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.     

A study on shear coagulation and heterocoagulation

Coagulation and heterocoagulation of spherical particles in a simple shear flow have been studied by means of trajectory analysis. Effects of particle size and size ratio have been extensively examined. Some new features of shear coagulation and heterocoagulation have been recognized. Primary and secondary shear coagulations differ in many aspects. The nonequatorial effective capture cross-sections can be attributed to the pure secondary shear coagulation. Shear stability can be low at small and large particle size ranges due to secondary and primary shear coagulation, respectively, with a high stability range at medium particle sizes. A second range of high stability may appear at even larger sizes. On the basis of relative coagulation rate, shear heterocoagulation between particles of the same material but different sizes may or may not be favored over the respective homocoagulations. In the case of primary coagulation, the two homocoagulations are favored over the heterocoagulation. The opposite is true in the case of secondary coagulation. In a suspension composed of particle species of different materials and different sizes, if the larger particles are less stable at an assumed same size with the smaller particles, the homocoagulation of the larger species is still favored over heterocoagulation in the case of primary shear coagulation. In the case of secondary shear coagulation, the heterocoagulation may be favored over the homocoagulation of the larger species, if the above mentioned stability difference is not very large, the particle size difference is not small, and the size of the larger particles is within a certain range.     

聚合物纳米微粒静电组装行为及其表征

使用2,2′-偶氮二异丁基脒二盐酸盐自由基引发剂,改变甲基丙烯酰氧乙基十六烷基二甲基溴化铵阳离子功能单体的量与苯乙烯进行乳液聚合获得不同粒径的阳离子乳胶粒,使用十二烷基硫酸钠为乳化剂和过硫酸钾为引发剂制备阴离子聚合物乳胶粒.采用基于静电相互作用的异凝聚法将以上2种带有相反电荷的乳胶粒组装,获得了表面粗糙程度不同的复合微粒.对异凝聚过程中复合液透光率和微粒大小及分布进行跟踪测试,并用透射电子显微镜表征了阳离子微粒、阴离子微粒以及复合微粒的形态和大小.结果表明,在一定范围内可以通过控制阴离子乳胶粒与阳离子乳胶粒的复合比例改变单个复合微粒表面阳离子小微粒的数目.     

The liquid flow force on a particle in the bubble-particle interaction in flotation

In this paper the problem of calculating the liquid flow force on a particle in interaction with an air bubble with a mobile surface in flotation as a function of the separation distance was solved. The force equation was obtained by first deriving the disturbed flow confined between the surfaces. The model for the force includes the separation distance between the bubble and the particle, the particle size, the bubble's Reynolds number, the bubble rise velocity, and the polar position of the particle on the bubble surface. The proposed equations provide an exact solution to the situation where the particle and the bubble are very close together. The attractive flow force and the surface forces are of similar orders of magnitude. Consequently, the models presented in this paper should provide a better estimate for calculating the forces on particles interacting with air bubbles in mineral flotation and other separation operations involving colloidal interactions.     

Interaction between an ion-penetrable particle and a solid particle. II. Criteria for heterocoagulation

The potential energy of the total interaction between two spherical colloidal particles of different nature is calculated, i. e., of an ion-penetrable particle and an ion-impenetrable solid particle having a constant surface potential or constant surface charge density. The criteria for heterocoagulation are derived. The obtained results suggest a possibility of selective coagulation in the mixed system.     

Selective recovery of micrometer particles from mixtures using a combination of selective aggregation and dissolved-air flotation

Particle–particle separation in biotechnology has gained interest over the years due to the large number of processes that yield particle mixtures. Direct isolation of the product-containing particles is a logical and efficient downstream processing route in these processes. Dissolved-air flotation is applicable for these separations when the particles that require separation have different interactions with the air bubbles and/or differ in aggregation behaviour.

In this work, model particles consisting of micrometer-sized protein-coated polystyrene particles were used to investigate the requirements for the application of dissolved-air flotation for particle–particle separation in biotechnology. These model particles have heterogeneous surfaces with surface groups (brushes) that extend out into the solution. Therefore, steric (or brush) repulsion and so-called hydrophobic interactions between the particles need to be taken into account. The flotation behaviour of the protein-coated particles was related to the size of the aggregates and the foaming behaviour of the proteins. Prediction of their aggregation behaviour was performed on the basis of calculations of the Van der Waals, electrostatic, hydrophobic and brush interactions. The brush interaction force proves to be essential for the prediction of the aggregation behaviour of the particles.     

