Microflotation Suppression and Enhancement Caused by Particle/Bubble Electrostatic Interaction

The processes of attachment and detachment of small or medium-sized particles to relatively large bubbles during microflotation are considered in terms of the heterocoagulation theory. Calculations are made for the conditions that the surface potentials are of similar sign and constant, that one of the surface potentials is small, that hydrophobic attraction is absent, and that there are no surface deformations. Under these conditions bubble-particle aggregates may form as a result of an electrostatic attraction which exceeds the repulsive van der Waals force at intermediate distances. Next to electrostatic and van der Waals forces, hydrodynamic and gravitational forces are considered. These forces may overcome the electrostatic repulsion at large distances and promote particle bubble attachment. Strong electrostatic attraction at small distances, arising at a large difference of the surface potentials of the bubble and the particle and of low electrolyte concentrations, can prevent subsequent detachment by hydrodynamic and gravitational forces. With increasing electrolyte concentration the electrostatic barrier increases and the attractive electrostatic force diminishes. As a result, a critical electrolyte concentration for microflotation exists. Above this concentration attachment may still occur but it is followed by detachment. At lower electrolyte concentrations the electrostatic attractive force prevents the detachment. The dependence of the critical electrolyte concentration on the values of the bubble and particle potentials and the Hamaker constant is calculated. The critical concentration does not depend on particle or bubble size if the absolute values of the total detachment force and the total pressing force coincide, which is the case for Stokes and potential flow. For every electrolyte concentration lower than the critical value there are two critical particle sizes that limit the flotation possibility. For small particle sizes attachment is impossible because the pressing force is smaller than the electrostatic barrier. For large particle sizes detachment cannot be prevented because the detachment force exceeds the maximum electrostatic attraction. A microflotation domain of intermediate particle sizes exists in which irreversible heterocoagulation occurs. Copyright 2001 Academic Press.     

Influence of very small bubbles on particle/bubble heterocoagulation

Very small bubbles which partially coat the surface of particles influence whether or not heterocoagulation between a particle and a bubble occurs. The electrostatic and van der Waals forces of interaction between particles and bubbles were calculated as a function of electrolyte concentration, particle size, and the size and distributions of these very small bubbles present on the particle surface. The height of the surface force barrier was compared with the hydrodynamic pressing force under conditions of flotation. The presence of these very small bubbles has a profound effect on the interaction between particles and bubbles and, in particular, strongly decreases the critical particle radius for heterocoagulation.     

Collision efficiencies of diffusing spherical particles: hydrodynamic,van der waals and electrostatic forces

A practical limitation of the application of Smoluchowski's classical estimate for the collisions probability of two diffusing spherical particles in Brownian motion is the non-consideration of interparticle forcves. For suspended particles in water such forces can arise from the disturbance the particle causes in the fluid (hydrodynamic forces), from the cloud of ions which surround an electrically charged particle (double layer forces) or they can be of molecular origin (van der Waals forces). In this paper corrections to Smoluckhowski's collision probability are computed when such forces operate Scoluchowski's collision probability are computed when such forces operate between two approaching particles of various sizes. Results for several values of the van der Waals energy of attraction and the ionic strength of the electrolyte are presented in a way convenient for particle collision modeling.     

Determination of van der Waals forces in monolayer films of lipids & biopolymers. Equation of state for two-dimensional films

Amphiphile molecules are characterized by the dual property arising from the interactions between the apolar [alkyl] and the polar part and the surrounding solvent, i.e., water. In assemblies which amphiphiles form in diverse systems, e.g., micelles, soap bubbles, monolayers or bilayers at interfaces, the attractive forces are attributed to the van der Waals forces. It is not easy to estimate the magnitude of van der Waals forces in some of these systems by any direct method.The magnitude of van der Waals forces in spread monolayers of lipids and biopolymers has been reported to be estimated from experimental data. The magnitude of these forces has been estimated by using an equation of state of a very general form, as delineated herein. In the current literature no such attempt has been reported in the analyses of these monolayers spread on aqueous surfaces. These analyses suggest that the predominant surface forces arise from van der Waals interactions, if the magnitude of electrostatic charge repulsions is weak. The equation-of-state as derived indicates that it is useful in providing information about the molecular interaction in monolayers, for both lipids and biopolymers.     

