Classical DLVO Theory Research Articles

Ultrafine Coal Cleaning using Selective Hydrophobic Coagulation

ABSTRACT Studies have shown that ultrafine hydrophobic materials such as coal and graphite can be selectively coagulated and separated from hydrophilic impurities without using oily agglomerants, flocculants, or electrolytes. This process, which is referred to as Selective Hydrophobic Coagulation (SHC), has been used in laboratory tests to significantly reduce the ash and sulfur contents of several ultrafine, run-of-mine coal samples. The selective coagulation occurs at ζ-potentials significantly higher than those predicted by the classical DLVO theory due to the presence of an attractive interaction energy between hydrophobic particles such as coal. To account for this additional attraction, the interaction energies for the coal-mineral system have been calculated using an extended DLVO theory that incorporates the hydrophobic interaction energy in addition to the traditional dispersion and the electrostatic energies. The results of these theoretical calculations correlate well with separation response obtained using the SHC process.

Stabilization of magnetorheological suspensions by polyacrylic acid polymers

This work is devoted to the synthesis and stabilization of magnetorheological suspensions constituted by monodisperse micrometer-sized magnetite spheres in aqueous media. The electrical double-layer characteristics of the solid/liquid interface were studied in the absence and presence of adsorbed layers of high molecular weight polyacrylic acids (PAA; Carbopol). Since the Carbopol-covered particles can be thought of as “soft” colloids, Ohshima's theory was used to gain information of the surface potential and the charge density of the polymer layer. The effect of the pH of the solution on the double-layer characteristics is related to the different conformations of the adsorbed molecules provoked by the dissociation of the acrylic groups present in polymer molecules. The stability of the suspensions was experimentally studied for different pH and polymer concentrations, and in the absence or presence of a weak magnetic field applied. The stability of the suspensions was explained using the classical DLVO theory of colloidal stability extended to account for hydration, steric, and magnetic interactions between particles. Diagrams of potential energy vs interparticle distance show the predominant effect of steric, hydrophilic/hydrophobic, and magnetic interactions on the whole stability of the system. The best conditions to obtain stable suspensions were found when strong steric and hydrophilic repulsions hinder the coagulation between polymer-covered particles, simultaneously avoiding sedimentation by the thickening effect of the polymer solution. When a not too high molecular weight PAA was employed in a low concentration, the task of a long-time antisettling effect compatible with the desired magnetic response of the fluid was achieved.

Equilibrium profile and rupture of wetting film on heterogeneous substrates

There is abundant experimental evidence, indicating that the non-homogeneity of solid substrates plays substantial role in the behavior of wetting films. Drainage and rupture of wetting films are among the most comprehensively studied phenomena that are influenced by the characteristics of the solid substrate state. Experimental data on silica/water/air wetting films reported in previous studies show that film lifetime is strongly dependent on the substrate degree of hydrophobicity, while the rate of drainage was observed to remain practically unaffected. It has been found also, that both van der Waals and electrostatic forces in these wetting films are repulsive and according to the classical DLVO theory, such films should remain stable. The proposed explanation of the paradox (finite lifetimes in the presence of repulsive surface forces)—that the rupture of these films is caused by nanosized bubbles adhering to the hydrophobic silica surface, is a typical demonstration of the crucial effect of the surface non-homogeneities. The aim of this paper is to analyze the previously proposed model of wetting film with adhered to the solid substrate nanobubble and use the solution to discuss the consistency of the nanobubble rupture mechanism.

ULTRAFINE COAL CLEANING USING SELECTIVE HYDROPHOBIC COAGULATION

ABSTRACT Studies have shown that ultrafine hydrophobic materials such as coal and graphite can be selectively coagulated and separated from hydrophilic impurities without using oily agglomerants, flocculants, or electrolytes. This process, which is referred to as Selective Hydrophobic Coagulation (SHC), has been used in laboratory tests to significantly reduce the ash and sulfur contents of several ultrafine, run-of-mine coal samples. The selective coagulation occurs at ζ-potentials significantly higher than those predicted by the classical DLVO theory due to the presence of an attractive interaction energy between hydrophobic particles such as coal. To account for this additional attraction, the interaction energies for the coal-mineral system have been calculated using an extended DLVO theory that incorporates the hydrophobic interaction energy in addition to the traditional dispersion and the electrostatic energies. The results of these theoretical calculations correlate well with separation response obtained using the SHC process.

