A regime map for granule formation by drop impact on powder beds

“Tunneling,” “Spreading,” and “Crater Formation” are the three granule formation mechanisms known to occur when single drops impact static powder beds. To quantify the conditions under which each mechanism will occur, dimensional analysis was performed, and a new regime map was created that plots the powder bed porosity against the modified granular Bond number (Bo_g*), which is a ratio of the capillary force to the gravitational force acting on a particle. Tunneling occurred for Bo_g* > 65,000 for all values of bed porosity, whereas Spreading and Crater Formation occurred when Bo_g* < 65,000 for all values of bed porosity below the minimum fluidization porosity. The granule formation mechanism regime map provides a useful tool to design and predict wet granulation processes by predicting the granule formation mechanism, and thereby general granule shape, from a few key dimensionless groups involving formulation properties and process parameters that can be calculated a priori. © 2012 American Institute of Chemical Engineers AIChE J, 59: 96–107, 2013     

A square‐force cohesion model and its extraction from bulk measurements

Accurate modeling of interparticle forces in DEM is critical to predicting the rheology of cohesive particles. Rigorous cohesion models usually include parameters associated with particle surface roughness. However, both roughness measurement and its distillation into appropriate model parameters remain challenging. We propose a square‐force cohesion model, where cohesive force remains constant until a cutoff separation, above which cohesion vanishes. We demonstrate the square‐force model is a valid surrogate of more rigorous models. Specifically, when two parameters of square‐force model are chosen to match the two key quantities governing dense and dilute flows, namely maximum cohesive force and critical cohesive energy, respectively, DEM results using square‐force and more rigorous models show good agreement. For practical application of the square‐force model to lightly cohesive systems, a method is established to extract its parameters via defluidization, enabling determination of particle–particle cohesion from simpler bulk measurements than complicated and expensive scans on individual grains. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2329–2339, 2018     

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     

On Geldart Group A behaviour in fluidized beds with and without cohesive interparticle forces: A DEM study

This paper presents a 2D soft sphere discrete element method (DEM) simulation study of fluidization behaviour of Geldart Group A powders and Geldart Group B powders in the presence of externally imposed cohesive interparticle force. In the presence of externally imposed cohesive interparticle force, beds of Group B powders exhibit some of the characteristics of Group A powders (homogeneous bed expansion and pressure drop hysteresis), but show other characteristics (e.g. bed collapse) which are quite different. The homogeneous bed expansion for Group B particles with imposed cohesive interparticle force is found to follow the Richardson-Zaki relationship, with the exponent n being independent of the magnitude of interparticle force and with the degree of expansion increasing with the magnitude of interparticle force. Group A particles show homogeneous bed expansion even in the absence of cohesive interparticle force.     

Is there any contradiction between the stress and energy failure criteria in micromechanical tests? Part III. Experimental observation of crack propagation in the microbond test

A direct observation of crack propagation in the microbond test was carried out for five different fiber/polymer matrix systems. This technique appeared to be a very effective tool for interface characterization. Experimental plots of the force required for further crack propagation as a function of debond length were analyzed using both energy-based and stress-based models of debonding. The fracture mechanics analysis was used to construct families of crack resistance or R-curves which showed the variation of energy release rate, G, with the debond length, and included the effect of interfacial friction in debonded regions. For the first time, analogs of the R-curves were created within the scope of the stress-based model to present the local shear stress near the crack tip, τ, as a function of crack length. In both models, the behavior of the interfacial parameter (G or τ) strongly depends on the assumed value of the interfacial frictional stress (τ_f). However, for each matrix/fiber system there exists such a τ_f value for which the investigated parameter is nearly constant over the whole region of stable crack propagation (70–90% of the embedded length). Moreover, these best-fit τ_f values for each specimen appeared to be practically the same for both energy-based and stress-based approaches. Thus, both interfacial toughness, G _ic, and local interfacial shear strength, τ_d, adequately characterize the strength of a fiber/matrix interface. Extrapolation of R-curves and their analogs to zero crack length allows measurement of the interfacial parameters with good accuracy.     