Forces between a hard surface and an air–aqueous interface with and without films

The adsorption of particles to air–aqueous interfaces is vital in many applications, such as mineral flotation and the stabilization of food foams. The forces in the system determine whether a particle will attach to an air–aqueous interface. The forces between a particle and an air–aqueous interface are influenced by Derjaguin–Landau–Verwey–Overbeek forces (i.e. van der Waals and electrostatic forces), non–Derjaguin–Landau–Verwey–Overbeek forces (e.g. hydrophobic, hydrodynamic, structural, and capillary forces), liquid drainage, and liquid flow. As an air–aqueous interface can be deformed by a particle, the forces measured between an air–aqueous interface and a particle can differ from those measured between two hard surfaces separated by liquid. The presence of a film at an air–aqueous interface can also change the forces.     

A modeling approach to describe the adhesion of rough, asymmetric particles to surfaces

A combined theoretical and experimental study of the adhesion of alumina particles and polystyrene latex spheres to silicon dioxide surfaces was performed. A boundary element technique was used to model electrostatic interactions between micron-scale particles and planar surfaces when the particles and surfaces were in contact. This method allows quantitative evaluation of the effects of particle geometry and surface roughness on the electrostatic interaction. The electrostatic interactions are combined with a previously developed model for van der Waals forces in particle adhesion. The combined model accounts for the effects of particle and substrate geometry, surface roughness and asperity deformation on the adhesion force. Predictions from the combined model are compared with experimental measurements made with an atomic force microscope. Measurements are made in aqueous solutions of varying ionic strength and solution pH. While van der Waals forces are generally dominant when particles are in contact with surfaces, results obtained here indicate that electrostatic interactions contribute to the overall adhesion force in certain cases. Specifically, alumina particles with complex geometries were found to adhere to surfaces due to both electrostatic and van der Waals interactions, while polystyrene latex spheres were not affected by electrostatic forces when in contact with various surfaces.     

Bubble particle heterocoagulation under turbulent conditions

An analytical model that enables the calculation of the flotation rate constant of particles as a function of particle size with, as input parameters, measurable particle, bubble, and hydrodynamic quantities has been derived. This model includes the frequency of collisions between particles and bubbles as well as their efficiencies of collision, attachment, and stability. The generalized Sutherland equation collision model and the modified Dobby-Finch attachment model developed previously for potential flow conditions were used to calculate the efficiencies of particle-bubble collision and attachment, respectively. The bubble-particle stability efficiency model includes the various forces acting between the bubble and the attached particle, and we demonstrate that it depends mainly on the relative magnitude of particle contact angle and turbulent dissipation energy. The flotation rate constants calculated with these models produced the characteristic shape of the flotation rate constant versus particle size curve, with a maximum appearing at intermediate particle size. The low flotation rate constants of fine and coarse particles result from their low efficiency of collision and low efficiencies of attachment and stability with gas bubbles, respectively. The flotation rate constants calculated with these models were compared with the experimental flotation rate constants of methylated quartz particles with diameters between 8 and 80 micro m interacting with gas bubbles under turbulent conditions in a Rushton flotation cell. Agreement between theory and experiment is satisfactory.     

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.     

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.     

Estimation of the Hamaker constants by sedimentation field-flow fractionation

van der Waals forces are one of several forces that control the adhesion between two materials. These forces are important to quantify in adhesion studies because they are always present and are always attractive. The major problem in calculating the van der Waals interaction between colloidal particles is that of evaluating the Hamaker constant. Hence, an accurately determined Hamaker constant for a given material is needed when interfacial phenomena such as adhesion are discussed in terms of the total potential energy between a particle and a substrate. In this paper, a new simple and accurate methodology for the estimation of the Hamaker constant is introduced. The results are in good agreement with those values found in literature.     

Van der Waals Emulsions: Emulsions Stabilized by Surface‐Inactive,Hydrophilic Particles via van der Waals Attraction

Surface‐inactive, highly hydrophilic particles are utilized to effectively and reversibly stabilize oil‐in‐water emulsions. This is a result of attractive van der Waals forces between particles and oil droplets in water, which are sufficient to trap the particles in close proximity to oil–water interfaces when repulsive forces between particles and oil droplets are suppressed. The emulsifying efficiency of the highly hydrophilic particles is determined by van der Waals attraction between particle monolayer shells and oil droplets enclosed therein and is inversely proportional to the particle size, while their stabilizing efficiency is determined by van der Waals attraction between single particles and oil droplets, which is proportional to the particle size. This differentiation in mechanism between emulsification and stabilization will significantly advance our knowledge of emulsions, thus enabling better control and design of emulsion‐based technologies in practice.     

