Elsevier

Powder Technology

Volume 381, March 2021, Pages 129-140
Powder Technology

Assessment of bi-disperse solid particles mixing in a horizontal paddle mixer through experiments and DEM

https://doi.org/10.1016/j.powtec.2020.11.041Get rights and content

Highlights

  • The performance of a paddle blender comprising bi-disperse particles was studied.

  • The particle number ratio had the most decisive effect on mixing quality.

  • The particle loading arrangement did not play a significant role on mixing quality.

  • The diffusion mechanism was the dominant mechanism in the mixing system.

  • The mixing system has a low segregation tendency for the operating conditions used.

Abstract

In the current study, the mixing of bi-disperse particles in a horizontal paddle mixer was investigated through the sampling experimental technique and discrete element method (DEM). LIGGGHTS software was employed as the DEM solver. A close agreement between the simulation and experimental data was observed. Using the calibrated DEM model, the influence of some operating parameters such as impeller rotational speed, vessel fill level, particle number ratio (rn) and particle loading arrangement on the mixing quality was analyzed. A detailed analysis of this specific type of mixer comprising bi-disperse particles has not been reported in literature. It was found that rn had the most significant effect on the mixing performance. It was also found that the diffusion mechanism was dominant over the convection mechanism and in the cases in which the values of the diffusion coefficients of 5 mm and 3 mm particles were close, the best mixing performance was achieved.

Introduction

The mixing of solid particles is a vital operation in numerous industrial applications such as polymers, food, pharmaceuticals, cosmetics, ceramic, and mineral processing [1]. Powder blending often involves mixing of two or more particle components to a desired degree of uniformity [2]. For instance, in the pharmaceutical industry, tablets with specific compositions are produced from the mixing of particle components with distinct properties (i.e. various sizes, shapes and densities) to a pre-specified degree of homogeneity to satisfy the desired product specification [3]. Particle assemblies involving distinct components however tend to undergo segregation due to differences in the aforementioned physical properties. As a result, processes involving the mixing of particle components with different physical properties becomes a challenging endeavor [3,4]. One of the most commonly encountered types of segregation mechanisms in particle-particle interactions is the sieving mechanism [5,6]. This segregation mechanism occurs when larger particles move toward the upper region of the mixture bed and the smaller particles tend to mobilize toward the lower region of the bed. The particle size difference is reported to be the main contributor to the segregation in particle assemblies [7]. Therefore, choosing a suitable mixer with low segregation tendency is a key step in industries dealing with particle blending.

The application of various non-intrusive and intrusive experimental measurement techniques for the analysis of mixing systems has been reported in literature [[8], [9], [10], [11], [12]]. In general the main advantage of the non-intrusive measurement techniques is that they do not disturb the particle mixture to obtain informatin about the particle position and velocity. The non-intrusive techniques however have some shortcomings. For instance, Particle Image Velocimetry (PIV) and Near-Infrared (NIR) Spectroscopy can only provide experimental data regarding the areas near the mixer geometry or the free surface of bed of material [13]. Therefore, a 3D structure of the mixture cannot be attained by employing these measurement techniques. Other non-intrusive techniques such as Positron Emission Particle Tracking (PEPT) and Electrical Capacitance Tomography (ECT) techniques enable the 3D visualization of particle flow patterns throughout the mixing process. These techniques, however, are costly [14]. Moreover, in the PEPT technique the information about the trajectory of a single tracer particle is recorded to study a mixing system. The tracer acts as a representative of all particles in the mixing system. However, using a tracer may not be sufficient to accurately represent the entirety of the mixer [13]. The use of the ECT technique is also limited to the mixing systems in which the particles have a considerable difference in their permitivity or dielectric constant [14]. Asachi et al. [14] recently reviewed the application of various non-intrusive experimental techniques to analyze the blend uniformity in mixing systems and have summarized the advantages and disadvantages of various experimental measurement techniques in their detailed study. A mixing system can also be investigated by using intrusive measurement methods such as direct sampling [15,16]. Several samples from different regions of the mixture can be taken as representative of the entire mixing system. The main disadvantage of direct sampling is that as the sampler (e.g. a thief sampler) is penetrated into the bed of material it disturbs the mixture and can introduce some errors in the sample composition.

