Double-layer interaction between parallel solid cylinders partially immersed in an oil/water interface

We consider two identical, parallel, infinitely long solid cylinders at a given separation, lying flat on a plane oil/water interface and both immersed to the same extent in the oil and water phases. The part of the surface of each cylinder in contact with the aqueous phase is charged, forming an electric double layer in a symmetrical aqueous binary electrolyte. The electrical potential in the overlapping electric double layers in the aqueous phase satisfies the Poisson-Boltzmann equation. The potentials within the uncharged interiors of the solid cylinders and in the oil phase satisfy Laplace's equation. The equations for the three potentials are solved simultaneously using the finite element method with Galerkin weighted residuals. The double-layer interaction per unit length of the cylinders is then calculated. Of the numerical results obtained, three deserve special mention. First, a short-range double-layer repulsion, decaying exponentially with separation between the two cylinders, acts through the aqueous electrolyte medium, whereas in the case of an uncharged oil/water interface a weaker, but much longer-ranging, repulsive interaction acts through the oil medium. Second, reasonable estimates of the short-range interaction between cylinders in a planar interface can be obtained from the Derjaguin approximation for thin double layers. Third, in addition to the repulsive force between the cylinders parallel to the oil/water interface, a force normal to the interface acts on the cylinders in the direction of the aqueous electrolyte phase.     

Electrical interaction between two rod-like particles covered by an ion-penetrable membrane in a water–oil interface

The electrical interaction between two long, parallel rod-like particles in a water–oil interface is investigated based on a Green function method, which is applicable to a system containing particles with different physical parameters. This is a highly desirable feature from practical considerations. We consider the case where each particle is covered by a membrane, and assumes a general class of shapes. This extends previous results in the literature in that they can be recovered as the special cases of the present model. We show that: (1) The higher the ionic strength in bulk water phase, the less stable the system concerned. (2) The closer the shape of the particles to a cylinder, the more stable the system under consideration. (3) The larger the fraction of particle immersed in the water phase, the greater the electrical interaction force. (4) The electrical interaction force increases with the increase in both the surface potential ratio between two particles and the fixed charge density in the membrane.     

The load supported by small floating objects

We consider the equilibrium flotation of a two-dimensional cylinder and a sphere at an interface between two fluids. We give conditions on the density and radius of these objects for them to be able to float at the interface and discuss the role played by the contact angle in determining these conditions. For cylinders with a small radius, we find that the maximum density is independent of contact angle but that, for spheres, the contact angle enters at leading order in the particle radius. Our theoretical predictions are in agreement with experimental results.     

General solution to two-dimensional nonslipping JKR model with a pulling force in an arbitrary direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Deltagamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.     

The lateral electric force on an off-axis sphere in a circular cylinder

The electrophoretic velocity of a sphere within a liquid-filled circular cylinder in a direction parallel to the cylinder axis has been studied by Yariv and Brenner (Phys. Fluids 2002, 14, 3354–3357; SIAM J. Appl. Math. 2003, 64, 423–441). We use their analyses of the electric field in order to determine the electrical force on the sphere along the cylinder radius (i.e., perpendicular to its axis) when either the radius of the sphere is small compared to that of the cylinder, or when the radius of the sphere is only slightly smaller than that of the cylinder. In both cases the force acts towards the centreline of the cylinder, and hence this force tends to stabilize electrophoresis of the sphere along the cylinder axis.     

Particle-interface interaction across a nonpolar medium in relation to the production of particle-stabilized emulsions

Quantitative theory of the particle-interface interaction across a nonpolar medium is developed. We consider a spherical dielectric particle (phase 1), which is immersed in a nonpolar medium (phase 2), near its boundary with a third dielectric medium (phase 3). The interaction originates from electric charges at the particle surface (e.g., the surface of a silica particle immersed in oil). The theoretical problem is solved exactly, in terms of Legendre polynomials, for arbitrary values of the dielectric constants of the three phases. As a result, expressions for calculating the interaction force and energy are derived. These expressions generalize the known theory of the electrostatic image force (acing on point charges) to the case of particles that have finite size and uniform surface charge density. For typical parameter values (silica or glass particles immersed in tetradecane), the image-force interaction becomes significant for particles of radius R > 30 nm. At fixed relative particle-to-interface distance, the force increases with the cube of the particle radius. In general, this is a strong and long-range interaction. For micrometer-sized particles, the interaction energy could be on the order of 10(5) k(B)T at close contact, and, in addition, the interaction range could be about 10(5) particle radii. The sign of the interaction depends on the difference between the dielectric constants of phases 2 and 3. When phase 3 has a smaller dielectric constant (e.g., air), the interface repels the particle. In contrast, when phase 3 has a greater dielectric constant (e.g., water), the interaction is attractive. Especially, water drops attract charged hydrophobic particles dispersed in the oily phase, and thus favor the formation of reverse particle-stabilized (Pickering) emulsions. The particle-interface interaction across the oily phase is insensitive to the concentration of electrolyte in the third, aqueous phase.     