Van der Waals Emulsions: Emulsions Stabilized by Surface‐Inactive,Hydrophilic Particles via van der Waals Attraction

Surface‐inactive, highly hydrophilic particles are utilized to effectively and reversibly stabilize oil‐in‐water emulsions. This is a result of attractive van der Waals forces between particles and oil droplets in water, which are sufficient to trap the particles in close proximity to oil–water interfaces when repulsive forces between particles and oil droplets are suppressed. The emulsifying efficiency of the highly hydrophilic particles is determined by van der Waals attraction between particle monolayer shells and oil droplets enclosed therein and is inversely proportional to the particle size, while their stabilizing efficiency is determined by van der Waals attraction between single particles and oil droplets, which is proportional to the particle size. This differentiation in mechanism between emulsification and stabilization will significantly advance our knowledge of emulsions, thus enabling better control and design of emulsion‐based technologies in practice.     

Specific and nonspecific interaction forces between Escherichia coli and silicon nitride, determined by poisson statistical analysis

The nature of the physical interactions between Escherichia coli JM109 and a model surface (silicon nitride) was investigated in water via atomic force microscopy (AFM). AFM force measurements on bacteria can represent the combined effects of van der Waals and electrostatic forces, hydrogen bonding, steric interactions, and perhaps ligand-receptor type bonds. It can be difficult to decouple these forces into their individual components since both specific (chemical or short-range forces such as hydrogen bonding) and nonspecific (long-range colloidal) forces may be present in the overall profiles. An analysis is presented based on the application of Poisson statistics to AFM adhesion data, to decouple the specific and nonspecific interactions. Comparisons with classical DLVO theory and a modified form of a van der Waals expression for rough surfaces were made in order to help explain the nature of the interactions. The only specific forces in the system were due to hydrogen bonding, which from the Poisson analysis were found to be -0.125 nN. The nonspecific forces of 0.155 nN represent an overall repulsive interaction. These nonspecific forces are comparable to the forces calculated from DLVO theory, in which electrostatic-double layer interactions are added to van der Waals attractions calculated at the distance of closest approach, as long as the van der Waals model for "rough" spherical surfaces is used. Calculated electrostatic-double layer and van der Waals interactions summed to 0.116 nN. In contrast, if the classic (i.e., smooth) sphere-sphere model was used to predict the van der Waals forces, the sum of electrostatic and van der Waals forces was -7.11 nN, which appears to be a large overprediction. The Poisson statistical analysis of adhesion forces may be very useful in applications of bacterial adhesion, because it represents an easy way to determine the magnitude of hydrogen bonding in a given system and it allows the fundamental forces to be easily broken into their components.     

Mechanism of hydrodynamic separation of biological objects in microchannel devices

In this study, the separation mechanism employed in hydrodynamic chromatography in microchannel devices is analyzed. The main purpose of this work is to provide a methodology to develop a predictive model for hydrodynamic chromatography for biological macromolecules in microchannels and to assess the importance of various phenomenological coefficients. A theoretical model for the hydrodynamic chromatography of particles in a microchannel is investigated herein. A fully developed concentration profile for non-reactive particles in a microchannel was obtained to elucidate the hydrodynamic chromatography of these particles. The external forces acting on the particles considered in this model include the van der Waals attractive force, double-layer force as well as the gravitational force. The surface forces, such as van der Waals attractive force as well as the double-layer repulsive force, can either enhance or hinder the average velocity of the macromolecular particles. The average velocity of the particles decreases with the molecular radius because the van der Waals attractive force increases the concentration of the particles near the channel surface, which is the low-velocity region. The transport velocity of the particles is dominated by the gravity and the higher density enlarges the effect caused by gravity.     

