Numerical investigation of the effect of insoluble surfactants on drop deformation and breakup in simple shear flow

The effect of insoluble surfactants on drop deformation and breakup in simple shear flow is studied using a combination of a three-dimensional boundary-integral method and a finite-volume method to solve the coupled fluid dynamics and surfactant transport problem over the evolving interface. The interfacial tension depends nonlinearly on the surfactant concentration, and is described by the equation of state for the Langmuir isotherm. Results are presented over the entire range of the viscosity's ratio lambda and the surface coverage x, as well as the capillary number Ca that spans from that for small deformation to values that are beyond the critical one Ca(cr). The values of the elasticity number E, which reflects the sensitivity of the interfacial tension to the maximum surfactant concentration, are chosen in the interval 0.1 < or = E < or = 0.4 and a convection dominated regime of surfactant transport, where the influence of the surfactant on drop deformation is the most significant, is considered. For a better understanding of the processes involved, the effect of surfactants on the drop dynamics is decoupled into three surfactant related mechanisms (dilution, Marangoni stress and stretching) and their influence is separately investigated. The dependence of the critical capillary number Ca(cr)(lambda) on the surface coverage is obtained and the boundaries between different modes of breakup (tip-streaming and drop fragmentation) in the (lambda; x) plane are searched for. The numerical results indicate that at low capillary number, even with a trace amount of surfactant, the interface is immobilized, which has also been observed by previous studies. In addition, it is shown that for large Péclet numbers the use of the small deformation theory to measure the interfacial tension in the case where surfactants are present can introduce a significant error.     

Dynamics of Growth and Breakup of Viscous Pendant Drops into Air

This paper presents a numerical study of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical tube into ambient air. A model is developed to predict the evolution of the drop shape and its breakup based on RIPPLE, which is a solution algorithm for computing transient, two-dimensional, incompressible fluid flow with surface tension on free surfaces of general topology (D. B. Kothe and R. C. Mjolsness, AIAA J. 30, 2694 (1992)). The full Navier-Stokes system is solved by using finite-difference formulation on a Eulerian mesh. The mesh is fixed in space, with the flow and surface moving through it to ensure accurate calculations of complex free surface flows and topology, including surface breakup and coalescence. The novel feature of the numerical algorithm is the use of a Eulerian volume-tracking approach which allows the calculations to pass the breaking point during formation of a drop continuously without interruption or numerical modification and, therefore, to explore the features of generation of satellite droplets. The effects of physical and geometric parameters on the nonlinear dynamics of drop growth and breakup are investigated. The focus here is on drop breakup and subsequent formation of satellite droplets. The effects of finite inertial, capillary, viscous, and gravitational forces are all accounted for to classify different formation dynamics and to elucidate features of satellite droplet generation. The numerical predictions are compared with experimental measurements for water drops, and the results show good agreement. Copyright 1999 Academic Press.     

Dynamic surface tension measurements with submillisecond resolution using a capillary-jet instability technique

An oscillating capillary jet method is implemented to measure surface tension of aqueous nonionic surfactant solutions as a function of surface age from the jet orifice. The experimental technique captures the evolution of jet swells and necks continuously along the jet propagation axis and is used in conjunction with an existing linear, axisymmetric, constant-property model to determine surface tension of liquids. The method is first validated using deionized water and isopropyl alcohol (constant surface tension test fluids) and a procedure is described to identify the optimum wavelength from the breakup point, which produces the smallest error in surface tension measurements. Dynamic surface tension data of concentrated aqueous Tergitol NP-8 surfactant solutions is then presented. The measurements are performed over a spatial length of approximately 1.5 wavelengths, a span corresponding to 0.6-4.2 ms time window from the jet orifice. Submillisecond surface age measurements are made possible by decreasing the jet diameter. Increased surfactant concentrations make the liquid jet more stable and allow measurements at higher surface ages. The correlation of Hua and Rosen fits well the dynamic surface tension data, which includes submillisecond surface ages. Finally, the time required for surface tension to reach equilibrium levels is estimated using a simple adsorption kinetics theory of surfactant molecules on the liquid/air interface.     