Although the experimental techniques provide valuable information regarding the general behavior of mixing systems, they cannot fully reveal the underlying phenomena happening during mixing. For instance, the current development of experimental techniques does not allow for the quantification of the mixing mechanisms or the magnitude of shear forces acting on particles in a mixing system. Computational simulations on the other hand, have been proven to be effecitve in revealing fundamental data regarding the mechanisms and mixing kinetics of particles which would be complex, time-consuming, costly, and in some cases impossible to achieve through experimental techniques [17]. The Discrete Element Method (DEM) is the most commonly used numerical technique to simulate the flow of granular material [[18], [19], [20]]. In the DEM technique the particle-particle and particle-wall contact forces are calculated in order to obtain the velocity and position of each individual particle within the process [21]. This method has been widely applied in order to examine the mixing peformance of blenders [8,[22], [23], [24]].

Agitated blenders are one of the most industrially relevant mixing systems due to their inherently high operating capacity. An agitated powder blender consists of a stationary vessel (vertical or horizontal) and a shaft (single or twin) which has an agitating device attached to it [4,19,[25], [26], [27]]. Depending on the impeller shape, some common types of this blender include paddle, plow, ribbon, and screw mixers. Numerous experimental and numerical investigations have been carried out on the mixing performance of agitated blenders containing mono-disperse particle mixtures [8,12,13,17,[28], [29], [30], [31], [32], [33]]. However, limited investigations are found in literature focusing on the mixing performance of agitated blenders containing a binary mixture composed of two particle components with different sizes. Zhou et al. [34] examined the flow and segregation of bi-disperse particles in an agitated vertical bladed mixer by using DEM simulations and experiments. The simulation results were found to be in good agreement with the Positron Emission Particle Tracking (PEPT) experimental results retrieved from a mono-disperse system. The effects of impeller rotational speed, particle size, volume fraction and particle density on mixing kinetics and mixing quality were investigated. It was observed that the larger particles collected in the top region of the mixing bed and the smaller particles assembled in the bottom region of the bed. This trend was also reported in other studies conducted by Remy et al. [3] and Alchikh-Sulaiman et al. [1]. It was also reported that as the size or density differences between particles were reduced, the mixing performance was enhanced. In addition, it was shown that the higher impeller speeds resulted in better mixing during the initial stages of the mixing process. The final mixing quality however did not change with variations in the impeller speed. Remy et al. [3] investigated the flow and segregation of bi-disperse and poly-disperse particles in an agitated vertical bladed mixer through DEM and experiments. It was reported that the binary system had the faster segregation occurrence compared to the poly-disperse mixture. Moreover, the authors calculated the Peclet number to determine the mobility strength of particles and the dominant mixing mechanism within the agitated mixer. It was reported that, regardless of the particle size used for the binary system, the dominant mixing mechanism was convection. Alchikh-Sulaiman et al. [1] studied the mixing of bi-disperse, tri-disperse, and poly-disperse particles in a double cone slanted tumbling blender via DEM and experiments. The validated model was utilized to study the effect of particle loading arrangement, particle size, vessel speed and impeller rotational speed on the mixing index. It was concluded that for the bi-disperse mixture the Top-Bottom (TB) particle loading arrangement, 70% vessel fill level, and vessel rotational speed of 45 RPM yielded the best mixing performance. Arratia et al. [35] analyzed the effect of particle loading arrangement and vessel fill level on the mixing of bi-disperse particles in a bin blender through experiments and simulations. It was demonstrated that the TB particle loading arrangement yielded a higher mixing index than the Front-Back (FB) particle loading arrangement. In addition, it was reported that as the vessel fill level was increased from 40% to 80% the mixing efficiency decreased accordingly. Halidan et al. [36] investigated the influence of the particle size ratio (ratio of small particle diameter to large particle diameter), particle density ratio (ratio of light particle density to heavy particle density) and volume fraction of large particle on the mixing behavior of the binary mixtures in a vertically bladed mixer. The authors found that there is an optimum particle size ratio and particle density ratio which can lead to the best mixing performance, at a given volume fraction. They also mentioned that the volume fraction of mixing particles had a decisive influence on the mixing behavior.

The objective of this investigation is to examine the mixing performance of a horizontal agitated paddle blender for a binary mixture composed of particles with a diameter of 3 mm and 5 mm by using DEM simulations and experiments. No such comprehensive study has been reported on this specific type of mixer. Initially the DEM model was validated by comparing the simulation results with experimental data obtained through a common direct sampling method [12,13,15,16]. Subsequently, the validated DEM model was used to perform simulations in order to study the effect of critical operating parameters on the degree of mixing. These parameters included three impeller rotational speeds (i.e. 40, 70, 100 RPM), two vessel fill levels (i.e. 40 and 60%), particle number ratio (rn = Ns/Nl, where Ns is the number of small particles and Nl is the number of large particles) and particle loading arrangement. The Relative Standard Deviation (RSD) mixing index and Segregation Index (SI) were used to evaluate the degree of mixing. In addition, the mixing mechanisms were analyzed by calculating the particle diffusivity and Peclet number obtained from simulations.

