Fluid dynamics simulation of the high shear mixing process
Introduction
Granulation in high shear mixers is an important unit operation often used in the development and manufacturing of tablets in the pharmaceutical industry. The process comprises a dry mixing step, where the active substances and excipients are mixed together in order to form a homogeneous mixture, followed by a wet mixing step, where binder liquid is added in order to build up agglomerates. Many researchers have focused on agglomeration and breakage mechanisms in the high shear mixer, e.g. Iveson et al. [1] and Reynolds et al. [2]. However, a better understanding of the local mixing and the flow pattern in the granulator is necessary in order to implement the agglomeration and breakage models and to develop quantitative process models that enable predictive scale-up and process optimization. This is highlighted by several authors, e.g. Cameron et al. [3], Faure et al. [4] and Niklasson Björn et al. [5].
The aim of this study is to obtain a quantitative understanding of the flow behaviour of particles in a high shear mixer via fluid mechanics calculations based upon the two-fluid model. The calculated results are compared to the experimental data obtained by Darelius et al. [8] using a high speed camera. In the simulation of fluidized beds, the kinetic theory of granular flow (KTGF), where colliding particles are treated in a similar fashion to colliding molecules in an ideal gas, has been shown to be a promising model for modelling particle–particle interactions (see e.g. van Wachem et al. [6]) and this model is therefore employed here as well. However, for the present flow it is expected that particles will be in sustained contact to a greater extent than in a fluidized bed so that the stresses between particles becomes larger than what is predicted by KTGF. Thus, a frictional stress model is used in combination with KTGF.
Section snippets
The Eulerian–Eulerian approach
In the Eulerian–Eulerian two-fluid approach for modelling multiphase flows, the fluid and dispersed phases are averaged over a fixed volume that is large in comparison with the size of the individual particles. The conservation equations for momentum and mass for the gas phase in a gas–solid flow can be written as (Anderson and Jackson [9])where αg is the volume fraction of the gas, ρg is the gas density, ug is the gas
The high shear system studied
The system considered is a MiPro high shear mixer (ProCept, Belgium) with an inner diameter of 150 mm, a volume of 1900 ml and a three-bladed bevelled impeller. To be able to compare the simulated results with experimental data, the simulated powder was assumed to be mono-disperse and to have properties similar to coarse microcrystalline cellulose (MCC) with particle diameter of 59 μm. Owing to symmetry, it would be possible to model only a third of the tank (a three-bladed impeller), but larger
Experimental
The experiments were performed in the MiPro equipment described in the previous section. MCC (Avicel PH102 special grade, FMC Biopolymer) with a number average diameter of 59 μm was used. A high speed camera with a capacity of 2000 frames per second was used to measure the surface velocities of the MCC powder at the wall of the transparent glass vessel. The experimental procedure is described in detail by Darelius et al. [8]. Laser Doppler Anemometry (LDA) measurements were also performed but
KTGF model
After approximately 50 simulated impeller revolutions, a stable slowly pulsating bed behaviour was observed. This could be observed as a slow fluctuation in the volume fraction and powder velocity. The frequency of the pulsations corresponded to approximately two impeller revolutions and was considered to represent low frequency macro-instabilities, such as the ones described by Kilander and Rasmuson [21] for mixing of liquids in square tanks. Fig. 2 shows the simulated average volume fraction
Conclusions
In this study, the Eulerian–Eulerian two-fluid approach to modelling multiphase flows was applied to the dense gas–solid flow in a high shear mixer. The Kinetic Theory of Granular Flow combined with frictional stress models was used to model the solids phase stress. Different boundary conditions for the solid phase at the vessel wall were used, i.e. the free and partial slip conditions. The partial slip condition that was implemented is a function of the coefficient of wall restitution for the
Acknowledgement
Financial support from AstraZeneca R&D, Mölndal, Sweden is gratefully acknowledged.
References (24)
- et al.
The importance of wet-powder dynamic mechanical properties in understanding granulation
Powder Technology
(2003) - et al.
Breakage in granulation: a review
Chemical Engineering Science
(2005) - et al.
Process systems modelling and applications in granulation: a review
Chemical Engineering Science
(2005) - et al.
Process control and scale-up of pharmaceutical wet granulation processes: a review
European Journal of Pharmaceutics and Biopharmaceutics
(2001) - et al.
