Search

The rotary kiln is an essential device in chemical and metallurgical industries, with applications in a wide range of solids manufacturing processes. In particular, in the preparation of industrial chemical catalysts, the kiln has become a popular reactor for continuous calcination of catalysts ranging from millimeter-sized extrudates to micron-sized powders. As granular and powder flow behaviors are difficult to characterize, the design and scale-up of rotary calcination processes are often performed empirically. The goal of this research is to improve the fundamental understanding of powder flow in rotary kilns to aid in optimization of the continuous calcination process. For successful calcination to occur, the residence time of the particles must exceed the time required for heating and subsequent treatment. For uniform treatment of the feed, the particles must also exhibit low axial dispersion. In this work, the mean residence time and axial dispersion coefficient for a cohesive fluid catalytic cracking powder were determined in a pilot plant kiln by measuring the residence time distribution. This study utilized a pulse test developed by Danckwerts. Results were fit to the Taylor solution of the axial dispersion model and compared to the Sullivan prediction for mean residence time. It was found that the mean residence time decreases as the feed rate, kiln incline, and rotation rate increase. It was also found that the axial dispersion coefficient increases with speed of rotation and angle of incline. However, the axial dispersion coefficient decreases as the feed rate is increased.

As the pharmaceutical industry modernizes its manufacturing practices and incorporates more efficient processing approaches, it is important to reevaluate which process design elements affect product quality and the means to study these systems. The purpose of this work is to provide insight on a methodology to correlate the effect of raw material properties to equipment and process performance using both data-driven and semi-empirical models. In this work, lubricated blends of pharmaceutically-relevant materials were made using varying levels of magnesium stearate, ranging from 0.25 to 1.5%. Materials characterization (e.g., compressibility, permeability, density, particle size) was performed for all materials and blends. The blends were compressed using a two by three experimental design, varying tablet fill cam depth and tablet thickness, respectively. Tablet properties (e.g., weight, tensile strength, and thickness) were collected for all tablets. Using the collected tablet property results, models coefficients for the semi-empirical Kuentz and Leuenberger equation, which relates the tablet tensile strength to changes in porosity, were regressed. Empirical models were then developed to correlate the values of the Kuentz and Leuenberger equation coefficients to the blend material properties. The empirical models were then used in conjunction with the Kuentz and Leuenberger equation to evaluate the compression design and operational space, accounting for material properties. This proof of concept work aimed at developing correlations between raw material properties and unit operation models can aid process development, especially in design space characterization and robustness analysis.

This paper provides a method for prediction of weight variability of tablets made in rotary tablet presses as a function of material attributes and processing parameters. The goal was to be able to predict whether or not a formulation is suitable for direct compaction continuous manufacturing using the tablet weight variability as a criterion. The work focused on identifying the significant factors affecting the weight variability in tablets, within the design space studied. A wide range of blends with different powder properties were prepared. It was shown that among powder properties, cohesion, bulk density, and particle size were the most significant and sufficient material attributes to explain tablet weight variability. A response surface model was built and validated with three different blends. The model is not formulation dependent and can be expanded to include other blend properties or processing parameters effects.

Purpose Accurate and consistent delivery of materials by well-designed feeders ensures overall process stability. Importantly, feeding performance is strongly dependent on material flow properties. The purpose of this study is to develop a methodology that identifies predictive correlation between material flow properties and feeder performance. Method The proposed methodology includes techniques to characterize material flow properties, methods to quantify feeding performance of a loss-in-weight feeder, and predictive multivariate analysis. Two approaches to correlate feeding performance and material flow properties were examined in the study: principal component analysis, followed by similarity scoring (PCA-SS), and partial least squares regression (PLSR). Results Experimental results showed that selection of the optimal feeder screw to achieve optimum feeding performance is heavily dependent on material flow properties. Both approaches to predict feeding performance based on material properties were validated. In addition, a strong correlation between the initial feed factor of each material and its flow properties were observed. Conclusion The work presented here has demonstrated an efficient approach to correlate material properties with gravimetric feeder performance. This approach is especially powerful in the early phase of process and product development, when the amount of a material is limited.

While continuous rotary calcination is a widely used thermal treatment in large-scale catalyst manufacturing, the process's heat and mass transfer mechanisms remain a challenge to characterize and to predict. Thus, the goal of this research is to improve fundamental understanding of rotary calcination to aid in the creation of a scientific methodology for process design and scale-up. For successful calcination to occur, the residence time of the particles must exceed the time required for heating and calcination at a set temperature. The optimal residence time therefore depends on both of these competing time scales, each of which is function of feed material properties, kiln geometry and kiln operating conditions. For uniform treatment of the feed, the particles must also exhibit low axial dispersion. In this work, the residence time distribution and axial dispersion coefficient for a dry cohesive fluid cracking catalyst powder were measured in a pilot plant kiln using a tracer study developed by Danckwerts. Results were successfully matched to the Taylor fit of the axial dispersion model and the Sullivan prediction for mean residence time. It was found that an increase in feed rate, kiln incline and rotary speed decreased mean residence time and overall axial dispersion. Such results have been established previously for free-flowing material like millimeter-sized extrudates, but have not been previously reported for the cohesive powders such as the one used in our work. As in free-flowing material, the axial dispersion coefficient was found to vary with kiln conditions. The values of the axial dispersion coefficients were lower for the powder than for free-flowing material, showing a dependency of axial dispersion on material properties as well as bulk flow behavior.

