Extended DLVO interactions between spherical particles and rough surfaces

An "extended DLVO" approach that includes Lifshitz-van der Waals, Lewis acid-base, and electrostatic double layer interactions is used to describe interaction energies between spherical particles and rough surfaces. Favorable, unfavorable, and intermediate deposition conditions are simulated using surface properties representing common aquatic colloids and polymeric membranes. The surface element integration (SEI) technique and Derjaguin's integration method are employed to calculate interaction energy. Numerical simulations using SEI demonstrate that nanometer scale surface roughness features can produce a distribution of interaction energy profiles. Local interaction energies are statistically analyzed to define representative interaction energy profiles-minimum, average, and maximum-for various combinations of simulated particles and surfaces. In all cases, the magnitude of the average interaction energy profile is reduced, but the reduction of energy depends on particle size, asperity size, and density of asperities. In some cases, a surface that is on average unfavorable for deposition (repulsive) may possess locally favorable (attractive) sites solely due to nanoscale surface roughness. A weighted average of the analytical sphere-sphere and sphere-plate expressions of Derjaguin reasonably approximates the average interaction energy profiles predicted by the SEI model, where the weighting factor is based on the fraction of interactions involving asperities.     

Numerical study on the adhesion and reentrainment of nondeformable particles on surfaces: the role of surface roughness and electrostatic forces

In this paper, the reentrainment of nanosized and microsized particles from rough walls under various electrostatic conditions and various hydrodynamic conditions (either in air or aqueous media) is numerically investigated. This issue arises in the general context of particulate fouling in industrial applications, which involves (among other phenomena) particle deposition and particle reentrainment. The deposition phenomenon has been studied previously and, in the present work, we focus our attention on resuspension. Once particles are deposited on a surface, the balance between hydrodynamic forces (which tend to move particles away from the surface) and adhesion forces (which maintain particles on the surface) can lead to particle removal. Adhesion forces are generally described using van der Waals attractive forces, but the limit of these models is that any dependence of adhesion forces on electrostatic forces (due to variations in pH or ionic strength) cannot be reproduced numerically. For this purpose, we develop a model of adhesion forces that is based on the DLVO (Derjaguin and Landau, Verwey and Overbeek) theory and which includes also the effect of surface roughness through the use of hemispherical asperities on the surface. We first highlight the effect of the curvature radius on adhesion forces. Then some numerical predictions of adhesion forces or adhesion energies are compared to experimental data. Finally, the overall effects of surface roughness and electrostatic forces are demonstrated with some applications of the complete reentrainment model in some simple test cases.     

Effect of Rough Nanoparticle Orientation on DLVO Energy Interaction

This study investigated the effect of the orientation of rough nanoparticles on Derjaguin and Landau, Verwey and Overbeek (DLVO) energy interaction. Rippled sphere model was used to survey van der Waals attraction energy and repulsive double-layer interaction energy between nanoparticles. The effect of particle size, asperity size, number of asperities, and concentration was studied for different orientations. Spherical coordinates were used to evaluate the effect of changes in orientation under controlled conditions. Surface element integral method was used to calculate DLVO energy interactions between rough particles at specific orientations. The DLVO energy results show that a change in orientation significantly affected the stability of the nanoparticles. The stability of dispersion varied as the contact surface between nanoparticles changed.     

Modelling colloid transport in groundwater; the prediction of colloid stability and retention behaviour

The association of contaminants with mobile colloidal particles present in groundwaters has been recognised as a potentially important mass transfer mechanism for contaminant migration in the environment. To predict the fate of environmental contaminants there is a need to develop numerical models which include colloid-mediated transport. The mobility of groundwater colloids is controlled by their stability towards aggregation and attachment to rock surfaces. For inorganic particles, the conceptual framework for predicting their stability and deposition behaviour is provided by the DLVO theory. However, under conditions unfavourable to coagulation or surface attachment (ie. when particles and surfaces are of like charge) there are significant discrepancies between theory and experimentally measured coagulation and deposition rates.Predictive shortcomings of the DLVO theory arise from the simplicity of the original model, which was formulated for smooth bodies with ideal geometries and uniform surface properties. However, surfaces are by nature rough, non-uniform and heterogeneous in composition. In addition, the theory does not consider the dynamics of particle interactions. Furthermore, the presence of additional forces, which may be either attractive or repulsive, acting at short range, which arise from interactions between surfaces and water, are not accounted for. Significant developments have been made to extend and modify the DLVO model to account for the discrepancies between theory and experiment. In this paper the prediction of colloid stability and deposition behaviour under unfavourable conditions is reviewed. Emphasis is placed on the phenomenological behaviour of inorganic colloids in aqueous systems that may need to be accounted for in a transport model.     