Measurement of the adsorption at solid-liquid interfaces from the pressure dependence of contact angles

Earlier studies have indicated that in an isothermal three-phase system, the liquid-phase pressure at the three-phase line, xL3, may be viewed as the independent variable of the contact angle, theta, and that adsorption at the solid-liquid interface is the mechanism relating them. When the liquid-vapor interface is axi-symmetric, we show that theta can be predicted as a function of xL3 and that by measuring theta(xL3), the amount adsorbed at the solid-liquid interface can be determined. We consider water in differently sized borosilicate glass cylinders. For progressively larger cylinders, xL3 increases with cylinder radius, but when a particularly sized cylinder is rotated about it longitudinal axis, xL3 is decreased. The observed value of theta in each case is found to be in close agreement with that predicted. A Gibbs model of the interphase is used, and the Gibbs adsorption at the solid-liquid interface is found to be negative. As xL3 increases above its value at wetting, the amount adsorbed at the solid-liquid interface becomes progressively more negative. Negative adsorption is shown to mean that the concentration of the fluid component is greater in the bulk liquid than in the interphase and that the difference in concentration increases as xL3 is increased. The data is used to investigate the hypothesis that the curvature of the three-phase line affects theta through line tension, but we find no relation between line tension and theta. There is an apparent relation between the curvature of the liquid-vapor interface, CLV and theta, but this is shown to be because CLV affects xL3.     

四甲基氢氧化铵改性聚偏氟乙烯一步接枝聚苯乙烯磺酸油水分离膜的制备及性能

利用四甲基氢氧化铵(TMAH)聚偏氟乙烯(PVDF)进行改性,以过氧化苯甲酰(BPO)为引发剂,将苯乙烯磺酸(SSA)接枝到改性的PVDF骨架上,制得聚偏氟乙烯接枝聚苯乙烯磺酸(PSSA-g-PVDF)油水分离膜。 研究了TMAH质量分数对PSSA的接枝率和油水分离膜性能的影响,同时采用傅立叶变换红外光谱(FTIR)、扫描电子显微镜(SEM)和视频光学接触角测量仪测试了膜的结构和表面接触角。 结果表明,TMAH使PVDF脱去部分氟化氢(HF)产生碳碳双键,硫元素均匀地分布在分离膜中。 PSSA的接枝率随着TMAH的质量分数增加而升高,分离膜的水通量随接枝率的升高先增加后降低。 当TMAH质量分数为20%,分离膜的接触角在30 s内降低到37.2°,接枝率和水通量分别为22.1%、643.3 L/(m·h),截留率和水通量恢复率分别达到90.6%和93.7%,衰减率为7.1%。 循环测试显示膜的水通量恢复率和油水通量恢复率均在90%以上。     

Fabrication of blend hydrophilic polyamide imide (Torlon®)-sulfonated poly (ether ether ketone) hollow fiber membranes for oily wastewater treatment

Blend hydrophilic polyamide imide (PAI)-sulfonated poly (ether ether keton) (SPEEK) hollow fiber membranes were fabricated for oil-water emulsion separation. The structure and performance of the membranes were examined by FESEM analysis, N₂ permeation, overall porosity, collapsing pressure, water contact angle, pure water flux, molecular weight cutoff (MWCO), and oil rejection tests. By studying ternary phase diagrams of polymer/solvent-additive/water system, the higher phase-inversion rate was confirmed for the solutions prepared at higher PAI/SPEEK ratio. A more open structure with larger finger-likes was observed by increasing PAI/SPEEK ratio. Mean pore size of 81 nm, overall porosity of 79% and water contact angle of 58° were obtained for the improved membrane prepared by PAI/SPEEK ratio of 85/15. Increasing SPEEK ratio resulted in lower mechanical stability in terms of collapsing pressure. Pure water flux of about 2.5 times of the plain PAI membrane was found for the improved membrane. MWCO of 460 kDa was found for the improved blend membrane. From oil rejection test, all the membranes demonstrated an oil rejection of over 95%. The improved membrane showed a lower rate of permeate flux reduction compared to the plain membrane which was related to the smaller fouling possibility. Less fouling resistance of the improved membrane was related to the higher flux recovery ratio (about 92%). For all the membranes, the dominant fouling mechanism was found to be the cake filtration. The improved PAI-SPEEK hollow fiber membranes was found to be practical for ultrafiltration of oily wastewaters.     

