Effect of particle and fluid properties on the pickup velocity of fine particles

Systems involving fluid-particle flows are a key component of many industrial processes, but they are not well-understood. One important parameter to consider when designing a conveying system is pickup velocity, the minimum fluid velocity required for particle entrainment. Many theoretical and experimental analyses have been performed to better understand pickup velocity, but there is little consistency with regard to system conditions, fluid properties, and particle characteristics, which makes comparisons between these studies very difficult. Although the proper design of many conveying systems requires the utilization of expressions that are applicable across a broad range of operating parameters, most expressions are system specific, which means that they are not extendable to other conditions. Also, there is currently an absence of a universal expression to predict particle entrainment in both gases and liquids.In this work, the pickup velocity of glass spheres, crushed glass, and stainless steel spheres in water has been measured for particles less than 450 μm. The effects of particle size, particle shape, and particle density are discussed and compared to the pickup velocity trends previously determined for similar gas-phase systems. In addition, the experimental data are used to assess an existing force balance model previously developed for gas-phase systems.     

Effects of bulk and surface properties of materials on adhesion-induced deformations between submicrometer diameter particles and substrates

—Spherical particles of polyvinylidene fluoride (PVF₂), of 0.3 μm diameter, were deposited onto various substrates including polyester, a polyester-polydimethylsiloxane block copolymer (hereafter referred to as PSBC), and polished silicon. The adhesion force-induced deformations between the particles and substrates were then observed using scanning electron microscopy (SEM). It was found that the particles embedded most deeply into the soft PSBC. No embedding of the particles into the Si wafers was observed, although the particles, themselves, appeared to flatten. The particles were also observed to embed into the polyester, although to a lesser extent than they did into the PSBC. Moreover, when the particles contacted samples of polyester which had been plasma-treated in argon, the embedding decreased. Measured contact area diameters are compared to predictions of various models of adhesion. The effect of the thickness of a conducting (Au/Pd) coating on the appearance of the contact zone is also discussed.     

Self Assembly of Nano Metric Metallic Particles for Realization of Photonic and Electronic Nano Transistors

In this paper, we present the self assembly procedure as well as experimental results of a novel method for constructing well defined arrangements of self assembly metallic nano particles into sophisticated nano structures. The self assembly concept is based on focused ion beam (FIB) technology, where metallic nano particles are self assembled due to implantation of positive gallium ions into the insulating material (e.g., silica as in silicon on insulator wafers) that acts as intermediary layer between the substrate and the negatively charge metallic nanoparticles.     

The Effect of Time and Humidity on Particle Adhesion and Removal

Time and humidity greatly influence particle adhesion and removal in many particlesubstrate systems. The effect of time (aging) and humidity on the adhesion and removal of 22 μm PSL (Polystyrene Latex) particles on polished silicon wafers is investigated. The results show that the effect of time on the adhesion and removal of the 22 μm PSL particles on silicon substrates in high humidity environment is very significant. The removal efficiency of PSL particles significantly decreased after the samples were aged for more than one day in high humidity environment. The combined effect of the van der Waals force and the capillary force tend to accelerate the adhesion-induced deformation process. When capillary force occurs at the particle substrate interface, the removal efficiency decreases quickly by more than 50% within 24 hours. Without the capillary force, the adhesion-induced deformation is negligible within the first 24 hours.     

The Effect of Time and Humidity on Particle Adhesion and Removal

Time and humidity greatly influence particle adhesion and removal in many particlesubstrate systems. The effect of time (aging) and humidity on the adhesion and removal of 22 μm PSL (Polystyrene Latex) particles on polished silicon wafers is investigated. The results show that the effect of time on the adhesion and removal of the 22 μm PSL particles on silicon substrates in high humidity environment is very significant. The removal efficiency of PSL particles significantly decreased after the samples were aged for more than one day in high humidity environment. The combined effect of the van der Waals force and the capillary force tend to accelerate the adhesion-induced deformation process. When capillary force occurs at the particle substrate interface, the removal efficiency decreases quickly by more than 50% within 24 hours. Without the capillary force, the adhesion-induced deformation is negligible within the first 24 hours.     