Foam films stabilized by dodecyl maltoside. 1. Film thickness and free energy of film formation.

Foam films stabilized by a sugar-based nonionic surfactant, beta-dodecyl maltoside, are investigated. The film thickness and the film contact angle (which is formed at the transition between the film and the bulk solution) are measured as a function of NaCl concentration, surfactant concentration, and temperature. The film thickness measurements provide information about the balance of the surface forces in the film whereas the contact angle measurements provide information about the specific film interaction free energy. The use of the glass ring cell and the thin film pressure balance methods enables studies under a large variety of conditions. Thick foam films are formed at low electrolyte concentration. The film thickness decreases (respectively the absolute value of the interaction film free energy increases) with the increase of the electrolyte concentration according to the classical DLVO theory. This indicates the existence of a repulsive double layer electrostatic component of the disjoining pressure. An electrostatic double layer potential of 16 mV was calculated from the data. A decrease of the film thickness on increase of the surfactant concentration in the solution is observed. The results are interpreted on the basis of the assumption that the surface double layer potential originates in the adsorption of hydroxyl ions at the film surfaces. These ions are expelled from the surface at higher surfactant concentration.

Mathematical modeling of polymer-induced flocculation by charge neutralization

A detailed mathematical model for flocculation of colloidal suspensions in presence of salts and polymers is described and validated. In former case, the classical DLVO theory, which accounts for relevant variables such as pH and salt concentration, is incorporated into a geometrically sectioned discrete population balance model. For processes involving polymers, flocculation via simple charge neutralization is modeled using a modified DLVO theory in which the effect of adsorbed polymer layers on van der Waals attraction is included. The fractal dimension of aggregates is obtained by dynamic scaling of experimental data for time evolution of mean aggregate size. The particle surface potential is assumed to be approximately equal to the zeta potential. The model predictions are in close agreement with experimental results for flocculation of colloidal hematite suspensions in the presence of KCl and polyacrylic acid at different concentrations. In particular, given values of model parameters, e.g., Hamaker constant, fractal dimension, surface potential, and thickness of adsorbed polymer layer, the model can realistically describe the kinetics of flocculation by a simple charge neutralization mechanism and track the evolution of floc size distribution. Representative examples of sensitivity of the flocculation model to perturbations in surface potential and fractal dimension and to modification in the DLVO theory for polymer-coated particles are included.

The viscous behaviour and structure of aqueous suspensions of goethite

Abstract Aqueous suspensions of goethite, prepared at neutral pH, were found to be flocculated, highly viscous and extremely shear thinning at particle volume fractions from 0.01 to 0.08. Then a suspension having a volume fraction of 0.02 was observed by optical microscopy over a range in pH values, and fluid structure correlated with viscous behaviour, that is, a pH that produced a more dispersed structure yielded a lower viscosity and a lower degree of shear thinning. Flocculation and high viscosity were found to persist at high zeta potentials (ζ). The persistence could not be predicted using classical DLVO theory, which indicated the presence of an attractive force in addition to van der Waals forces. It was hypothesized that the different crystal faces of goethite possess different charges and thus provide an additional attractive force, one that is electrostatic. The theory was supported by electron microscopy studies of mixtures of goethite and charged latex spheres.

Hydrophobic aggregation of alumina in surfactant solution

The aggregation behavior of ultrafine alumina in surfactant solution is examined by particle size analyzer. Electrokinetic and contact angle measurements are used to discuss the adsorption mechanism of sodium dodecyl sulfate (SDS) and dodecylamine (DDA) chloride at alumina. The PZC value of alumina is 9.1. SDS and DDA made alumina surface hydrophobic, respectively at pH < PZC and pH > PZC, and hydrophobic aggregation between alumina particles take place. The interfacial interaction energies between alumina particles in solution have been obtained based on polar interfacial interaction theory and contact angle measurements. The classical DLVO theory only considering the electrostatic and van der Waals interaction fails to explain the hydrophobic aggregation of ultrafine alumina, which can be well explained in the extended DLVO theory concerning polar interfacial interaction.

