Adhesion of solid particles to gas bubbles. Part 2: Experimental

In slurry bubble columns, the adhesion of solid catalyst particles to bubbles may significantly affect the G-L mass transfer and bubble size distribution. This feature may be exploited in design by modifying the hydrophilic or hydrophobic nature of the particles used. Previously we have proposed a generalised model, describing the adhesion of particles to G-L interface under stagnant conditions. In this work, we studied the adhesion of particles characterised by different degree of hydrophobicity and porosity: non-porous polystyrene and glass beads, unmodified and hydrophobised mesoporous silica, and activated carbon particles. Images recorded at high optical magnification show the particles adhering to gas bubbles individually or as aggregates. In aqueous media, higher liquid surface tension and particle surface hydrophobicity increase the adhesion strength and the tendency of particles to agglomerate, in agreement with the model. The adhesion of non-porous rough-surface particles to gas bubbles can be characterised by the receding contact angle. The advancing contact angle represents better the adhesion of the same particles to liquid droplets. We found that the “effective” contact angle of porous particles is much lower than an “intrinsic” contact angle calculated from the heat of immersion in water, or measured by sessile drop method. An equivalent contact angle derived from the Cassie rule explains the wetting behaviour of particles having the pores filled with liquid.     

Determination of the collision frequency between bubbles and particles in flotation

Collision efficiency for a spherical bubble rising in a uniform concentration of small non-inertial particles is studied by direct numerical simulations (DNS). The Stokes number of the particles is negligibly small so that the particle trajectories follow the streamlines. The effect of the bubble interface contamination is studied for the flow surrounding the bubble using the spherical cap model. Numerical results are obtained for a wide range of bubble Reynolds number (based on bubble diameter d_b) ranging from 0.01 to 1000 and for different angles of contamination ranging from 0^° to 180^°. The collision efficiency is found to be increased with the Reynolds number and significantly decreased with the level of contamination. Correlations of the numerical results are proposed for efficiencies versus d_p/d_b (d_p being the particle diameter), bubble Reynolds number and interface contamination degree. For clean (respectively, fully contaminated) spherical bubbles, the efficiency evolves as d_p/d_b (respectively (d_p/d_b)²) whatever the bubble Reynolds number and the particle size. For partially contaminated bubbles, efficiency can be scaled with d_p/d_b or (d_p/d_b)² depending on both the level of contamination and the particle size.     

Attachment of solid particles to air bubbles in surfactant-free aqueous solutions

This paper presents a mechanism to explain the attachment of solid particles to air bubbles in surfactant-free aqueous solutions where both solids and air bubbles have the same sign of zeta potential via investigating the mechanical properties of micro air bubbles and the adsorption of hydroxide on air bubble surfaces.Particle-bubble attachment was measured in a Hallimond tube. The results indicate that purified quartz particles attached to air bubbles in surfactant-free deionised water, and the attachment increased with the pH of the aqueous solutions. The mechanical properties of micro air bubbles in aqueous solutions were measured using a novel micromanipulation technique. It was found that the micro air bubbles were pseudo-elastic and spherical in the solutions. The rigidity of the air bubbles decreased with increasing pH of the solutions. When a moving particle with a certain kinetic energy collided with an air bubble in a surfactant-free aqueous solution, the deformation of the air bubble varied with pH of the solution. In an alkaline solution, the micro air bubble was much softer and the deformation was larger than that in an acidic solution. The larger deformation of the softer air bubble resulted in a large contact area between the solid particle and the air bubble, therefore increasing the attachment, and reducing the rebound.The attachment of purified quartz particles to air bubbles in surfactant-free aqueous solutions was possibly due to hydrogen bond formation. The OH⁻ ions on air bubble surfaces formed hydrogen bonds with silicon and oxygen atoms in ≡Si-O-Si≡ or with the adsorbed OH group on quartz surfaces.     