Stick slip contact mechanics between dissimilar materials: effect of charging and large friction

Measurements of the contact radius as a function of applied force between a mica surface and a silica surface (mica/silica) in air are reported. The load/unload results show that the contact radius generally increases with applied force. Because of the presence of charging due to contact electrification, both a short-range van der Waals adhesion force and longer-range electrostatic adhesive interaction contribute to the measured force. The results indicate that approximately 20% of the pull-off force is due to van der Waals forces. The contact radius versus applied force results can be fit to Johnson-Kendall-Roberts (JKR) theory by considering that only the short-range van der Waals forces contribute to the work of adhesion and subtracting a constant longer-range electrostatic force. Also, an additional and unexpected step function is superimposed on the contact radius versus applied force curve. Thus, the contact diameter increases in a stepped dependence with increasing force. The stepped contact behavior is seen only for increasing force and is not observed when symmetric mica/mica or silica/silica contacts are measured. In humid conditions, the contact diameter of the mica/silica contact increases monotonically with applied force. Friction forces between the surfaces are also measured and the shear stress of a mica/silica interface is 100 times greater than the shear stress of a mica/mica interface. This large shear stress retards the increase in contact area as the force is increased and leads to the observed stepped contact mechanics behavior.     

Physical properties of nanobubbles on hydrophobic surfaces in water and aqueous solutions

In recent years there has been an accumulation of evidence for the existence of nanobubbles on hydrophobic surfaces in water, despite predictions that such small bubbles should rapidly dissolve because of the high internal pressure associated with the interfacial curvature and the resulting increase in gas solubility. Nanobubbles are of interest among surface scientists because of their potential importance in the long-range hydrophobic attraction, microfluidics, and adsorption at hydrophobic surfaces. Here we employ recently developed techniques designed to induce nanobubbles, coupled with high-resolution tapping-mode atomic force microscopy (TM-AFM) to measure some of the physical properties of nanobubbles in a reliable and repeatable manner. We have reproduced the earlier findings reported by Hu and co-workers. We have also studied the effect of a wide range of solutes on the stability and morphology of these deliberately formed nanobubbles, including monovalent and multivalent salts, cationic, anionic, and nonionic surfactants, as well as solution pH. The measured physical properties of these nanobubbles are in broad agreement with those of macroscopic bubbles, with one notable exception: the contact angle. The nanobubble contact angle (measured through the denser aqueous phase) was found to be much larger than the macroscopic contact angle on the same substrate. The larger contact angle results in a larger radius of curvature and a commensurate decrease in the Laplace pressure. These findings provide further evidence that nanobubbles can be formed in water under some conditions. Once formed, these nanobubbles remain on hydrophobic surfaces for hours, and this apparent stability still remains a well-recognized mystery. The implications for sample preparation in surface science and in surface chemistry are discussed.     

The viscous drag of three-dimensional model fibrous filters

Dependences of the viscous drag of the model filter consisting of two parallel cylinder rows arranged perpendicular to the Stokes flow and to each other, on a step and a distance between rows are found. The approximation formula for the drag force of a cylinder in contacting rows is obtained. The drag was calculated for the three-dimensional model filter where two hexagonal grids of cylinders are inserted into each other at a right angle. The drag force of a cylinder for this model is close to that for the fan model filter.     

Fabrication,characterization, and performance evaluation of polyethersulfone/TiO2 nanocomposite ultrafiltration membranes for produced water treatment

In the present work, development of neat and nanocomposite polyethersulfone membranes composed of TiO₂ nanoparticles is presented. Membranes are fabricated using nonsolvent phase inversion process with the objective of improving antifouling, hydrophilicity, and mechanical properties for real and synthetic produced water treatment. Membranes are characterized using scanning electron microscopy, Fourier‐transform infrared, contact angle, porosity measurement, compaction factor, nanoparticles stability, and mechanical strength. The performance of prepared membranes was also characterized using flux measurement and oil rejection. Fourier‐transform infrared spectra indicated that noncovalence bond formed between Ti and polyethersulfone chains. The contact angle results confirmed the improved hydrophilicity of nanocomposite membranes upon addition of TiO₂ nanoparticles owing to the strong interactions between fillers and water molecules. The increased water flux for nanocomposite membranes in comparison with neat ones can be due to coupling effects of improved surface hydrophilicity, higher porosity, and formation of macrovoids in the membrane structure. The membrane containing 7 wt% of TiO₂ nanoparticles was the best nanocomposite membrane because of its high oil rejection, water flux, antifouling properties, and mechanical stability. The pure water flux for this membrane was twice greater than that of neat membrane without any loss in oil rejection. The hydrophilicity and antifouling resistance against oil nominates developed nanocomposite membranes for real and synthetic produced water treatment applications with high performance and extended life span.     