Effect of sodium stearate and calcium ion on dispersion properties of precipitated calcium carbonate suspensions

The adsorptions of sodium stearate and calcium ion on calcium carbonate particles in aqueous media were investigated in terms of zeta potential and yield stress. The zeta potentials of calcium carbonate particles were fluctuated strongly by the co-adsorption of stearate molecules and calcium ions, showing the counter effect on the potential change. At the high concentration of stearate, zeta potentials varied with the surface state of adsorbed surfactant layer. The co-adsorption of stearate and calcium ion indicated a strong interaction of calcium ion with solid/liquid interface at low concentrations, however, showed a similar trend with the case of stearate at high concentrations. Since the zeta potential presents the potential at shear plane, practically it is responsible for the interaction of particles and the destabilization of solution structure at yield stress (τ0). The yield stresses of suspensions determined by Casson’s plots were postulated to present the persistency of stagnant bulk state of dispersions near zero shear rate and inverse to the square of zeta potential. Further, the stability of calcium carbonate suspension mainly depends on an electrostatic repulsion force given by the classical DLVO theory.

Evaluation of DLVO theory with disjoining-pressure and film-conductance measurements of common-black films stabilized with sodium dodecyl sulfate

We develop a unique film holder combining a thin-film balance with AC impedance spectroscopy to measure disjoining pressure, film conductance, and film thickness simultaneously. Foam films stabilized by sodium dodecyl sulfate (SDS) are investigated with and without added sodium chloride (NaCl) electrolyte. Classical colloidal theory, Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, is tested rigorously over a wide range of solution conditions by comparing the surface charge densities fit to disjoining-pressure isotherms with those estimated independently from film-conductance and surface-tension data. Film-conductance measurements strongly suggest that the adsorbed anionic surfactant is partially complexed with counterions. Therefore, to reconcile the different values of charge densities calculated from surface tension and film conductance with those from disjoining pressure, we propose a simple ion-binding electrostatic model. The ion-complexation framework predicts increased ion complexing with increasing solution ionic strength, in agreement with surface-tension and film-conductance data. Unfortunately, it is not possible to describe similarly the trends of the measured disjoining-pressure isotherms because the diffuse-layer charge density increases, or equivalently, the ion complexation decreases with increasing ionic strength. Accordingly, the ion-binding extension of classical DLVO theory does not permit agreement between theory and independent experimental data from surface tension, disjoining pressure, and film conductance.

Observation and characterization of colloids derived from leached cement hydrates

The possibility of colloid generation from cement hydrates in a cementitious repository environment has been investigated through leaching experiments. Pulverized samples of High Flyash and Silica fume-content Cement (HFSC) and 1:9 ordinary portland cement/blast furnace slag (1:9 OPC/BFS) hydrate were leached in low-salinity groundwater at three solid-to-liquid (S/L) mass ratios (1:5, 1:50 and 1:100), and two temperatures (20 and 60 °C) for durations of nearly 2 and 8 months. Detailed characterization of colloid populations has been undertaken by TEM coupled with X-ray analysis. In addition, the surface charge and stability behavior of colloids have been investigated. The colloid concentrations in HFSC hydrate leachates generated at 20 and 60 °C show similar trends with S/L ratio. The colloid concentrations of leachates with the lower S/L ratio (1:50 and 1:100) are in the range of 10 11–10 12 particles per liter. The majority of these particles are composed predominantly of Si, Ca, and Al; the mean particle size is less than 100 nm. The lowest colloid concentrations are found in the leachates with the highest S/L ratios, and the colloid populations tend to be dominated by larger particles. HFSC-derived colloid stability is due to a high negative zeta potential at alkaline pH values, combined with a calcium concentration that is below the critical coagulation concentration (CCC) for the colloids. A preliminary interpretation of HFSC-derived colloid stability based on classical DLVO theory provides a semi-quantitative explanation of the dependence of colloid populations on the S/L ratio in the leaching experiments.