Adhesion as an interplay between particle size and surface roughness

Surface roughness plays an important role in the adhesion of small particles. In this paper we have investigated adhesion as a geometrical effect taking into account both the particle size and the size of the surface features. Adhesion is studied using blunt model particles on surfaces up to 10 nm root-mean-square (RMS) roughness. Measurements with particles both smaller and larger than surface features are presented. Results indicate different behavior in these areas. Adhesion of particles smaller than or similar in size to the asperities depend mainly on the size and shape of the asperities and only weakly on the size of the particle. For large particles also the particle size has a significant effect on the adhesion. A new model, which takes the relative size of particles and asperities into account, is also derived and compared to the experimental data. The proposed model predicts adhesion well over a wide range of particle/asperity length scales.     

Breakdown of colloid filtration theory: role of the secondary energy minimum and surface charge heterogeneities

The mechanisms and causes of deviation from the classical colloid filtration theory (CFT) in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions were investigated. The deposition behavior of uniform polystyrene latex colloids in columns packed with spherical soda-lime glass beads was systematically examined over a broad range of physicochemical conditions, whereby both the fluid-phase effluent particle concentration and the profile of retained particles were measured. Experiments conducted with three different-sized particles in a simple (1:1) electrolyte solution reveal the controlling influence of secondary minimum deposition on the deviation from CFT. In a second series of experiments, sodium dodecyl sulfate (SDS) was added to the background electrolyte solution with the intent of masking near-neutrally charged regions of particle and collector surfaces. These results indicate that the addition of a small amount of anionic surfactant is sufficient to reduce the influence of certain surface charge inhomogeneities on the deviation from CFT. To verify the validity of CFT in the absence of surface charge heterogeneities, a third set of experiments was conducted using solutions of high pH to mask the influence of metal oxide impurities on glass bead surfaces. The results demonstrate that both secondary minimum deposition and surface charge heterogeneities contribute significantly to the deviation from CFT generally observed in colloid deposition studies. It is further shown that agreement with CFT is obtained even in the presence of an energy barrier (i.e., repulsive colloidal interactions), suggesting that it is not the general existence of repulsive conditions which causes deviation but rather the combined occurrence of "fast" and "slow" particle deposition.     

Probing surface charge potentials of clay basal planes and edges by direct force measurements

The dispersion and gelation of clay suspensions have major impact on a number of industries, such as ceramic and composite materials processing, paper making, cement production, and consumer product formulation. To fundamentally understand controlling mechanisms of clay dispersion and gelation, it is necessary to study anisotropic surface charge properties and colloidal interactions of clay particles. In this study, a colloidal probe technique was employed to study the interaction forces between a silica probe and clay basal plane/edge surfaces. A muscovite mica was used as a representative of 2:1 phyllosilicate clay minerals. The muscovite basal plane was prepared by cleavage, while the edge surface was obtained by a microtome cutting technique. Direct force measurements demonstrated the anisotropic surface charge properties of the basal plane and edge surface. For the basal plane, the long-range forces were monotonically repulsive within pH 6-10 and the measured forces were pH-independent, thereby confirming that clay basal planes have permanent surface charge from isomorphic substitution of lattice elements. The measured interaction forces were fitted well with the classical DLVO theory. The surface potentials of muscovite basal plane derived from the measured force profiles were in good agreement with those reported in the literature. In the case of edge surfaces, the measured forces were monotonically repulsive at pH 10, decreasing with pH, and changed to be attractive at pH 5.6, strongly suggesting that the charge on the clay edge surfaces is pH-dependent. The measured force profiles could not be reasonably fitted with the classical DLVO theory, even with very small surface potential values, unless the surface roughness was considered. The surface element integration (SEI) method was used to calculate the DLVO forces to account for the surface roughness. The surface potentials of the muscovite edges were derived by fitting the measured force profiles with the surface element integrated DLVO model. The point of zero charge of the muscovite edge surface was estimated to be pH 7-8.     