Particle-bubble collision models--a review

A critical review of the various models existing in the literature for the calculation of the collision efficiency between particles and single, rising gas bubbles is presented. Although all of these collision models predict that the collision efficiency increases with particle size, their dependence on the latter is different because of the various assumptions and hydrodynamic conditions used in each model. Collision efficiencies of quartz particles with single bubbles have been obtained from experimental flotation experiments under conditions where the attachment and stability efficiencies were at, or near, unity. These collision efficiencies were then used to test various collision models. Good agreement between the experimental and calculated collision efficiencies was only obtained with the Generalised Sutherland Equation. The differences in collision efficiencies obtained between the various models were mainly explained in terms of, firstly, the degree of mobility of the bubble surface and, secondly, a consideration of the inertial forces acting on the particles.     

DLVO interactions of tungsten oxide and cobalt oxide surfaces measured with the colloidal probe technique

We have investigated the DLVO surface forces of oxidized tungsten and cobalt surfaces using the atomic force microscope (AFM) colloidal probe technique. It was shown by X-ray photoelectron spectroscopy (XPS) and electrokinetic measurements that this model system is representative of industrial tungsten carbide (WC) and cobalt powders used in the production of hard metals. We found that the attractive van der Waals forces are well described by Hamaker constants, calculated from optical data for WO(3) and CoOOH. The repulsive electrostatic double layer forces between WO(3) surfaces increase with increasing pH due to an increasingly negative surface potential. This surface potential decreases with increasing ionic strength at pH 7.5. The electrostatic interaction between WO(3) and CoOOH is attractive at pH 10, suggesting a positively charged CoOOH surface.     

Ionic liquid nanotribology: stiction suppression and surface induced shear thinning

The friction and adhesion between pairs of materials (silica, alumina, and polytetrafluoroethylene) have been studied and interpreted in terms of the long-ranged interactions present. In ambient laboratory air, the interactions are dominated by van der Waals attraction and strong adhesion leading to significant frictional forces. In the presence of the ionic liquid (IL) ethylammonium nitrate (EAN) the van der Waals interaction is suppressed and the attractive/adhesive interactions which lead to "stiction" are removed, resulting in an at least a 10-fold reduction in the friction force at large applied loads. The friction coefficient for each system was determined; coefficients obtained in air were significantly larger than those obtained in the presence of EAN (which ranged between 0.1 and 0.25), and variation in the friction coefficients between systems was correlated with changes in surface roughness. As the viscosity of ILs can be relatively high, which has implications for the lubricating properties, the hydrodynamic forces between the surfaces have therefore also been studied. The linear increase in repulsive force with speed, expected from hydrodynamic interactions, is clearly observed, and these forces further inhibit the potential for stiction. Remarkably, the viscosity extracted from the data is dramatically reduced compared to the bulk value, indicative of a surface ordering effect which significantly reduces viscous losses.     

The Effect of van der Waals Forces on the Deposition of Highly Dispersed Aerosol Particles on Ultrafine Fibers

The effect of van der Waals forces on the collection of highly dispersed aerosol particles with ultrafine fiber filters was studied theoretically. The capture coefficient was found from the numerical solution of the equation of convective diffusion with the account of the particle size, the effect of van der Waals forces acting between a particle and a fiber, and the gas slip effect at the surface of ultrafine fibers. It was shown that allowance being made for van der Waals forces markedly affects the capture coefficient within the maximal particle penetration range and that the radius of the most penetrating particles decreases with the rising effect of these forces.     

Dependence of the floatability of antimonite on the value of zeta-potential

The case of flotation of a ‘bulk’ hydrophobic mineral in the absence of a collector is considered. The theory developed takes into consideration the van der Waals and electrostatic forces and leads to a simple quantitative criterion of floatability containing the zeta-potential.

Experiments with the flotation of antimonite confirm the theory and the quantitative form of criterion of floatability revealing the role of zeta-potential.     

Drying and hydrophobic collapse of paraffin plates

We perform molecular dynamics simulations of the hydrophobic collapse of two paraffin plates to examine how the collapse is mediated by realistic paraffin-water attractive van der Waals forces. We explore several aspects of the drying transition between the plates, including the critical separation for drying and the critical size of the vapor bubble required for the nucleation of the drying event. We also investigate the kinetics of hydrophobic collapse and find that the hydrophobic collapse occurs in about 100 ps. We compare these results with the simulations with the plate-water van der Waals attractions turned off and with recent results on the hydrophobic collapse of multidomain proteins. Last, we discuss the relationship among the dewetting transition critical distance, van der Waals potential well depth, and water contact angle on solute surface using a simple macroscopic theory.