Consolidation behavior in sedimentation of TiO 2 suspensions in the presence of electrolytes

The consolidation of TiO 2 suspensions (anatase and rutile) due to gravity sedimentation in the presence of electrolytes has been investigated as a function of pH. Sodium and barium nitrate were used as flocculating electrolytes. The particle interaction was related to the ζ potential and the thickness of the electrical double layer, κ −1, by utilizing the repulsive barrier in the classical DLVO theory. The stability of the suspensions was represented as the average final solids content of the sediment cake, φ fin. The batch sedimentation process was followed by scanning the sample cell with X-rays, from which the solids content and the particle size were calculated. Generally, dense sediments, with φ fin up to volume fractions of 0.5, were found for stable suspensions. Flocculated suspensions produced sediments with low φ fin. The φ fin was observed to increase linearly with increasing repulsive barrier. However, at pH values only slightly higher than the isoelectric point (pH iep) the φ fin remained low until it returned to linearity at a pH much higher than pH iep. This was attributed to the stronger affinity of sodium than of nitrate for the particle surface, which may be explained by the higher negative hydration energy of sodium. The stronger affinity of sodium was also shown as unsymmetrical distribution of φ fin around pH iep, with stronger flocculation at pH>pH iep. The interpretation of φ fin as a function of the repulsive barrier (or κ −1) also made it possible to distinguish between the adsorption mechanisms of ions from solution. Addition of electrolyte at a fixed low and high pH (surface positively and negatively charged, respectively) clearly showed the specificity in adsorption and consequent flocculation of the barium ion from the indifferent nitrate. Sodium was, however, again observed to flocculate the TiO 2 suspensions slightly more strongly than nitrate.

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.

Sugar-based gemini surfactant with a vesicle-to-micelle transition at acidic pH and a reversible vesicle flocculation near neutral pH.

A sugar-based (reduced glucose) gemini surfactant forms vesicles in dilute aqueous solution near neutral pH. At lower pH, there is a vesicle-to-micelle transition within a narrow pH region (pH 6.0-5.6). The vesicles are transformed into large cylindrical micelles that in turn are transformed into small globular micelles at even lower pH. In the vesicular pH region, the vesicles are positively charged at pH < 7 and exhibit a good colloidal stability. However, close to pH 7, the vesicles become unstable and rapidly flocculate and eventually sediment out from the solution. We find that the flocculation correlates with low vesicle zeta-potentials and the behavior is thus well predicted by the classical DLVO theory of colloidal stability. Surprisingly, we find that the vesicles are easily redispersed by increasing the pH to above pH 7.5. We show that this is due to a vesicle surface charge reversal resulting in negatively charged vesicles at pH > 7.1. Adsorption, or binding, of hydroxide ions to the vesicular surface is likely the cause for the charge reversal, and a hydroxide ion binding constant is calculated using a Poisson-Boltzmann model.

Membrane–Colloid Interactions: Comparison of Extended DLVO Predictions with AFM Force Measurements

Theoretical predictions of interaction energies for several membrane–colloid pairs were made using the classical DLVO theory and an extended DLVO (XDLVO) approach. The XDLVO approach accounts for acid-base (polar) interactions that are not considered in the classical DLVO theory. For all membranecolloid pairs studied, DLVO interactions were similar. However, inclusion of acid-base interactions resulted in substantially different predictions of short-range (separation distance <10 nm) interaction energies for several of the membrane–colloid pairs investigated. Predicted interaction energies were compared with atomic force microscopy (AFM) force measurements. The colloid probe technique was used to directly measure the force of interaction between a single colloid and a membrane surface. It was found that for strongly hydrophilic systems where the XDLVO approach predicts substantially different interaction energies than the DLVO theory, the measured force curves agree with the interaction sequence predicted...

Study on Osmotic Pressures for Aqueous Lysozyme and α-Chymotrypsin—Electrolyte Solutions with Two Yukawa Potentials

The equation of state (EOS) of Duh and Mier-y-Terán for one Yukawa potential is expanded to two Yukawa potentials to describe the nonidealities of the charged lysozyme and α-chymotrypsin solutions. Instead of the classical DLVO theory, the attractive dispersion and double-layer repulsion interactions are represented by two Yukawa potentials, respectively. For the aqueous lysozyme solutions, the only adjustable dispersion energy parameter ε/k is regressed and the average deviation is 1.76%. For the aqueous α-chymotrypsin solutions, two adjustable parameters (the molecular weight and dispersion energy parameter) are regressed and the average deviation is 7.62%. Some correlation and prediction results are discussed.