Micromechanics of agglomeration forced by the capillary bridge: The restitution of momentum

The formation of capillary bridge formed by a liquid adsorbate is one of the main reasons for agglomeration in multiphase flows. Agglomeration takes place when the relative momentum of two colliding particles is fully consumed by the bridge. This article presents a theoretical study of the collisions of particles with adsorbed liquid taking into account the influence of capillary and viscous dissipative forces. The article proposes an approximate analytical solution for the dynamics of the bridge formed during the collision, together with a more complete numerical model, which is validated with experimental data. The restitution of the relative momentum of the colliding particles, depending on a series of dimensionless parameters characterizing the bridge, is investigated. A criterion for prediction of agglomeration, or “collision efficiency,” in a flow involving cohesive particles is given. An expression is proposed for the coefficient of restitution for the case of collision via a liquid bridge. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4045–4057, 2013     

EXPERIMENTAL INVESTIGATION ON FLOW AND DRYING CHARACTERISTICS OF A VERTICAL AND SEMI-CYCLIC COMBINED IMPINGING STREAMS DRYER

Abstract

Flow characteristics of a vertical and semi-cyclic combined impinging streams dryer(VSCIS) was investigated. Results show that centrifugation and gravity have obvious influences on pressure drop and on momentum commutation between gas and particles in impingement zones. The effects of various operating parameters on water removal from particles have been studied experimentally. It is found that initial hot air temperature Tin, μ and initial moisture content of particles X₀ play important roles on water removal from particles. Based on the experimental data, dimensionless correlations for flow and drying characteristics in the system were obtained. VSCIS has shown to be a good way to overcome the shortcomings of single configuration of either vertical or semi-cyclic impinging streams. It can take full advantages of both arrangement to remove more water from particles.     

Heat and mass transfer in calcination of limestone particles

The heat and mass‐transfer phenomena occurring during the calcination of limestone particles was studied by means of modeling. The applicability of two modeling methods for calcination was compared under different conditions. An unsteady numerical particle model with mass, momentum, energy balance, and shrinking core models were chosen for the study. The influence of different phenomena (chemical kinetics, advective and diffusive mass transfer, and heat transfer) in different conditions was evaluated with the aid of dimensionless parameters, and their relative importance was shown in a regime chart. Especially, the significance of advection was studied and its importance in high CO₂ concentration was observed. Local temperatures inside the particle were obtained by solving a dynamic energy balance in each particle layer including calcination reaction energy and conduction heat transfer. Noticeable temperature differences between constant ambient conditions and the particle were observed. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2563–2572, 2012     

Spectral analysis of force fluctuations during probe penetration into cohesive powders

We investigate force fluctuations during probe penetration into cohesive powders consisting of ∼ 5 μm lactose particles with varying surface properties prepared by spray drying. The results obtained for the more cohesive powders were remarkably similar to those previously reported for orders of magnitude larger noncohesive particles. For the less cohesive powders, the spectral densities were instead found to exhibit two distinct power-law regions. Furthermore, the spectra were found to be independent of the geometry of the penetrating probe and dimensions of the die cavity. These findings suggest that the response is dominated by particle aggregate or agglomerate movement for the more cohesive powders, whereas the behaviour of the less cohesive ones is consistent with a response dominated by relatively weak force chains, with the fluctuations resulting from the recurring creation and collapse of jammed states being damped for length scales > 0.1 mm.     

Adhesion strength and fracture behavior between carbon black-filled rubber sheets

Adhesion behavior at the interface between a partially-crosslinked and a fully-crosslinked sheet of carbon black-filled rubber compound was investigated over a temperature range from 30 to 120°C. The values of adhesion fracture energy G_a were compared with those of cohesive tear energy G_c. A considerable chemical, as well as physical, interfacial bonding is formed when the uncrosslinked or partially-crosslinked sheet is crosslinked in contact with even a fully-crosslinked sheet. However, there is only a small possibility of chemical bonding when the two fully-crosslinked rubber layers are again crosslinked in contact with each other. An interesting failure mode, termed 'interfacial knotty tearing' was found for a strain-induced crystallizable natural rubber.     

Breakage of wet flexible fiber agglomerates impacting a plane

The breakage of an agglomerate of wet flexible fibers impacting a plane is computationally investigated in this work using the discrete element method. In the agglomerate, the fibers stick together due to cohesive liquid bridge forces. Agglomerate breakage with various impact conditions, initial configurations, fiber properties, and liquid bridge properties is systematically investigated. The degree of breakage is governed by the impact energy, the cohesion energy due to liquid bridges, the energy dissipation/absorption through fiber–fiber contacts and fiber deformation, and the efficiency of force transmission within the agglomerate. More specifically, breakage is promoted by increasing impact velocity, decreasing agglomerate size, increasing initial compaction, increasing fiber bending modulus, decreasing liquid surface tension, and decreasing liquid-to-solid volume ratio. Breakage is strongly dependent on the modified Weber number, that is, the ratio of the Weber number to a dimensionless rupture distance, which is a measure of the impact energy relative to the cohesion energy.     

