Deviation from the classical colloid filtration theory in the presence of repulsive DLVO interactions

A growing body of experimental evidence suggests that the deposition behavior of microbial particles (e.g., bacteria and viruses) is inconsistent with the classical colloid filtration theory (CFT). Well-controlled laboratory-scale column deposition experiments were conducted with uniform model particles and collectors to obtain insight into the mechanisms that give rise to the diverging deposition behavior of microorganisms. Both the fluid-phase effluent particle concentration and the profile of retained particles were systematically measured over a broad range of physicochemical conditions. The results indicate that, in the presence of repulsive Derjaguin-Landau-Verwey-Overbeek (DLVO) interactions, the concurrent existence of both favorable and unfavorable colloidal interactions causes significant deviation from the CFT. A dual deposition mode model is presented which considers the combined influence of "fast" and "slow" particle deposition. This model is shown to adequately describe both the spatial distribution of particles in the packed bed and the suspended particle concentration at the column effluent.     

Colloid particle and protein deposition - electrokinetic studies

Recent developments in the electrokinetic determination of particle, polyelectrolyte and protein deposition at solid/electrolyte interfaces, are reviewed. In the first section basic theoretical results are discussed enabling a quantitative interpretation of the streaming current/potential and microelectrophoretic measurements. Experimental results are presented, pertinent to electrokinetic characteristics of simple (homogeneous) surfaces such as mica, silica and various polymeric surfaces used in protein studies. The influence of the ionic strength, background electrolyte composition and pH is discussed, and the effective (electrokientic) charge of these interfaces is evaluated. In the next section, experimental data obtained by streaming potential measurements for colloid particle mono- and bilayers are presented and interpreted successfully in terms of available theoretical approaches. These results, obtained for model systems of monodisperse colloid particles are used as reference data for discussion of more complicated experiments performed for polyelectrolyte and protein covered surfaces. Results are discussed, obtained for cationic polyelectrolytes (PEI, PAH) and fibrinogen adsorbing on mica, interpreted quantitatively in terms of the theoretical approach postulating a heterogeneous 3D charge distribution. The Gouy-Chapman model, based on the continuous charge distribution proved inadequate. Interesting experimental data are also discussed, obtained by electrophoretic methods in the case of protein adsorption on colloid latex particles. In the last section, supplementary results on particle deposition on heterogeneous surfaces produced by controlled protein adsorption are discussed. Quantitative relationships between the amount of adsorbed protein, zeta potential of the interface and the particle coverage are specified. Possibility of evaluating the heterogeneity of protein charge distribution is pointed out. The anomalous deposition of colloid particles on protein molecules bearing the same sign of zeta potential, which contradicts classical DLVO theory, is interpreted in terms of the fluctuation theory. It is concluded that theoretical and experimental results obtained for model colloid systems and flat interfaces can be effectively used for interpretation of protein adsorption phenomena, studied by electrophoresis. In this way the universality of electrokinetic phenomena is underlined.     

Coupled Influence of Colloidal and Hydrodynamic Interactions on the RSA Dynamic Blocking Function for Particle Deposition onto Packed Spherical Collectors

The influence of electrostatic double-layer and hydrodynamic interactions on random sequential adsorption (RSA) of colloidal particles onto packed spherical collectors was investigated using inverse analysis of colloid breakthrough data obtained from well-controlled particle deposition experiments. Deposition experiments were carried out using monodisperse aqueous suspensions of positively charged latex colloids and packed columns of negatively charged uniform glass beads for different combinations of ionic strength, particle size, and approach velocity. From the experimental particle breakthrough data, the initial particle deposition rates and the virial coefficients of the dynamic blocking function based on RSA mechanics were determined. The magnitudes of the virial coefficients were observed to increase from the hard sphere values with increasing flow rates and decreasing ionic strengths of the background electrolyte. Particle size also plays a significant role in governing the deposition dynamics. The deviation from the hard sphere RSA behavior becomes more prominent for larger particles. Copyright 2000 Academic Press.     

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.     