Effects of soluble surfactants on the deformation and breakup of stretching liquid bridges

Surfactants are routinely used to control the breakup of drops and jets in many applications such as inkjet printing, crop spraying, and DNA or protein microarraying. The breakup of surfactant-free drops and jets has been extensively studied. By contrast, little is known about the closely related problem of interface rupture when surfactants are present. Solutions of a nonionic surfactant, pentaethylene glycol monododecyl ether, or C12E5, in water and in 90 wt % glycerol/water are used to show the effects of surfactant and viscosity on the deformation and breakup dynamics of stretching liquid bridges. Equilibrium surface tensions for both solutions can be fitted with the Langmuir-Szyskowski equation. All experiments have been done at 24 degrees C. The critical micelle concentrations for C12E5 are 0.04 and 0.4 mM in water and the glycerol/water solution, respectively. With high-speed imaging, the dynamic shapes of bridges held captive between two rods of 3.15 mm diameter are captured and analyzed with a time resolution of 0.1-1 ms. The bridge lengths are 3.15 mm initially and about 5-7 mm at pinch-off. Breakup occurs after stretching for about 0.2-0.3 s, depending on the solution viscosity and the surfactant concentration. When the liquid bridges break up, the volume of the sessile drop left on the bottom rod is about 3 times larger than that of the pendant drop left on the top rod. This asymmetry is due to gravity and is influenced by the equilibrium surface tensions. Surfactant-containing low-viscosity water bridges are shown to break up faster than surfactant-free ones because of the effect of gravity. With or without surfactant, water bridges form satellite drops. Surfactant-containing high-viscosity glycerol/water bridges break up more slowly than surfactant-free ones because of strong viscous effects. Moreover, the shapes of the sessile drops close to breakup exhibit a "pear-like" tip; whether a satellite forms depends on the surface age of the bridge before stretching commences. These unexpected effects arising from the addition of surfactants are due to the capillary pressure reduction and Marangoni flows linked to dynamic surface tension.     

HYDRODYNAMIC AND THERMODYNAMIC EFFECTS IN PHASE INVERSION EMULSIFICATION PROCESS OF EPOXY RESIN IN WATER

The mechanism of phase inversion emulsification process （PIE） was studied for waterborne dispersion of highly viscous epoxy resin using non-ionic polymeric surfactants. Drop deformation and breakup, rheological properties, conductivity, and particle size measurements reveal the micro-structural transition amid emulsification. It is revealed that strong flow causes water drop to burst with the formation of droplets and huge interface. Phase inversion corresponds to an abrupt rheological transition from a type of viscous melt with weak elasticity to a highly elastic type of aqueous gel. This implies that the phase inversion equivalent to a curvature inversion. Based on this, a geometric model is postulated to correlate process variables to the particle size. The coverage and conformation of the surfactant plays key role for the particle size of the final emulsion. The interactions of thermodynamic and hydrodynamic effects are also discussed. It is concluded that the thermodynamics control the PIE while the hydrodynamics drives the creation of interface and involves every step of PIE.     

A numerical study of the effect of insoluble surfactants on the stability of a viscous drop translating in a Hele-Shaw cell

A circular drop is a linearly stable solution for the buoyancy-driven motion of drops in a Hele-Shaw cell [Gupta et al. J. Colloid Interface Sci.218(1), 338 (1999)]. In the absence of surface-active agents, an initially prolate drop always goes to a steady circular shape while initially oblate drops exhibit complex dynamics [Gupta et al. J. Colloid Interface Sci.222, 107 (2000)]. In this study, the effect of insoluble surfactant impurities on the critical conditions for drop breakup is explored by using the Langmuir adsorption framework in conjunction with a physically based expression for the depth-averaged tangential stress exerted on a two-phase interface in a Hele-Shaw cell. It is shown that the presence of surfactants can have both a stabilizing and a destabilizing effect on the shape of the drop, depending on the Bond number, the magnitude of the initial perturbation, and the strength of surface convection. Similar to the clean drop dynamics, two marginally stable branches are found. Increasing the surface Peclet number results in the stabilization of the main branch while the secondary branch shifts to higher Bond numbers. The mode of breakup is also found to be strongly influenced by the strength of surface convection.     