On the onset of incipient fluidization

The onset of incipient fluidization is investigated theoretically and simulated by a computational fluid dynamics (CFD) procedure. The onset of incipient instability in a particle bed is preceded by stable gas diffusion in the interstices and is caused by a critical momentum force that may overcome the inertia of the particles. The critical momentum force is provided by the critical superficial gas velocity U_c in the form of critical mass flux of diffusion. It is found that the first movement of particles may be predicted by a critical transient Rayleigh number determined by a critical superficial velocity equals to the minimum fluidization velocity, U_mf. The onset of incipient fluidization was found to occur at a critical transient Rayleigh number of 3.1, which is close to the lowest theoretical value for buoyancy convection in a porous medium bounded by free surfaces. Consequently the onset times of incipient fluidization may be predicted accurately. The finding has been found to be supported by the present CFD study, past experiments and simulations in the literature.     

Facile self-assembly of sandwich-like MXene V2CTx/Ag/rGO/MWCNTs layered multiscale structure nanocomposite

MXene is widely used in the supercapacitors, fuel cells and other fields due to its excellent conductivity and hydrophilicity. V has multiple oxidation states that allow V₂CT_x to participate in more redox reactions, and has good energy storage potential. Ag particles, rGO and MWCNTs are used to modify V₂CT_x to fully exploit the electrochemical properties of V₂CT_x. The doping of Ag particles, rGO and MWCNTs can well prevent the collapse and accumulation of V₂CT_x. A number of Ag particles, rGO and MWCNTs enter into the layers of V₂CT_x, which can increase the layer spacing. The expansion of interlayer spacing can expose more active contact sites and shorten the diffusion path of electrolyte ions. Ag particles, rGO and MWCNTs transform the original two-dimensional structure into a three-dimensional structure, which can provide a fast transport channel for charge transport and ion diffusion. Moreover, the close contact of Ag particles, rGO and MWCNTs enables the cross-boundary transport of carriers more rapid and convenient. The capacitance contribution rate of V₂CT_x + Ag + rGO + MWCNTs composite that is modified with Ag particles, rGO and MWCNTs reaches 86.6%. The results show that the electrochemical performance of V₂CT_x + Ag + rGO + MWCNTs composites has a more promising future.     

Method for inferring contact angle and for correlating static liquid hold-up in packed beds

Static liquid hold-up (SLH), which is an upper bound measure of the passive liquid volume fraction in packed beds, comes into play in several reaction-separation-transport design models and in correlations of fundamental hydrodynamic variables such as total liquid hold-up, wetting efficiency and pressure gradient. Early reported experimental SLHs in packed beds seemed to level off at a plateau of ca. 5% when capillary force dominates over gravity. Hence, most of the published correlations were constructed taking this asymptotic feature into account, despite the fact that reliable SLH values well beyond 5% were also reported particularly for Bond numbers tending towards zero. Thermodynamics and dimensional analysis of the interfacial momentum balance (Young-Laplace) equation suggests that SLH depends, besides the Bond number (Bo) and some packing and bed characteristic lengths, on an effective contact angle at the junction where the gas-liquid interface and the packing-gas boundary meet. The contact angle, being difficult to measure, was generally disregarded in most analyses, and in practice, seldom incorporated as a computable quantity in the majority of published SLH correlations. Therefore in this work, a method was proposed for inferring theoretically the contact angle from an energy analysis of the meniscus interfaces’ area obtained from solving the 2-D Young-Laplace equation for two vertically aligned touching equivalent spheres. The approach showed that the intuited contact angles matched the measured ones, when available, with an average error of 8.6%. Following this determination, a new SLH correlation based on the contact angle (θ_c), the Bond number (Bo), the solid-to-void volume ratio (1−ε)/ε, the packing sphericity (φ), and the bed-to-packing volume ratio, BPR, was proposed and analysed in the light of most published SLH data, i.e., 239 measurements over the past five decades. The SLH correlation yielded an average error of 23%. Sensitivity analysis of its weights showed an important impact of the contact angle as an input variable. The correlation was also found to capture SLH values exceeding 5% in the limit of Bo→0.     