The effect of air on the packing structure of fine particles

A numerical study of the effect of air on the packing structure of fine particles has been performed by a combined continuum and discrete numerical model. The forces considered are gravity, contact force, drag force, and van der Waals forces. The results are analyzed in terms of particle rearrangement, local porosity, coordination number, radial distribution function, and the distribution of contact forces. The results indicate the degree to which drag and van der Waals forces promote mean porosity increases and mean coordination number decreases. Drag forces allow contacts of particles reaching a state of rest in a packing to be closer to the Coulomb failure criterion for shear displacement when van der Waals forces are small. Increasing van der Waals forces imposes contact conditions that are far away from the Coulomb failure criterion. Increased drag and van der Waals forces tends to lead to more heterogeneous structure. It is demonstrated that average normal contact force is related to the ratio of van der Waals forces to particle weight.     

Pickup (critical) velocity of particles

This work presents experimental results on pickup velocity (critical velocity) measurements for a variety of particulate solids. The present experiments together with previously published experiments of a number of researchers encompass about 100 measurements of 24 materials for a wide range of particle sizes, shapes and densities. Based on the experimental results, three zones are defined by establishing simple relationships between the Reynolds and Archimedes numbers. The empirical relationships were further modified by taking into account the pipe diameter and particle shape (sphericity). The three-zone model was shown to reasonably correlate to Geldart's classification groups.     

Electric-Field Induced Morphological Transitions in Elastic Contact Instability of Soft Solid Films

A soft elastic film, when placed in adhesive proximity with a contactor in a crack-like geometry, spontaneously undergoes a surface instability to form finger patterns with a characteristic wavelength of approximately 4h, where h is the film thickness. We study the morphological evolution and control of this elastic contact instability under the influence of an external electric field. The distinct electric field induced morphological changes, leading to the formation of two-dimensional hexagonally arranged pillars, large-amplitude fingers, and straightening of contact edge, which are studied comprehensively. The conditions for the evolution of morphologically distinct patterns are governed by the film parameters, such as its shear modulus and thickness. A theoretical model and its stability analysis provide an approximate estimate of the critical voltage required for the onset of changes and its scaling with the film parameters (thickness and shear modulus). Further, three-dimensional simulations based on energy minimization are presented to provide important clues regarding the physics of pattern evolution on soft elastic interfaces.     

Electric-Field Induced Morphological Transitions in Elastic Contact Instability of Soft Solid Films

A soft elastic film, when placed in adhesive proximity with a contactor in a crack-like geometry, spontaneously undergoes a surface instability to form finger patterns with a characteristic wavelength of approximately 4h, where h is the film thickness. We study the morphological evolution and control of this elastic contact instability under the influence of an external electric field. The distinct electric field induced morphological changes, leading to the formation of two-dimensional hexagonally arranged pillars, large-amplitude fingers, and straightening of contact edge, which are studied comprehensively. The conditions for the evolution of morphologically distinct patterns are governed by the film parameters, such as its shear modulus and thickness. A theoretical model and its stability analysis provide an approximate estimate of the critical voltage required for the onset of changes and its scaling with the film parameters (thickness and shear modulus). Further, three-dimensional simulations based on energy minimization are presented to provide important clues regarding the physics of pattern evolution on soft elastic interfaces.     

The Effect of Relative Humidity on Particle Adhesion and Removal

The removal of small particles is vital for contamination-free manufacturing. In humid environments liquid can condense between the particle and substrate and give rise to a very large capillary force, which increases the total force of adhesion. The removal and adhesion forces of polystyrene latex (PSL) particles and pigmented coating chips were measured on silicon, polyethylene terephthalate, metallized and polyester coating substrates as a function of humidity. The results indicate that the capillary force is significant at a relative humidity above 50% and dominates at a relative humidity above 70%. At relative humidity below 45%, the electrostatic force becomes significant. The adhesion forces varied depending on the particles and substrates used, but the trend of high adhesion at high and low relative humidity was observed for all PSL particles/substrate systems. The pigmented coating chips/substrate system however, exhibited high adhesion at high relative humidity and low adhesion at low relative humidity.     

The Effect of Relative Humidity on Particle Adhesion and Removal

The removal of small particles is vital for contamination-free manufacturing. In humid environments liquid can condense between the particle and substrate and give rise to a very large capillary force, which increases the total force of adhesion. The removal and adhesion forces of polystyrene latex (PSL) particles and pigmented coating chips were measured on silicon, polyethylene terephthalate, metallized and polyester coating substrates as a function of humidity. The results indicate that the capillary force is significant at a relative humidity above 50% and dominates at a relative humidity above 70%. At relative humidity below 45%, the electrostatic force becomes significant. The adhesion forces varied depending on the particles and substrates used, but the trend of high adhesion at high and low relative humidity was observed for all PSL particles/substrate systems. The pigmented coating chips/substrate system however, exhibited high adhesion at high relative humidity and low adhesion at low relative humidity.     