The role of bentonite addition in UF flux enhancement mechanisms for oil/water emulsion

The main problem in treating oil/water emulsion from car wash waste-water by ultrafiltration (UF) is fouling caused by oil adsorption on the membrane surface and internal pore walls. This study demonstrates that the addition of bentonite clay can reduce the adsorption layer on cellulose acetate UF membrane, resulting in a reduction of total membrane resistance (R_t). Experiments were conducted to identify and describe three possible mechanisms: (i) bulk oil emulsion concentration reduction; (ii) particle aggregation and (iii) detachment of the adsorbed gel layer by shear force. Adsorption of oil emulsion by bentonite can lead to a significant reduction of bulk oil emulsion concentration, one of the major causes of flux enhancement. Results show that contact of oil emulsion with bentonite forms larger particles resulting in flux increment. An optimum particle size of 37 μm, corresponds with a bentonite concentration of 300 mg/l and provided the highest flux. Beyond this limiting concentration, flux improvement gradually declined, possibly due to the formation of packed cake of particles on the membrane surface. The presence of bentonite in the oil emulsion promotes high shear stress which acts against the gel layer. This high shear stress, caused by bentonite particles and cross-flow velocity, reverses the adsorbed gel layer to the bulk of the liquid phase.     

Preparation and Evaluation of iPP/GO Microfiltration Membrane with Enhanced Antifouling Property

Isotactic polypropylene(iPP) and graphene oxide(GO), dispersed in dibutyl phthalate(DBP) and dioctyl phthalate(DOP), were blended to prepare organic-inorganic-blended microfiltration membranes using thermally induced phase separation(TIPS). These membranes were characterized by scanning electron microscopy(SEM), Fourier transform infrared spectroscopy(FTIR), contact angle measurements, mechanical properties, permeation tests, and porosity measurements. The morphology studied by SEM shows larger pores of the GO-blended membranes when compared to those of unmodified iPP membranes. Composite iPP/GO membranes achieve better performance in terms of water fluxes and pure water fluxes recovery ratio due to the hydrophilic nature of GO when compared with the pure iPP membranes. The addition of GO increases the permeability and the tensile strength by 352.98% and 123%, respectively, and also decreases the contact angle from 125° to 52.33°. We concluded that the composite membrane with 0.3% GO has the best antifouling ability of the membranes tested because it has the highest values of mean pore radius, porosity, and water flux observed in this study.     

Janus cylinders at liquid-liquid interfaces

We describe the first study on the self-assembly behavior of Janus cylinders at liquid/liquid interfaces. The Janus cylinders are characterized by a phase separation along the major axis into two hemicylinders of different wettability. The pendant drop technique and microscopic imaging were used to characterize the adsorption behavior and self-assembly of Janus cylinders at perfluorinated oil/dioxane and perfluorinated oil/dimethyl sulfoxide interfaces. According to the evolution of the interfacial tension and a series of TEM images taken during the cylinder adsorption, we will specify the characteristics of early to late stages of the Janus cylinder adsorption at a liquid-liquid interface and discuss the effect of Janus cylinder length and their concentration. We also establish that the broken symmetry of the corona leads to significantly higher interfacial activity as compared to homogeneous core-shell cylinders. The adsorption is characterized by three different adsorption stages: first, free diffusion to the interface, followed by continuous adsorption of cylinders including ordering and domain formation and, finally, additional packing with a rearrangement of domains and formation of a loose multilayer system.     

Analytical Dispersion Force Calculations for Nontraditional Geometries

Presented in this paper are first-principle-based approximate macroscopic models of the van der Waals adhesion force for a variety of particle shapes interacting with an infinite cylinder. In particular, expressions for the van der Waals adhesion force and interaction energy are developed for a (1) spherical particle/infinite cylinder, (2) disk-like particle/infinite cylinder, (3) disk-like particle oriented edgewise to an infinite cylinder, and (4) a deformed slice/infinite cylinder. The models presented depict expected trends in the behavior of both the force of adhesion and the interaction energy between different geometric configurations. These results are also used to demonstrate the impact of contact time on the adhesion force for cylindrical fibers in contact with a disk-shaped particle. After long time intervals where the disk-like particles have remained in contact with the cylinder, the adhesion force may lead to significant deformation of the attached particle. Hence, the adhesion force for a fourth geometric set which represents the most likely scenario for attached particles with long contact times is developed. As will be shown, this scenario results in the highest values of adhesion force and interaction energy. Copyright 2000 Academic Press.     

