On the relative importance of the kinetic and frictional contributions to granular motion in an annular Couette flow

A quantitative assessment is made on the relative importance of the kinetic and frictional contributions to the motion of dry granular materials under shear in an annular Couette flow configuration. The assessment is based on comparing the modelling results using the kinetic-frictional model with the experiments. It is shown that the kinetic-theory-based model with equal weight of the collisional and frictional contributions, commonly used in the literature, gives a great deviation from the experimental results in the point of view of the dominant solids motion, while an increase in the weight of the frictional contribution improves the modelling towards the experimental results. An increase in the weight of the frictional contribution by 25-50% leads to the best match, suggesting the current constitutive relationship with equal weight of the kinetic and frictional contributions need to be refined in order to reflect the real dense granular flows.     

Applying dry powder coatings to pharmaceutical powders using a comil for improving powder flow and bulk density

A method for applying nano-sized silicon dioxide guest particles onto host pharmaceutical particles (a.k.a. “dry-coating” or “nanocoating”) has been developed using conventional pharmaceutical processing equipment. It has been demonstrated that under selected conditions, a comil can be used to induce sufficient shear to disperse silicon dioxide particles onto the surfaces of host particles such as active pharmaceutical ingredients (API) without significant host particle attrition. In accordance with previous studies on dry coating, the dispersed silicon dioxide adheres to the host particle surface through van der Waals attractions, and reduces bulk powder cohesion. In this work, laboratory and pilot scale comils were used to dry coat pharmaceutical API and excipient powders with 1% w/w silicon dioxide by passing them through the mill with an appropriate combination of screen and impeller. In general, the uncoated powders exhibited poor flow and/or low bulk density. After dry coating with a comil, the powders exhibited a considerable and in some cases outstanding improvement in flow performance and bulk density. This coating process was successful at both the laboratory and pilot scale with similar improvements in flow. The superior performance of the coated powders translated to subsequent formulated blends, demonstrating the benefit of using nanocoated powders over uncoated powders. This particle engineering work describes the first successful demonstration of using a traditional pharmaceutical unit operation that can be run continuously to produce uniform nanocoating and highlights the substantial improvements to powder flow properties when this approach is used.     

Influence of agitator design on powder flow

Design influences the flow within a powder mixer but quantitative guidance is lacking. Here the performance of mixers of different geometry was compared using positron emission particle tracking. One mixer had six long flat blades; the other carried short paddles. With the former, blade angle and number of axial compartments had little effect on agitation in the transaxial plan but axial dispersion was enhanced by longer axial compartments. A loop of circulation was found below the shaft. For the short paddle device, the transaxial agitation was more uniform, with a lower mean angular velocity and narrower ranges of velocities. The mixing elements inhibited the formation of the loop of circulation. In both cases, the axial flow had a cellular structure created by the radial supports for the blades but the short paddles mixer showed more chaotic behaviour, the axial dispersion coefficient being typically five times higher and increasing with fill rather than decreasing as seen with the six-blade device. A rationale for the design of powder mixers is thus emerging.     

Instability-induced clustering and segregation in high-shear Couette flows of model granular materials

Controlling unwanted segregation of components within a particle mixture is a longstanding goal in particle processing technologies. We investigate flow-induced clustering and consequent segregation of cohesionless particulate mixtures flowing rapidly in high-shear Couette geometries, comparing results from particle-dynamic (PD) simulations, kinetic theory and experiments. Using spheres and disks and a simplified plug instability as a surrogate for the variety of coherent flow structures, we find that density, velocity, and granular temperature gradients, and possibly, initiation of vorticity, influence the onset and nature of segregation. For equal density particles, simulations and experiments show that there exists a critical solids fraction at which the direction of segregation is reversed and streamwise diffusivity drops significantly, which appears to correspond to a point where the thermal diffusion flux no longer dominates over other terms. Results compare favorably to those from binary kinetic theories with one exception. We find that the 1D steady-state theoretical solutions do not capture the flux reversal observed in PD simulations of the equal density mixtures. Finally, we illustrate how local density variations can severely affect particle size distribution measurements.     