A full factorial design of experiments was used to study the effect of blend shear strain on the compaction process, relative density and strength of pharmaceutical tablets. The powder blends were subjected to different shear strain levels (integral of shear rate with respect to time) using an ad hoc Couette shear cell. Tablets were compressed at different compaction forces using an instrumented compactor simulator, and compaction curves showing the force-displacement profiles during compaction were obtained. Although the die-fill blend porosity (initial porosity) and the minimum in-die tablet porosity (at maximum compaction) decreased significantly with shear strain, the final tablet porosity was surprisingly independent of shear strain. The increase in the in-die maximum compaction with shear strain was, in fact, compensated during post-compaction relaxation of the tables, which also increased significantly with shear strain. Therefore, tablet porosity alone was not sufficient to predict tablet tensile strength. A decrease in the ‘work of compaction’ as a function of shear strain, and an increase in the recovered elastic work was observed, which suggested weaker particle-particle bonding as the shear strain increased. For each shear strain level, the Ryskewitch Duckworth equation was a good fit to the tensile strength as a function of tablet porosity, and the obtained asymptotic tensile strength at zero porosity exhibited a 60% reduction as a function of shear strain. This was consistent with a reduced bonding efficiency as the shear strain increased.

Modeling conductive heat transfer from rotary drum walls to a particle bed via discrete element method simulations, three time scales were determined: 1) the characteristic heating time of the bed, τ; 2) the particle thermal time constant, τp; and 3) the contact time between a particle and the wall, τc. Results fall onto a monotonic curve of τ/τc vs. ϕ (τp/τc), with three heating regimes. At low ϕ, conduction dominates, and the system heats quickly as a solid body. At high ϕ, granular convection dominates, and the bed heats slowly at a nearly uniform temperature. At intermediate ϕ, the system heats as a cool core with warmer outer layers. The results of this work have important implications for improving the design and operation of rotary drums (e.g., energy-intensive calcination processes). By calculating τp and τc from material and operating parameters, the characteristic heating time, τ, can be predicted a priori.

Purpose The shear cell test has been widely used to characterize flow properties of powders and granular materials. The purpose of this study is to address the gap between the extensive usage of the test and the limited methods available to analyze the data, and to introduce methodologies for comparing results for different initial consolidation stresses, materials, and testing devices. Method A library of shear cell data was established. Forty-one powders were included, and each material was tested under four different initial consolidation stresses. For each initial consolidation stress, 3 sampling replicates were performed. Results A dimensionless cohesion, C*, was defined as the cohesion divided by the initial consolidation stress. By identifying a correlation between the flow function coefficient (ffc) and C*, the effects of the initial consolidation stress and the testing device were separated. In addition, by identifying a mathematical correlation between the unconfined yield strength and the cohesion, the yield loci from different initial consolidation stresses could be collapsed into a single material characteristic line, enabling one to characterize each material by a single number (the characteristic slope). This approach can be used to economically compare different materials, or different testing devices. Conclusion The proposed method augments shear cell data analysis and significantly reduces the complexity of the shear cell data.

Rotating drums are encountered in numerous industrial applications, including blenders, rotary calciners, impregnators, coaters, granulators, and cement mixers. In all of these devices, the rotation of the drum is used to engender mixing of the granular material in the radial direction. Axial mixing, because of its significantly lower rate, can also have an impact on the process performance, especially when control of residence time is important. Typically, the particle dynamics in rotating drums are quantified as a function of process conditions, such as rotation speed, fill level, and cylinder size. Particle properties are also important, but previous studies have largely been limited to the effects of particle size. In this work, the quantification of the axial particle dynamics has been expanded to include the effect of bulk flow properties by studying a number of cohesive powders. Fick's second law was found to describe the axial dispersion behavior of cohesive particles. Therefore, changes in behavior can be characterized using the axial dispersion coefficient. The effect of material flow properties was found to be statistically significant; the flowability of the material (as measured using bulk flow properties) correlated significantly to the axial dispersion coefficient. Partial least squares was used to determine that 95% of the variation observed in the axial dispersion coefficient measurement can be explained using particle size, compressibility, and shear cell measurements.

This paper compares the micro-mixing dynamics of three active pharmaceutical ingredients (APIs) varying in particle size, bulk density and cohesion. Chlorpheniramine maleate, acetaminophen and caffeine, in a common blend of excipients, were used in this study. Micro-mixing was studied in a 1-L bin-blender using in-line near infrared chemical imaging (NIR-CI) to monitor the aggregate size distribution of the APIs and excipients. A science-based calibration chemometric method was used to calculate the concentration maps of ingredients in the blends. Chlorpheniramine maleate, smallest in particle size with lowest bulk density, resulted in the highest relative standard deviation (RSD) for all concentrations. The RSDs obtained for acetaminophen and caffeine were similar and dependent on their concentrations. Chlorpheniramine remained in large aggregates throughout the blending process. Overall, other ingredients (e.g. Avicel) required longer blending times to become well dispersed in the presence of chlorpheniramine maleate, as evidenced by the aggregate size measurements. This in-line NIR-CI technique was able to approximate the number of API aggregates and their size during a common blending process. Although further development of this technique is necessary, metrics measured using this technique could potentially be used as a critical quality attributes during pharmaceutical processing.