Heterocoagulation in Bidisperse Magnetorheological Fluids Containing Like-Charged Nanosized and Micron Particles Without a Magnetic Field

Based on extended Derjaguin–Landau–Verwey–Overbeek theory, a heterocoagulation model is proposed for magnetorheological (MR) fluids containing like-charged nanosized and micron particles without a magnetic field. This model considers three major interactions, namely van der Waals attraction, electrical double layer (EDL) interaction, and steric repulsion. The EDL interaction has been identified as the most important factor. The surface potential ratio β (ψ₂/ψ₁) between two dissimilar particles with like charge plays an important role in controlling the change of EDL interaction. At higher β ratios, the EDL interaction becomes attractive when the surface separation falls within a certain range. Two groups of MR fluid samples have been used in experimental studies based on electroacoustic measurements. In the first group, the ratio and the sum of the zeta potentials between carbonyl iron particles and ceria were 4 and ?734.57 mV, respectively. In the second group, these parameters were 1.38 and ?108.17 mV, respectively. The experimental results suggested that the second group did not undergo heterocoagulation, whereas the first group showed extensive heterocoagulation. The difference in surface potentials between particles of two different phases has been found to be critical for determining the state of dispersion or heterocoagulation in concentrated MR fluid systems.     

Selective particle trapping using an oscillating microbubble

The ability to isolate and sort analytes within complex microfluidic volumes is essential to the success of lab-on-a-chip (LOC) devices. In this study, acoustically-excited oscillating bubbles are used to selectively trap particles, with the selectivity being a function of both particle size and density. The operating principle is based on the interplay between the strong microstreaming-induced drag force and the attractive secondary Bjerknes force. Depending upon the size of the bubble, and thus its resonant frequency, it is possible to cause one force to dominate over the other, resulting in either particle attraction or repulsion. A theoretical analysis reveals the extent of the contribution of each force for a given particle size; in close agreement with experimental findings. Density-based trapping is also demonstrated, highlighting that denser particles experience a larger secondary Bjerknes force resulting in their attraction. This study showcases the excellent applicability and versatility of using oscillating bubbles as a trapping and sorting mechanism within LOC devices.     

Preparation of composite fine particles by heterocoagulation

To prepare regular composite particles comprised of organic and inorganic compounds, based on heterocoagulation theory, the properties of the mixture of small amphoteric latices (2a=250 nm) and large spherical silica (2a=240–1590 nm) were investigated as a function of pH, particle number ratio, particle size ratio and electrolyte concentration in the medium. It is apparent that under suitable conditions, we may prepare a stable mixed suspension comprising uniform composite particles, which are made up of many latices regularly adsorbed on silica surfaces, and each composite particle is undergoing Brownian motion as an isolated unit. This new composite particle is very stable for electrolyte, base and acid medium, and its surface charges (sign and magnitude) can be controlled by changing the pH of the medium.     

Interaction force between two charged plates immersed in a solution of charged particles. Coupling between double layer and depletion forces

When two parallel plates are immersed in a solution of small charged particles, the center of the particles is excluded from a region of thickness D/2 near the plate, where D is their diameter. The approach which Langmuir developed for the double layer repulsion in the presence of an electrolyte with ions of negligible size is extended to the case in which one of the "ions" is a charged particle of finite, relatively small size. A general expression for the force generated between the two charged plates immersed in an electrolyte solution containing relatively small charged particles is derived. In this expression, only the electrical potential at the middle distance between the plates is required to calculate the force. A Poisson-Boltzmann equation which accounts for the volume exclusion of the charged particles in the vicinity of the surface is solved to obtain the electrical potential at the middle between the two plates. Starting from this expression, some results obtained previously for the depletion force acting between two plates or two spheres are rederived. For charged plates immersed in a solution of an electrolyte and charged small particles, the effects of the particle charge, particle charge sign, particle size, and volume fraction of the particles on the force acting between the two plates are examined.     

Influence of surface properties of particles on their adhesion and removal

The effect of surface properties of particles on their adhesion and removal was investigated using an immersed system consisting of nylon particles and a quartz plate. The nylon particles were dyed with a reactive dye in order to change their properties and were used for the adhesion and removal experiments in comparison with undyed particles. The electrokinetic potentials of the particles were measured by micro-electrophoresis and the Hamaker constants were independently evaluated using experimental values of dispersive component of surface free energy determined by the Wilhelmy technique. The experimental results were used for the discussion of particle adhesion and removal on the basis of the heterocoagulation theory. The differences in adhesion and removal efficiencies between dyed and undyed particles were explained in terms of the electrostatic and dispersive van der Waals interaction by considering the differences in thier properties, the electrokinetic potential and the Hamaker constant, due to dyeing.     