Section snippets

Experimental method and setup

The experimental setup in the current study was similar to what was used in our previous studies for the mixing of mono-disperse particles [12,13]. In brief, the setup was made up of three main components: the cylindrical PVC vessel with a diameter of 0.216 m and 0.500 m in length, six PVC paddle impellers arranged in an alternating 90 degree pattern, and a motor equipped with a speed controller. The impellers were mounted on a rotating shaft, which was aligned along the center of the vessel.

Modelling approach

In the current study, the DEM approach was used in order to analyze the mixing performance of a horizontal paddle blender containing bi-disperse particles. Applying the DEM technique the position of each individual particle within simulation domain is tracked by integrating Newton's second law of motion with respect to a specified time-step [1,17,21,40]. In this investigation, LIGGGHTS(R)-PUBLIC v.3.3.1, an open source DEM particle simulation platform was used as the numerical solver [41]. The

Results and discussion

In this section, the DEM model validation is initially discussed. Subsequently, the influence of operational parameters on the mixing performance quantified by RSD and segregation index (SI) is presented. Analysis of the mixing mechanisms is also covered in this section.

Conclusions

The mixing performance of a horizontal agitated blender comprising bi-disperse 3 and 5 mm glass beads particles was studied by the use of the thief sampling technique and discrete element method (DEM). A series of experimental data was used in order to calibrate and validate the DEM model. A good agreement between the DEM results and the experimental measurements was achieved. The performance of the blender due to the variation of the impeller rotational speed (40, 70 and 100 RPM), vessel fill

Nomenclature

    D

    Diffusion coefficient [m2/s]

    e

    Coefficient of restitution [−]

    F

    Force [N]

    G

    Shear modulus [Pa]

    I

    Particle moment of inertia [kg.m2]

    Is

    Segregation index [−]

    K

    Total number of samples [−]

    M

    Torque [N.m]

    m

    Mass [kg]

    mn

    Number of individual granular in each sample [−]

    R

    Particle radius [m]

    Rmixer

    Mixer vessel radius [m]

    Rxx, Ryy, Rzz

    Ratio between the diffusion coefficients of 5 mm and 3 mm particles in different directions [-]

    v

    Particle velocity [m/s]

    v¯

    Averaged particle velocity [m/s]

    xi

    Concentration of one type of

Declaration of Competing Interest

None.

Acknowledgements

The financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

References (50)

  • M. Asachi et al.

    A review of current techniques for the evaluation of powder mixing

    Adv. Powder Technol.

    (2018)
  • T.A.H. Simons et al.

    Characterization of granular mixing in a helical ribbon blade blender

    Powder Technol.

    (2016)
  • F.J. Muzzio et al.

    Sampling practices in powder blending

    Int. J. Pharm.

    (1997)
  • S. Golshan et al.

    Granular mixing in nauta blenders

    Powder Technol.

    (2017)
  • H.P. Zhu et al.

    Discrete particle simulation of particulate systems: a review of major applications and findings

    Chem. Eng. Sci.

    (2008)
  • A. Hassanpour et al.

    Analysis of particle motion in a paddle mixer using Discrete Element Method (DEM)

    Powder Technol.

    (2011)
  • R.K. Soni et al.

    Numerical analysis of mixing of particles in drum mixers using DEM

    Adv. Powder Technol.

    (2016)
  • B. Freireich et al.

    Incorporating particle flow information from discrete element simulations in population balance models of mixer-coaters

    Chem. Eng. Sci.

    (2011)
  • S. Radl et al.

    Mixing characteristics of wet granular matter in a bladed mixer

    Powder Technol.

    (2010)
  • G.R. Chandratilleke et al.

    Effects of blade rake angle and gap on particle mixing in a cylindrical mixer

    Powder Technol.

    (2009)
  • P.W. Cleary et al.

    Assessing mixing characteristics of particle-mixing and granulation devices

    Particuology

    (2008)
  • M. Alian et al.

    Analysis of the mixing of solid particles in a plowshare mixer via discrete element method (DEM)

    Powder Technol.

    (2015)
  • G. Basinskas et al.

    Numerical study of the mixing efficiency of a ribbon mixer using the discrete element method

    Powder Technol.

    (2016)
  • M. Sakai et al.

    Discrete element simulation for the evaluation of solid mixing in an industrial blender

    Chem. Eng. J.

    (2015)
  • J.R. Jones et al.

    Axial mixing in a ploughshare mixer

    Powder Technol.

    (2007)
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