DNA and cationic surfactant complexes at hydrophilic surfaces. An ellipsometry and surface force study

The adsorption and formation of DNA and cationic surfactant complexes at the silica-aqueous interface have been studied by ellipsometry. The interaction between the DNA-surfactant complexes at the mica-aqueous interface has been determined by the interferometric surface force apparatus. Adsorption was as expected not observed on negatively charged hydrophilic surfaces for DNA and when DNA-cationic surfactant complexes were negatively charged. However, adsorption was observed when there is an excess of cationic surfactant, just below the point of phase separation. The adsorption process requires hours to reach steady state. The adsorbed layer thickness is large at low surface coverage but becomes more compact and thinner at high coverage. A long-range repulsive force was observed between adsorbed layers of DNA-cationic surfactant complexes, which was suggested to be of both electrostatic and steric origin. The forces were found to be dependent on the equilibration time and the experimental pathway.     

Enhanced surfactant determination by ion-pair formation using flow-injection analysis and dynamic surface tension detection

Chemical analysis of surface active species (surfactants) is of interest for many applications, such as in process monitoring, biomedical applications, environmental monitoring and surface science investigations. Recently, we reported a dynamic surface tension detector (DSTD) based upon optically probing the size of a repeating drop resulting from constant flow of an aqueous solvent out of the end of a capillary. Presence of a surfactant in a growing drop reduces the surface tension at the air-solvent interface, causing the drop to detach at a smaller volume, which is detected. The DSTD has a kinetic dependence, and with increasing flow rate the sensitivity decreases due to diffusional and adsorption effects. We report that for the sodium salt of dodecylsulfate (DS), the DSTD performs significantly better with a stainless steel (S.S.) capillary dropper than with a fused silica dropper because the S.S. dropper exhibits a smaller adsorption effect as a function of time. Flow-injection analysis with the DSTD of DS was found to enhance sensitivity 50-fold by in-situ reaction with the ion-pair reagent tetrabutylammonium hydroxide (TBA) in water, even though the TBA alone was not very surface active. The TBA-DS system serves as a model for a selective detection method in which surface activity is exploited and enhanced. The detection limit for DS, as TBA-DS, was 400 ppb. Additionally, weakly surface active species such as TBA could be analyzed "indirectly" by ion-pair formation with DS. The enhanced sensitivity is due to increased packing of the ion-pairs at the air-aqueous solvent interface. The flow rate dependence on the sensitivity of detecting the TBA-DS ion-pair was examined. Two limiting conditions were observed as a function of ion-pair concentration: sensitivity decreases linearly with inverse flow rate at high flow rates and approaches a steady state at slower flow rates.     

A Surface Rheological Study of Silwet L-77 Surfactant at the Air/Water Interface

The dilational viscoelastic properties of Silwet L-77, a trisiloxane surfactant of the general formula (Me₃SiO)₂SiMe(CH₂)₃(OCH₂CH₂)_7.5OH, at the air/water interface were investigated. Aqueous solutions of Silwet L-77 were spread onto a pendant drop and the dynamic surface tensions were measured by means of axisymmetric drop shape analysis. The surface dilatational elasticity, viscosity, and phase angle of the adsorption monolayer were also determined using the oscillating drop technique. The influences of frequency and concentration on the surface dilational properties were expounded. It is shown that the surface dilational modulus and elastic modulus increased with the increase of frequency, the viscous modulus was complex, while the phase angle decreased with the increase of frequency. Surface dilational modulus, elastic modulus, and viscous modulus passed through the maximum with the increase of bulk concentration and the phase angle increased with the increase of concentration.     