Preparation of core-shell polymer colloid particles by encapsulation

 By means of heterocoagulation anionic poly-[styrene] particles were coated with smaller electrosterically stabilised cationic particles of poly-[butyl methacrylate]. On heating the heterocoagulated units 45 °C above the glass transition temperature of poly-[butyl methacrylate], as predicted theoretically, the latter polymer spread over the surface of the poly-[styrene] particle to give a composite particle with a core-shell structure. It was found that the extent of packing of the small particles on the larger core particle was a critical feature of the coating process. Received: 12 September 1996 Accepted: 18 September 1996     

Analysis of particle-wall interactions during particle free fall

In this study, the vertical motion of a particle in a quiescent fluid falling toward a horizontal plane wall is analyzed, based on simplified models. Using the distance between the particle and wall as a parameter, the effects of various forces acting on the particle and the particle motion are examined. Without the colloidal and Brownian forces being included, the velocity of small particles is found to be approximately equal to the inverse of the drag force correction function used in this study as the particle approaches the near-wall region. Colloidal force is added to the particle equation of motion as the particle moves a distance comparable to its size. It is found that the particle might become suspended above or deposited onto the wall, depending on the Hamaker constant, the surface potentials of the particle and wall, and the thickness of the electrical double layer (EDL). For strong EDL repulsive force and weaker van der Waals (VDW) attractive force, the particle will become suspended above the wall at a distance at which the particle velocity is zero. This location is referred to as the equilibrium distance. The equilibrium distance is found to increase with increased in EDL thickness when a repulsive force barrier appears in the colloidal force interaction. For the weak EDL repulsive force and strong VDW attractive force case, the particle can become deposited onto the wall without the Brownian motion effect. The Brownian jump length was found to be very small. Many Brownian jumps would be required in a direction toward the wall for a suspended particle to become deposited.     

Prevulcanisation of skim latex: morphology and its use in natural rubber based composite material

The prevulcanisation of skim latex, a by-product of field natural rubber (NR) latex concentrated by centrifugation, using sulphur and peroxide systems was investigated. Compared to the peroxide prevulcanisation, the lower swelling ratio of film casted from sulphur-prevulcanised skim (SPVS) latex was observed. The latter was then employed for preparation of NR/SPVS core–shell particles by using heterocoagulation technique whose driving force was an interpolymer complex between poly(ethylene oxide) (PEO) moieties of a non-ionic surfactant (Nonidet) adsorbed on small SPVS particles and the indigenous surfactant (protein–lipid) on a large NR particle. The value of zeta potential of heterocoagulated particle and the better oil resistance of films casted from the composite latex when compared to that of the NR film revealed the NR/SPVS core–shell structure.     

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.     

Composite natural rubber–polychloroprene latex particles produced by the heterocoagulation technique

Composite natural rubber (NR) based latex particles were prepared using the heterocoagulation technique. A nonionic surfactant (Tween 80) whose molecules bear poly(ethylene oxide) (PEO) was adsorbed on polychloroprene (CR) latex particles and allowed to form complexes between PEO and indigenous surfactant (protein–lipid) on the NR particle surface. The heterocoagulated NR/CR–Tween particles produced were characterised by particle size, zeta-potential and glass-transition temperature measurements and the data indicated the presence of CR–Tween on the outer layer of the composite polymer particles. The results agreed well with the better oil resistance of films cast from heterocoagulated latex when compared with that of the NR film. Received: 22 August 2000 Accepted: 8 January 2001     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

Electrostatic double layer force between a sphere and a planar substrate in the presence of previously deposited spherical particles

A finite element model of the electrostatic double layer interaction between an approaching colloidal particle and a small region of a charged planar surface containing four previously deposited particles is presented. The electrostatic interaction force experienced by the approaching particle is obtained by solving the Poisson-Boltzmann equation with appropriate boundary conditions representing this complex geometry. The interaction forces obtained from the detailed three-dimensional finite element simulations suggest that for the many-body scenario addressed here, the electrostatic double layer repulsion experienced by the approaching particle is less than the corresponding sphere-plate interaction due to the presence of the previously deposited particles. The reduction in force is quite significant when the screening length of the electric double layer becomes comparable to the particle radius (kappaa approximately 1). The results also suggest that the commonly used technique of pairwise addition of binary interactions can grossly overestimate the net electrostatic double layer interaction forces in such situations. The simulation methodology presented here can form a basis for investigating the influence of several previously deposited particles on the electrostatic repulsion experienced by a particle during deposition onto a substrate.     

Bubble colloidal AFM probes formed from ultrasonically generated bubbles

Here we introduce a simple and effective experimental approach to measuring the interaction forces between two small bubbles (approximately 80-140 microm) in aqueous solution during controlled collisions on the scale of micrometers to nanometers. The colloidal probe technique using atomic force microscopy (AFM) was extended to measure interaction forces between a cantilever-attached bubble and surface-attached bubbles of various sizes. By using an ultrasonic source, we generated numerous small bubbles on a mildly hydrophobic surface of a glass slide. A single bubble picked up with a strongly hydrophobized V-shaped cantilever was used as the colloidal probe. Sample force measurements were used to evaluate the pure water bubble cleanliness and the general consistency of the measurements.