Electrical double-layer effects on the deposition of zeolite A on surfaces

Zeolite particles formed from an aluminosilicate solution possess a negative surface charge due to the substitution of aluminum atoms into a SiO4 tetrahedral structure making it difficult to form a continuous layer in solution. The particle interactions with surfaces and each other can be studied using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The interaction energy between zeolite-zeolite and zeolite-substrate on various materials can be estimated in this fashion. The zeolite LTA particles show a stronger repulsion interaction on all substrates and on the each other as compared to the ZSM-5 particles. This repulsive energy also increases as the particles size increases. This results in the formation of conglomerate in the solution rather than forming an adhered layer on the substrate.     

The Electrochemical Surface Forces Apparatus: The Effect of Surface Roughness, Electrostatic Surface Potentials, and Anodic Oxide Growth on Interaction Forces, and Friction between Dissimilar Surfaces in Aqueous Solutions

We present a newly designed electrochemical surface forces apparatus (EC-SFA) that allows control and measurement of surface potentials and interfacial electrochemical reactions with simultaneous measurement of normal interaction forces (with nN resolution), friction forces (with μN resolution), and distances (with ? resolution) between apposing surfaces. We describe three applications of the developed EC-SFA and discuss the wide-range of potential other applications. In particular, we describe measurements of (1) force-distance profiles between smooth and rough gold surfaces and apposing self-assembled monolayer-covered smooth mica surfaces; (2) the effective changing thickness of anodically growing oxide layers with ?-accuracy on rough and smooth surfaces; and (3) friction forces evolving at a metal-ceramic contact, all as a function of the applied electrochemical potential. Interaction forces between atomically smooth surfaces are well-described using DLVO theory and the Hogg-Healy-Fuerstenau approximation for electric double layer interactions between dissimilar surfaces, which unintuitively predicts the possibility of attractive double layer forces between dissimilar surfaces whose surface potentials have similar sign, and repulsive forces between surfaces whose surface potentials have opposite sign. Surface roughness of the gold electrodes leads to an additional exponentially repulsive force in the force-distance profiles that is qualitatively well described by an extended DLVO model that includes repulsive hydration and steric forces. Comparing the measured thickness of the anodic gold oxide layer and the charge consumed for generating this layer allowed the identification of its chemical structure as a hydrated Au(OH)(3) phase formed at the gold surface at high positive potentials. The EC-SFA allows, for the first time, one to look at complex long-term transient effects of dynamic processes (e.g., relaxation times), which are also reflected in friction forces while tuning electrochemical surface potentials.     

DLVO interaction of colloidal particles with topographically and chemically heterogeneous surfaces

The DLVO force and potential energy of interaction between microspheres and topographically and chemically heterogeneous surfaces in aqueous solution are computed using a modification of the surface element integration approach. The heterogeneous surface has an array of cylindrical pillars of varying height, diameter, and arrangement to model different nano-topographies. In agreement with previous studies, the nano-topography decreases the size of the potential energy barrier for unfavorable surfaces because the pillars limit the minimum separation distance. The influence of topography is significant even for pillars several nanometers high and is more pronounced if the surface potential of the pillar tops differs from that of the underlying surface. A new force- and energy-averaging model is introduced as a simple method to compute the mean interaction energy or force between the particle and a heterogeneous surface, which differs significantly from a mean-field approach based on the average or nominal surface potential. Small variations in topography are found to remove large energy barriers to colloidal deposition. These results help explain the increased attraction of patchy surfaces towards particles relative to expectations based on typical DLVO calculations, which is particularly significant for surfaces with adsorbed polyelectrolytes.     

Interpretation of conservative forces from Stokesian dynamic simulations of interfacial and confined colloids

This paper presents Stokesian dynamics simulations of experiments involving one or two charged colloids near either a single charged wall or confined between parallel charged walls. Equilibrium particle-particle and particle-wall interactions are interpreted from dynamic particle trajectories in simulations involving (1) a single particle levitated above a wall, (2) two particles below a wall, and (3) two particles confined between two parallel walls. By specifying only repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek (DLVO) potentials and including multibody hydrodynamics, we successfully recover expected potentials in some cases, while anomalous attraction is observed in other cases. Attraction inferred in the latter simulations displays quantitative agreement with literature measurements when particle dynamics are interpreted using reported analyses. Because anomalous attraction is reproduced in simulations using only electrostatic repulsive DLVO potentials, our results reveal the one-dimensional analyses to be invalid for configurations that are inherently multidimensional via multibody hydrodynamics. Parameters related to experimental sampling of particle dynamics are also found to be critical for obtaining accurate potentials. We explain the anomalous attraction in each experiment using effective potentials, which can be employed in an a priori fashion to assist the confident design of future experiments involving interfacial and confined colloids. Ultimately, our findings reveal the importance of dimensionality and multibody hydrodynamics for understanding nonequilibrium dynamics of colloids near surfaces.     