Drop profile analysis tensiometry with drop bulk exchange to study the sequential and simultaneous adsorption of a mixed β-casein /C12DMPO system

The formation of mixed protein/surfactant adsorption layers is studied by the drop profile analysis tensiometry equipped with a special tool for drop volume exchange during experiments. This arrangement allows investigating in the traditional way by simultaneous adsorption from a mixed solution and also by a subsequent adsorption of the protein followed by surfactant. The experiments are performed for β-casein as the protein in the presence of different amounts of the non-ionic surfactant C₁₂DMPO. The surface layers formed via the two routes show similar equilibrium surface properties. However, the dynamics of desorption of the protein complexes into the pure buffer solution deviate significantly, which is explained by the different locations of the protein/surfactant interaction. Although in both cases the complex formation is based on hydrophobic interaction, the accessibility of the hydrophobic parts of pre-adsorbed proteins due to unfolding is more favourable by the surfactant than in the solution bulk. Therefore, the amount desorbed from surface layers formed from mixed solutions is significantly less as compared to the displacement of proteins by subsequently injected surfactants interacting at the surface.     

Transient Surface Tension of an Expanding Liquid Sheet

We address the problem of dynamic surface tension using measurements of sheet diameters that results from the impact of a liquid jet of diameter d(0) on a small disk of diameter d(i) (d(i)/d(0) approximately 4). At low velocities, the sheet diameter D is related to d(0) by the Weber number We, constructed with the liquid density rho, the jet velocity u(0), and the surface tension sigma at the rim: D/d(0)=18 We=18 [rho u(0)(2)/(sigma/d(0))]. This relation expresses the equilibrium between inertial forces and surface tension forces at the sheet rim. When a surfactant has been dissolved in the bulk of the liquid prior to the formation of the initial jet, the rim surface tension, and therefore the sheet diameter, depends on the amount of surfactant adsorbed at the rim. This amount is fixed by a competition between surface formation induced by radial extension and repopulation of the liquid interface in surfactant. The experimental setup proposed here provides a method to measure dynamic surface tension from sheet diameter measurements and symmetrically to monitor the adsorption of a surfactant on a liquid surface. The available adsorption time ranges from 10 to 100 ms. Experimental data obtained with two surfactants are in agreement with a model of a diffusion-controlled adsorption at the interface. Copyright 2000 Academic Press.     

AFM study on the wettability of mica and graphite modified with surfactant DTAB

In this work atomic force microscopy (AFM) was applied to study the wettability of mica and graphite modified with surfactant dodecyltrimethylammonium bromide (DTAB) at varying DTAB concentrations (below the cmc) and adsorption time. The coverage states of DTAB on surfaces were analyzed from the AFM images, while the contact angle measurement was made for the wettability of DTAB-modified surfaces. The experimental results have shown that the adsorption aggregates formed as needle-like dots covering on the mica surface with the surfactant concentration of 10^?6–10^?4?mol/L. The coverage of DTAB aggregates increased with the increasing concentration, leading to a strong hydrophobicity on the surfaces. However, the large aggregates which might be caused by bilayer adsorption of surfactant occurred on mica surface at surfactant concentration of 10^?3?mol/L, resulting in the reverse of the wettability as the adsorption time extended. In the case of hydrophobic graphite, DTAB aggregates mainly formed as stripe covering on the surfaces, leading to the reduction of hydrophobicity. This reduction became stronger as more DTAB aggregates covered on graphite surfaces.     

Double sample preconcentration by in‐line coupled large volume single drop microextraction and sweeping in capillary electrophoresis

Single drop microextraction (SDME) is a convenient and powerful preconcentration method for CE before injection. By simple combination of sample‐handling sequences without modification of the CE apparatus, a drop of an aqueous acceptor phase covered with a thin organic layer was formed at the tip of a capillary; 10 min SDME of fluorescein and 6‐carboxyfluorescein from a donor phase of pH 1 to an acceptor phase of pH 9 provided 110‐fold enrichments without stirring the donor phase. To improve the concentration effect further, SDME was coupled with an on‐line (after injection) sample preconcentration method, sweeping, in which analytes in a long sample zone are accumulated at the boundary of a pseudostationary phase penetrating into the sample zone. It is thus necessary to inject a sample of much larger volume than that of a drop in typical SDME. A Teflon sleeve over the capillary inlet allowed a large volume drop to be held stably during extraction. By in‐line coupling 10 min SDME and sweeping of a 30 nL sample using a cationic surfactant dodecyltrimethylammonium, enrichment factors of the double preconcentration were increased up to 32 000.     

