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.     

Capillary and van der Waals force between microparticles with different sizes in humid air

It is well known that surface effect forces, such as van der Waals force and capillary force, are the major contributions to adhesion when microsized particles are in contact in humid environment. But it is very complex to calculate the adhesion force between two smooth unequal particles. In conventional approaches, the effective particle radius approximation and the constant half-filling angle assumptions are often used for computing the van der Waals forces between two microparticles. However, the approximation and the assumption are actually difficult to accurately model the forces between unequal particle sizes when the surfaces are with different properties. In this paper, we present a theoretical study of the van der Waals force and capillary force between two microparticles with different radii and the surface properties linked by a liquid bridge. The proposed model provides the adhesion force predictions in good agreement with the previous formula and existing experiment data. Considering the solid particles are partially wetted by the liquid bridge, the van der Waals force is calculated by divided the particle surface into a wetted part and a dry portion in our stimulation. Since the wetted surface portion of the particle is determined by the half-filling angle, the relationship between two half-filling angles of the unequal size particles is developed from the geometrical consideration, which is relate to the size ratio of the particles, the contact angle, and the separation distance. Then, the van der Waals force is determined using the surface element integration. Moreover, the influences of humidity, particles size, contact angle, and separation distance toward the adhesion forces are discussed using the proposed method. Simulations indicate that a higher relative humidity leads to bigger liquid bridges, suggesting a higher capillary force, but at the same time, the van der Waals force decreases due to the decrease in surfaces energy. As for the influence of contact angle, results show that a higher contact angle, that is, a more hydrophobic surface, reduces the capillary force but increases the van der Waals force (absolute value). The simulations also show that the both the capillary force and the van der Waals force (absolute value) increase as the particle size increases. When the particles are separated from each other, the capillary force and van der Waals force decreases gradually. These results are helpful to understand and utilize the adhesion interaction between particles with unequal sizes at the ambient condition.     

Cohesive strength of alumina powder compacts

In order to characterize the nature of the interparticle forces that causes particle agglomeration in submicron size alumina particles, eight commercial alumina powders were investigated. Since the strength of the agglomerates depends upon the interparticle forces and the packing density of the particles the Hartley model which relates the tensile strength, packing density of a powder compact, to the interparticle force has been applied. The present experimental results suggest that in the absence of any electrostatic forces (either force of attraction or repulsion between particles) van der Waals force is responsible for the agglomeration of alumina particles.     

Interactions between fine combustion droplets

Interactions between fine combustion droplets were directly observed using microscopic flow visualization and high speed photography. The observations revealed “attracting-revolving-repulsing” interactions between the droplets. Force analyses showed that the traditionally considered interparticle forces, including drag, gravitation, the Coulomb force and the van der Waals force, cannot explain these interactions. However, the induced dipoles on the droplets due to the non-uniform distribution of surface charges on the fine droplets have important influence on such interactions. Therefore, the inter-dipole forces must be taken into account in the interaction force analysis as well as the Coulomb force between the net charges. The inter-dipole force includes components in the radial and azimuthal directions and is inversely proportional to r⁴. This force causes the particles to revolve and repel each other at small distance. The combined effects of the inter-dipole force and the traditionally considered forces give a complete explanation for the particle interactions.     

A numerical study of fluidization behavior of Geldart A particles using a discrete particle model

This paper reports on a numerical study of fluidization behavior of Geldart A particles by use of a 2D soft-sphere discrete particle model (DPM). Some typical features, including the homogeneous expansion, gross particle circulation in the absence of bubbles, and fast bubbles, can be clearly displayed if the interparticle van der Waals forces are relatively weak. An anisotropy of the velocity fluctuation of particles is found in both the homogeneous fluidization regime and the bubbling regime. The homogeneous fluidization is shown to represent a transition phase resulting from the competition of three kinds of basic interactions: the fluid-particle interaction, the particle-particle collisions (and particle-wall collisions) and the interparticle van der Waals forces. In the bubbling regime, however, the effect of the interparticle van der Waals forces vanishes and the fluid-particle interaction becomes the dominant factor determining the fluidization behavior of Geldart A particles. This is also evidenced by the comparisons of the particulate pressure with other theoretical and experimental results.     

