PEPT study of particle cycle and residence time distributions in a Wurster fluid bed

Particle cycle and residence time distributions are critical factors in determining the coating quality in the Wurster process. Positron emission particle tracking experiments are performed to determine the cycle and residence times of particles in different regions of a Wurster fluid bed. The results show that particles tend to recirculate in and sneak out below from the Wurster tube. The experiments also show that a larger batch size leads to a shorter cycle time and a narrower cycle time distribution (CTD). It is possible to avoid recirculations and obtain a shorter cycle time and a narrower CTD by selecting the operating conditions appropriately or via equipment design. Experiments using binary mixtures of particles with a diameter ratio of 1.5 show that large particles have a longer cycle time than small particles and that the cycle time is shorter for mixtures with approximately equal amounts of small and large particles. © 2014 American Institute of Chemical Engineers AIChE J, 61: 756–768, 2015     

Residence time distribution in spouted bed drying of maltodextrin solutions on a bed of inert particles

Residence time distributions (RTD) for aqueous maltodextrin solutions were determined in two kinds of spouted bed dryers: (1) conventional spouted bed (CSB) 0.305 m diameter with a bed of polypropylene beads and (2) spout‐fluid bed 0.143 m diameter with draft tube submerged in a bed of FEP® pellets (S‐FBDT). RTD, mean residence time t_m, and spread of the distribution σ², were determined at different drying temperatures, spouting velocities, bed depths, spraying pressures, and feed concentrations. Average values of t_m and σ² were 6.5 min and 26.6 min² for the CSB and 6.9 min and 36 min² for the S‐FBDT, respectively, for all operating conditions except spraying pressure. RTD curves were well represented by the response of an ideal stirred tank with a superimposed bypass of 15% on average for the CSB and 7% on average for the S‐FBDT dryer for all operating conditions. Increase in spraying pressure produced a reduction of t_m and an increase in the bypass fraction of the product in both dryers. © 2011 Canadian Society for Chemical Engineering     

MRI investigations of particle motion within a three-dimensional vibro-fluidized granular bed

The unique ability of magnetic resonance imaging (MRI) to provide spatial and temporal information from optically opaque systems, in three dimensions, make it an ideal tool to study the internal motion of rapid granular flows. This paper will focus on the use of ultra-fast velocity compensated MRI measurements to study particle velocity and density distributions in a granular gas, produced by vibrating vertically a bed of mustard seeds at 40 Hz. Specifically, a velocity compensated, double spin-echo, triggered, one-dimensional MRI profiling pulse sequence was developed. This gives an MRI temporal resolution of approximately 2 ms and also minimises MRI velocity artefacts. 12 phase measurements per vibration cycle were used. The data can be used to extract values of the mustard seed average velocity and velocity propagators (probability distributions functions) as a function of the phase of the vibration cycle and vertical height within the cell. The data show strong transient effects during the impact phase of the vibration. A detailed discussion of the temporal passage of the individual phase resolved, height resolved velocity distributions, along with seed velocity propagators at a fix height from the vibrating base is presented.     

Modulating the mean residence time difference of wide-size particles in a fluidized bed

For non-catalytic gas-solid reaction, it is desirable to match the mean residence time(MRT) of particles and complete conversion time(t_c) in a fluidized bed. In this study, the MRT differences(MRT ratios) between the coarse particles and the fine particles were investigated in a continuous fluidized bed with a side exit by varying the superficial gas velocity, feed composition and particle size ratio. The results show that the MRT ratio increases firstly and then decreases with increasing the gas velocity. By controlling the gas velocity and the feed composition of coarse particles, the MRT ratio can be modulated from 1.8 to 10.5 at the gas velocity of 1.0 m·s~(-1) for the binary mixture with the size ratio of 2.2. The MRT ratio can reach to ~ 12 at the gas velocity of 1.2 m·s~(-1)for the particle size ratio of 3.3. The present study has endeavored to obtain fundamental data for an effective plant operation to meet the need of synchronously complete conversion of particles with different sizes during the film diffusion controlling reaction.     

Experimental studies of particle flow dynamics in a two-dimensional spouted bed

In this paper, both time-averaged and fluctuating behaviors of granular solids in a two-dimensional spouted bed (2DSB) were investigated by particle image velocimetry (PIV). A self-developed algorithm for the high-gradient granular flow field was employed to measure particle velocity sequences together with power spectral density, mean particle velocity and granular temperature. The incoherent spout was characterized as an ‘X’ geometry marked with a periodic upwardly moving neck consisting of particle clusters. In the annulus, particles move periodically as a process of acceleration-deceleration-stagnation that has the same domain frequency as the pressure drop of 2DSB. The time-averaged downward velocities have a maximum at a certain position between the spout wall and conical wall. In the spout, the longitudinal profiles of vertical particle velocities along the axis exhibit a fast acceleration followed by a long flat peak, while the normalized lateral profiles at all bed levels tend to collapse into a third polynomial curve with an inflection point. A mushroom-like distribution of the granular temperature exists in 2DSB. The peaks of granular temperature occur not only near the spout-annulus interface, but also at the corner zone between the annulus and the fountain.     