Adhesion forces of charged particles

Adhesion forces of toner and polymer particles to aluminum substrates were measured by the centrifugal, detachment field and microelectrode detachment field methods, and factors affecting the adhesion forces are discussed. The adhesion forces of toner particles increased with an increase in either particle size or particle charge. The adhesion force of an irregularly shaped toner was larger than that of a spherical toner. The mean adhesion force of polymer particles to aluminum substrates decreased with an increase in surface roughness of the substrates. The CF₄ plasma treatment of the polymer particles shifted their adhesion force distribution in a smaller direction. It was confirmed that the results by the centrifugal and the detachment field methods were in good agreement with each other. The contribution of van der Waals, electrostatic and water bridging forces to the adhesion forces of toner particles are also discussed.     

Modelling of agglomeration in suspension: Application to salicylic acid microparticles

The agglomeration in suspension technique consists of adding directly into the suspension a small amount of a second liquid which acts as an interparticle bonding agent. The system (salicylic acid particles, aqueous solution, chloroform) is studied experimentally by in situ image analysis. After a brief period of wetting of the particles by the binding liquid, the agglomerates grow by a coalescence-like process until they reach a maximum size. Porosity measurements reveal that the agglomerates are then getting more compact. Eventually, the agglomeration mechanism is likely governed by the agglomerate deformability, as it is often suggested in granulation. A population balance modelling is proposed to describe the growth period. The agglomeration kernel is built according to the experimental observations. It is expressed as the product of two factors which relate the meeting probability and the sticking efficiency, respectively. The probability of encounter is governed by the hydrodynamics. The sticking efficiency compares the sticking force, directly linked to the deformation induced by the agglomerate-agglomerate impact under consideration, with the shear-induced disruptive force. This phenomenological model fits well the experimental results obtained for the salicylic acid particles.     

Modelling of direct-contact evaporation using a simultaneous heat and multicomponent mass-transfer model for superheated bubbles

A recently developed model for coupled heat and mass transfer in binary systems during the formation and ascension of superheated bubbles was extended to a multicomponent system comprising N volatile species. The model allows variable properties and bubble radius changes, assuming diffusive mass fluxes to be properly described by Fick's law. Experimental direct-contact evaporation tests were conducted with ethyl acetate aqueous solutions to provide data for assessing the developed model. In addition, the model was tested against available literature data for an air-stripper. In both cases, a good agreement between simulation and experimental results was verified.     

Particle Adhesion to Drops

The adhesion of spheroidal particles to spherical drops is calculated and discussed in terms of an equilibrium-penetration index. The present study emphasizes the case of particles that are sufficiently large to affect the drop volume upon penetration. It is shown that the more elongated the particles, the steeper the dependence of the penetration index on the contact angle. The effect of line tension on nanoscale particles is considered. Positive line tensions increase the steepness of the dependence of penetration index on contact angle whereas negative line tensions decrease this dependence. In addition, the energy barrier caused by positive line tensions is presented and discussed.     

Particle Adhesion to Drops

The adhesion of spheroidal particles to spherical drops is calculated and discussed in terms of an equilibrium-penetration index. The present study emphasizes the case of particles that are sufficiently large to affect the drop volume upon penetration. It is shown that the more elongated the particles, the steeper the dependence of the penetration index on the contact angle. The effect of line tension on nanoscale particles is considered. Positive line tensions increase the steepness of the dependence of penetration index on contact angle whereas negative line tensions decrease this dependence. In addition, the energy barrier caused by positive line tensions is presented and discussed.     