CALCULATION OF VAN DER WAALS FORCES WITH DIFFUSE COATINGS: APPLICATIONS TO ROUGHNESS AND ADSORBED POLYMERS

A novel method using Lifshitz continuum theory to account for the effects of surface roughness was developed. The method treats roughness as a diffuse film whose dielectric properties vary continuously between those of the substrate and those of the solvent: AFM measurements of surface topography are used to deduce the volume-fraction profile of substrate in solvent which in turn is converted into a dielectric-permittivity profile using the Clausius-Mossoti equation as a mixing rule. Calculations show orders of magnitude of reduction in the van der Waals force between rough surfaces at contact compared with smooth surfaces, with the amount of reduction dependent on the shape of the volume-fraction profile as well as the total depth of the roughness. These predictions help account for discrepancies observed previously between the Total Internal Reflection Microscopy (TIRM) data and calculations for smooth polystyrene surfaces in water, with or without physisorbed polymer, without introducing any adjustable parameters.     

CALCULATION OF VAN DER WAALS FORCES WITH DIFFUSE COATINGS: APPLICATIONS TO ROUGHNESS AND ADSORBED POLYMERS

A novel method using Lifshitz continuum theory to account for the effects of surface roughness was developed. The method treats roughness as a diffuse film whose dielectric properties vary continuously between those of the substrate and those of the solvent: AFM measurements of surface topography are used to deduce the volume-fraction profile of substrate in solvent which in turn is converted into a dielectric-permittivity profile using the Clausius-Mossoti equation as a mixing rule. Calculations show orders of magnitude of reduction in the van der Waals force between rough surfaces at contact compared with smooth surfaces, with the amount of reduction dependent on the shape of the volume-fraction profile as well as the total depth of the roughness. These predictions help account for discrepancies observed previously between the Total Internal Reflection Microscopy (TIRM) data and calculations for smooth polystyrene surfaces in water, with or without physisorbed polymer, without introducing any adjustable parameters.     

Dispersive forces of particle–surface interactions: direct AFM measurements and modelling

Fundamentals of particle–particle interaction are of great interest in agglomeration processes. Particle adhesion depends on dispersive forces (van der Waals force), local chemical bindings, Coulomb force and capillary attractions. Additionally, surface properties like roughness, adsorption layers and surface chemistry strongly affect adhesion forces. van der Waals interactions are poorly understood because popular ab initio force calculations for molecules like density functional theory (DFT) often do not lead to proper results. van der Waals forces are difficult to measure directly. We present direct measurements of particle–particle and particle–surface interactions in the gas phase carried out with an atomic force microscope (AFM). Special emphasis is given to a proper statistical treatment of the data. For modelling of particle adhesion, we use computer-assisted empirical potential methods. Parameters like adsorbed water and surface roughness are considered. We extract parameters for weak interactions from the Lifshitz theory and gas adsorption data. Adsorbing molecules can be used as probes to measure dispersive forces. Studying surface and particle properties combined with computer-assisted modelling is a basic requisite to reach the aim of predicting particle–particle interactions in industrial processes.     

On the relationship between porosity and interparticle forces

This paper presents an attempt to quantify the relationship between porosity and interparticle forces for mono-sized spheres. Two systems are considered: the packing of wet coarse spheres where the dominant interparticle force is the capillary force, and the packing of dry fine spheres where the dominant force is the van der Waals force. The interrelationships between porosity, capillary force and liquid content are first discussed based on the well-established theories and experimental observations. The resultant relationship between porosity and capillary force is then applied to the packing of fine particles to quantify the van der Waals force in a packing. A generalised relationship between porosity and interparticle forces results as an extension of this analysis. The usefulness of this relationship is finally demonstrated in depicting the fundamentals governing the relationship between porosity and particle size.     