Accurate assessment of tablet content uniformity is critical for narrow therapeutic index drugs such as phenytoin sodium. This work presents a near-infrared (NIR)-based analytical method for rapid prediction of content uniformity based on a large number of phenytoin sodium formulation tablets. Calibration tablets were generated through an integrated experimental design by varying formulation and process parameters, and scale of manufacturing. A partial least squares model for individual tablet content was developed based on tablet NIR spectra. The tablet content was obtained from a modified United States Pharmacopeia phenytoin sodium high-performance liquid chromatography assay method. The partial least squares model with 4 latent variables explained 92% of the composition variability and yielded a root mean square error of prediction of 0.48% w/w. The resultant NIR model successfully assayed the composition of tablets manufactured at the pilot scale. For one such batch, bootstrapping was applied to calculate the confidence intervals on the mean, acceptance value, and relative SD for different sample sizes, n = 10, 30, and 100. As the bootstrap sample size increased, the confidence interval on the mean, acceptance value, and relative SD became narrower and symmetric. Such a ‘large N’ NIR-based process analytical technology method can increase reliability of quality assessments in solid dosage manufacturing.

A novel manufacturing strategy based on continuous processing integrated with online/inline monitoring tools coupled with an advanced control system is highly desired for efficient Quality by Design (QbD)-based pharmaceutical manufacturing. A control system ensures the predefined end product quality, satisfies the high regulatory constraints, facilitates real time release of the product, and optimizes the resources. In this work, a systematic framework for the onsite design and implementation of the control system in continuous tablet manufacturing process has been developed. The framework includes a generic methodology and supporting tools through which the control system can be designed at the manufacturing site and can be implemented for closed-loop operation. The control framework has different novel features such as the option to run the plant in closed-loop (MPC/PID), open-loop and simulation mode. NIR sensor, an online prediction tool, a PAT data management tool, and a control platform have been used to close the control loop.

The present study introduces a new in situ near-infrared chemical imaging technique (imMixTM) designed to characterize micro-mixing in pharmaceutical powder blends. The technique uses in-line, non-contact monitoring of the blending process, eliminating the bias introduced by commonly used powder sampling techniques. A Science-Based Calibration (SBC) chemometric method, which uses pure component spectral data to create a calibration model, was used to create concentration maps of the blends studied here. The advantage of SBC over the alternative Partial Least Squares (PLS) or Principal Component Analysis (PCA) calibration methods is that it does not require a large number of samples to create a calibration. The imMix system proved to be useful in monitoring the spatial distribution and aggregate sizes of acetaminophen, used as the model drug, and of excipients in the blends. Using a 1-l bin-blender, measurements were able to detect changes in the constituents and other experimental parameters as a function of blending time. Such measurements can be used to determine the mixing time and shear requirements of blends during product and process development.

This paper focuses on two aspects of continuous powder mixing, namely characterizing the effects of material properties on the bulk powder flow behavior, and developing continuous blending strategies suitable for cohesive materials. The relative effects of process parameters and material properties on the bulk powder flow behavior were analyzed by performing a PLS analysis of the output parameters, including mean residence time, and axial dispersion coefficient as a function of input parameters (impeller speed, flow rate, bulk density and cohesion). The mean residence time was primarily affected by the bulk density and impeller speed, whereas the axial dispersion coefficient was affected by impeller speed and cohesion. Based on previously developed knowledge of mixing performance as a function of process parameters [1] , a design rule to select the optimal number of impeller passes based on the bulk density was proposed. Impeller speed and cohesion showed a significant interacting effect on the output variable, the axial dispersion coefficient. Increase in cohesion leads to increase in the axial dispersion coefficient at higher impeller speeds, whereas a negligible effect of cohesion on the axial dispersion coefficient was observed at lower impeller speeds. In the second part of the paper, a continuous blending methodology for blending cohesive materials was demonstrated. Considering the feeding limitations of cohesive materials, and limitations in the application of shear in the bladed continuous mixer, a combination of high shear and low shear mixing with high-shear mixing as a first step exhibited an optimal mixing strategy.

Reduced-order modeling (ROM) techniques are playing a very significant role in the recent literature bridging the gap between computationally expensive simulators and their application in optimization and control of distributed parameter systems. In modeling of solid-based processes, Discrete Element Method (DEM) is a very popular high-fidelity modeling approach which enables the tracking of discrete entities as they are processed inside complex geometries interacting with each other and with process boundaries. However, the computational cost of DEM models limits their applicability to simulation of specific and limited number of cases. In this work, we develop the DE–ROM (Discrete Element–Reducer-order model) approach which reduces the computational cost—while maintaining model accuracy—of expensive DEM models. The proposed methodology is based on Principal Component Analysis (PCA), combined with surrogate-model mapping and data imputation for the cases where there is missing information. The results of the application of the developed method to the powder mixing process, demonstrate that the DE–ROM model produces accurate profiles of distributed particle properties in real time. Finally, the developed model is used for the identification of the optimal design and operating conditions of the mixing process.

Near infrared spectroscopic (NIRS) calibration models for real time prediction of powder density (tap, bulk and consolidated) were developed for a pharmaceutical formulation. Powder density is a critical property in the manufacturing of solid oral dosages, related to critical quality attributes such as tablet mass, hardness and dissolution. The establishment of calibration techniques for powder density is highly desired towards the development of control strategies. Three techniques were evaluated to obtain the required variation in powder density for calibration sets: 1) different tap density levels (for a single component), 2) generating different strain levels in powders blends (and as consequence powder density), through a modified shear Couette Cell, and 3) applying normal forces during a compressibility test with a powder rheometer to a pharmaceutical blend. For each variation in powder density, near infrared spectra were acquired to develop partial least squares (PLS) calibration models. Test samples were predicted with a relative standard error of prediction of 0.38%, 7.65% and 0.93% for tap density (single component), shear and rheometer respectively. Spectra obtained in real time in a continuous manufacturing (CM) plant were compared to the spectra from the three approaches used to vary powder density. The calibration based on the application of different strain levels showed the greatest similarity with the blends produced in the CM plant.

