1
Mixing of Solids and case of V-Blender
Kishuk Goyal1, Anshuman Kumar2, Gaurav Singh3
1
Senior undergraduate, Chemical engineering Department, IIT Delhi, goyal95.k@gmail.com
2
Senior undergraduate, Chemical engineering department, IIT Delhi, anshuman053@gmail.com
3
Senior undergraduate, Chemical engineering department, IIT Delhi, grvsingh64@gmail.com
1.
Abstract
The mixing of granular systems such as powders is a fundamental operation, important for a range of
industries including pharmaceuticals, plastics, house-hold products (such as detergents) and food processing. The
quality of products depends on the degree of mixing of their constituent materials. The desired mixing should be
achieved throughout the batch if the mixing is batch operation or it should be same throughout the time if the
operation is continuous. Degree of mixing is obtained from the various samples taken from different places at
different times of the mixer. The locations from which the samples are to be taken depends on the mixer geometry.
The samples taken are analysed for the uniformity individually and then using the methods of statistics the
representation of the whole batch is created. Individual samples are taken from the mixer using mostly the thief
sampling method and then methods like image analysis, FBRM can tell the distribution of particles in the sample. The
next task is to find the mixing uniformity based on the samples obtained. For that task in the literature various mixing
indices are developed, and there is no universal mixing index which is suggested so the user should be able to find
the one depending on his requirements. Mixing indices mostly use variance of the samples for their calculation.
Variance is calculated based on the assumption that the distribution obtained is normal distribution.
Keyword: V-Blender, Mixing, Froude.
2.
Introduction
However, the homogeneity of the final mixture relies on the nature of the mixing procedure used, type of
the mixture as well as handling after mixing. Ideally speaking we want to achieve the random mixing step but any
systematic mixing process is incapable of creating a completely random mixture since the likelihood of it re-ordering
the particles increases with the degree of mixing. Mixing time is also very important variable as both mixing and
demixing happen simultaneously initially with different rates but after some time an equilibrium point is reached
where the mixing and de-mixing mechanisms are in balance and there is a natural cessation of mixing. So if we keep
running the device demixing may dominate after some time and it will deteriorate the quality of the mixture. For
different mixing devices, the equilibrium states will depend on the design of the device as well as the conditions at
which the operations are taking place. In many cases it may not be possible to reach the desired mixing uniformity
fundamentally as the process involves complex flow regions inside the mixer having significant different in
properties, and there may be segregation due to some pattern formation or self-organisation due to the particle
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shape ,size and density. To study the flows in the granular devices is very limited as there is no technology to visualize
the mixing in the mixer itself especially for the large ones so the only option available is to remove the samples and
analyse which has many limitations. But recent advances in discrete element modelling (DEM) have resulted in this
method becoming a useful simulation tool that can provide detailed experimental information which cannot be
observed during experiments. The flow properties of the powders depend on the flow properties of the mixture
which can be obtained from the component properties. The selection of the mixer as well as the type of dominant
mixing mechanism is decided by the properties of the mixture.
Here we are basically focussing on the V-blender which is found to be more efficient in the pharmaceutical
mixing compared to the other mixers. The flow regimes inside the mixer will be discussed along with the
experimental observations such as the effect on the uniformity due to variables such as mixture flow properties,
speed of mixing, size of mixer, loading pattern etc. Scale-up of the V-blender is discussed based on the experimental
scale–up observations and some empirical relations which are used in the industry. A procedure is developed which
is helpful in designing the experiments so that scale up can be done considering the critical variables of importance.
3.
Understanding the Mixing
The phenomenon of mixing is not completely understood but a lot of research has been done about the
mechanisms involved in the mixing. There are a lot of devices available industrially and they can be grouped based
on the mixing mechanism which is predominant inside them. Since mixing strongly depends on the properties of the
materials to be mixed such as their shape, size and density there is a need to understand how these properties affect
the flowability and thus the mixing. The problems associated with the mixing such as agglomeration and segregation
also need to be looked upon and steps should be taken to avoid such problems.