A mechanistic study of agglomeration in fluidised beds at elevated pressures

Effect of operating pressure on the hydrodynamics of agglomerating gas–solid fluidised bed was investigated using a combination of discrete element method (DEM) for describing the movement of particles and computational fluid dynamic (CFD) for describing the flow of the gas phase. The inter‐particle cohesive force was calculated based on a time dependent model developed for solid bridging by the viscous flow. Motion of agglomerates was described by the multi‐sphere method. Fluidisation behaviour of an agglomerating bed was successfully simulated in terms of increasing the size of agglomerates. The results showed that increasing the operating pressure postpones de‐fluidisation of the bed. Since the DEM approach is a particle level simulation and study about particle–particle interactions is possible, a micro‐scale investigation in terms of cohesive force and repulsive force during agglomeration at elevated pressures was done. The micro‐scale results showed that although the number of contacts between particles was decreased by increasing operating pressure, stronger solid bridge formed between colliding particles at higher pressures. © 2012 Canadian Society for Chemical Engineering     

A coupled DEM/CFD analysis of the effect of air on powder flow during die filling

Die filling from a stationary shoe in a vacuum and in the presence of air was numerically analyzed using an Eulerian‐Lagrangian model, which employs a discrete element method (DEM) for the particles and computational fluid dynamics (CFD) for the air with a two‐way air‐particle interaction coupling term. Monodisperse and polydisperse powder systems have been simulated to explore the effect of the presence of air on the die filling process. For die filling with monodisperse powders, the influences of particle size and density on the flow behavior were explored. The numerical simulations revealed that the presence of air has a significant impact on the powder flow behavior, especially for systems with smaller and/or lighter particles. Flow has been characterized in terms of a dimensionless mass flow rate, and it has been shown that for die filling in a vacuum this is constant. The flow characteristics for die filling in air can be classified into two regimes. There is an air‐inert regime in which the particle size and density are sufficiently large that the effect of air flow becomes negligible, and the dimensionless mass flow rate is essentially identical to that obtained for die filling in a vacuum. There is also an air‐sensitive regime, for smaller particle sizes and lower particle densities, in which the dimensionless mass flow rate increases as the particle size and density increase. The effects of particle‐size distribution and adhesion on the flow behavior have also been investigated. It was found that, in a vacuum, the dimensionless mass flow rate for polydisperse systems is nearly identical to that for monodisperse systems. In the presence of air, a lower dimensionless mass flow rate is obtained for polydisperse systems compared to monodisperse systems, demonstrating that air effects become more significant. Furthermore, it has been shown that, as expected, the dimensionless mass flow rate decreases as the surface energy increases (i.e., for more cohesive powders). © 2008 American Institute of Chemical Engineers AIChE J, 2009     

Spreading,wetting, and contact angles

The thermodynamic energies associated with conventional wetting, spreading, adhesion, cohesion, and disjoining pressure, as defined in classical equations, are re-examined for their significance in a force field. They are then converted into dimensionless form such that the equilibrium properties of both wetting and spreading all fall on the same line when the dimcnsionless spreading coefficient is plotted as a function of the dimensionless work of adhesion. The effects of a force field such as gravity are examined and it is further shown that spreading is always thickness-dependent, whether in a force field or in a gravity-free field. Non-equilibrium processes such as autophobicity are shown on the same dimensionless plot and indicate clearly that the speed with which the process approaches equilibrium depends on the difference between the initial and equilibrium spreading coefficients. All these processes are expressed in terms of a dimensionless group P_n, the reduced wetting energy, which, when lying between the values of + 1 and -1, equals the cosine of the contact angle, . The implication of this approach to non-equilibrium processes is discussed.     

Product Design of Cohesive Powders – Mechanical Properties,Compression and Flow Behavior

The fundamentals of cohesive powder consolidation and flow behavior are explained using a reasonable combination of particle and continuum mechanics. By the model “stiff particles with soft contacts”, universal models are presented which include the elastic‐plastic and viscoplastic particle contact behavior with adhesion, load‐unload hysteresis and thus energy dissipation, a history‐dependent and a nonlinear adhesion force function. With this as the physical basis, incipient powder consolidation, yield and cohesive steady‐state flow, consolidation and compression functions, compression and preshear works are explained. As an example, the flow properties of an ultrafine limestone powder are shown. These constitutive models are used to evaluate shear cell test results for apparatus design to ensure reliable powder flow. Finally, conclusions are drawn concerning particle stressing, powder handling behavior and product quality assessment in processing industries.     

Numerical simulation of the ENF test for the mode-II fracture characterization of bonded joints

In this work, the End Notched Flexure (ENF) test is analyzed in order to obtain the critical strain energy release rate in mode-II fracture of bonded joints. A cohesive model based on specially developed interface elements, including a linear softening damage process, is employed. The adequacy of the experimental ENF test is evaluated by numerical simulation. The objective is to compare the critical strain energy release rate in mode-II (G _{II c} ) obtained by different data reduction schemes with the real value which is an inputted parameter in the cohesive model. The effect of the Fracture Process Zone (FPZ) ahead of the crack tip is evaluated. A crack equivalent concept is proposed in order to account for the energy dissipated in the FPZ. A data reduction scheme avoiding the need to measure crack length is proposed. A good agreement with the inputted value of G _{II c} was obtained.