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.

Assessing short-range membrane–colloid interactions using surface energetics

The contribution of acid–base (AB) (polar) interactions to the total interaction energy between membranes and colloids was investigated. The surface energetics of several membranes and colloids were evaluated using the Lifshitz–van der Waals acid-base approach. This provides the van der Waals (LW) and polar interaction energies between various surfaces from measurements of contact angles of different probe liquids on these surfaces. In addition, the surface potentials of the membranes and colloids were determined using electrokinetic measurements, yielding the electrostatic (EL) interaction between these surfaces. The three interaction energy components (LW, EL, and AB) were combined according to the extended Derjaguin–Landau–Verwey–Overbeek (extended DLVO or XDLVO) approach to evaluate membrane–colloid interaction energies. Predictions of interaction energy based on the XDLVO approach were compared to the corresponding predictions from the classical DLVO theory. For all the membrane–colloid combinations studied, the DLVO potentials were quite similar. However, inclusion of AB interactions resulted in a substantially different (qualitative and quantitative) prediction of short-range (separation distances <5 nm) interaction energies for several of the membrane–colloid combinations investigated. Finally, all of the membranes studied were found to have substantially low surface energies compared to the colloids and the interaction energy between the membranes and colloids was primarily dictated by the surface energies of the colloids. Fouling experiments for a membrane and three colloids supported the fouling trends predicted by the XDLVO approach.

Stability of Dispersions of Colloidal Nickel Ferrite Spheres

The stability of suspensions of nickel ferrite spheres is investigated for different compositions of the dispersion medium, in the absence and in the presence of an external magnetic field. The time-dependence of the optical absorbance of the suspensions is the quantity used for experimentally determining the stability. Two approaches have been used for the calculation of the interaction energy of the particles: first, the classical DLVO theory, in which the net interaction is considered as the superposition of electrostatic double-layer repulsion and van der Waals attraction; and second, the so-called extended-DLVO model, in which short-range hydrophobic (hydrophilic) attractions (repulsions) are also considered. Calculation of all these interactions required the determination of (i) the diffuse double-layer potential of the ferrite particles (that was approximated by the zeta potential, as deduced from electrophoresis measurements); (ii) the Hamaker constant of the particles in aqueous media; and (iii) the acid/base components of the surface free energy of the solids. The quantities in (ii) and (iii) above were obtained from contact-angle measurements for selected liquids on layers of the magnetic oxide. When a magnetic field is applied, another interaction, of magnetic origin, has to be accounted for. It was found that the suspensions are more stable the farther their pH is from the isoelectric point, and the lower the ionic strength of the medium is, in full agreement with the predictions of both the classical and extended-DLVO models. The application of the external magnetic field was found to provoke significant changes in the rate of variation of absorbance with time: The results are coherent with an increased velocity of particle aggregation due to magnetic attractions between the magnetized colloids. The DLVO theory (in any of its versions) including magnetic interactions can explain this behavior, since the calculated force between particles is more attractive when the field is present.

Correlation and Prediction of Osmotic Pressures for Aqueous Bovine Serum Albumin–NaCl Solutions Based on Two Yukawa Potentials

A new equation of state is proposed to correlate and predict the osmotic pressure data for aqueous bovine serum albumin (BSA) solutions with different NaCl concentrations and pH values with only one adjustable parameter. The Carnahan–Starling equation represents the contribution of the hard sphere repulsion to the osmotic pressure. The attractive dispersion and double-layer repulsion interactions are represented by two Yukawa potentials, respectively. The equation of state of Duh and Mier-Y-Teran for one Yukawa potential is expanded to two Yukawa potentials to describe the nonidealities of the charged BSA–aqueous NaCl solution, instead of the classical DLVO theory. The average relative deviation of correlation of the osmotic pressure in 0.15 M NaCl solution is 18%. The average relative deviation of prediction in 1–5 M NaCl solutions is 20.33%. A comparison with other models and the limitations of our model are discussed.