Particle adsorption and deposition: role of electrostatic interactions

This work demonstrates how electrostatic interactions, described in terms of the classical DLVO theory, influence colloid particle deposition phenomena at solid/liquid interfaces. Electrostatic interactions governing particle adsorption in both non-polar and polar media (screened interactions) are discussed. Exact and approximate methods for calculating the interaction energy of spherical and non-spherical (anisotropic) particles are presented, including the Derjaguin method. Phenomenological transport equations governing particle deposition under the linear regime are discussed with the limiting analytical expressions for calculating initial flux. Non-linear adsorption regimes appearing for higher coverage of adsorbed particles are analysed. Various theoretical approaches are exposed, aimed at calculating blocking effects appearing due to the presence of adsorbed particles. The significant role of coupling between bulk transport and surface blocking is demonstrated. Experimental data obtained under well-defined transport conditions, such as diffusion and forced convection (impinging-jet cells), are reviewed. Various experimental techniques for detecting particles at interfaces are discussed, such as reflectometry, ellipsometry, streaming potential, atomic force microscopy, electron and optical microscopy, etc. The influence of ionic strength and flow rate on the initial particle deposition rate (limiting flux) is presented. The essential role of electrostatic interactions in particle deposition on heterogeneous surfaces is demonstrated. Experimental data pertinent to the high-coverage adsorption regime are also presented, especially the dependence of the maximum coverage of particles and proteins on the ionic strength. The influence of lateral electrostatic interactions on the structure of particle monolayers is elucidated, and the links between colloid and molecular systems are pointed out.     

Particle capture via discrete binding elements: systematic variations in binding energy for randomly distributed nanoscale surface features

This work examines how the binding strength of surface-immobilized "stickers" (representative of receptors or, in nonbiological systems, chemical heterogeneities) influences the adhesion between surfaces that are otherwise repulsive. The study focuses on a series of surfaces designed with fixed average adhesive energy per unit area and demonstrates quantitatively how a redistribution of the adhesive functionality into progressively larger clusters (stronger stickers) increases the probability of adhesive events. The work employs an electrostatic model system: relatively uniform, negative 1 μm silica spheres flow gently over negative silica flats. The flats contain small amounts of randomly positioned nanoscale cationic patches. The silica-silica interaction is repulsive; however, the cationic patches (present at sufficiently low levels that the overall surface charge remains substantially negative) produce local attractions. In this study, the attractions are relatively weak so that multiple patches engage to capture flowing particles. Experiments reveal an adhesion signature characteristic of a renormalized random distribution when the sticker strength is increased at an overall fixed binding strength per unit area of surface. The form of the particle capture curves are in good quantitative agreement with a simple model that assumes only a fixed adhesion energy needed for particle capture. Aside from the quantitative details that provide a simple formalism for anticipating particle adhesion, this work demonstrates how increasing the heterogeneities in the surface functionality can cause a system to go from being nonadhesive to becoming strongly adhesive. Indeed, systems containing small amounts of discretized adhesive functionality are always more adhesive than systems in which the same functionality is distributed uniformly over the surface (the mean field scenario).     

Charge heterogeneity of surfaces: mapping and effects on surface forces

The DLVO theory treats the total interaction force between two surfaces in a liquid medium as an arithmetic sum of two components: Lifshitz–van der Waals and electric double layer forces. Despite the success of the DLVO model developed for homogeneous surfaces, a vast majority of surfaces of particles and materials in technological systems are of a heterogeneous nature with a mosaic structure composed of microscopic and sub-microscopic domains of different surface characteristics. In such systems, the heterogeneity of the surface can be more important than the average surface character. Attractions can be stronger, by orders of magnitude, than would be expected from the classical mean-field DLVO model when area-averaged surface charge or potential is employed. Heterogeneity also introduces anisotropy of interactions into colloidal systems, vastly ignored in the past. To detect surface heterogeneities, analytical tools which provide accurate and spatially resolved information about material surface chemistry and potential — particularly at microscopic and sub-microscopic resolutions — are needed.Atomic force microscopy (AFM) offers the opportunity to locally probe not only changes in material surface characteristic but also charges of heterogeneous surfaces through measurements of force–distance curves in electrolyte solutions. Both diffuse-layer charge densities and potentials can be calculated by fitting the experimental data with a DLVO theoretical model. The surface charge characteristics of the heterogeneous substrate as recorded by AFM allow the charge variation to be mapped. Based on the obtained information, computer modeling and simulation can be performed to study the interactions among an ensemble of heterogeneous particles and their collective motions. In this paper, the diffuse-layer charge mapping by the AFM technique is briefly reviewed, and a new Diffuse Interface Field Approach to colloid modeling and simulation is briefly discussed.     