The coefficient of restitution for normal incident, low velocity particle impacts

This paper examines the theoretical regimes underlying the collision and recoil of elasto-plastic particles in low-velocity normal impacts. The coefficient of restitution is shown to be an approximate function of the ratio of the relative impact velocity to the system compressional wave speed, and the ratio of yield pressure to Young's modulus. The system compressional wave speed is further a function of the relative radii of the impacting particles, and it is predicted that the coefficient of restitution for equally sized sphere-sphere impacts is about 19% small than for sphere-plate impacts of otherwise identical particles. This result is confirmed experimentally. Theory is also developed to quantify an increase in restitution coefficient following identical impacts at the same point. Progressive plastic deformation about the impact point leads to a collision that is increasingly more elastic, and the restitution coefficient for typical particles approaches unity after about five to 10 impacts. This is also approximately confirmed experimentally.     

Experimental investigation of solid particles flow in a conical spouted bed using radioactive particle tracking

Solid particles flow in a conical spouted bed is characterized by radioactive particle tracking. The influence of operating conditions on key parameters of this flow is evaluated and discussed: the morphology of the solid bed is not strongly influenced by the forces exerted by the gas on the solid particles, but rather by geometrical considerations; the particles spend approximately 8% of their time in the spout in all experiments; it is the force exerted on the solid particles by the gas that directly controls the volumetric flow rate between adjacent regions, and not the amount of particles in the bed; as U/U_ms increases, the volume of solid particles in the annulus decreases, the volume of solid particles in the fountain increases and the volume of solid particles in the spout remains constant. Correlations to predict key flow parameters as functions of operating conditions are also established and discussed. © 2015 American Institute of Chemical Engineers AIChE J, 62: 26–37, 2016     

Incipient motion of a bed of particles resting on a submerged oscillating plate

A model for the incipient motion of a particle resting on a bed of like particles carried by a submerged oscillating plate is presented. The model is developed by extending the theory of Stevenson et al. (Chem. Eng. Sci. 57, (2002) 4505) who gave a force balance for limiting equilibrium of a particle within the viscous sublayer at a pipe wall to the present case by including a d'Alembert type force due to the oscillatory motion of the plate. Simultaneous equations are presented that can estimate the phase and frequency of first motion as a function of system parameters. The new model is compared with the data of Bagnold (Proceedings of the Royal Society, London A 187, (1946) 1-15) and is shown to be in excellent agreement.     

An improved integral non-linear model for the contact of particles in distinct element simulations

In this paper we consider a non-linear model for the elastic-frictional contact of spherical particles based on a modification of the classical Hertz-Mindlin no-slip solution. The characteristics of the original model are described and discussed in terms of the capabilities to simulate collisions using the distinct element method (DEM). Perfectly elastic collisions in normal direction and elastic-frictional mechanisms in tangential direction are considered for impacts of a sphere with a flat wall at various angles. On this basis, we suggest a mathematical modification of Mindlin's tangential solution and demonstrate formally its advantages with respect to the commonly used model. We illustrate a comparison of the proposed model with other commonly used models and a validation of the models against experimental data, available under similar conditions (Kharaz et al., Powder Technology 120 (2001) 281). It is shown that an improved realism and consistency is obtained with our modification, especially regarding the tangential displacement and force-displacement relation, at the cost of a very simple modification of the model algorithm.     

The effect of vibrating conditions on the electrostatic charge in a vertical vibrating granular bed

In this study, we carried out experiments to measure the electrostatic charge of a granular matter in a vertical shaker device. The purpose was to quantify the effect of the vibrating conditions on electrostatic charging in the granular matter. In each experimental run, 3 mm glass beads were first discharged to remove any residual charge prior to subsequently studying their electrostatic charging. The accumulative electrostatic charges of the granular materials were measured using a Faraday cage. The findings show that the vibrating conditions play an important role in the saturated electrostatic charge and time constant. The electrostatic charges of granular materials are mainly generated by the contact potential difference mechanism in the vibrating granular system. The results show that the saturated accumulation charge increases as the dimensionless vibrating acceleration increases, and decreases with increasing vibrating frequency. The time constant is small when a higher vibrating frequency is applied in the vibrating granular system. Finally, we demonstrate that the saturated accumulation charge increases linearly with the increase of the dimensionless vibrating velocity regardless of the vibrating frequency.     