While continuous powder mixing has been an area of active research in recent years, effects of operating conditions on the mixing performance has not been well understood yet. Based on our previously developed periodic section modeling ( Gao et al., 2012 ), this paper examines the effects of operating conditions on two significant parameters of the continuous blending processes: axial velocity and local mixing rate of the mixture. Four mixing cases differing in particle size, density and cohesiveness are simulated. Results show that when the local mixing rate improves at low fill levels and high blade speed, particles also move faster in the axial direction and reside for a shorter time inside the mixer. This trade-off between ascending local mixing rate and descending residence time indicates a non-optimal overall blending performance even when the best operating condition is applied. Based on these results, strategies that can further improve the blending performance are performed, which are proposed by increasing the blade speed while keeping a constant axial velocity. These strategies guarantee that the variance decay rate along the mixing axis is proportional to the blade speed in continuous blending processes. Dramatic improvements are observed when these strategies are applied, which shows the merit of this work on design and optimization of continuous power blending processes.

A combination of analytical and statistical methods is used to improve a tablet coating process guided by quality by design (QbD) principles. A solid dosage form product was found to intermittently exhibit bad taste. A suspected cause was the variability in coating thickness which could lead to the subject tasting the active ingredient in some tablets. A number of samples were analyzed using a laser-induced breakdown spectroscopy (LIBS)-based analytical method, and it was found that the main variability component was the tablet-to-tablet variability within a lot. Hence, it was inferred that the coating process (performed in a perforated rotating pan) required optimization. A set of designed experiments along with response surface modeling and kriging method were used to arrive at an optimal set of operating conditions. Effects of the amount of coating imparted, spray rate, pan rotation speed, and spray temperature were characterized. The results were quantified in terms of the relative standard deviation of tablet-averaged LIBS score and a coating variability index which was the ratio of the standard deviation of the tablet-averaged LIBS score and the weight gain of the tablets. The data-driven models developed based on the designed experiments predicted that the minimum value of this index would be obtained for a 6% weight gain for a pan operating at the highest speed at the maximum fill level while using the lowest spraying rate and temperature from the chosen parametric space. This systematic application of the QbD-based method resulted in an enhanced process understanding and reducing the coating variability by more than half.

A computational study using the discrete element method was performed to study the effect of pan speed, fill level and the design of the spray pattern on the coating variability of tablets coated in a rotating pan. The method simulates the movement of tablets in the pan and calculates the residence time of each tablet inside the spray zone, which is directly related to the amount of coating received by the tablet. The computational method was experimentally validated using a Laser Induced Breakdown Spectroscopy based analytical method. The simulations showed that the axial mixing was the most critical parameter affecting the coating variability. Although axial mixing was found to be better at higher pan speed, it did not affect the coating variability significantly. Lower variability was obtained when a 100% fill level was used as compared to 67% fill. Four spray patterns were used, two idealized (full surface spray and a symmetric band spray) and two realistic (5-ellipse and 5-circular spray guns). The full and band spray showed similar results while the ellipse and circular patterns were similar to each other (and much worse than the other two patterns) at all speeds and fill levels.

Previous experimental and computational work has demonstrated that the geometry of the impeller has a significant effect on the mixing performance of continuous powder mixers. In particular, different blade patterns using either all blades pushing the powder forward (‘forward pattern’) are less effective than patterns where some of the blades push the powder backwards (‘alternate pattern’). In this article, we use Discrete Element Method to investigate this issue, as well as to examine whether batch mixers can be used to estimate the cross-sectional mixing rate of continuous mixing process. Mixing and flow of particles are examined in simple geometries consisting of a cylindrical cross-section agitated by impellers. In these geometries, blades are designed ‘forward’ and ‘alternate’ to study different blade patterns. Periodic boundary conditions are used to approximate an idealised cross-section of a continuous mixer. In addition, to examine whether an experimentally realisable batch system could be used to validate these cross-sectional simulations, we examine mixing in geometries with solid end walls. Performance in these elemental systems is compared qualitatively in terms of radially averaged velocity vectors, and quantitatively in terms of the mixing rate and the fill level profile. Results show that end walls and symmetric blade pairs of the ‘alternate’ blade patterns lead to faster mixing. Non-symmetric elemental systems display both increased fill level uniformity and similar mixing performance for both blade patterns. Results demonstrate the need for caution when attempting to use batch mixing information to estimate the cross-sectional mixing rate of continuous powder mixers.

Continuous powder mixing is an efficient alternative in high volume manufacturing of powder-based products. A new method is communicated in this paper to determine the effects of different operating conditions and mixer configurations on mixing performance. The main idea of the proposed methodology is the utilization of experimental residence time distribution (RTD) measurements to (a) determine the contributions of feeding variability, powder segregation and RTD variability on output composition variance and (b) develop a predictive model of the output variance of a continuous mixer. The method is illustrated using experimental data for mixing acetaminophen and lactose in convective continuous mixer.

In this paper, we examine the movement of particles within a continuous powder mixer using PEPT (Positron Emission Particle Tracking). The benefit of the approach is that the particle movement along the vessel can be measured non-invasively. The effect of impeller rotation rate, powder flow rate, and powder cohesion on the particle trajectory, dispersive axial transport coefficient, and residence time is examined. Increase in the impeller rotation rate decreased the residence time, increased the axial dispersion coefficient, and resulted in longer total path length. Effect of flow rate was different at two different rotation rates. At lower rotation rate, increase in flow rate increased the residence time, decreased the axial dispersion, and resulted in longer total path length. At higher rotation rate, increase in flow rate decreased the residence time, increased the total path length and showed a complex dependence on the axial dispersion coefficient. Increasing cohesion (measured using the flow index, dilation, and the Hausner ratio) did not affect the axial dispersion coefficient significantly, but had significant effects on the total particle path length traveled and the residence time. These results, relevant to pharmaceutical powders, provide better physical understanding of the influence of operating parameters on the flow behavior in the continuous mixer. In addition, one of the main obstacles of modeling continuous mixing of particles is to know the appropriate values for the modeling parameters as well as validate modeling approaches. One example is the dispersion coefficient which leads to an analytical solution for the axial dispersion model of a continuous blending process.