2.1 Mixing mechanisms
There are three main type of mixing mechanisms which regulate the mixing in devices. Though there is no
such device which has only one type of mixing, most of them have either one or two of these three as the dominating
mechanism which decide the rate and quality of the mixing. The three mechanisms of mixing are 2.1.1 Convection
This mechanism arises due to the mixing of materials inside the mixer as large clumps. The motion of the
vessel or the baffles inside the vessel force the material to move in form of clumps. In simple words baffles pick one
large chunk of the materials from one place and put it at another place in the mixer thus leading to convection. The
homogeneity at the macroscopic level is achieved due to the convective mixing. Surface area between the
components is improved due to this mechanism. This mechanism is very fast compared to other mechanisms of
mixing especially the diffusive mixing.
2.1.2 Diffusion
This mechanism is responsible for the mixing at the length scale of the particle in the mixer. This should not
be confused with the molecular diffusion in the fluids which has well defined equations. Rather it arises when the
dense packed material is distributed over the surface by the mixer action and thus developing the new set of particleparticle contact. This method helps to achieve uniformity at the particle size scale so final mixing quality depends a
lot on this mechanism. The mechanism is very slow and takes orders of magnitude more time than the convective
mixing and so it is the rate determining mechanism of the mixing process.
2.1.3 Shear
This mechanism is related to the convection, as clumps of the powder move in convection the velocity
gradient is created between the region of two clumps. This region is called slip zone and here the velocity gradient
is very high. In this region due to high shear strain the breaking of agglomerates take place and also the area of
contact of two group of particles are extended here. This mechanism helps in mixing when the mixture is showing
cohesive properties. But, phenomenon like percolation which cause demixing especially in non-cohesive mixtures
take place in the slip zone.
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2.2 Important component properties
The selection of the mixer as well as mixing quality that can be achieved is mostly determined by the
properties of the individual components such as shape, size, density and flowing properties. In this section the effect
of the shape and cohesiveness is discussed, the effect due to density and the size will be covered in the section of
problems related to the mixing and cohesion section.
2.2.1 Particle shape
The shape of the particle is very important in particle industries as the properties of the final product
depends critically on the shape of the components. For e.g. in pharmaceutical industry the shape of the API (active
pharmaceutical ingredient) governs the rate of dissolving the drug in the body and so is of paramount importance.
Shape of the particle should not change while mixing. The shape vary dramatically with the feed and to account for
that in modelling is daunting task and we have not been able to completely take into account the effect of shape on
mixing for different shapes. Spherical particles have low resistance to shear compared to more angular or blocky
particles. So where the flow regime and mixing patterns for realistic particle assemblies depart significantly from
that of spheres the prediction of the mixing rates correctly is a major problem. For characterising the effects of shape
on particulate flows and microstructures angularity and aspect ratio are important parameters. Angularity leads to
tighter packing as neighbours lose their ability to freely roll over each other. Elongated particles which have high
aspect ratio lead to complicated interlocking of the microstructure and restrict the flow and also generate complex
force network within the system. In order to mimic the flow behaviour of particles of more complex shapes rolling
and sliding friction coefficients are used, but this is unable to account for the many important aspects such as the
packing fraction and the extent of dilation of granular bed in slip zones. Shape plays an important role in determining
packing efficiency, strength of a microstructure, flowability and segregation.
2.2.2 Cohesivity
There are two types of powder behaviour, cohesionless and cohesive. There are different set of problems
faced while mixing these different type of powders. To make the matter more complicated the given powder can
behave as cohesive at some conditions and cohesionless at some other conditions. This can arise either from a spatial
variation of the velocity field in a mixer or from the system containing materials of a range of sizes, densities or
surface properties. Two types of forces compete to decide which type of behaviour a powder is going to show the
forces between the particles and the force of the gravity. If the force of gravity dominates it shows cohesionless
behaviour and if the interparticle forces dominate cohesive behaviour is seen.
