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.     

Dielectrophoretic force on a sphere near a planar boundary

The small gap distance separating a spherical colloidal particle in electrophoretic motion from a planar nonconducting surface is a required parameter for calculating its electrophoretic mobility. In the presence of an externally applied electric field, this gap distance is determined by balancing the van der Waals, electrical double layer interaction, and gravitational forces with a dielectrophoretic (DEP) force. Here, the DEP force was determined analytically by integration of the Maxwell stress over the surface of the particle. The account of this force showed that its previous omission from the analysis always resulted in underpredicted gap distances. Furthermore, the DEP force dominated under conditions of low particle density or high electric field strength and led to much higher gap distances on the order of a few microns. In one particular case, a combination of low particle density and small particle size produced two possible equilibrium gap distances for the particle. However, the particle was unstable in the second equilibrium position when subjected to small perturbations. In general, larger particles had smaller gap sizes. The effects of four other parameters on gap distance were studied, and gap distances were found to increase with lower particle density, higher electric field strength, higher particle and wall zeta potentials, and lower Hamaker constants. Retardation effects on van der Waals attraction were considered.     

Direct measurement of hydrophobic particle–bubble interactions in aqueous solutions by atomic force microscopy: Effect of particle hydrophobicity

Direct measurements of the interaction forces between a spherical silica particle and a small air bubble have been conducted in aqueous electrolyte solutions by using an atomic force microscope (AFM). The silica particle was hydrophobized with a silanating reagent, and the interaction forces were measured by using several particles with different surface hydrophobicities. In the measured force curves, a repulsive force was observed at large separation distances as the particle moved towards the bubble. The origin of the repulsive force was attributed to an electrostatic double-layer force because both the particle and bubble were negatively charged. After the repulsive force, an extremely long-range attractive force acted between the surfaces. These results indicate that the intervening thin water film between the particle and bubble rapidly collapsed, resulting in the particle penetrating the bubble.

The instability of the thin water film between the surfaces suggests the existence of an additional attractive force. By comparing the repulsive forces of the obtained force curves with the DLVO theory, the rupture thickness was estimated. The hydrophobicity of the particle did not significantly change the rupture thickness, whereas the pH of the solution is considered to be a critical factor.     

Detachment of Particles from Surfaces: An AFM Study

We have measured interactions between hydrophilic and hydrophobic surfaces in an aqueous medium at various pH and ionic strengths as well as in some organic solvents using atomic force microscopy and analyzed them in terms of particle adhesion and detachment from surfaces. In hydrophilic systems the forces observed were found to be well described by DLVO theory at large separation distances. Very long range hydrophobic forces were not observed in hydrophilic-hydrophobic systems. Nevertheless, the jump into contact was found to occur at distances greater that those predicted by just van der Waals attraction. The interaction between two hydrophobic surfaces was dominated by the long-range attraction due to hydrophobic forces. This interaction was found to be sensitive to the type of substrate as well as to the pH and electrolyte concentration. Measured pull-off forces showed poor reproducibility. However, average values showed clear trends and were used to estimate interfacial energies or work of adhesion for all systems studied by means of the Derjaguin approximation. These values were compared to those calculated by the surface tension component theory using the acid-base approach. Good qualitative agreement was obtained, giving support for the usefulness of this approach in estimating interfacial energies between surfaces in liquid media. A comparison of the measured adhesion force with hydrodynamic detachment experiments showed good qualitative agreement. Copyright 2001 Academic Press.     

Trajectory Analysis and Collision Efficiency during Microbubble Flotation

The hydrodynamic interaction between a rising bubble and a sedimenting particle during microbubble flotation is considered. The effects of attractive van der Waals forces and attractive or repulsive electrostatic forces are included. A mathematical model is presented which is used to perform a trajectory analysis and to calculate collision efficiencies between the bubble and particle. It is shown that collision efficiencies and the nature of the bubble-particle interactions are strongly dependent on the relative strengths of the van der Waals and electrostatic forces and on the lengthscales over which these forces act. It is demonstrated that optimal operating conditions can be suggested to achieve efficient microbubble flotation by correctly accounting for the interaction of van der Waals, electrostatic, and hydrodynamic forces. Copyright 1999 Academic Press.     

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.     