Role of van der Waals force in latex film formation

Capillary pressure force and direct surface tension force are known to be sufficient though probably not necessary to drive the compaction stage of latex film formation. There is abundant evidence that van der Waals force can draw particles together progressively more around the perimeters of interparticle contacts, but their role in compaction remains unanswered. With the powerful technique of high-resolution cryogenic scanning electron microscopy (cryo-SEM), together with fast-freezing and freeze-drying followed by controlled annealing at temperatures below and around the nominal glass transition temperature, we have documented the role of van der Waals force in film formation in the water-free condition, i.e., with capillary pressure and surface tension forces absent. Results of imaging the freeze-dried and annealed coatings are fully consistent with the hypothesis that van der Waals force alone can compact a latex coating. The rate at which particles flatten and thus the coating compacts by annealing increases, as expected, with temperature and time. The results of rewetting tests of coatings annealed at various temperatures demonstrate that compacted coating is not necessarily coalesced, and that even full compaction of solid particles can be elastic, hence reversible, rather than viscoelastic or viscoplastic. Some of the results suggest that soluble ionic surfactant and oligomeric and grafted polymeric stabilizers at particle surfaces, collapse to undetectable dimensions during freeze-drying, yet reswell to detectable size during rewetting, if they have not dissolved into polymer particles during annealing. Presented at 2006 FutureCoat! Conference, sponsored by Federation of Societies for Coatings Technology, November 1–3, 2006 in New Orleans, LA.     

Numerical simulation of cohesive particle motion in vibrated fluidized bed

The effect of vibration on the cohesive particle motion in the bed was examined by using discrete element method(DEM). The bed of dried fine particles was treated as the objective of calculation. The van der Waals force was used as the cohesive force because the van der Waals force was considered to be the main cohesive force in this case. Since the actual calculation time was too long, the fine cohesive particle was difficult to be treated. So a relatively large particle (1.0 mm in diameter) was used in calculation and the van der Waals force was assumed that the ratio of gravity force to van der Waals force of particle used in this calculation was equal to that of a fine particle (6.0 μm in diameter), to express the effect of van der Waals force significantly. The calculation results were compared with that case of cohesionless particle.In the case with vibration, the cohesive particle motion in the bed is observed, though no fluidization state appears in the case without vibration, and there is no bubble in the bed even the fluidization state. In the case of cohesive particle, the collision energy between particle and wall caused by vibration gap propagates from the bottom to top of bed, and the particle moves vigorously at the top of bed in the case with vibration. As the vibration gap increases, the effect of vibration on the cohesive particle motion becomes larger, i.e., the low vibration frequency at the same vibration strength or the large vibration strength at the same vibration frequency promotes the fluidization of the bed.     

The role of the van der Waals force in the agglomeration of powders containing submicron particles

A model has been developed which relates the tensile strength and packing density of powder compacts containing submicron particles to the interparticle force. Hamaker's expression for the van der Waals force and the law of corresponding states are used to develop an expression for the reduced inter-particle force R which is used to evaluate an energy parameter ?_o for a given powder on an absolute scale. The tensile strength of several carbon black and titanium dioxide powders was measured using a split-cell apparatus. Analysis of plots of R against separation distance for the carbon blacks gives an average value of ?_o = 2.1 × 10^?19 J which compares favorably with the literature value of 1.09 × 10^?19 J for the Hamaker constant. This is taken as confirmation that the van der Waals force is dominant in agglomerates of submicron carbon black particles. Similar plots for titanium dioxide powders give values of ?_o that are much higher than that attributed to the van der Waals force alone; the extra force may be due to water on the particle surfaces in the form of adsorbed layers or liquid bridges.     