A non-destructive NIR spectroscopic method was used to acquire on-line spectra of a continuous mixing process, and evaluate the performance of this novel system. Partial least squares (PLS) calibration models were developed and used for real-time determination of active ingredient concentration on the blends produced with a continuous mixer. The NIR method was developed for concentrations ranging from 0 to 15% (w/w) of acetaminophen (APAP), the active pharmaceutical ingredient used in the experiments. The calibration model's overall accuracy was 0.41% (w/w), and estimated through the root mean square error of cross validation (RMSECV) for samples predicted using leave-class-out cross validation. In this cross validation, each concentration was defined as a class, and when a sample of a specific concentration was predicted all samples of that concentration were left out of the calibration model. The precision of the calibration model was also estimated at various concentration levels, to facilitate the differentiation between the variation in drug concentration due to the analytical method's measurement uncertainty and the variation in the drug distribution throughout the powder blend. The results obtained are very promising since in three of the five powder mixes, the variation in the drug concentration in the powder blends was similar to that of the analytical method indicating a high degree of blend homogeneity

Objective: The purpose of this study was to investigate the effect of mechanical shear on hydrophobicity of pharmaceutical powder blends as a function of composition and particle size, and to determine the impact on drug release from tablets. Methods: Four powder formulations were subjected to three different shear strain conditions (40 rev, 160 rev, and 640 rev) in a controlled shear environment operating at a shear rate of 80 rpm. A total of 12 blends were tested for hydrophobicity. Subsequently, sheared blends were compressed into tablets at 8 kN and 12 kN in a rotary tablet press. During tablet compression, powder samples were collected after the feed frame and their hydrophobicity was again measured. Results: Results indicated that increase in shear strain could significantly increase hydrophobicity, predominantly as an interacting function of blend composition. Blends with both colloidal silica and magnesium stearate (MgSt) were found to show higher hydrophobicity with shear than other blends. Additional shear applied by the tablet press feed frame was found to change the powder hydrophobicity only in the absence of MgSt. Conclusions: Studies showed that the drug release rates dropped with shear more for the blends with both colloidal silica and MgSt than the other blends. Furthermore, the rate of drug release dropped with a decrease in particle size of the main excipient. Surprisingly, the relationship between the relative increase in hydrophobicity and a corresponding drop in the drug release rate was not found when either MgSt or colloidal silica was mixed alone in the blends.

This communication empirically correlates flow in two systems; an instrumented rotating drum (GDR) and a set of bench scale hoppers. A flow index obtained from measurements in the GDR is directly correlated to the flow through hoppers, providing a predictive method for hopper design and a convenient experimental test for screening materials and determining their suitability for specific hopper systems. Simulations were performed to understand the dynamics of flow in hoppers by using the same flow parameters in hoppers and rotating cylinders. Simulations showed that as cohesion increased it becomes harder for the particles to flow through the hoppers, in good agreement with the experiments. The effect of hopper angle also yields similar findings to experiments for Avicel, K =60, where the powder does not flow through the 45° hopper but flows well in a 75° hopper. Simulations were also used to calculate the normal forces on the walls of the hopper and the wall pressure distributions in both hoppers. As depth increases, the wall pressure increases for all cases. Finally, the simulations also helped understand the different flow behaviors (funnel and mass flow) that take place in a hopper. The simulated dynamics of flow in the rotating drum and in the hopper correlate very closely to experiments, indicating that the model cohesion parameters are, as desirable, material-specific but independent of geometry.

The problem of the Andersen cascade impactor data inversion is studied using the maximum entropy method to recover the particle size distribution function from a set of measured masses collected on the impactor stages. The classical entropy maximization and its modification to accommodate data errors are reviewed using the techniques of convex optimization. Numerical experiments were performed to test the method on several unimodal and multimodal distributions commonly observed in practice. The Maximum Entropy Method for data inversion produced excellent agreement between the recovered and test Particle Size Distribution Functions without the need for a priori assumptions.

Laminar flow structure and mixing patterns in stirred tanks with eccentrically located impellers is examined using tracer visualization techniques and laser induced fluorescence (LIF). The displacement of the shaft from the centerline of the tank has a remarkable effect on the manifold structure of the flow: segregated regions of regular motion observed in concentric systems are destroyed, impeller mid-plane separatrices are eliminated, and the axial circulation is greatly improved even in systems agitated even by radial impellers. On examine par des techniques de visualisation par traceurs et la fluorescence laser (LIF) la structure de l'ecoulement laminaire et les modeles de melange dans des reservoirs agites munis de turbines decentrees. Le deplacement de l'axe de l'agitateur par rapport a l'axe central du reservoir a un effet notable sur la structure d'ensemble de l'ecoulement : les regions isolees a mouvement regulier observees dans les systemes concentriques sont detruites, les separatrices au plan median de la turbine sont supprimees et la circulation axiale est grandement amelioree meme dans des systemes agites par des turbines radiales.