Gravity pipe flow of polymeric bulk solids in pneumatic conveying system

Various physical parameters of gravity pipes such as gravity pipe diameter, the inclination of the gravity pipe, the cone angle, temperature of the discharged material and the rate of air counter flow into the gravity pipe were studied. The results obtained from the pipe diameter and cone angle experiments showed that the mass flow rate was proportional to (D-1.4d)^2.5 and also to θ^-0.5. The results from the pipe inclination experiment showed the existence of an angle of inclination for maximum flow, which was also reported by Wieghardt [Uber einige versuche an stromungen in sand. Ingenieur Archived 20, 109-115]. The air flow experiment also showed that the mass flow rate was inversely proportional to the air counter-flow rate, and strongly influenced by the material properties. Results from the temperature experiment showed that the temperature of the material had slight effect on the mass flow rate for the temperature range that was used in the experiment. Flow visualization images showed formation of solid plugs in the pipe that played a part in influencing the behaviour and mass flow rate of solids in the system.     

Measurement of the velocity field and frictional properties of wet masses in a high shear mixer

In order to develop predictive process models and to enhance process understanding in high shear granulation, there is an ongoing search for non-intrusive methods for measuring the wet mass velocities in the mixer. In this study, a high speed CCD camera is used in combination with software for particle image velocimetry (PIV) calculations to obtain information about the wet mass velocities. The focus has been on obtaining good spatial and angular resolution for the velocities along the glass bowl wall. In a Jenike shear cell, both internal and wall frictional properties have been measured and together with velocity data, this information is used for prediction of the impeller torque. It has been shown that the near wall velocities are strongly dependent on the coefficient of wall friction, which decreases during liquid addition. The decrease in the coefficient of wall friction results in increased wet mass velocities close to the bowl wall. It is also found that the wet mass velocity has a strong angular dependence, resulting in a high frequency pulsing bed behaviour which cannot be detected by visual inspection. The predictive impeller torque model developed by Knight et al. [2001. Prediction of impeller torque in high shear powder mixers. Chemical Engineering Science 56, 4457-4471] has been generalized to account for cohesive materials and with frictional and velocity data, the level of the impeller torque is well predicted. However, the model is based on crude assumptions regarding the velocity distribution and hence, it cannot capture the dynamics in the measured torque curve satisfactorily.     

Couette grain flow experiments: The effects of the coefficient of restitution, global solid fraction, and materials

Granular flows are complex flows of solid granular material which are being studied in several industries. However, it has been a challenge to understand them because of their non-linear and multiphase behavior. The present experimental work investigates granular flows undergoing shear, by specifically studying the interaction between rough surfaces and granular flows when the global solid fraction and the material comprising the rough shearing surface are varied. A two-dimensional annular shear cell, with a stationary outer ring and inner driving wheel, and digital particle tracking velocimetry (DPTV) technique were used to obtain local granular flow properties such as velocity, local solid fraction, granular temperature, and slip. A customized particle drop test apparatus was built to experimentally determine the coefficient of restitution (COR) between the granular and surface materials using high-speed photography. Results showed that wheel surface materials that produce higher COR values exhibit higher velocity and granular temperature values near the wheel, and lower slip velocities. The local solid fraction appears inversely related to the COR values. The global solid fraction seemed to correspond with velocity and granular temperature, while displaying an inverse relationship to slip. Results also showed an initial decrease in the kinetic energy of the flow as the global solid fraction increased, due to the formation of a distinct contact region. This was followed by a rise in kinetic energy as the global solid fraction continued to increase, based on the increase of particles present in the kinetic region of the flow.     

Modeling rheological behavior of bentonite suspensions as Casson and Robertson-Stiff fluids using Newtonian and true shear rates in Couette viscometry

The Casson model and the Robertson-Stiff model have been used to determine whether they can describe the rheology of aqueous bentonite suspensions. The assessment utilized a total of twelve sets of experimental viscometric data from literature and from this work. Equations have been presented which allowed the determination of the true shear rates experienced by the fluids within the gap of the rotational viscometer for both rheological models. Non-linear regression has been applied to determine the two rheological parameters for the Casson model and the three rheological parameters for the Robertson-Stiff model using true shear rates and Newtonian shear rates, which are used most often in the analysis of rheometric data. The results showed that both models describe well the experimental data of these bentonite suspensions with good statistical indicators. Furthermore, analysis showed that true shear rates are always higher than Newtonian shear rates for both models. The differences depend on the particular suspension and are larger at low shear rates while they become smaller at higher shear rates indicating that the fluid behavior approaches Newtonian behavior at higher shear rates. The shapes of the rheograms remained essentially unchanged indicating that the rheological parameters determined with the use of true shear rates are very similar to the rheological parameters determined with the use of Newtonian shear rates. This was further confirmed with the computation of the rheological parameters for both models and both approaches. For the Casson model differences in the yield value computed with true shear rates were at most at 7% while for the plastic viscosity at 3%. For the Robertson-Stiff model, differences of the order of 2 to 5% were observed for the K-values, of 7% for γ˙₀-values while no differences were observed for the n-values. These small differences, however, do not justify use of Newtonian shear rates when analytical solutions exist which allow use of true shear rates without any compromise.     