2.2.2.1 Cohesionless materials
These are the materials for which the force of gravity dominates the interparticle forces and these have the
tendency to flow freely. The biggest problem in mixing such type of powders is that of the segregation. It has been
seen that large difference in size causes materials to segregate and for the rotating drums the size ratio above 1.2
tend to segregate. Since segregation is main problem for such kind of materials so even after the mixing is complete
special care should be taken so that segregation is avoided during downstream processing and transport. For
cohesionless materials important mixing mechanisms are convective and diffusive, shear mixing which is mainly used
for breaking of agglomerates is largely unimportant for the mixing of such powders. So for the selection of the mixer
for such powders one with the dominant mixing mechanism as convective should be chosen so that the rate of
mixing is fast.
2.2.2.2 Cohesive materials
These are the materials in which the inter-particle forces dominate the force of the gravity and hence the
flow inside the mixers require more amount of the force. These kind of the powders agglomerate while mixing and
the size of agglomerate depends on the relative strength of the interparticle forces over gravity. Shear mixing is very
important for such mixtures to break the agglomerates and the selection of the mixer should be accordingly. Mostly
the mixers for cohesive materials have baffles or rods inside which provide the impact to break the agglomerates.
These are the basic forces responsible for cohesion:
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• Surface tension – Surface tension is significant when there is solid liquid interface considering the solid-solid mixing
it is largely unimportant. But even in solid-solid mixing additives are added and then surface tension should be taken
into account.
• Electrostatic forces – These forces arise when solids are in rubbing contact of each other. They charge each other
via movement of electrons from one species to other and a potential difference is developed between them. But
these forces are magnitudes of order smaller than the der Walls forces.
• Van der Waals forces - The van der Waals forces are related to electromagnetic fluctuation phenomena in solids.
These forces originate when the random movement of electrons on a particle's surface momentarily concentrate to
form dipoles which, in turn, are attracted to other dipoles nearby. The van der Waals forces are only noticeable
when the particles can come sufficiently close together, at separation distances of the order of the size of a molecule,
0.2 to 1 nm. Whilst the gravitational force is proportional to the cube of the particle diameter, the van der Waals
force is proportional to the diameter and, therefore, the magnitude of the attractive van der Waals force becomes
negligible compared with that of the body force when the particle size exceeds a certain value (of the order of a few
microns) . The most important parameter determining the van der Waals attraction force is the interparticle
separation distance which is affected by the surface roughness and the presence of spacers (small molecules or fines
adsorbed) on the particle surface.
2.3 Mixing devices
There are mainly two categories of the mixing devices. First one is rotating shell devices in which the shell
rotates and the material slopes inside the mixer, and mixes due to action of gravity. Diffusion and the shear are the
main mixing mechanisms here. These are available in various geometries, a few examples of such devices are given
in Table 1(S. No. 1-4).
Table 1
Different types of mixers and their description
S. No.
1.
2.
3.
4.
5.
6.
7.
Name of the mixer
Drum Mixer
Octagonal
Double cone
V blender
Centrifugal Mixer
Ribbon mixer
Orbiting Screw mixer
Mixing
Mechanism
Materials Suited
Comments
Diffusion
Free flowing
Cleaning is easy.
Slightly cohesive
Suited for continuous operation.
Free flowing
Ensures good quality of mixture.
Slightly cohesive
Very less RPM is required.
Shear and
Diffusion
Free flowing
Easy to clean.
Slightly cohesive
Can be sealed during operation.
Shear and
Diffusion
Free flowing
Better performance than the other
rotating shell devices.
Shear and
convection
Cohesive
Shear and
convection
Slightly cohesive or
Cohesive
Less RPM and less time required.
Convection
and diffusion
Free flowing
Confined to batch operation.
Diffusion
Slightly cohesive
Removes agglomerates.
Hard to clean.
Wide range of materials handling.
Reduces segregation.
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The second kind of the mixers are in which the shell is kept stationary and inside there are blades and
impellers which rotate. These are suitable for the mixing of cohesive powders as the main mixing mechanism is the
shear and convection. These are highly effective in breaking of the agglomerates. Some examples of such type of
mixers are in Table 1(S. No. 5-7).