This communication correlates two empirical methods; flow in a rotating drum with flow in bench scale hoppers. The flow characteristics of 13 cohesive granular materials were studied in the gravitational displacement Rheometer (GDR) and compared to flow in hoppers of varying angle and discharge diameter at fixed temperature and moisture conditions. The GDR proved to be an effective and convenient tool for examining flow properties of pharmaceutical materials, both pure and mixtures. A flow Index obtained from GDR measurements is directly correlated to the flow through hoppers, providing a predictive method for hopper design and a convenient experimental test for screening materials and determining their suitability for specific hopper systems. Analysis of industrial scale hoppers will be addressed in future communication.

Mammalian cells are extremely sensitive to mechanical stress. Ideally, a bioreactor design for mammalian cell culture should assure adequate mixing at low mechanical stress. This paper focuses on the mixing characterization of a novel stirred tank bioreactor configuration, proposed for the culture of mammalian cells, based on the principle of displacing the agitation shaft to an eccentric position and replacing the impellers normally used for mammalian cell culture with a disc impeller with no blades. Experiments in a 1.0 L prototype are conducted to study flow patterns using UV light visualization techniques. Three different impeller shaft positions are tested E = 0.0 , 0.21 , and 0.42. For the purposes of this work, eccentricity ( E ) is defined as the distance between the shaft and the vertical centerline of the tank/tank radius. The mixing performance of two different impeller disc diameters (3.0 and 5.0 cm) are compared. Experimental results show that adequate mixing conditions are achieved at very low Re numbers for some of the eccentric cases considered. Computations are used to illustrate mixing improvement caused by eccentricity, and to validate the existence of globally chaotic conditions for the eccentric cases tested experimentally.

Heat transfer in particulate materials affects a wide variety of applications ranging from multi-phase reactors to kilns and calciners. In catalyst manufacturing, heat transfer through granular media (catalyst) occurs in the impregnation and calcinations stages. We use the discrete element model to simulate flow, mixing, and heat transport in granular flow systems in rotary calciners and impregnators. Granular flow and heat transport properties are taken into account in order to develop a fundamental understanding of their effect on dryer and calcination performance. Simulations have shown that as rotation speed decreases, both heat transfer and temperature uniformity of the granular bed for both calciner and impregnator increase. Depending on baffle size, baffles can either increase or decrease heat transfer in double cone impregnators. Granular cohesion does not affect heat transfer in the range of values examined.

Mixing of shear-thinning fluids with yield stress is investigated in a three-dimensional (3-D) flow both in experiments and in simulations. Experiments are conducted in a stirred tank using tracer visualization and velocity measurements. Bulk flow visualization shows the familiar cavern formation around the impeller with stagnant zones surrounding it. Detailed flow visualization inside caverns reveals the main ingredients of chaotic flow: lobe formation, stretching, folding, and self-similar mixing patterns. For multiple impeller systems, however, we find strong compartmentalization characterized by robust segregation between adjacent caverns, hindering mixing performance. Mixing efficiency is enhanced by moving the shaft off-center, which breaks spatial symmetry. The displacement of the shaft from the tank centerline has a beneficial effect on manifold structure: segregated regions are destroyed, separatrices are eliminated, and axial circulation is improved. Numerical simulations are performed by solving the incompressible Reynolds Averaged Navier Stokes equation with a Galerkin Least-Squares finite-element formulation and a macroscopic rheological model. Simulations are able to capture the main features of the flow and are used to investigate stretching statistics and scale behavior. © 2006 American Institute of Chemical Engineers AIChE J, 2006

The mixing performance of a batch stirred tank with four Ekato Intermig® impellers is investigated in this paper by experimental and computational methods. We considered three impeller speeds corresponding to Reynolds numbers 37, 50 and 100, all in the laminar regime. For the purposes of model development and flow validation, Newtonian rheology is assumed, where the fluid density and viscosity is set to 1247.6 kg/m 3 and 0.4 kg/(m s) , respectively. The computed velocity field and mixing patterns are validated using Particle Image Velocimetry, acid-base visualization experiments and Planar Laser-Induced Fluorescence. All three techniques reveal excellent agreements between the experiments and computations. Also, detailed Lagrangian analysis of mixing, using particle tracking and stretching simulations, is presented for two flowrates in the laminar regime. It is shown that severe compartmentalization exists in the vessel and transport in the axial direction is very slow. Characterization of local micromixing intensities is presented by computing the distribution of intermaterial area density and striation thickness distribution (STD) from the stretching field. It is found that the STDs at both flowrates are identical despite significant differences in the stretching field, suggesting that at low stirring rates micromixing performance is independent of agitation speed.

Using visualization techniques, including acid/base reactions and UV fluorescence, we provide experimental evidence of segregated regions (islands) during mixing of viscous Newtonian fluids under laminar flow conditions in continuous stirred tank reactors (CSTRs). The effect of inlet/outlet stream position and Reynolds number on the dynamics of the mixing processes is examined. Numerical experiments in 3-D map were able to capture the main features of the CSTR flow by perturbing a Batch system using an imposed axial flow. Asymmetric flow patterns produced by off-center positioning of inlet and outlet pipes cause a reduction in size of the segregated region, enlarging the chaotic region and leading to more efficient mixing. Under dynamic inlet flow conditions, the laminar steady flow is perturbed, giving rise to an asymmetric flow pattern that is able to destroy toroidal segregated regions. Counter-intuitively, higher agitation speed (higher Re) did not enhance overall mixing efficiency. Faster agitation stabilized the toroidal regions, making it harder to destroy them. In addition, dynamic mixing protocols are investigated to enhance mixing performance. We demonstrate that time-dependent pumping and stirring protocols are able to efficiently destroy long-lasting toroidal regions.