The deformation and adhesion of randomly rough and patterned surfaces

Using a surface forces apparatus (SFA) and an atomic force microscope (AFM) we have studied the effects of surface roughness (root-mean-square (RMS) roughness between 0.3 and 220 nm) on the "contact mechanics", which describes the deformations and loading and unloading adhesion forces, of various polymeric surfaces. For randomly rough, moderately stiff, elastomeric surfaces, the force-distance curves on approach and separation are nearly reversible and almost perfectly exponentially repulsive, with an adhesion on separation that decreases only slightly with increasing RMS. Additionally, the magnitude of the preload force is seen to play a large role in determining the measured adhesion. The exponential repulsion likely arises from the local compressions (fine-grained nano- or submicron-scale deformations) of the surface asperities. The resulting characteristic decay lengths of the repulsion scale with the RMS roughness and correlate very well with a simple finite element method (FEM) analysis based on actual AFM topographical images of the surfaces. For "patterned" surfaces, with a nonrandom terraced structure, no similar exponential repulsion is observed, suggesting that asperity height variability or random roughness is required for the exponential behavior. However, the adhesion force or energy between two "patterned" surfaces fell off dramatically and roughly exponentially as the RMS increased, likely owing to a significant decrease in the contact area which in turn determines their adhesion. For both types of rough surfaces, random and patterned, the coarse-grained (global, meso- or macroscopic) deformations of the initially curved surfaces appear to be Hertzian.     

Mixed-emulsifier stabilised emulsions: Investigation of the effect of monoolein and hydrophilic silica particle mixtures on the stability against coalescence

An experimental circulating water loop has been constructed to study the deposition of hematite particles of average diameter 320 nm on polypropylene pipe walls in the ranges pH 4–11, Re 3300–17,700 at 25 °C. Real-time turbidimetric measurements were used to measure the deposited concentrations. Results showed that the deposition rate increased when pH decreased and when the flow rate increased. Adhesion was observed even under repulsive electrostatic conditions (pH > 7), where the surfaces of hematite and polypropylene were both negative, indicating that the kinetic energy of at least a part of the particles surpassed the electrostatic repulsive potentials. The experimental curves were fitted by a model assuming simultaneous adhesion and removal of particles, leading to adhesion and removal rate constants, whose values depend on pH and flow rate. Removal is negligible below pH 9.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.     

Force measurements between Teflon AF and colloidal silica particles in electrolyte solutions

The interaction force between a very hydrophobic polymer surface and colloidal silica particles with a roughness of 10–15 nm has been measured in aqueous solutions of KOH and KCl using an atomic force microscope. The interaction can be described according to the DLVO theory by an electrical double-layer force that is repulsive at long distances and attractive at short distances and an attractive van der Waals force. The electrical double-layer potentials are compared to the zeta potentials of Teflon AF and the silica spheres. The roughness of the silica particles leads to an underestimation of the short-range attraction and the surface potential. Both KCl and KOH solutions affect the potential of the interacting surfaces. OH⁻ ions that adsorb preferentially to the Teflon AF surface create higher potentials than Cl⁻ ions. Range and strength of the attractive interaction are not affected by KCl solutions but reduced by addition of KOH. This can be explained by decreasing potential differences between the silica sphere and Teflon AF with increasing KOH concentration. In addition, the preferential adsorption of OH⁻ ions may lead to a reduction of the van der Waals interaction. The presence of nanobubbles, too, might play a role.     