For any mixing operation selection of the blender is done considering that, ideally the mixer should be able
to achieve the acceptable blend uniformity in reasonable time and without damaging the product. But there are
many other factors which should be kept in mind in selection, design and operation of the equipment. In general
mixer should be dust tight, require low energy and can be cleaned and discharged easily. The surface of the mixer
should be such that it does not react with the components of the mixture and it should not resist the flow of the
components to be mixed. It should be designed such that taking samples is easy for the determination of the quality
of the mixture and also the samples taken should be sufficient enough to represent the whole batch. While operating
the mixer if one component is in very small amount which is the case of APIs in pharmaceutical industry first a preblend of higher percentage should be made and it should be mixed with main components in next step to get the
desired percentage. Segregating mixtures should be dealt with addition of some appropriate liquid to increase the
cohesiveness. Particle damage, reduction of size should be monitored during the operation along with the conditions
of blender such as temperature and pressure. The way mixer is started and stopped also affects the product quality
and when the material is discharged care should be taken so that it does not segregate.
2.4 Mixing problems
There are two important problems which should be addressed while doing the mixing: Segregation and
Agglomeration, while segregation occur as the mixture is more flowing in nature, the existence of the agglomeration
is due to cohesive nature of the mixture. As the presence of these can heavily deteriorate the quality so there is a
need to control these via controlling the process conditions and variables.
2.4.1 Segregation
In the process where the particles move relative to each other the difference in size, shape or density leads
to the separation of bulk mass into different regions each region containing one of the components in amounts more
than it’s overall percentage. It has been seen that particle size is most dominating factors of all which causes
segregation. Segregation is seen in case of free flowing mixtures but sometimes the agglomerates in cohesive
powders also tend to segregate. There are some mechanisms of segregation
2.4.1.1 Inter particle Percolation
In the convective movement of chunks while mixing there is a small thin layer of particles (usually 10 particle
diameter in thickness) between the two blocks which are moving with different velocity, the region is called the
failure zone. The failure zone has more mobility due to velocity gradient and particles move in different directions
based on difference in size, shape, density etc. but the particle size is seen to be most deterministic factor. In failure
zone smaller particles move downwards and larger ones move in the direction of the increasing strain rate.
2.4.1.2 Trajectory segregation
This mechanism can cause segregation when the particle travel through the air or when they are freely
falling and simultaneously have horizontal component of velocity. When stokes law is applied the particle is seen to
travel the horizontal distance proportional to the square of the diameter. So the particles with more diameter travel
more and segregation occurs.
2.4.1.3 Free Surface segregation
This is related to interparticle percolation and trajectory segregation. To understand this phenomenon
consider a mixture having one component in small amount and the mixture is poured to form a heap. It is found that
the minor component in the heap is either close to the top or towards the bottom of the slope (Drahun & Bridgwater,
1983). If the minor component is smaller than the bulk, the minor component is found near the top of the heap. This
arises from the percolation of small particles through the deforming array of larger ones. If the minor component is
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larger than the bulk, then it is found at the bottom of the heap. Here the large particles float on the surface of the
small ones to the bottom of the heap. If the velocity of the particles onto the top of the heap is increased, then a
smaller minor component is found near the bottom of the heap and a larger minor component at the top. The
greater momentum of the individual particles when impacting on the surface is the important factor. Smaller
particles are reflected off large ones into the space above the free surface and bounce over the free surface to the
bottom, with surface avalanches being avoided. In the case of the minor component being large, particles then get
buried in the heap and avoid the action of the surface avalanches. There is a significant effect of particle density.
More dense particles of the same size as the bulk are found at the top of the heap and less dense ones at the bottom.
2.4.1.4 Elutriation segregation
This happens when one of the components has size less than 50 micrometre. While mixing when the air
passes through the bed of particles it may be possible that the velocity of air is more than the terminal velocity of
smaller particle and thus they form a suspension in the air and remain there hampering the mixing.