We report that the formation of much reported axial segregation bands in rotating cylinders loaded with different sized particles depends critically on scale and inertia. Specifically, when the ratio, δ, of the diameter of the cylinder to the average diameter of the particles is large, axial bands invariably appear, when δ is small, bands never appear, and between these extremes lies a reversible state where the presence or absence of bands depends on container rotation speed. Our results indicate that banding is associated with a Rayleigh-like instability of a granular core of fine particles, and that this instability is controlled by the inertia of the larger species – and consequently on scale.

A detailed Lagrangian analysis of partially mixed structures in an SMX static mixer is presented, with emphasis on laminar flows with Reynolds numbers between 1 and 100. The distribution of a small amount of equal-viscosity additive is examined based on computing the trajectories of passive tracer particles through the mixer. Three radial positions (one centerline and two off-center) are chosen for injection and the mixing patterns are compared in order to investigate the effect of injection location on mixing. Mixing measures, such as the decrease in the variation coefficient with axial distance, and the increase in the average rate of stretching, are discussed in order to quantify mixing performance. It is found that mixing rates for the centerline injections are larger than for the off-center injection positions investigated. The presence of self-similarity in the stretching field and the mixing patterns, and the exponential decrease in variation coefficient with increasing axial distance provides evidence for chaotic mixing behavior in this device.

We report several segregation patterns in V-blenders partially filled with mixtures of glass beads differing in size. Three dominant patterns are found, including one in which larger and smaller particles migrate to opposite halves of the blender. Changes in the rotation rate by as little as 3% can cause a change of pattern. Analysis of particle pathlines suggests that segregation in this vessel may be dominated by ‘trajectory segregation’, i.e. the inability of larger, more inertial, particles to navigate sharp bends in pathlines.

We present experimental and computational analyses of three-dimensional chaotic laminar mixing in one of the most widely utilized mixing devices, the stirred tank. We 7nd that 98% of the power expended in mechanical stirring produces no detectable mixing at all, and in fact convective mixing is generated solely by tiny perturbations to a dominant non-chaotic :ow. By analyzing the role of these perturbations, dramatic improvements in performance are easily achieved: for example, minor judicious, changes in agitator design produce order of magnitude improvements in mixing e>ectiveness. ? 2002 Elsevier Science Ltd. All rights reserved.

The blending performance in a resonant acoustic mixer (RAM) was characterized. The system showed to be highly effective in blending low concentrations of cohesive active pharmaceutical ingredients (APIs) and lubricants. A summary of these results will be described and changes in material properties were observed. Those changes, and their effects on tablet characteristics, were also studied. Changes in particle size, powder flow properties, and hydrophobicity of the blend were investigated. Tablets were then compressed, using a tablet press simulator, and characterized. The tableting compression force, tablet hardness, tablet weight, and tablet dissolution were considered. Results indicated that the powder blend material properties and tablet characteristics were significantly affected by acceleration (mixing intensity), blending time, and thus, total energy input. The RAM was shown to be an excellent choice for blending low concentrations of cohesive APIs, but care must be taken when blending hydrophobic lubricants because the high-energy input can adversely affect the final tablet properties such as hardness and dissolution. In addition, the material properties of the blends and tablets were correlated to the total energy input. These correlations demonstrated that total energy, in the RAM, determines, and can be used to predict, the performance of final blends and finished product.

Mixing in an unbaffled stirred tank equipped with a 6-blade radial flow impeller is examined computationally. Results demonstrate that the flow generated by constant impeller speed is partially chaotic. Under these conditions, the stretching experienced by fluid elements located within segregated toroidal regions of the flow increases slowly at a linear rate characteristic of regular (non-chaotic) flows. Within the bulk flow region, since the flow is chaotic, stretching increases at the expected exponential rate. The use of dynamic flow perturbations enhances mixing; when time-dependent RPM are applied, a globally chaotic flow is generated. We investigate computationally the effect on mixing performance of protocols in which the agitation speed oscillates between two steady values. Different frequencies of speed change and several RPM settings are compared. Under variable RPM schemes, the segregated torii are periodically relocated and fluid elements have the opportunity to abandon the regular regions. Under these conditions stretching increases exponentially throughout the entire flow domain. In general, mixing protocols with higher frequency of speed fluctuation produce the largest increase in stretching rates. Counter-intuitively, at a given RPM fluctuation frequency, stretching rates were higher for the lower RPM settings, either per revolutions or per unit of energy spent.

We examine the spontaneous formation of numerous previously unreported patterns in deep beds of fine grains vibrated at frequencies ranging from 10 to 100 Hz and accelerations ranging from 1 to 14 times gravity. Similarly to shallow beds, we find stripes, closed cells and labyrinthine patterns. In addition, we observe traveling waves, cannibalizing cells and other behaviors that are unexpected and remain unexplained. All of these patterns vary spatiotemporally, and unlike shallow bed patterns, are harmonic rather than subharmonic.

This paper explores in some detail the spatial structure and the statistical properties of partially mixed structures evolving under the effects of a time-periodic chaotic flow. Numerical simulations are used to examine the evolution of the interface between two fluids, which grows exponentially with a rate equal to the topological entropy of the flow. Such growth is much faster than predicted by the Lyapunov exponent of the flow. As time increases, the partially mixed system develops into a self-similar structure. Frequency distributions of interface density corresponding to different times collapse onto an invariant curve by a simple homogeneous scaling. This scaling behavior is a direct consequence of the generic asymptotic directionality property characteristic of 2D time-periodic flows. Striation thickness distributions (STDs) also acquire a time-invariant shape after a few (∼5–10) periods of the flow and are collapsed onto a single curve by standardization. It is also shown that STDs can be accurately predicted from distributions of stretching values, thus providing an effective method for calculation of STDs in complex flows.