How nano‐scale roughness impacts the flow of grains influenced by capillary cohesion

We show that nano‐scale changes in surface roughness affect the macro‐scale (many‐particle) behavior of granular materials influenced by cohesion. Macro‐scale effects of roughness are investigated for conditions where cohesion is dominated by either humidity‐induced or van der Waals‐induced forces. Surface‐topography measurements are used to calculate the relevant interparticle cohesive forces. The (force‐dominated) macro‐scale cohesion measurements are explained via the ratio of the predicted interparticle cohesive force to gravity, thus reinforcing the importance of roughness to cohesion. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5250–5257, 2017     

粘性糊料颗粒间的作用力及其机理分析

在阴极炭块组装过程中，粘性糊料颗粒间的相互作用导致颗粒的成团和破碎，由此影响糊料的微观和宏观行为。本文对两颗粒间的毛细力、范德华力、粘性力、接触力、静电力和重力六种相互作用力的计算进行了阐述。通过对这些相互作用力的量级分析，得到了导致糊料中颗粒成团和破碎行为的主要作用力，并分析了颗粒尺寸对相互作用力的影响。最后对碰撞变形过程中主要作用力随碰撞时间的变化规律进行了研究，通过对比这些力在碰撞过程中的相对大小对颗粒成团的机理进行力学解释。     

The effect of van der Waals and charge induced forces on bed modulus of elasticity in ac/dc electrofluidized beds of fine powders—a unified theory

Perturbation theory is applied to an ac electrofluidzed bed of fine powder (glass and FCC) using electric field bubble control to infer the relation between interparticle forces (microscale) and the bulk bed modulus of elasticity (macroscale). Electrostatically induced and permanent van der Waals forces are modeled in a unified theory with bulk fluidized bed behavior. The extrapolation of the electric field to zero strength gives the permanent bed force and bulk bed modulus of elasticity as limiting cases. The resulting equations involve atomic as well as macros-scale parameters. The charge induced forces are identified through the bed modulus of elasticity as a function of the applied electric field strength. The semi-empirical approach is based on the principle that the conservation equations for the perturbed fluidized bed become unstable at the onset of bubbling giving characteristic eigenvalues for the bed modulus, a condition that is readily identifiable experimentally. Eigenvalues from the one-dimensional linearized conservation equations for the fluidized state are examined for growth, neutrality, or decay from the perturbation, which together with bed data are evaluated at bubbling conditions to give the bed modulus of elasticity. Both Richardson-Zaki and Carman-Kozeny bed expansion models of fluidization are examined. The former approach is found to give self-consistent results in which the bed modulus varies linearly with the electric field strength. The results are extended to dc beds as a limiting case of zero field frequency.The modulus of elasticity (a macroscopic bed property) is finally related to particle charge separation at the particle level through an interparticle force model applicable to ac-dc electric fields.     

Gravitational discharge of fine dry powders with asperities from a conical hopper

The effects of particle properties, especially the surface roughness and particle type, on the gravity discharge rate and flow behavior of fine dry powders from a conical hopper are studied in detail. The van der Waals force is considered to dominate the discharge of small particles, while the empty annulus effect dominates the discharge of large particles. To predict the van der Waals force between two rough spherical particles, a model based on Rumpf theory is adopted. The effect of surface roughness can be reflected by Bond number Bo_g which is correlated with discharge rate. By modifying the powder bed porosity and Beverloo constant, the discharge rates of fine dry powders can be well predicted by an empirical correlation. Finally, not only the ratio of hopper outlet size to particle size D₀/d_p but also the Bond number Bo_g is found to be an important indicator to determine the powder flowability. © 2017 American Institute of Chemical Engineers AIChE J, 64: 427–436, 2018     

Berechnung der Haftung von Pulverpartikeln an strukturierten Oberflächen

The adhesion of powder particles on solid surfaces is influenced by many parameters. Among these influence factors the van‐der‐Waals‐forces and the humidity of the surrounding atmosphere play a dominant role. Since current models often neglect important parameters, in this paper different possibilities to calculate particle adhesion forces are presented. The calculated values allow the interpretation of adhesion force distribution and the assignment of adhesion forces to certain mechanisms.     