Modelling the motion of cylindrical particles in a nonuniform flow

The models currently used in computational fluid dynamics codes to predict solid fuel combustion rely on a spherical shape assumption. Cylinders and disks represent a much better geometrical approximation to the shape of bio-fuels such as straws and woods chips. A sphere gives an extreme in terms of the volume-to-surface-area ratio, which impacts both motion and reaction of a particle. For a nonspherical particle, an additional lift force becomes important, and generally hydrodynamic forces introduce a torque on the particle as the centre of pressure does not coincide with the centre of mass. Therefore, rotation of a nonspherical particle needs to be considered. This paper derives a model for tracking nonspherical particles in a nonuniform flow field, which is validated by a preliminary experimental study: the calculated results agree well with measurements in both translation and rotation aspects. The model allows to take into account shape details of nonspherical particles so that both the motion and the chemical reaction of particles can be modelled more reasonably. The ultimate goal of such a study is to simulate flow and combustion in biomass-fired furnaces using nonspherical particle tracking model instead of traditional sphere assumption, and thus improve the design of biomass-fired boilers.     

Adhesion of charged particles

The adhesion properties of charged particles are of considerable importance in the electrophotographic process. Measurements on irregularly-shaped, pigmented particles, called toner in the electrophotographic industry, show that adhesion increases with toner charge but that the magnitude is much larger than expected from a simplified electrostatic image force model. An enhanced electrostatic adhesion is also seen in electric field detachment measurements on spherical charged particles. In both cases, this unexpected large adhesion can be attributed to a nonuniform distribution of charge on the surfaces of the particles.     

Numerical simulation of gas bubbles behaviour using a three-dimensional volume of fluid method

In this paper a three-dimensional (3D) volume of fluid (VOF) method is presented featuring (i) an interface reconstruction technique based on piecewise linear interface representation, (ii) a 3D version of the CSF model of Brackbill et al. [1992, Journal of Computational Physics 100, 335]. Our model can handle a large density and viscosity ratio and a large value of the surface tension coefficient.First the results of a number of test cases are presented to assess the correctness of the advection and interface reconstruction algorithms and the implementation of the 3D version of the CSF model. Subsequently the computed terminal Reynolds numbers and shapes of isolated gas bubbles rising in quiescent liquids are compared with data taken from the bubble diagram of Grace (1973). Finally results of two calculations are reported involving the co-axial and oblique coalescence of two gas bubbles. The computed bubble shapes compared very well with the experimentally observed bubble shapes of Brereton and Korotney [1991, In: Dynamics of Bubbles and Vortices Near a Free Surface, AMD-vol. 119. ASME, New York].     

Time-Dependence of the Adhesion of Micrometer-Size Particles to Substrates: Correlation with Postdeposition Particle Rotation

The time dependence of the detachment force of 7-µm ground polyester particles coated with silica nanoparticles from a ceramer-coated substrate was determined by ultracentrifugation. The detachment force of the particles from the substrate was found to increase with the time since the particle deposition. Scanning electron microscopy (SEM) results show that, following deposition, the particles rotate at approximately the same scale as the observed increase in the detachment force. This suggests that the increase in adhesion may be due to particle rotation from their initial positions obtained upon deposition to a more stable position that results from torques generated by either electrostatic or van der Waals forces acting on the particles.     

The motion of electrolytic gas bubbles near electrodes

Several reports in the literature mention oscillatory bubble motions close to, or in contact with electrodes. Such behaviour is obviously related to a time-variable force, but it was not apparent what the origin of this variable force was. Recent advances in understanding of the surfactant behaviour of gases, and in particular the gases liberated during electrolysis, have cast a new light on the underlying mechanism of these oscillations. Other unexpected, but not necessarily oscillatory bubble behaviour is discussed, and the role of electrolytic gas acting as a surfactant illuminates these non-oscillatory motions as well. Finally, the paradox of bubbles remaining attached to electrodes with zero contact angle is resolved.     

Modelling acid attack on concrete: Part I. The essential mechanisms

At present, a computer model is being developed to predict the corrosion of concrete construction components subjected to acidic solutions with pH values ranging between 4.0 and 6.5, i.e. exposure classes XA3 down to XA1 according to DIN EN 206-1. The concrete may contain Portland cement based binders with dissolvable or acid resistant aggregate. Calcium aluminate cement is also considered. The concrete degradation is characterised by a corroded layer of high porosity whose thickness is determined by the combination of dissolution, precipitation and transport processes which depend on cement chemical composition, binder reactivity, aggregate reactivity, grading curve as well as concrete composition. It is also intended to include the effect of abrasion. The model components will be described in detail in forthcoming publications.     