Layer-by-layer adsorption of polyelectrolyte and surfactant and adsorption of their complexes on solid surface

The capillary electrokinetics method (measurement of streaming potential and current in a capillary with a radius of 5–7 μm made of fused quartz) is employed to study the structure formation at interfaces between quartz and solutions containing a cationic polyelectrolyte (poly(diallyldimethylammonium chloride) with molecular mass M = 100000−200000) and an anionic surfactant (sodium dodecyl sulfate). The kinetics of surface layer formation is studied upon the layer-by-layer adsorption of the components and the adsorption of their complexes at the same component ratios. It is established that the formation time and the electrokinetic potentials of the surface layers are almost independent of the procedure of their formation. In the case of the layer-by-layer adsorption, the first layers of the polyelectrolyte appear to be virtually undeformed, thus indicating that molecules with a planar conformation prevail in the adsorption layer. Surfactant adsorption enhances the deformation (layer loosening), which decreases with time (layer aging). Layers formed from the complexes have a denser (less deformable) structure. Variations in the electrokinetic potentials of the layers during the long-term pumping of a background electrolyte solution through a capillary witnesses the prevailing desorption of the anionic surfactant, with the desorption being noticeably more pronounced for the layers resultant from the adsorption of the complexes.     

Surfactant-assisted spreading of a liquid drop on a smooth solid surface

Axisymmetric spreading of a liquid drop covered with an insoluble surfactant monolayer on a smooth solid substrate is numerically investigated. As the drop spreads, the adsorbed surfactant molecules are constantly redistributed along the air-liquid interface by convection and diffusion, leading to nonuniformities in surface tension along the interface. The resulting Marangoni stresses affect the spreading rate by altering the surface flow and the drop shape. In addition, surfactant accumulation in the vicinity of the moving contact line affects the spreading rate by altering the balance of line forces. Two different models for the constitutive relation at the moving contact line are used, in conjunction with a surface equation of state based on the Frumkin adsorption framework, to probe the surfactant influence. The coupled evolution equations for the drop shape and monolayer concentration profile are integrated using a pseudospectral method to determine the rate of surfactant-assisted spreading over a wide range of the dimensionless parameters governing the spreading process. The insoluble monolayer enhances spreading through two mechanisms; a reduction in the equilibrium contact angle, and an increase in the magnitude of the radial pressure gradient within the drop due to the formation of positive surface curvature near the moving contact line. Both mechanisms are driven by the accumulation of surfactant at the contact line due to surface convection. Although the Marangoni stresses induced at the air-liquid interface reduce the rate of spreading during the initial stages of spreading, their retarding effect is overwhelmed by the favorable effects of the aforementioned mechanisms to lead to an overall enhancement in the rate of spreading in most cases. The spreading rate is found to be higher for bulkier surfactants with stronger repulsive interactions. With the exception of monolayers with strong cohesive interactions which tend to retard the spreading process, the overall effect of an insoluble monolayer is to increase the rate of drop spreading. Simulation results for small Bond numbers indicate the existence of a power-law region for the time-dependence of the basal radius of the drop, consistent with experimental measurements.     

Regularities of the Two-Layer Adsorption of Anionic Surfactant and Cationic Polyelectrolyte on the Fused Quartz Surface

The adsorption of sodium dodecyl sulfate (SDS) on the quartz capillary surface that was preliminarily covered with a layer of cationic polyelectrolyte (CPE) is studied. The charge sign change of the modified quartz surface and subsequent increase of negative surface charge observed upon the adsorption of SDS indicate the formation of the second adsorption layer composed of surfactant molecules. It is shown that the surfactant layer is stronger attached to the surface at a higher charge of the CPE adsorption layer. Upon the formation of the surfactant layer on a looser CPE adsorption layer, the desorption of SDS molecules decreases, which can be associated with the partial penetration of these molecules into the CPE layer.__________Translated from Kolloidnyi Zhurnal, Vol. 67, No. 4, 2005, pp. 573–574.Original Russian Text Copyright © 2005 by Sergeeva, Ermakova, Anuchkina, Sobolev, Churaev.     