It is by now well established that curvature plays a fundamental role in the description of the topology emerging from the partially mixed structures advected by chaotic flows. This article focuses on the dynamics of curvature in volume-preserving time-periodic flows. Previous work on the subject dealt with the evolution of curvature in the time-continuous framework. Here we derive the dynamical equations for the time-discrete dynamical system associated with the Poincare return map of the flow. We show that this approach allows one to gain more insight into understanding the mechanisms of folding of material lines as they are passively stirred by the mixing process. By exploiting the incompressibility assumption, we analyze dependence on initial conditions (i.e. on the initial curvature and tangent vectors), and discuss under which circumstances the dependence on the initial curvature vector becomes immaterial as time increases. This analysis is closely connected with the properties of an invariant geometric structure referred to as the global unstable manifold associated with the flow system. Direct numerical simulations for physically realizable systems are used to provide concrete examples of the results that arise from theoretical considerations. The impact of this information on the prediction of the behavior of diffusing-reacting mixing processes (e.g. pattern formation and generation of lamellar structures) is also addressed.

This paper demonstrates that the geometry and topology of material lines in 2D time-periodic chaotic flows is controlled by a global geometric property referred to as asymptotic directionality . This property implies the existence of local asymptotic orientations at each point within the chaotic region, determined by the unstable eigendirections of the Jacobian matrix of the n th iterative of the Poincare map associated with the flow. Asymptotic directionality also determines the geometry of the invariant unstable manifolds, which are everywhere tangent to the field of asymptotic eigendirections. This fact is used to derive simple non-perturbative methods for reconstructing the global invariant manifolds to any desired level of detail. The geometric approach associated with the existence of a field of invariant unstable subspaces permits us to introduce the concept of a geometric global unstable manifold as an intrinsic property of a Poincare map of the flow, defined as a class of equivalence of integral manifolds belonging to the invariant unstable foliation. The connection between the geometric global unstable manifold and the global unstable manifold of hyperbolic periodic points is also addressed. Since material lines evolved by a chaotic flow are asymptotically attracted to the geometric global unstable manifold of the Poincare map, in a sense that will be made clear in the article, the reconstruction of unstable integral manifolds can be used to obtain a quantitative characterization of the topological and statistical properties of partially mixed structures. Two physically realizable systems are analyzed: closed cavity flow and flow between eccentric cylinders. Asymptotic directionality provides evidence of a global self-organizing structure characterizing chaotic flow which is analogous to that of Anosov diffeomorphisms, which turns out to be the basic prototype of mixing systems. In this framework, we show how partially mixed structures can be quantitatively characterized by a nonuniform stationary measure (different from the ergodic measure) associated with the dynamical system generated by the field of asymptotic unstable eigenvectors.

The laminar flow structure inside an unbaffled stirred tank generated by a 6-blade radial flow impeller was characterized using flow visualization experiments, particle imaging velocimetry (PIV) experiments, and computational fluid dynamics (CFD) simulations. As expected from a previous study (Lamberto et al., 1996), the dominant flow structures in the system were two ring vortices above and below the impeller. These secondary circulation regions were segregated from the bulk of the flow and, for low impeller Reynolds numbers (5

A parallel-competitive reaction system, A+B 1 →2P and A+B 2 →2W, where A and B 1 are the reactants, B 2 is a reactive impurity, P is the desired product, and W is a byproduct, is simulated in a chaotic flow by solving the differential convection–diffusion–reaction equations. Three different flow conditions are investigated: a predominantly regular system, a globally chaotic flow, and an intermediate case that displays predominantly chaotic behavior but which has four small islands of regular flow. The time evolution and spatial distribution of species concentration depend strongly both on the nature of the flow and on the relative rates of the two reactions. Even in the globally chaotic flow, significant spatial heterogeneity exists throughout the duration of the reactive mixing simulation. Product and waste accumulate in different spatial regions, depending on the relative characteristic times of the two reactions. When the primary reaction is the faster one, waste tends to accumulate in local A-rich regions and the selectivity of product to waste is strongly affected by the degree of chaos in the system. On the other hand, when the side reaction is faster, waste accumulates in segregated regions which have local excesses of B 2 , but mixing has minimal effect on the quantity of waste produced.

There are several types of instabilities in fluid mechanics that lead to spontaneous chaotic mixing and intricate patterns. Classical examples include the Kelvin–Helmholtz instability1,2 in shear layers, the instability of Taylor–Couette flow between rotating cylinders3,4 and the Rayleigh-Benard instability in thermal convection5. More recently, a variety of two- and three-dimensional chaotic mixing phenomena have been observed in other geometries6,7,8,9. Mixing in granular flows10,11, unlike that in stirred fluids, is thought to be diffusive—although periodic forcing has been used to enhance granular mixing12,13, spontaneous chaotic granular mixing has not previously been reported. Here we report the observation of chaotic granular mixing patterns in simple cylindrical tumblers partially filled with fine grains. The patterns form spontaneously when sufficiently fine grains (≲300 µm diameter) are blended. We identify the mechanism by which the chaotic patterns are produced: a periodic stick–slip behaviour occurs in the shear layer separating static and flowing regions of grains. This causes weakly cohesive grains to mix at rates overwhelmingly exceeding those achievable for previously studied11,14 freely flowing grains.