Colloidal deposition on remotely controlled charged micropatterned surfaces in a parallel-plate flow chamber

This article describes a method to influence colloid deposition by varying the zeta potential at microelectrodes with remotely applied electric potentials. Deposition experiments were conducted in a parallel-plate flow chamber for bulk substrates of glass, indium tin oxide (ITO), and ITO-coated glass microelectrodes in 10 and 60 mM potassium chloride solutions. Colloid deposition was found to be a function of solution chemistry and the small locally delivered electric surface potentials. Electric fields and physical surface heterogeneity can be ruled out as cause of the observed deposition. Results are reported using experimentally determined Sherwood numbers and compared to the predictions of a previously developed patch model. Minor deviations between predicted and experimental Sherwood numbers imply that physical and chemical interactions occur. Specifically, we propose that colloidal particles respond to local variations in surface potential through electrostatic interactions, altering particle streamlines flowing along the surface and ultimately the extent of deposition.     

Image charges and dispersion forces in electric double layers: the dependence of wall-wall interactions on salt concentration and surface charge density

The interaction pressure between two planar charged walls is calculated for a range of conditions. The diffuse electric double layers between the two wall surfaces are treated with ion-wall dispersion forces and ionic image charge interactions taken into account. Both these interactions are due to dielectric discontinuities at the surfaces. Ion-ion and ion-image charge correlations are explicitly included. The ion-wall dispersion interactions can give rise to appreciable ion specific effects, which are particularly strong when the counterions to the surfaces are highly polarizable. The mechanisms of these effects are investigated, and their influence on the net interaction pressure between the walls is studied for a range of surface charge densities, strengths of the anion-wall dispersion interaction and bulk electrolyte concentrations. When the strength of the anion-wall dipersion interaction is increased, the pressure generally becomes less repulsive (or more attractive) for positive surfaces. The opposite happens in general for negative surfaces but to a much lesser extent. The effects are largest for large surface charge densities and high electrolyte concentrations. The image charge interactions give rise to a considerable depletion attraction between the walls for low surface charge densities.     

Atomic force microscopy study of cellulose surface interaction controlled by cellulose binding domains

Colloidal probe microscopy has been used to study the interaction between model cellulose surfaces and the role of cellulose binding domain (CBD), peptides specifically binding to cellulose, in interfacial interaction of cellulose surfaces modified with CBDs. The interaction between pure cellulose surfaces in aqueous electrolyte solution is dominated by double layer repulsive forces with the range and magnitude of the net force dependent on electrolyte concentration. AFM imaging reveals agglomeration of CBD adsorbed on cellulose surface. Despite an increase in surface charge owing to CBD binding to cellulose surface, force profiles are less repulsive for interactions involving, at least, one modified surface. Such changes are attributed to irregularity of the topography of protein surface and non-uniform distribution of surface charges on the surface of modified cellulose. Binding double CBD hybrid protein to cellulose surfaces causes adhesive forces at retraction, whereas separation curves obtained with cellulose modified with single CBD show small adhesion only at high ionic strength. This is possibly caused by the formation of the cross-links between cellulose surfaces in the case of double CBD.     

Effect of ionic size on the deposition of charge-regulated particles to a charged surface

The deposition of charge-regulated particles to a rigid, planar charged surface is modeled theoretically, taking the effects of the excluded area arising from deposited particles and finite ionic sizes into account. Here, a particle comprises a rigid core and an ion-penetrable charged membrane layer, which represents a general type of particle. If the membrane layer has a negligible thickness, the particle simulates a regular inorganic particle, and if the membrane layer has a finite thickness, it simulates biocolloids such as cells. The results of numerical simulation reveal that the rate of particle deposition is faster under the following conditions: (1) lower potential of the planar surface, (2) thicker membrane, (3) higher counterion valance, (4) lower fixed charge density, (5) smaller counterions, (6) larger co-ions, (7) larger functional group, and (8) lower pH. Neglecting the sizes of ionic species may lead to an appreciable deviation in both the electrical repulsive force between particle and surface and the rate of deposition. Typical deviation for the former is approximately 20%, and that for the latter is approximately -75%.     

Influence of natural organic matter on the deposition kinetics of extracellular polymeric substances (EPS) on silica

The influence of humic acid and alginate, two major components of natural organic matter (NOM), on deposition kinetics of extracellular polymeric substances (EPS) on silica was examined in both NaCl and CaCl(2) solutions over a wide range of environmentally relevant ionic strengths utilizing a quartz crystal microbalance with dissipation. Deposition kinetics of both soluble EPS and bound EPS extracted from four bacterial strains with different characteristics was investigated. EPS deposition on humic acid-coated silica surfaces was found to be much lower than that on bare silica surfaces under all examined conditions. In contrast, pre-coating the silica surfaces with alginate enhanced EPS deposition in both NaCl and CaCl(2) solutions. More repulsive electrostatic interaction between EPS and surface contributed to the reduced EPS deposition on humic acid-coated silica surface. The trapping effect induced by the rough alginate layer resulted in the greater EPS deposition on alginate-coated surfaces in NaCl solutions, whereas surface heterogeneities on alginate layer facilitated favorable interactions with EPS in CaCl(2) solutions. The presence of dissolved background humic acid and alginate in solutions both significantly retarded EPS deposition on silica surfaces due to the greater steric and electrostatics repulsion.     