2.4.2 Agglomeration
The problem of agglomeration occurs in the cohesive powders. Here the interparticle forces are strong
enough so that particles bond with each other and form large chunk called agglomerates. The chunk size is seen to
be directly proportional to the surface tension and inversely proportional to the product of density and acceleration
due to gravity.
4.
Sampling and Assessment
There are generally two types of methods for studying the quality of mixing first one is to take out samples
from different locations at different times to analyse it and the second is in which material remains in the container
and using some techniques it is analysed. In the first type sometimes probes can be inserted rather than taking out
the samples, use of the optic fibre probes hold the potential to do that but due to several issues their use is not
widespread(Kaye, Brushenko, Ohlhaber, & Pontarelli, 1969). The second type of study mainly relies on the free
surface or transparent surface photographs. These methods cannot be used for 3-D study of mixing. But now with
the help of DEM (discrete elemental method) it is now possible to tack the motion of each and every particle, but
this method is computation expensive and so is not used for the large systems. The two methods of thief sampling
and the DEM are discussed below3.1 Thief Sampling and Statistical analysis
Earlier this method mostly used the scoops to take out the samples but Keye developed a more consistent
equipment in 1997which reduced the errors in the sampling. It consists of a first cylindrical tube with a conical base,
there being a number of holes drilled in a line along the wall in the axial direction. There is a second cylindrical tube
of external diameter slightly smaller than the inner diameter of the first tube. It is split apart internally into a number
of axial compartments, with a handle on the end. There are holes, drilled in the wall of this inner cylinder, these
having the same spacing as those in the first tube. To carry out sampling, the smaller tube is inserted into the larger
with the three sets of holes out of alignment. The device is inserted into the mixture with the holes of the outer tube
on the top. The inner tube is then rotated so the two sets of holes are aligned. Material falls into each of the three
compartments. The inner tube is then rotated again to take the holes out of alignment and the whole assembly is
withdrawn.
The next task is to characterize the samples taken, for that each sample is first analysed for it’s components
and then spread in the compositing is determined by using the variance. The formulae for the variance are for the
two components system but in case of the multicomponent mixtures that can be applied by taking compound of
interest as the one component and rest as the other. There are two reference states of variance which correspond
to the completely unmixed state and completely mixed state, these can be calculated by the equation (1) and (2)
respectively
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σo2 = x(1−x)
(1)
σr2 = x(1−x)/N
(2)
Where x is the fraction of component in the original mixture σo2 is the variance of unmixed state and σr2 is the
variance of completely mixed random state. Now for the samples taken at the intermediate time variance can be
calculated using the equation
1
𝑛
𝜎 2 = (𝑛−1) ∑𝑙̇=1(𝑦ⅈ − 𝑦)2
(3)
Where 𝜎 2 is the variance of the intemediate samples, n is the number of the sample taken and y i is the mass
concentration of main component in sample i.Once we know all the variances the task remaining is to find the mixing
uniformity and for that a lot of mixing indices are described in the literature. There is no such best index and
selection of index depends on the user and the conditions of the operation and product specification.
The method in which the thief sample is used to take out the material is used widely in most of the places.
But there are a number of issues related to using a sample probe – it is slow and has to be followed by some
measurement techniques, insertion of the probe causes the material to displace thus changing the composition and
microstructure near the probe. Also many samples are needed to give a sufficiently reliable estimate of σ 2. The taking
and analysis of these samples in itself can prove to be very tedious. Also the movement of components in the thief
is with different velocities and causes seperation. The force necessary to the probe in the bulk can be appreciable
which may lead to comapction and partcle attrition. Also it violates two golden rules of sampling i.e. to sample a
moving powder and sampling the entire stream rather than sampling the parts of stream. Considering the problems
related to thief sampling and the inherent error it adds to the results there is need of more precise technique to
analyze the powders.
