Fluid dynamics simulation of the high shear mixing process

https://doi.org/10.1016/j.cej.2009.12.020Get rights and content

Abstract

The Eulerian–Eulerian two-fluid approach for modelling multiphase flows is used to simulate the flow in a high shear mixer. The results are compared with experimental velocity profiles for the solids phase at the wall in the mixer obtained using a high speed camera (Darelius et al. Chem. Eng. Sci. 62 (2007) 2366).

The governing equations are closed using relations from the Kinetic Theory of Granular Flow (KTGF) combined with a frictional stress model due to Johnson and Jackson and Schaeffer and inter-phase drag due to Wen and Yu. In addition, calculations are presented for a model with a constant particle phase viscosity (CPV). Free slip and partial slip boundary conditions for the solid phase velocity at the vessel wall and the impeller have been utilized.

The results show that the bed height could be well predicted by the partial slip model, whereas the free slip model could not capture the experimentally found bed height satisfactorily. For the KTGF model, the swirling motion of the rotating torus that is formed by the moving powder bed was over-predicted and the tangential wall velocity was under-predicted, probably due to the fact that the frictional stress model needs to be further developed, e.g. to tackle cohesive particles in dense flow. The CPV model gave predictions in good agreement with the experiments for a solids viscosity of 0.1 Pa s and a wall slip parameter of 0.005 m/Pa s. However, for a very low or very high value of the particle phase viscosity and for a high value of the wall slip parameter the agreement with experiments was poor. Interestingly, values of the viscosity that are commonly employed for fluidized beds seem applicable also in the present case.

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])(αgρgug)t+(αgρgugug)=αgP+αgτg¯¯β(ugus)+F(αgρg)t+(αgρgug)=0where 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)

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Present address: Epsilon Utvecklingscentrum Väst, Lindholmspiren 9, SE-417 56 Göteborg, Sweden.

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