Deflection and pull-in instability of nanoscale beams in liquid electrolytes

An elastic beam suspended horizontally over a substrate in liquid electrolyte was subjected to electric, osmotic, and van der Waals forces. The problem, which is governed by four non-dimensional parameters, was solved using the finite element method. The sum of the electric and osmotic forces, the electrochemical force, is usually attractive. However, the electrochemical force can be repulsive for a narrow range of the ion concentration, the initial separation and surface potentials. Furthermore, the beam deflection is not a monotonic function of the applied surface potentials, the bulk ion concentration, or the initial separation between the beam and the substrate. As these parameters are increased monotonically, the beam bends up and then down. The pull-in voltage increases as the bulk ion concentration increases. The pull-in voltage of a double-wall carbon nanotube suspended over a graphite substrate in liquid can be less than or greater than the pull-in voltage in air, depending on the bulk ion concentration. The critical separation between the DWCNT and the substrate increases with the bulk ion concentration. However, for a given bulk ion concentration, the critical separation is independent of the electric potentials. Furthermore, the critical separation is approximately equal in liquid and air.     

Generalizations for the potential of mean force between two isolated colloidal particles from Monte Carlo simulations

A substantial amount of experimental and numerical evidence has shown that the Derjaguin-Landau-Verwey-Overbeek theory is not suitable for describing those colloidal solutions that contain multivalent counterions. Toward improved understanding of such solutions, the authors report Monte Carlo calculations wherein, following Rouzina and Bloomfield, they postulate that, in the absence of van der Waals forces, the overall force between two isolated charged colloidal particles in electrolyte solutions is determined by a dimensionless parameter Gamma=z(2)l(B)/a, which measures the electrostatic repulsion between counterions adsorbed on the macroion surface, where z = counterion valence, l(B)=Bjerrum length, and a = average separation between counterions on the macroion surface calculated as if the macroion were fully neutralized. The authors find, first, that the maximum repulsion between like-charged macroions occurs at Gamma approximately 0.5 and, second, that onset of attraction occurs at Gamma approximately 1.8, essentially independent of the valence and concentration of the surrounding electrolyte. These observations might provide new understanding of interactions between electrostatic double layers and perhaps offer explanations for some electrostatic phenomena related to interactions between DNA molecules or proteins.     

The bridging force between two plates by polyelectrolyte chains

The interaction between particles in a colloidal system can be significantly affected by their bridging by polyelectrolyte chains. In this paper, the bridging is investigated by using a self-consistent field approach which takes into account the van der Waals interactions between the segments of the polyelectrolyte molecules and the plates, as well as the electrostatic and volume exclusion interactions. A positive contribution to the force between two plates is generated by the van der Waals interactions between the segments and the plates. This positive (repulsive) contribution plays an important role in the force when the distances between the plates are small. With increasing van der Waals interaction strength between segments and plates, the force between the plates becomes more repulsive at small distances and more attractive at large distances. When the surfaces of the plates have a constant surface electrical potential and a charge sign opposite to that of the polyelectrolyte chains, the force between the two plates becomes less attractive as the bulk polyelectrolyte concentration increases. This behavior is due to a higher bulk counterion concentration dissociated from the polyelectrolyte molecules. At short distances, the force between plates is more repulsive for stiffer chains. A comparison between theoretical and experimental results regarding the contraction of the interlayer separation between the platelets of vermiculite clays against the concentration of poly(vinyl methyl ether) was made.     

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.     

Interaction forces between α-alumina fibres in aqueous electrolyte measured with an atomic force microscope

The surface charging properties of polycrystalline α-alumina fibres in aqueous electrolyte solutions have been investigated by direct force and streaming potential measurements. The presence of both Al and Si on the surface of the fibres resulted in a chemically heterogeneous surface. The heterogeneous distribution of Si resulted in large attractive forces between the fibres at moderate to low pH values and a pzc/iep at a pH value of approximately 5.5. The origin of this force was electrostatic in nature as the force profiles were well described by the DLVO theory of colloid stability. The agreement between the direct force and streaming potential measurements was good both in terms of the magnitude of the potentials and the position of the pzc/iep. By acid washing the fibres the chemical heterogeneity of the surface was reduced and the attractive force profiles at lower pH values were not observed. Instead repulsive forces were observed which were well described by DLVO theory at all separation distances greater than 8 nm. At smaller separation distances an additional repulsive force was measured which was attributed to the presence of a Al(OH)₃ like layer on the surface of the alumina. The acid washing treatment also resulted in a shift in the pH at which the pzc/iep occurred to a value of 6.5, presumably due to a lower surface silica concentration.     