The Effect of Adhesion on the Rheological and Frictional Behavior of a Confined Lubricant Film

We investigated the rheological and frictional behavior of a model system of lubricated, atomically-smooth, solid surfaces at zero and negative external normal load. The measurements were performed with a surface forces apparatus modified for oscillatory shear. For low deflection amplitudes, and negative loads up to the point when the surfaces jumped apart, the confined liquid layer (0.7 ± 0.2 nm perfluorinated heptaglyme) showed a highly elastic behavior independent of load. In the sliding regime at large amplitudes, the behavior was mostly dissipative but also independent of normal load. The force necessary to separate the surfaces was not affected by any sliding conditions. However, the friction force showed a very pronounced decrease as a consequence of sliding at large amplitudes. Thus, for our system, friction and adhesion are decoupled. We propose a mechanism of in-plane rearrangements of the molecules and explain the shear-induced reduction of friction by the formation of shear-bands.     

The Effect of Adhesion on the Rheological and Frictional Behavior of a Confined Lubricant Film

We investigated the rheological and frictional behavior of a model system of lubricated, atomically-smooth, solid surfaces at zero and negative external normal load. The measurements were performed with a surface forces apparatus modified for oscillatory shear. For low deflection amplitudes, and negative loads up to the point when the surfaces jumped apart, the confined liquid layer (0.7 ± 0.2 nm perfluorinated heptaglyme) showed a highly elastic behavior independent of load. In the sliding regime at large amplitudes, the behavior was mostly dissipative but also independent of normal load. The force necessary to separate the surfaces was not affected by any sliding conditions. However, the friction force showed a very pronounced decrease as a consequence of sliding at large amplitudes. Thus, for our system, friction and adhesion are decoupled. We propose a mechanism of in-plane rearrangements of the molecules and explain the shear-induced reduction of friction by the formation of shear-bands.     

Prediction of agglomerate sizes in bubbling fluidized beds of group C powders

A mathematical model to predict an equilibrium agglomerate size in agglomerating fluidized beds of Geldart group C powders was derived based on the balance of bed expansion force caused by bubbles and agglomerate-to-agglomerate cohesive rupture force. The bed compaction force caused by bubbles of ordinary sizes was found not sufficient to break agglomerates. Among the two solutions the one corresponding to a stable equilibrium was calculated by a simple iteration. The model was successfully validated by experimental data in the literature and additional new data in the present work. Previous models are also critically reviewed and evaluated.     

Multicomponent phase equilibria of thin liquid films and their vapour

Subject of the paper are multicomponent phase equilibria between extremely thin liquid films and their vapour phase on curved or planar solid surfaces. The solid surface is either heated or cooled, so that the liquid films are evaporating or the vapour is condensing.The curvature of the film surface and long range molecular forces due to the van der Waals attraction acting over distances of about 0.2- between solid and liquid film can lead to a composition shift in liquid and vapour phase compared to the composition that would be observed at planar and not extremely thin liquid films in equilibrium with their vapour phase.The Kelvin equation for the interfacial pressure is derived, as well as the equations for the composition shift. As a numerical example shows the van der Waals forces considerably influence the pressures at the liquid-vapour interface. Responsible for the composition shift is a dimensionless thermodynamic quantity . For small values D_i→0, liquid-vapour phase equilibria become identical with those of planar surfaces. For D_i?0 the vapour phase contains less and for D_i?0 more of the lighter volatiles than planar interfaces.     

Effects of binary particle size distribution on minimum pick-up velocity in pneumatic conveying

Minimum pick-up velocities (U_pu) for entrainments of particle mixtures having binary particle size distributions (PSD) are measured in a horizontal pneumatic-conveying line using the weight-loss method. Geldart's groups A, B, and C glass beads having diameters of 400, 170, 40, and 5 μm are used. Variations in U_pu as a function of particle mass fraction (m) are examined. The capability of empirical correlations of monodisperse U_pu in predicting U_pu of binary mixtures is investigated. For group B particle mixtures (i.e. 400 & 170 μm), the particles are entrained separately resulting in linear U_pu variations with m, which is accurately predicted by the monodisperse U_pu correlation. For mixtures involving group A and B particles (i.e. 170 & 40, 400 & 40 μm), the two particles are collectively entrained resulting in U_pu that vary non-linearly with m and that cannot be predicted by the correlation. For mixtures involving group B and C particles (i.e. 400 & 5, 170 & 5 μm), U_pu are comparable to that of the monodisperse group B particles, therefore they are accurately predicted by the correlation. The significant impacts of binary PSD on U_pu found presently indicates that PSD effects on particle entrainment process warrants further investigations.