3.2 Discrete Element Modelling (DEM)
The challenges associated with the development of computational models for industrial blenders is their
large size and the particles inside them can be as small as few microns and can have very complex shapes. To
accomodate for complex shapes and such size ranges is not feasible. In DEM approach, particles are permitted to
suffer minute deformations, and these small deformations are used to calculate elastic, plastic and frictional forces
between particles. The motion of particles is described by the Newton’s laws of motion. This model can handle
multiple contacts which are of importance in modelling quasi-static systems. Newton’s laws are applied to describe
both the velocity and rotation of each particle, which are mostly taken to be spherical, the equations are solved for
velocities and trajectories. The models describing the inter-particle forces are generally linear ones. When
considering the torque balances on a particle, it is argued that rolling friction is also needed. Rolling friction accounts
for the energy dissipation associated with rolling of particles on each other or on other contact surfaces. Cohesive
forces due to van der Waals’ forces, electrostatic effects, steric forces and capillary action can also be included. The
method can be used for particles of shapes other than spheres but this makes calculations much slower. Each particle
in the flow is tracked and all collisions between particles and between particles and boundaries are modelled. The
particles are allowed to overlap and the extent of overlap is used in conjunction with a contact force law to give
instantaneous forces from knowledge of the current positions, orientations, velocities and spins of the particles.
Here we used the simplest of the force laws which is the linear spring-dashpot model. A search grid is maintained
which keeps list for all neighbouring interactions between particle-partile and particle-wall which can result in
collision in a given time period. The forces are calculated using the contact force model and then summed over to
form the net force and net torque which when put in the Newton’s laws of motion gives the position,speed and
orientation of particles.
5.
V-Blender Case Study
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The V-Blender (also known as a twin shell blender) is one of the most commonly used tumbling blenders. It
has been seen that it’s performance is better than a lot of blenders like drum blender, bin blender etc. It offers short
blending time and efficient blending. The mechanism of mixing in the V-blender is seen to be convection and
diffusion. Diffusion leads to the uniformity at the length scale of the blender. Therefore when precise blend
uniformity is reqiuired V-Blenders are used. They also show excellent mixing when one of the components is in very
small amount like API in pharmaceutical industry. A V-blender uses a V shaped mixing vessel for batch mixing. Each
arm of the V has a cylindrical cross-sectional shape and there is typically an access port at the bottom of the V for
filling and discharge of the particulates. This is sealed during mixing operation. The blender has a horizontal shaft
attached to the V and the blender rotates around this shaft. The configuration is symmetric to reflection in a vertical
plane through the V. The advantages of using the V-Blender is that the particle size reduction and attrition is
minimized and loading and discharge of material is easy. Cleaning of the Blender is also easy and there are no chances
of product contamination. Next section talks about the flow pattern inside the blender and the effect of various
paramters like rotation rate, vessel size, time of operation, vessel fill level on the performance of blender. Different
mixtures have different flowing properties which lies between free flowing and cohesive so the next section is
divided into two parts and mixing of both type of powders are discussed seperately.
4.1 Free flowing mixtures in V-Blender
In this section various experimental results are discussed along with the DEM of blender for free flowing
powders.
4.1.1 DEM of free flowing powder in V-Blender
In the DEM analysis of the scaling of the blender the data was analysed by ##for the blenders of the volume
1.8 litre to the volume 210 litre. DEM modelling of industrial scale mixers for coarser materials (mm scale) is now
feasible, but mixing of finer powders (10μm to 1 mm) is
Table 1
Table 2 mixing rate with scale up
still not feasible at the industrial scale. The experiment was performed for the free flowing particels. The particles
used had a mean size of 2.75 mm with a range of 0.25 mm above or below this size. The same particle sizes are used
in all the different scale mixers. The solid packing fraction was 0.5564. The particle density was 1500 kg/m3 and the
blenders were filled to 50.1% by volume. The physical length of blender and the number of particles in the model
for each blender scale are given in Table 1.