Surface interaction forces mediated by poly(N-isopropylacrylamide) (PNIPAM) polymers: effects of concentration and temperature

Total internal reflection microscopy was used to directly measure the interaction potentials between a micron-sized silica sphere and a flat silica surface in the presence of a linear poly(N-isopropylacrylamide) (PNIPAM) aqueous solution. When the PNIPAM concentration was low, no discernible forces were detected. A further increase in PNIPAM concentration resulted in a long-range attraction which was likely due to a combined of the reduced electrostatic interaction between the silica particle and the flat surface after the polymer adsorption and polymer bridges formation. On the other hand, for a fixed PNIPAM concentration, the interaction potential profiles between the particle and flat surface were once again characterized by attraction as temperature was increased. This attractive force can be explained in terms of the conformational changes of PNIPAM chains at the surfaces, which subsequently affected the polymer adsorption and enhanced the segment–segment interaction among the adsorbed polymer chains.     

Bubble-solid interactions in water and electrolyte solutions

Surface forces between an air bubble and a flat mica surface immersed in aqueous electrolyte solutions have been investigated using a modified surface force apparatus. An analysis of the deformation of the air bubble with respect to the mutual position of the bubble and the mica surface, the capillary pressure, and the disjoining pressure allows the air-liquid surface electrical potential to be determined. The experiments show that a long-range, double-layer repulsion acts between the mica (which is negatively charged) and an air bubble in water and in various electrolyte solutions at low concentration, thereby indicating that the air bubble surface is negatively charged. However, there is clear evidence that charge regulation occurs at the air-water interface to maintain a constant surface potential, and as a result of this, the charge at this interface changes from negative to positive as the bubble approaches the mica surface. Because of the attraction that arises as a result of the charge reversal, a finite force is required to separate the bubble from the mica, though the mica remains wetted by the aqueous phase. At the low concentrations investigated, the potential on the gas-liquid interface is independent of the electrolyte type within experimental uncertainty.     

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

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

Surface Potential of Coal Particles in Coal-Oil Mixture and Control of Settling Stability Under Gravity

This work deals with the problem of settling under gravity for coal-oil mixtures when the concentration of particles is large. The repulsive force necessary to ensure stability of coal particle is vital. The net forces acting on the particle include gravity, buoyancy, viscous drag force, and electrostatic repulsive force. Accordingly, the equation at the terminal velocity at settling is obtained along with a critical surface potential to prevent settling under gravity.     

Surface Forces in Nanodispersions

The stability of nanodispersions are analyzed on the basis of data on interaction forces between nanoparticles calculated using more precise (than Derjaguin's approximation) approaches. When calculating the dispersion attraction between nanoparticles in dispersions, we use Mitchell and Ninham equations for the case of small (compared to particle radii) interlayer thickness. For the calculation of electrostatic interaction in nanodispersions, the approximation of low potentials of particle surfaces developed by McCartney and Levine are employed. Estimates based on more precise approaches demonstrate that the energy of electrostatic repulsion between particles lowers with a decrease in their sizes (other conditions being equal) that can bring a nanodisperse system closer to the coagulation threshold.     

Effect of added salt on the depletion attraction caused by non-adsorbing clay particles

Total internal reflection microscopy (TIRM) has been used to study the effect of a model clay colloid (laponite) on the interparticle forces acting between a 6 μm polystyrene sphere and a glass slide when the two are separated by 50–350 nm of an aqueous solution containing up to 1 mM of NaCl. In the absence of clay, the Brownian sphere samples elevations in the vicinity of the secondary minimum formed by gravitational attraction, van der Waals attraction and double-layer repulsion. The addition of clay induces a discernible depletion attraction at concentrations greater than 100 ppm and for separation distances as large as 200 nm, which greatly exceeds the diameter of the laponite disks (25 nm). Increasing the clay concentration increases the magnitude of this attraction without changing the range (defined as the largest separation distance at which the attractive potential is 1 kT). Increasing the concentration of an indifferent electrolyte (NaCl) reduces both the magnitude and range of the depletion attraction. These observations are in quantitative agreement with the primitive theory in which depletion attraction is computed as the product of the osmotic pressure of the polyelectrolyte (calculated from Donnan’s equation) and the area of overlap of the depletion layers. Besides the effect of the polyelectrolyte on the Debye length, the only adjustable parameter is the depletion layer thickness or ‘effective radius’ of the platelets which is found to be the radius of the laponite disks plus five Debye lengths.     

Experimental determination of energy barrier to particle detachment

The estimation of energy barrier to detachment of particles from a substrate was carried out. Detachment processes of 4 m polyethylene particles from a quartz wall under the gravitational force in aqueous solutions were investigated by a direct observation technique. The magnitude of energy barriers was experimentally determined by the temperature dependence of the rate constant of detachment and was compared with that estimated theoretically from the superposition of electrostatic and London—van der Waals energies calculated using the experimental electrokinetic potentials and Hamaker constants, respectivley. Both were in fairly good agreement.     

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.