The DLVO Energy Interaction of Nanorough Surfaces by Spherical Coordinates

By a new method of modeling, the DLVO energy interaction between rough nanoparticles and rough surfaces is investigated at various conditions. Rippled sphere model and surface element integration method are used. For calculation of energy interaction, the spherical coordinates are used and by increasing the radius ratio of two particles, the pseudo flat surfaces are generated. With increasing the radius ratio of two particles to 50, the large particle behaves as flat surface in front of small particle. Roughness, size of particles, temperature, zeta potential, capacity, and concentration of ions, which influence the stability of nanocolloidal solutions, are considered by the new method. Spherical coordinates enable to model the rough nanoparticles and rough surfaces so that no simplifying assumptions are needed, which was very difficult and time-consuming in Cartesian coordinate system. New method could predict the effect of different parameters on the stability of nanocolloidal systems precisely, easily, and at short times in comparison to Cartesian coordinate.     

Roughness models for particle adhesion

The effects of different surface roughness models on a previously developed van der Waals adhesion model were examined. The van der Waals adhesion model represented surface roughness with a distribution of hemispherical asperities. It was found that the constraints used to define the asperity distribution on the surface, which were determined from AFM scans, varied with scan size and thus were not constant for all surfaces examined. The greatest variation in these parameters occurred with materials that had large asperities or with materials where a large fraction of the surface was covered by asperities. These rough surfaces were modeled with fractals and also with a fast Fourier transform algorithm. When the model surfaces generated using the Fourier transforms are used in the adhesion model, the model accurately predicts the experimentally observed adhesion forces measured with the AFM.     

Electrostatic interactions between double layers: influence of surface roughness, regulation, and chemical heterogeneities

Electrostatic interactions between two surfaces as measured by atomic force microscopy (AFM) are usually analyzed in terms of DLVO theory. The discrepancies often observed between the experimental and theoretical behavior are usually ascribed to the occurrence of chemical regulation processes and/or to the presence of surface chemical or morphological heterogeneities (roughness). In this paper, a two-gradient mean-field lattice analysis is elaborated to quantifying double layer interactions between nonplanar surfaces. It allows for the implementation of the aforementioned sources of deviation from DLVO predictions. Two types of ion-surface interaction ensure the adjustment of charges and potentials upon double layer overlap, i.e., specific ionic adsorption at the surfaces and/or the presence of charge-determining ions for the surfaces considered. Upon double layer overlap, charges and potentials are adjusted via reequilibrium of the different ion adsorption processes. Roughness is modeled by grafting asperities on supporting planar surfaces, with their respective positions, shapes, and chemical properties being assigned at will. Local potential and charge distributions are derived by numerically solving the nonlinear Poisson-Boltzmann equation under the boundary conditions imposed by the surface profiles and regulation mechanism chosen. Finite size of the ions is taken into account. A number of characteristic situations are briefly discussed. It is shown how the surface irregularities are reflected in the Gibbs energy of interaction.     

Deposition of spherical particles onto cylindrical solid surfaces. II. Experimental studies

This paper presents experimental studies of the deposition of silicone oil drops onto two different solid surfaces in an aqueous solution. A series of deposition tests were conducted to measure the dimensionless mass transfer rate (Sherwood number). The effects of three kinds of aqueous solutions and two solid surfaces on the deposition process were studied and compared with the numerical predictions based on the well-known DLVO theory. More specifically, both the experimentally measured and the numerically predicted Sherwood numbers monotonically decrease as the pH value of the aqueous solution increases. It was also found that two ionic surfactant solutions have similar influences while the electrolyte solutions have opposite effects on the deposition rate on different solid surfaces. Finally, comparison of all the experimental results for the bare glass surface with the numerical simulations shows that the deposition process of the silicone oil drops onto the hydrophilic solid surface can be satisfactorily described by the classical DLVO theory. However, the deposition data for the FC725 precoated surface are significantly larger than the numerical predictions. This fact suggests that the so-called non-DLVO attractive interaction is involved in the deposition process with the hydrophobic solid surface. This additional non-DLVO attractive interaction, which is generally called the hydrophobic interaction, still remains to be incorporated into the existing DLVO theory, if this is possible.     

表面力仪的改进及溶液中DLVO理论的验证

改进了现有表面力仪,使之具有更低的造价和更高的实验精度.利用改进后的表面力仪测量了0.1mol/L的NaCl溶液中两云母表面间的作用力-距离曲线;通过与计算得到的曲线对比验证了DLVO理论.结果表明:在0.1mol/L的NaCl溶液中,两云母表面间在距离较大时的作用力测量值与DLVO理论值相符合,但在距离较小时测量值出现附加的短程斥力,且此斥力呈现指数衰减规律.