As the blender rotates slowly around its horizontal axis the free surface changes its angle until it reaches
the angle of failure of the material which then avalanches down the slope settling at the angle of repose. Each
increment of rotation causes some particles to exceed the angle of failure leading to continuous avalanching from
across the high side of the blender. In the first half revolution the avalanching flow is directed down into the angled
cylindrical sections of the blender shell. In the second half of the revolution particles flow down the slope in the
direction of rotation but also converge back towards the middle of the blender as the particles pack into the apex
region. It was seen that both type of mixing mechanisms i.e. convective and diffusive mixing were present and the
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mixing in each arm was very fast compared to the cross arm mixing suggesting that the flow pattern developed was
symmetrical in nature. Also the mixing rate initially was high which keep on decreasing with time asymptotically
which suggests that to acheive complete uniformity may take very long time. From the mixing rates summarised in
Table 2 it is clear that the rate of mixing does change with increasing scale when the speed of the mixer was scaled
to maintain the same Froude number. For this V-blender, scaling up the volume by 31.6 times has led to a halving of
the mixing rate when measured in revolutions.
4.1.2 Flow pattern and Circulation Intensity
## performed Positron Emission Particle Tracking (PEPT) study for mixing of 3 mm large cohesionless
particles in V-blender with the operating conditions summerized in table 3. The motion showed some trends of the
rotating drums , it has a convective component driven by vessel rotatin and a diffusive component driven by gravity.
The circulation in the left arm was in the anti-clockwise direction when the fill percentage is relatively low (20% and
28%), whereas the direction of the flow reverses at a greater fill (46%). It is also apparent that at the intermediate
fill of 34% fill, the motion is much less ordered. Although mixing within a single arm is considered to be very fast
compared to mass transfer between arms, the convective mixing mechanism can be
Table 3
suppressed at intermediate fills and hence reduces the quality of mixing within the arms. The change of the direction
of the flow due to the free volume available in the arms. The rotation of the vessel can be divided into two steps:
the division step and the combination step. During the division step, the surface particles move towards the two
ends of the arms under the influence of gravity. When the fill level is relatively low, the trajectories of the particles
in the surface flow region are closer to the plane of symmetry of the V-mixer than those in the high fill level condition.
During the combination step, the surface particles move towards the joint of the V-mixer. The trajectories of the
particles in the surface flow region are closer to the bottom of the arm when the fill level is relatively low. It is
therefore the surface flow regime which determines the direction of the circulation. The flow in the arm reverses as
the fill level increases and the occurrence of the flow reversal is system-dependent. Circulation intensity is the term
which is calculated using the velocity vectors at the different positions in each cross section and it represents the
rate of mixing. When the shaft rotational speed increases, an increase of the particle circulation intensity was
observed.The dependence of the circulation intenstiy on rotation rate was quadratic. This is the expected result if
the circulation intensity is controlled by the kinetic energy of the particles and their mean velocity is directly
proportional to the rotational speed of the mixer. The inertia of the particles is then roughly proportional to the
square of the rotational speed. As the fill level increases, the circulation intensity decreases dramatically. There is a
minimum value of the circulation intensity and this occurs approximately where the flow reversal occurs. This again
suggests that the convective mixing mechanism is hindered at intermediate fills.
4.1.3 Effect of fill level
Fill level as discussed changes the circulation intensity and thus the rate of mixing. So operations should not
be performed with the ~50% fill as at that point the convection is hampered and the rate of mixing is very slow. Fill
level along with the rotation rate basically decides the type of segregation which may occur in the blender. There
are normally 4 types of segregating pattern - stripes, inverse-stripes, small-out and big-out. In general operations
are performed for fill level ranging from 40 % to 80 %.
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Table 4 Experiment for loading pattern effect
determination
Figure 1 Different segregating patterns in V-blender
4.1.4 Effect of Loading pattern
There are three types of loading pattern – Top-bottom, Front-back and Left-Right loading patterns. As can
be seen in Fig. 2, all three curves exhibit a similar profile that is a rapid decrease with time followed by a slow
transition leading to an asymptotic plateau. The loading profiles have a critical influence on the evolution of the RSD.