Particle deposition onto Janus and patchy spherical collectors

An Eulerian model (convection-diffusion-migration equation) is presented to study colloid deposition behavior on Janus and patchy spherical collectors using Happel cell geometry. The model aims to capture the effect of the collector surface charge heterogeneity on the particle deposition rate. Two separate cases of surface charge distribution are presented. In the first case, the surface heterogeneity is modeled as half the collector favoring deposition and the other half hindering it (Janus collectors). For the second case, the surface heterogeneity is modeled as alternate stripes of attractive and repulsive regions on the collector (patchy collectors). The model also considers fluid flow approaching the collector at different angles in addition to the standard gravity assisted and gravity hindered flow conditions to analyze the effect of the collector orientation on the deposition. It was observed that particles tend to deposit at the edges of the favorable stripes and the extent of this preferential accumulation varies along the tangential position of the collector due to the nonuniform nature of the collector. The predicted deposition behavior is compared to the patchwise heterogeneity model. The study brings to fore how recent developments in synthesis of chemically heterogeneous particles and beads can be used for improved particle capture in porous media and for designing filter beds with enhanced life.     

Particle deposition onto micropatterned charge heterogeneous substrates: trajectory analysis

A trajectory analysis of particles near a micropatterned charged substrate under radial impinging jet flow conditions is presented to investigate the effect of surface charge heterogeneity on particle trajectory and deposition efficiency. The surface charge heterogeneity is modeled as concentric bands of specified width and pitch having positive and negative surface potentials. The flow distribution is obtained using finite element analysis of the governing Navier-Stokes equations. The particle trajectory analysis takes into consideration the hydrodynamic interactions, gravity, van der Waals and electrostatic double layer interactions. The presence of surface charge heterogeneity on the substrate gives rise to an oscillating particle trajectory near the collector surface due to repulsive and attractive forces. As a result of the coupled effects of hydrodynamic and colloidal forces, the particle trajectories and deposition efficiencies are increasingly affected by surface charge heterogeneity as one moves radially away from the stagnation point. The results indicate that it is possible to render collectors with up to 50% favorable surface fraction completely unfavorable by modifying the ratio of the radial to normal fluid velocity. Utilizing the real favorable area fraction of the collector, the patch model expression for calculating the deposition efficiency is modified for impinging jet flow geometry.     

Dielectrophoretic levitation in the presence of shear flow: implications for colloidal fouling of filtration membranes

The ability of dielectrophoretic (DEP) forces created using a microelectrode array to levitate particles in a colloidal suspension is studied experimentally and theoretically. The experimental system employs microfabricated electrode arrays on a glass substrate to apply repulsive DEP forces on polystyrene latex particles suspended in an aqueous medium. A numerical model based on the convection-diffusion-migration equation is presented to calculate the concentration distribution of colloidal particles in shear flow under the influence of a repulsive DEP force field. The results obtained from the numerical simulations are compared against trajectory analysis results and experimental data. The results indicate that by incorporating ac electric field-induced DEP forces in a shear flow, particle accumulation and deposition on the flow channel surfaces can be significantly reduced or even completely averted. The mathematical model is then used to indicate how the deposition behavior is modified in the presence of a permeable substrate, representative of tangential flow membrane filtration operations. The results indicate that the repulsive dielectrophoretic (DEP) forces imparted to the particles suspended in the feed can be employed to mitigate membrane fouling in a cross-flow filtration process.     

Application of the extended RSA models in studies of particle deposition at partially covered surfaces