Empirical to mechanistic modelling in high shear granulation
Chemical Engineering Science
(2005) - et al.
LDA measurements of near wall powder velocities in a high shear mixer
Chemical Engineering Science
(2007) - et al.
Measurement of the velocity field and frictional properties of wet masses in a high shear mixer
Chemical Engineering Science
(2007) - et al.
Fundamentals of turbulent gas–solid flows applied to circulating fluidized bed combustion
Progress in Energy and Combustion Science
(1998) Instability in the evolution equations describing incompressible granular flow
Journal of Differential Equations
(1987)- et al.
CFD simulation of the high shear mixing process using kinetic theory of granular flow and frictional stress models
Chemical Engineering Science
(2008)
Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements
Chemical Engineering Science
Prediction of impeller torque in high shear powder mixers
Chemical Engineering Science
Cited by (10)
Clean iron removal from zinc leaching solution by shear enhancement: Industrial pilot campaign and strengthening mechanism
2022, Journal of Cleaner ProductionCitation Excerpt :Further study is necessary to improve this process. High-speed shear homogeneous machine, a new type of process intensification equipment, has great advantages in chemical reaction and is widely applied in material preparation, food processing, bio-pharmaceutical, environmental protection, and other fields (Cheng et al., 2021; Darelius et al., 2010; Yang et al., 2018; Zeng et al., 2022). Mehrotra et al. (2007) investigated the influence of shearing speed on blends and tables of lactose and cellulose properties, obtained the flow characteristics of the mixture under a high shear speed, and found that increasing the shearing speed is beneficial to the mixing process.
Continuum modeling of multi-regime particle flows in high-shear mixing
2015, Powder TechnologyCitation Excerpt :According to experimental observations, particles mostly move in a correlated tangential direction, and movements in the axial direction were hardly visible. Similar studies on the same equipment, filled with different materials, have reported a drastic overestimation in simulations of particle movements in the axial direction [3,9]. The mentioned studies applied the traditional formulation of KTGF + friction [15,16] to estimate transport coefficients.
Quality by design for wet granulation in pharmaceutical processing: Assessing models for a priori design and scaling
2013, Powder TechnologyCitation Excerpt :Considerable progress has been made for modeling fluidized bed granulation in this way, as the particle motion in fluidized beds is relatively well understood [17,23–27]. Some progress has been made on modeling high shear wet granulation using this approach [28–34], but this work is proof of concept only, given the challenges of understanding granulation processes and the wet mass flow in the granulator. Thus, these models have significant assumptions and are limited mostly to developing qualitative understanding as opposed to quantitative prediction.
A particle-particle Reynolds stress transportation model of swirling particle-laden-mixtures turbulent flows
2012, Advanced Powder TechnologyCitation Excerpt :This two granular temperature model is used to simulate the segregation of binary mixtures [35]. Because the CPU time necessary to obtain results from discrete particle model can be several orders of magnitude higher than that of corresponding results from the two-fluid model, two-fluid models have been widely applied in the field of practical engineering, such as bubble formation, distribution of time-averaged particle concentration, cluster formation and the time-averaged particle concentration and mass flux distribution in circulating fluidized beds, riser and bubble fluidization bed, etc. [36–41]. To date, as for swirling binary mixture of particles using second-order-moment model, it has never been reported.
Numerical investigation on hydrodynamics of gas-binary particles flows using a second-order-moment turbulent model
2012, Acta AstronauticaCitation Excerpt :At the same time, closure probability-density-function (PDF) transport equations are established and developed [23–28]. Because the CPU time necessary to obtain results from discrete particle model can be several orders of magnitude higher than those of the two-fluid models, two-fluid models have been widely applied in the field of practical engineering, such as bubble formation, distribution of time-averaged particle concentration, cluster formation and the time-averaged particle concentration and mass flux distribution in circulating fluidized beds, riser, bubble fluidization bed, etc. [29–34]. Moreover, an advanced Euler-Lagrangian methods combining the deterministic and stochastic approaches presented by Smirnov et al. [35–37] have been widely used to sedimentation, ignition and porous combustion of turbulent dust-air and atmospheric flows.
110th Anniversary: Continuum Modeling of Granular Mixing in a Rotating Drum
2019, Industrial and Engineering Chemistry Research
- 1
Present address: Epsilon Utvecklingscentrum Väst, Lindholmspiren 9, SE-417 56 Göteborg, Sweden.