Granular flow and segregation in a four-bladed mixer

In this study, we experimentally examine flow and segregation of granular material in a cylindrical mixer geometry agitated by four 45 pitched blades, which is representative of equipment such as high-shear granulators and filter-dryers. We observe that the free surface of the granular bed deforms, rising where the blades are present and falling between blades passes. Using particle image velocimetry (PIV), we measure the instantaneous, average, and fluctuating velocity fields at exposed surfaces (top surface and near the wall), for both near-monodisperse and polydisperse granular materials. The radial and axial point-velocity profiles indicate three-dimensional recirculation patterns indicative of avalanching and bed penetration. For polydisperse mixtures, we find that depending on the shear rate, different segregation mechanisms can take place. Under low shear, complex lobe and striation segregation patterns occur through stretching and folding due to surface avalanching. This leads to enhanced initial mixing rates in a manner consistent with spontaneous chaotic granular mixing. At high-shear rates, segregation is controlled by the rotation of the blades. As a result, coarse particles have a tendency to migrate both to the free surface and the outer wall independently of initial bed loading conditions.     

Numerical investigation of coarse powder and air flow in an electrostatic powder coating process

The work presented here reports on the numerical simulation of an electrostatic powder coating process that uses a commercial computational fluid dynamic code, FLUENT v6.1. The purpose of this study was to understand the gas and particle flow fields inside a coating booth under given operating conditions and the effect of particle sizes on its trajectories and the final coating quality. The air and powder particle flows in a coating booth were modeled as a three-dimensional turbulent continuous gas flow with solid particles as a discrete phase. The continuous gas flow was calculated by solving Navier-Stokes equations including the standard k − ε turbulence model with non-equilibrium wall function and the discrete phase was modeled based on the Langrangian approach. Since the solid phase volumetric fraction was less than 0.1%, the effect of particle-particle interaction on particle trajectories was not taken into account. In addition to drag force and gravity, the electrostatic force including the effect of space charge due to the free ions was considered in the equation of motion and implemented using user defined scalars and functions. The governing equations were solved using the second order upwind scheme. Information was provided on the particle trajectories with respect to the particle diameters that could be used to develop suitable operating conditions for the use of fine powders in a powder coating process.     

Lattice Boltzmann simulation of 2D and 3D non-Brownian suspensions in Couette flow

In this study, the Lattice Boltzmann (LB) method is applied for computer simulation of suspension flow in Couette systems. Typical aspects of Couette flow such as wall effects and non-zero Reynolds numbers can be studied well with the LB method because of its time-dependent character. Couette flow of single, two and multi-particle systems was studied, where two-dimensional (2D) systems were compared with three-dimensional (3D) systems.Computations on multi-particle 3D suspensions, for instance to assess the viscosity or shear-induced diffusivity, were found to be very intensive. This was only partly a consequence of the 3D system size. The critical particle grid size, necessary for accurate results, was found to be relatively large, increasing the system to impractical sizes.It is however demonstrated that it is possible to carry out computer simulations on 2D suspensions and use relatively simple, linear scaling relations to translate these results to 3D suspensions, in this way avoiding intensive computations. By doing so, the LB method is shown to be well-suited for study of suspension flow in Couette systems, particularly for aspects as particle layering near solid walls, hydrodynamic particle interactions and viscous stresses at non-zero Reynolds numbers, which cannot be easily solved with alternative methods. It also opens the way to employ the LB method for other unexplored aspects, such as particle polydispersity and high Reynolds number flow, with large relevance to practical processing of suspensions.     