Adhesion of polymer coils to a solid surface: influence of the depletion effect

The specific properties of polymer coils are often disregarded in theories of adhesion, but polymer properties are essential for the strength of the adhesive bond. Polymer coils are repelled entropically from impenetrable surfaces. This causes the depletion effect and creates a layer of reduced concentration right at the interface. To bond a polymer coil to a substrate, it must be forced actively towards the interface, driven by the gaining of adsorption energy. The adsorption of specific groups in the (co)polymer, which interact with 'polar' sites on the substrate, must be used to suppress the depletion. Adsorption diminishes the effective distance between the surface and the adhesive polymer. The balance between adsorption and depletion (rather than the effect of polar groups or pretreatments on the work of adhesion as such) is the most important chemical possibility of affecting adhesion. The strength of the bond between polymeric materials and solid surfaces varies as H^-3, with the effective distance H between the polymer and substrate. Therefore, it changes by an order of magnitude when the polymer adhesive is pulled towards the substrate by adsorption.     

Effect of microbubbles and particle size on the particle collection in the column flotation

Particle-bubble collection characteristics from microbubble behavior in column flotation have been studied theoretically and experimentally. A flotation model taking into account particle collection has been developed by particle-bubble collision followed by the particle sliding over the bubble during which attachment may occur. Bubble size and bubble swarm velocity were measured as a function of frother dosage and superficial gas velocity to estimate the collision and collection efficiency. Separation tests were carried out to compare with theoretical particle recovery. Fly ash particles in the size range of <38, 38-75, 75-125, >125 mm were used as separation test particles. Theoretical collision and collection efficiencies were estimated by experimental data on the bubble behavior such as bubble size, gas holdup and bubble swarm velocity. Collection efficiency improved with an increase of the bubble size and particle size but decreased in the particle size up to 52 mm. Also, flotation rate constants were estimated to predict the optimum separation condition. From the theoretical results on the flotation rate constant, optimum separation condition was estimated as bubble size of 0.3-0.4 mm and superficial gas velocity of 1.5-2.0 cm/s. A decrease of bubble size improved the collection efficiency but did not improve particle recovery.     

Time-Dependence of the Adhesion of Micrometer-Size Particles to Substrates: Correlation with Postdeposition Particle Rotation

The time dependence of the detachment force of 7-µm ground polyester particles coated with silica nanoparticles from a ceramer-coated substrate was determined by ultracentrifugation. The detachment force of the particles from the substrate was found to increase with the time since the particle deposition. Scanning electron microscopy (SEM) results show that, following deposition, the particles rotate at approximately the same scale as the observed increase in the detachment force. This suggests that the increase in adhesion may be due to particle rotation from their initial positions obtained upon deposition to a more stable position that results from torques generated by either electrostatic or van der Waals forces acting on the particles.     

Identification of thermal zones and population balance modelling of fluidized bed spray granulation

Air temperature measurements in a fluidized bed of glass beads top sprayed with water showed that conditions for particles growth were fulfilled only in the cold wetting zone under the nozzle which size and shape depended on operating conditions (liquid spray rate, nozzle air pressure, air temperature, and particles load). Evolution of the particle size distribution during agglomeration was modelled using population balance and representing the fluidized bed as two perfectly mixed reactors exchanging particles with particle growth only in the one corresponding to the wetting zone. The model was applied to the agglomeration of non-soluble glass beads and soluble maltodextrin particles spraying respectively an acacia gum solution (binder) and water. Among the three adjustable parameters, identified from experimental particle size distributions evolution during glass beads agglomeration, only one describing the kinetics of the size distribution evolution depended on process variables. The model allowed satisfying simulation of the evolution of the particle size distribution during maltodextrin agglomeration.