Recent Results in Particle Adhesion: UHV Measurements, Light-Modulated Adhesion and the Effect of Adsorbates

In the past few years, the force of adhesion F between small metal spheres (about 2 to 8 μm in diameter) and flat semiconducting or metallic substrates has been measured under a variety of conditions. Most of this work has been or is about to be published. This is a summarizing review of the results obtained. An ultracentrifuge technique has been employed. In measurements under ultra-high vacuum the adhesion between Au spheres and flat Si substrates was studied as a function of the oxide layer thickness on Si. Also flat Au substrates were used. The results fit with the Lifshitz theory of van der Waals forces. In another series of measurements the van der Waals component F_ndW of F was separated from the electrostatic one F_el which originates from the electrostatic double layer formed at the interface of the adherents. This was achieved by varying F_el by band-gap light of varying intensity. The adherents were Zr-coated Au spheres on CdS.     

Exploring forces between individual colloidal particles with the atomic force microscope

Forces between individual colloidal particles can be measured with the atomic force microscope (AFM), and this technique permits the study of interactions between surfaces across aqueous solutions in great detail. The most relevant forces are described by the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, and they include electrostatic double-layer and van der Waals forces. In symmetric systems, the electrostatic forces are repulsive and depend strongly on the type and concentration of the salts present, while van der Waals forces are always attractive. In asymmetric systems, the electrostatic force can become attractive as well, even when involving neutral surfaces, while in rare situations van der Waals forces can become repulsive too. The enormous sensitivity of the double layer forces on additives present is illustrated with oppositely charged polyelectrolytes, which may induce attractions or repulsions depending on their concentrations.     

Contribution of Colloidal Forces in Non-contact Area to the Adhesion Between a Micro-probe and a Substrate Surface: Theoretical Analysis

Colloidal forces outside the microscopic probe (particle)–substrate adhesion contact area were analyzed theoretically. Equations describing the van der Waals, electrical double layer, and hydrophobic forces were derived for the non-contact area of a probe–substrate system assuming a simple sphere–flat geometry. Two cases were considered: particles freely resting on the substrate surface and particles pulling off the substrate. The results of modeling presented in this communication suggest that the adhesion of fine particles (microscopic and sub-microscopic particles) to flat surfaces can be affected by the forces acting outside the contact area. However, due to increased distance between the particle and substrate during separation, both the van der Waals and electrostatic forces acting outside the contact area are negligibly small compared to the short-range adhesion forces and they do not contribute to the measured pull-off force to any great extent for most systems. On the contrary, our calculations suggest that the long-range hydrophobic forces can contribute to the strength of adhesion between hydrophobic fine particles and hydrophobic substrates.     

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.     

Cohesive forces between particles of fluid-bed catalysts

The importance of van der Waals and capillary interparticle forces with respect to particle weight is discussed. Evaluation of solid to solid interaction on the basis of particle diameter leads to exceedingly high values of cohesive forces. The need for detailed analysis of particle surfaces is shown.Electron scanning microscopy is used to investigate particle surface characteristics of a number of catalytic powders. There are surface irregularities even in the case of apparently perfect microspheres. For some of the materials tested the investigation provides local radii of curvature of particle surface required for the evaluation of particle to particle interactions.     

Random loose packing of small particles with liquid cohesion

Random packing of wet grains is numerically investigated using a multiscale discrete element method. The cohesion between wet grains is evaluated by the Weber number, with which the macroscopic and microscopic properties of wet packing are compared with those of dry systems. The effect of capillary force on wet packing partially resembles that of van der Waals force on the dry adhesive packing, because both packing fraction (ϕ) and coordination number (Z) of wet packing decrease with increasing surface tension, following a Boltzmann-like exponential decay that leads to a metastable state with ϕ ≈ 0.37 and Z ≈ 3.8. The decay processes of wet grains, however, are much faster than that of dry ones due to the additional liquid-phase viscous dissipation. Moreover, in the cases of strong cohesion, the relationship between Z and ϕ can be well interpreted by the Edwards' ensemble theory, while those with weak cohesion follow an exponential formula instead. © 2018 American Institute of Chemical Engineers AIChE J, 65: 500–511, 2019