Dynamic surface properties of polyelectrolyte/surfactant adsorption films at the air/water interface: poly(diallyldimethylammonium chloride) and sodium dodecylsulfate

The dynamic surface elasticity, dynamic surface tension, and ellipsometric angles of mixed aqueous poly(diallyldimethylammonium chloride)/sodium dodecylsulfate solutions (PDAC/SDS) have been measured as a function of time and surfactant concentration. This system represents a typical example of polyelectrolyte/surfactant complex formation and subsequent aggregation on the nanoscale. The oscillating barrier and oscillating drop methods sometimes led to different results. The surface viscoelasticity of mixed PDAC/SDS solutions are very close to those of mixed solutions of sodium polystyrenesulfonate and dodecyltrimethylammonium bromide but different from the results for some other polyelectrolyte/surfactant mixtures. The abrupt drop in surface elasticity when the surfactant molar concentration approaches the concentration of charged polyelectrolyte monomers is caused by the formation of microparticles in the adsorption layer. Aggregate formation in the solution bulk does not influence the surface properties significantly, except for a narrow concentration range where the aggregates form macroscopic flocks. The mechanism of the observed relaxation process is controlled by the mass exchange between the surface layer and the flocks attached to the liquid surface.     

Effect of coating electrolytes on two-tailed surfactant bilayer coatings in capillary electrophoresis

Surfactants such as dioctadecyldimethylammonium bromide (DODAB) form semi-permanent coatings that effectively prevent adsorption of cationic proteins onto the fused silica capillary in capillary electrophoresis (CE). The bilayer coating is generated by flushing the capillary with a 0.1 mM surfactant solution. However, formation of the bilayer is strongly dependent on the coating electrolyte. The effect of counter-ions, electrolyte concentrations and buffer co-ions were monitored based on: the separation of basic model proteins; the adsorption kinetics of DODA⁺ onto fused silica; and dynamic light scattering (DLS) to determine vesicle size. Low concentrations (≤10.0 mM) and/or weakly associating buffers such as phosphate (pH 3.0), acetate (pH 4.0) and chloride should be used for DODAB coating solutions. Dissolving the surfactant in strongly associating electrolyte, such as phosphate at pH 7.0, results in poor coating of the capillary surface. Effective cationic bilayer coatings are formed if the buffer conditions favor formation of vesicles with diameters < 300 nm. Monitoring turbidity at 400 nm provides a convenient means of verifying vesicle diameter variation of <5 nm; that is, that the coating solution is effective.     

Self-aggregation of cationic surfactants onto oxidized cellulose fibers and coadsorption of organic compounds

In this work, the adsorption of cationic surfactant and organic solutes on oxidized cellulose fibers bearing different amounts of carboxylic moieties was investigated. The increase in the amount of -COOH groups on cellulose fibers by TEMPO oxidation induced a general rise in surfactant adsorption. For all tested conditions, that is, cellulose oxidation level and surfactant alkyl chain length (C12 and C16), adsorption isotherms displayed a typical three-region shape with inversion of the substrate zeta-potential which was interpreted as reflecting surfactant adsorption and aggregation (admicelles and hemimicelles) on cellulose fibers. The addition of organic solutes in surfactant/cellulose systems induced a decrease in surfactant cac on the cellulose surface thus favoring surfactant aggregation and the formation of mixed surfactant/solute assemblies. Adsorption isotherms of organic solutes on cellulose in surfactant/cellulose/solute systems showed that solute adsorption is strictly correlated to (i) the surfactant concentration, solute adsorption increases up to the surfactant cmc, where solute partitioning between the cellulose surface and free micelles causes a drop in adsorption, and to (ii) solute solubility and functional groups. The specific shape of solutes adsorption isotherms at a fixed surfactant concentration was interpreted using a Frumkin adsorption isotherm, thus suggesting that solute uptake on cellulose fibers is a coadsorption and not a partitioning process. Results presented in this study were compared with those obtained in a previous work investigating solute adsorption in anionic surfactant/cationized cellulose systems to better understand the role of surfactant/solute interactions in the coadsorption process.