Membrane modification to avoid wettability changes due to protein adsorption in an emulsion/membrane bioreactor

This study addresses problems encountered with an emulsion/membrane bioreactor. In this reactor, enzyme- (lipase) catalyzed hydrolysis in an emulsion was combined with two in-line separation steps. One is carried out with a hydrophilic membrane, to separate the water phase, the other with a hydrophobic membrane, to separate the oil phase. In the absence of enzyme, sunflower oil/water emulsions with an oil fraction between 0.3 and 0.7 could be separated with both membranes operating simultaneously. However, two problems arose with emulsions containing lipase. First, the flux through both the hydrophilic and the hydrophobic membranes decreased with exposure to the enzyme. Second, the hydrophobic membrane showed a loss of selectivity demonstrated by permeation of both the oil phase and the water phase through the hydrophobic membrane at low transmembrane pressure. These phenomena can be explained by protein (i.e. lipase) adsorption to the polymer surface within the pores of the membrane. It was proven that lipase was present at the hydrophilic membrane and that this, in part, explains the flux decrease of the hydrophilic membrane. To prevent the observed loss of selectivity with exposure to protein, the hydrophobic polypropylene membrane (Enka) was modified with block copolymers of propylene oxide (PO) and ethylene oxide (EO). These block copolymers act as a steric hindrance for proteins that come near the surface. The modification was successful: After 10 days of continuous operation the minimum transmembrane pressure at which water could permeate through an F 108-modified membrane was 0.5 bar, the same value as that observed in the beginning of the experiment. This indicates that loss of selectivity due to protein adsorption is prevented by the modification of the membrane.     

Can we predict the spreading of a two-liquid system from the spreading of the corresponding liquid-air systems?

We present new data obtained from the spreading of a series of oil droplets, on top of a hydrophobic grafted silicon substrate, in air and immersed in water. We follow the contact angle and radius dynamics of hexane, dodecane, hexadecane, dibutyl phthalate, and squalane from the first milliseconds to approximately 1 s. Analysis of the images allows us to make several hundred contact angle and droplet radius measurements with great accuracy. The G-Dyna (Seveno et al. Langmuir 2010, 25, 13034) software is then used to fit the data with one of the wetting theories, the molecular-kinetic theory (MKT) (Blake et al. J. Colloid Interface Sci.1969, 30, 421), which takes into account the dissipation at the three-phase zone at the contact line. This theory allows us to extract the coefficient of friction of the contact line, which expresses the relationship between the driving force, that is, the unbalanced Young force, and the contact-line velocity V. It is first shown that the MKT is appropriate to describe the experimental data and then that the contact-line friction is a linear function of the viscosity as theoretically predicted. This is checked for oil-air and oil-water systems. A linear relation between the contact-line friction measured in oil-water systems and the contact-line frictions of the parent single liquid system seems plausible. To the best of our knowledge, this is the first trial to establish a link between the dynamics of wetting in liquid-liquid and in liquid-air systems.     

Deformation of cylinders in the hexagonal phase of sodium decyl sulphate/decanol/water on the introduction of decanol

X-ray scattering studies show that aggregates of amphiphilic molecules in the hexagonal phase of the binary system sodium decyl sulphate/water are infinite cylinders whose radius is very close to that of the extended molecule. When sodium decyl sulphate molecules are progressively substituted by decanol molecules the phase remains hexagonal, up to a decanol/soap molar ratio of 0.15, but the radius of its cylinders becomes larger than the molecular length. We have developed specific experiments to investigate this growth and see if it is isotropic or anisotropic. We have focused our attention on the evolution of the configuration of soap and decanol molecules within the aggregates. Neutron scattering experiments show that the two molecules do not distribute themselves uniformly and D.M.R. measurements show that they stay anchored at the amphiphile/water interface by their polar heads. The distribution of the two molecules along the interface is not therefore uniform. This induces an inhomogeneity of the interfacial curvature and the growth of the section of the cylinders cannot be isotropic. This anisotropy increases when the decanol/soap molar ratio increases. It provides a clue to understand the transformation of the hexagonal phase into a recangular one whose aggregates are infinite ribbons with non-circular section, above the decanol/soap molar ratio of 0.15.