Characterization of powder flow: Static and dynamic testing

Many characterization techniques are available to determine the flow properties of powders; however, it is debated which method(s) are the most appropriate. In this study, sample fine powders with a medium particle size between 22 and 31 µm were characterized using a variety of techniques that tested powders under different stress states, ranging from static to dynamic. It was found that characterization techniques that were more dynamic such as fluidized bed expansion were best suited for predicting the fluidization performance while characterization techniques that were more static such as cohesion were better for predicting agglomeration. It was also found that results from static and dynamic characterization do not necessarily agree, where fine powders that showed good fluidization performance also displayed increased agglomeration, and vice versa. This suggests that flow properties are dependent upon the stress state and that no single technique is suitable for the full characterization of a powder. In other words, both static and dynamic characterization techniques must be employed to completely understand the flow properties of a powder and predict how it will behave under different process conditions.     

Flow dynamics in Taylor–Couette flow reactor with axial distribution of temperature

In this study, the flow dynamics of a Taylor–Couette flow with an axial distribution of temperature was experimentally investigated. The flow can be classified into three patterns based on the balance between the centrifugal force and the buoyancy. If the buoyancy is dominant, global heat convection is observed instead of Taylor vortices (Case I). When the buoyancy is comparable to the centrifugal force, the Taylor vortices and global heat convection appear alternately (Case II). If the centrifugal force is sufficiently high to suppress the buoyancy, stable Taylor vortices are observed (Case III). The characteristics of the mixing/diffusion are investigated by conducting a decolorization experiment on a passive tracer. In Case II, the tracer is rapidly decolorized in the presence of the global heat convection instead of the Taylor vortices. This result implies that the interaction between the centrifugal force and the buoyancy would induce an anomalous transport. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1075–1082, 2018     

The onset of Taylor-Görtler vortices in the time-dependent Couette flow induced by an impulsively imposed shear stress

The onset of Taylor-Görtler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τ _c to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as V _i ∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (V _i =constant). Based on the present τ _c and the Foster’s [1969] comment, the manifest stability guideline is suggested.     

An experimental study of the flow of nonspherical grains in a rotating cylinder

The effect of particle aspect ratio on the rheology of the flow of granular materials is studied experimentally in a quasi–two‐dimensional rotating cylinder, using two varieties of prolate spheroidal grains with different aspect ratios. Image analysis of high speed videos is used to obtain the flow profiles near the centre of the cylinder. The dynamic angle of repose and apparent viscosity in the medium show significant increase with increasing aspect ratio. The mean velocity, root mean square velocity and shear rate profiles are qualitatively similar for nonspherical and spherical particles, however, their magnitudes increase with increasing aspect ratio. A simple scaling is shown to predict the maximum thickness of the flowing layer for all the particles. The predictions of a model for the flow match with the measured mean velocity profiles and layer thickness. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4307–4315, 2017     

Mechanisms of mixing of granular materials in drum mixers under rolling regime

Experimental investigations on mixing of non-ideal powders (granular tetraacetylendiamine (TAED)) are described. The evolution of mixing in rotating batch cylinders, in rolling regime has been addressed. Characterization and quantification of the local mixture composition have been obtained through an efficient solidification technique, coupled with computerized image analysis.Starting from a completely segregated configuration, the formation of a temporary, poorly mixed core at low rotation speed has been observed. Investigation of intermediate configurations during the mixing process allows to identify some unexpected granular mixing mechanism. The observed core has been explained in terms of transient axial convective fluxes superimposed on diffusive motion. Small differences of dynamic angle of repose between the two granular materials have been suggested to drive the axial convection, similarly to the mechanism reported in the literature to explain axial segregation phenomena. The differences in repose angle result from surface and shape irregularities typical of actual (i.e. non-ideal) granules.Convective fluxes due to the friction of powder with the end plates are also identified at the extremities of the mixer. Short-circuiting zones are created that hinder both axial diffusion and convection from the center of the vessel. Eventually, we suggest a mixing mechanism of non-ideal granular material where convection plays a major role.     

Setting the bar for powder flow properties in successful high speed tableting

An inadequate powder flow leads to problems in tablet manufacturing. The knowledge of minimum flow properties required for successful tableting on a high speed press is critically important to the efficient development of pharmaceutical tablets. This may be achieved by identifying a powder that exhibits minimally acceptable flow properties on a high speed tablet press. A grade of a common tablet excipient, microcrystalline cellulose (Avicel PH102) lies near the borderline between acceptable and poor flow regions during high speed tableting. It can therefore serve as a reference material for judging adequacy of flow properties of prototype formulations by the way of comparison. A powder exhibiting poorer flow properties than Avicel PH102 likely exhibits flow problems and should be avoided. An implementation of this simple approach in formulation development can minimize potential flow problems during large scale tablet manufacture.