Contact detection algorithms for DEM simulations of tablet-shaped particles

The shape of standard round tablet was represented by using the intersection of three spherical surfaces. Using this model, the contact criteria for tablet-flat surface and tablet-tablet contact were developed and were applied for tablet-tablet contact using a DEM simulation implemented in Matlab™ code. In addition, a high-speed digital imaging system was used to capture the images of one tablet hitting another fixed tablet anchored to a flat surface. Comparison of angular velocity showed good agreement between simulation and experimental results. The simulations were compared with alternative multi-sphere representations for the shape of the tablet and the results showed that the simulation times for 66- and 178-sphere representations were much larger than that for the tablet simulations. In addition, the simulation results for all the multi-sphere representations were significantly different from those of the tablet simulation.     

Mathematical modelling of solvent drying from a static particle bed

Distributed-parameter models of vacuum contact drying of a static particle bed have been formulated and a numerical solution of the resulting set of partial differential equations describing heat and mass transfer in the particle bed has been carried out. Systematic parametric study of the effect of jacket temperature, head-space pressure, bed depth, and gas- and liquid-phase relative permeability has been performed. Trends observed in vacuum contact drying experiments, namely the independence of drying rate on the mode of driving force realisation (by jacket temperature or head-space pressure), linear scaling of heat-transfer rate with bed depth during the constant-rate period, independence of drying rate on particle size above a certain critical size, and disappearance of the constant-rate period below a certain particle size, have been reproduced by the model both qualitatively and quantitatively. A study of the effect of gas-phase permeability on drying kinetics revealed an interesting phenomenon-a reversal of the direction of drying front propagation. The drying front was found to originate from the heat source (heated walls) for large permeability, and from the mass sink (head-space) for low permeability.     

Contact between a smooth microsphere and an anisotropic rough surface

This article discusses the effects of asperities on elastic and adhesive contact between a smooth sphere and a rough surface. Two numerical methods are introduced: an asperity-superposition method and a direct-simulation method. In the first method, geometric parameters such as asperity heights, orientations, and radii of curvature are identified by a least-squares regression of neighboring surface heights measured using an atomic force microscope. The rough surface is reconstructed by the superposition of these asperities. The modeling of adhesive and elastic contacts begins with the modeling of a single parabolic-shaped asperity contact. A generalized JKR model for an arbitrary parabola is developed to suit this purpose. The contact between the rough surface (represented by the supposition of parabolic-shaped asperities) and the sphere consequently is modeled bythe mapping and integration of individual asperity contacts. In the second method, pure-elastic contact is modeled by half-space elastic theory. A contact-search algorithm is used to find solutions on the displacement and the contact-pressure distribution that satisfy both the load-displacement equation and the contactboundary conditions. Results from both methods are compared to reveal the effects of asperities on adhesion and elastic-contact pressure.     

Characterizing bubble behavior in a pseudo-2D fluidized bed of wet particles

By applying digital image analysis on the bubble characteristics in a two dimensional wet-particle fluidized-bed, we report two-stage evolution of bubble characteristics with increasing liquid content. In the first stage, bubble number and uniformity of bubble fraction increase, while bubble average diameter and aspect ratio decrease. In the second stage, these characteristics shift toward an opposite direction. This two-stage evolution of bubble characteristics are analogous to that of reducing particle size in dry-particle fluidization, and the fluidizing properties of particles shifts from Geldart Group B to Group A and then to Group C. Furthermore, liquid addition causes a continuous decrease of bubble fraction and bubble flow rate. This is different from dry-particle fluidization, in which reducing particle size causes an increase trend. An explanation for this difference is that liquid addition increases the equivalent size of agglomerates in wet-particle fluidization, which is opposite to the effect of reducing particle size.     

热解分离的散状料层接触传热

根据对化合物散状料层接触传导热解分离的理论，对料床的热传导进行了分析。建立了不稳定热传导过程料床的热传导计算方法，为化合物散状料层热解分离加热设备的设计提供理论依据。     

Experimental investigation of particle contact time at the wall of gas fluidized beds

The contact time of particles at the walls of gas fluidized beds has been studied using a radioactive particle tracking technique to monitor the position of a radioactive tracer. The solids used were sand or FCC particles fluidized by air at room temperature and atmospheric pressure at various superficial velocities, covering both bubbling and turbulent regimes of fluidization. Based on the analysis of tracer positions, the motion of individual particles near the walls of the fluidized bed was studied. The contact time, contact distance and contact frequency of the particles at the wall were evaluated from these experimental data. It was found that in a bed of sand particles, the mean wall contact time of the fluidized bed of sand particles decreases by increasing the gas velocity in the bubbling and increases in the turbulent fluidization. In other words, the particle-wall contact time is minimum at the onset of turbulent fluidization in the bed of sand particles. However, the mean wall contact time is almost constant in both regimes of fluidization in the bed of FCC particles. All the existing models in the literature predict a decreasing contact time when the gas velocity in the bed is increased. It was also shown that the contact distance increases monotonously by increasing the gas velocity in the bed of sand particles, while it is almost constant for the bed of FCC particles. Contact frequency has a trend similar to that of the contact time for both sand and FCC particles.     

