one-dimensional surfactant flood was then simulated using an incompressible, two-dimensional, polymer-surfactant model that solves for the polymer-surfactant model that solves for the concentration using a point-tracking scheme based on the method of characteristics. This method eliminates numerical dispersion and results in sharp surfactant-slug interfaces. Several sets of runs were made, with each set using a different averaging scheme. The various schemes used are described in the next section. SPEJ P. 53