This paper reviews the application of the extended random sequential adsorption (RSA) approaches to the modeling of colloid-particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. Hard (noninteracting) particle systems are discussed first. We report on the numerical simulations we performed to determine the available surface function, jamming coverage, and pair-correlation function of the larger particles. We demonstrate the effect of the particle size ratio and the small particle surface coverage. We found that the numerical results were in reasonable agreement with the formula stemming from the scaled-particle theory in 2D with a modification for the sphere geometry. Next, we discuss three approximate models of adsorption allowing electrostatic interaction of colloid particles at a charged interface, employing a many-body superposition approximation. We describe two approaches of the effective hard-particle approximation next. We demonstrate the application of the effective hard-particle concept to the bimodal systems and present the effect of electrolyte concentration on the effective particle size ratio. We present the numerical results obtained from the theoretical models of soft-particle adsorption at precovered surfaces. We used the effective hard-particle approximation to determine the corresponding simpler systems of particles, namely the system of hard spheres and the system of hard discs at equilibrium. We performed numerical computations to determine the effective minimum particle surface-to-surface distance, available surface function, jamming coverage, and pair-correlation function of the larger particles at various electrolyte ionic strengths and particle size ratios. The numerical results obtained in the low-surface coverage limit were in good agreement with the formula stemming from the scaled-particle theory with a modification for the sphere geometry and electrostatic interaction. We compared the results of numerical computations of the effective minimum particle surface-to-surface distance obtained using the 2D, 3D, and curvilinear trajectory model. The results obtained with the 3D and curvilinear trajectory models indicate that large-particle/substrate attractive interaction significantly reduces the kinetic barrier to large, charged-particle adsorption at a surface precovered with small, like-charged particles. The available surface function and jamming-coverage values predicted using the simplified 3D and the more sophisticated curvilinear trajectory models are similar, while the results obtained with the 2D model differ significantly. The pair-correlation function suggests different structures of monolayers obtained with the three models. Unlike the three models of the electrostatic interaction, both effective hard-particle approximations give almost identical results. Results of this research clearly suggest that the extended RSA approaches can fruitfully be exploited for numerical simulations of colloid-particle adsorption at precovered surfaces, allowing the investigation of both hard and soft-particle systems.     

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.     

Surface and capillary forces encountered by zinc sulfide microspheres in aqueous electrolyte

The colloid probe technique was used to investigate the interactions between individual zinc sulfide (ZnS) microspheres and an air bubble in electrolyte solution. Incorporation of zinc ions into the electrolyte solution overcomes the disproportionate zinc ion dissolution and mimics high-volume-fraction conditions common in flotation. Determined interaction forces revealed a distinct lack of long-ranged hydrophobic forces, indicated by the presence of a DLVO repulsion prior to particle engulfment. Single microsphere contact angles were determined from particle-bubble interactions. Contact angles increased with decreasing radii and with surface oxidation. Surface modification by the absorption of copper and subsequently potassium O-ethyldithiocarbonate (KED) reduced repulsive forces and strongly increased contact angles.     

Immobilization of cationic polymer particles having active ester groups onto solid surfaces

Monodispersed cationic polymer particles with sulfonium groups and active ester groups at their surfaces were prepared by emulsifier-free emulsion copolymerization of styrene (ST) with a water-soluble active ester monomer, methacryloyloxyphenyldimethylsulfonium methylsulfate (MAPDS). The cationic polymer particle monolayers were fabricated on unmodified and aminated glass plates by electrostatic interactions and chemical reactions, respectively. The polymer particles were immobilized onto unmodified glass plates at relatively regular intervals in the absence of electrolytes, and the morphology of particle monolayers on the glass plates was changed with solid content of latex, electrolyte and cationic surfactant concentration. The polymer particles were immobilized onto aminated glass plate as aggregates by controlling the pH of latex and electrolyte concentration. Remaining active ester groups of the particle monolayers were confirmed to react easily with primary amino compounds.     

Stability of silicon and titanium carbide suspensions in electrolyte, poly(ethylene oxide), and PEO-surfactant solutions

It has been shown that the coagulation values of counterions for SiC and TiC suspensions with particle radius from 0.5 to 5 microm obey a z(2.5-3.5) law and there is an insufficient change in the critical concentration of 1-1 electrolytes (CCE) when the surface potential of particles increases more than two times. Also, the CCE values hardly depend on the position of counterions in the lyotropic sequence. This is explained by aggregation of SiC and TiC particles at a secondary minimum, which is proved by calculations of the potential curves of interparticle interactions using the DLVO theory. The adsorption of poly(ethylene oxide) on the surfaces studied does not cause--in contradiction to dispersions with smaller particles--an unlimited growth in the stability of suspensions. This is due to the aggregation of large particles with adsorbed PEO, as in polymer-free dispersions, under barrierless conditions in which the coordinates of the secondary minimum are determined by superposition of molecular attractive forces and steric repulsive forces of adsorbed polymeric chains, without a contribution from the electric repulsion term. PEO-anionic surfactant complexes possess higher stabilizing capacity compared to the individual components of the mixture. Our results show that the adsorbed polymer layers may hinder the aggregation both in the primary and in the secondary minimum for not very large particles only, the critical size of which depends on the dispersed phase nature and the molecular mass of the polymer.