The influence of the riser exit on the particle residence time distribution in a circulating fluidised bed riser

This paper reports measurements of the influence of riser exit geometry upon the particle residence time distribution in the riser of a square cross section, cold model, circulating fluidised bed. The bed is operated within the fast fluidisation regime. The fast response particle RTD technique developed by Harris et al. (Chem. Eng. J. 89 (2002) 127-142) was used to measure the residence time distribution.The geometry of the riser exit is shown to have a modest but consistent influence upon the particle RTD; the influence of operating conditions, i.e. superficial gas velocity and solids flux is more significant.Increasing the refluxing effect of the riser exit increases the mean, variance and breakthrough time and decreases the coefficient of variation of the residence time distribution. Changes in reflux do not have a systematic effect upon the skewness of the RTD.     

Magnetic particle tracking for nonspherical particles in a cylindrical fluidized bed

In granular flow operations, often particles are nonspherical. This has inspired a vast amount of research in understanding the behavior of these particles. Various models are being developed to study the hydrodynamics involving nonspherical particles. Experiments however are often limited to obtain data on the translational motion only. This paper focusses on the unique capability of Magnetic Particle Tracking to track the orientation of a marker in a full 3‐D cylindrical fluidized bed. Stainless steel particles with the same volume and different aspect ratios are fluidized at a range of superficial gas velocities. Spherical and rod‐like particles show distinctly different fluidization behavior. Also, the distribution of angles for rod‐like particles changes with position in the fluidized bed as well as with the superficial velocity. Magnetic Particle Tracking shows its unique capability to study both spatial distribution and orientation of the particles allowing more in‐depth validation of Discrete Particle Models. © 2017 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 63: 5335–5342, 2017     

Monitoring the particle-wall contact in a gas fluidized bed by RPT

Particle-wall contact behavior of the solids in a gas-solid fluidized bed was experimentally studied using the radioactive particle tracking (RPT) technique in which the position of a radioactive tracer is monitored when moving freely in the bed. The solids were sand particles, fluidized by air at room temperature and atmospheric pressure at various superficial velocities, covering both bubbling and turbulent regimes of fluidization. The motion of individual particles near the wall of the bed was studied based on the position of the tracer. The contact time, contact distance and contact frequency of the particles at the wall were evaluated. It was found that the distribution functions of these three parameters become wider by increasing the superficial gas velocity. Axial profiles of contact time and contact distance were also studied in this work. Axial profiles of the overall heat transfer coefficient in the fluidized bed were estimated based on the formulas reported in the literature and the experimental particle-wall contact time evaluated in the present study. Based on such profiles, in order to benefit from the maximum heat transfer coefficient along the bed, it is recommended to place the heat exchanging surface in the middle of the bed, i.e., not very close to the gas distributor as well as far from the top of the dense bed.     

Analytical solution for the problem of frictional-elastic collisions of spherical particles using the linear model

In the present paper, the problem of a frictional-elastic impact of two spheres is addressed with a novel approach. The set of equations arising from the linear model of the contact mechanics is analytically integrated considering the combined effects of the elastic and frictional mechanisms. The linear model is very commonly used in simulations based on the soft-sphere distinct element method (DEM) (Geotechnique 29 (1979) 47), where numerical methods are used for the integration of the equations of motion of the particles. The analytical approach presented in this work allows the examination of many important aspects related to the use of the linear model in dynamic simulation of multi-particle systems. The impact characteristics, in terms of the mechanisms governing the evolution of the force-displacement relation, can be classified in terms of the initial conditions, showing the same subdivision as that obtained with the more complex model of Maw et al. (Wear 38 (1976) 101). It is demonstrated how the values of many interesting variables at the end of the impact can be directly related to the impact initial conditions through a one-step calculation procedure. The model results of the tangential coefficient of restitution, rebound angles of the contact point and center of mass are validated with the experimental data on frictional-elastic collisions of Kharaz et al. (Powder Technol. 120 (2001) 281), showing, despite the simplicity of the considered model, an excellent agreement. However, it is demonstrated that the force evolution and time duration of the collisions strongly depend on the model parameters and can be improperly evaluated with incorrect material constants. Further analyses are carried out, for various impact angles, on the amount of energy loss due to the frictional mechanism. Also, an analysis of the direct influence of each model parameter on the properties of the particles at the end of the collision is carried out, with special emphasis on the normal elastic spring constant K_n. This helps clarifying why, in the literature, realistic macroscopic results were obtained even with very small values of K_n.