The system with the front-back loading profile shows the fastest RSD decrease. The system with the top–bottom
loading profile follows closely, the asymptotic plateau being attained after about 60 rotations (120 s). The system
with the worst mixing efficiency is the one with the right–left loading profile, for which the asymptotic plateau was
not yet reached after 60 revolutions. One can explain the differences obtained for these three loading profiles by
the fact that the convective transport between the two arms of the V-blender is slower than that within any of its
arms. Consequently, in the case of a right–left loading profile, the mixing of the two phases comes from the
(convective and diffusive) mass transfer across the plane of symmetry of the blender, that is between its two arms,
and the overall mixing dynamics is then slower than in the case of a front–back or top–bottom loading profile for
which the (convection-dominated) mass transfer mainly occurs within each of these arms. It is also seen that the
loading profile not only affects the rate of the mixing but it also affects the asymptotic value of the variance i.e. the
best mixing that possibly can be achieved also depends on the loading pattern.
11
Figure 2
Figure 3
4.1.5 Effect of rotation rate
There is a critical speed which, if approached will diminish blending efficiency considerably. As the
revolutions per minute increase, the centrifugal forces at the extreme points of the blender will exceed the
gravitation forces required for blending. Consequently the powder shall tend to gravitate to the outer walls of the
blender shell. As the size of the blender increases, the rotational speed decreases usually in proportion to the
peripheral speed of the blender extreme. V-Blenders are designed to operate at 50% to 80% of the critical speed.
Three flow regimes (tumbling, partial-inertia, and centrifugal) were characterized for the V-blender rotating at
variable speeds##. The first mode of particle motion was dominated by tumbling motion, characterized by particles
cascading from one end of the shell to the other, with the mixture splitting and reforming during each rotation. A
gradual transition to the second mode of particle motion began at about 70 rpm. In this regime, the mixer rotated
too fast for all the particles to complete tumbling from one end of the shell to the other. Since all particles did not
reach the end of the shell, some became airborne as they fell from a position no longer supported by the vessel to
another location that was supported. As the rotation rate increased, a gradual shift toward the third mode of particle
motion occurred, which was totally dominated by particle inertia. In Figure 4, results are compared for 8, 16, and 24
rpm. The data shows that rotation rate exerts little influence on the mixing process; in all cases, the evolution of the
standard deviation is independent of rotation rate and can be expressed solely as a function of the total number of
revolutions (which is the properly nondimensionalized mixing time). All these data are for the tumbling flow regime
in which all the industrial mixers run. Qualitative observations indicate that this tumbling motion, which is gravity
driven, is largely independent of the rotation rate for low enough Fr numbers. Particles within one shell are mixed
relatively quickly by convective rearrangement during the tumbling motion. Mixing between shells occurs more
slowly, as particles cross from one shell to the other only as
12
Table 5
the mixture is reassembled. Hence, the important factor determining the overall extent of mixing is the total number
of times the mixture splits and reforms, rather than the rotation rate. In terms of total mixing time, however, the
rotation rate is very important, because tripling the rotation rate from 8 to 24 rpm produces a uniform mixture three
times as fast.
4.2 Cohesive mixtures in V-Blender
An experiment was performed for the mixing of the MgSt with microcrystalline cellulose in V-blender, the
conditions are given in table 5. MgSt is widely used powder lubricant in the pharmaceutical industry.
4.2.1 Effect of blender fill volume
Blending performance, as characterized by the asymptotic RSD value, decreases as the fill volume increases,
which complies with what is generally observed in the case of free-flowing and cohesive powders in tumbling
blenders. The deleterious effect of fill volume on mixing performance can be explained here by the decrease in shear
stress per unit volume. It was seen that the MgSt concentration has little impact on mixing performance. Therefore,
the impact of the fill volume on MgSt mixing performance is related to the shear stress per unit volume alone.
4.2.2 Effect of loading profile
Loading profile has little impact on the mixing time at similar fill levels. Note that previous results from the
literature have shown that the difference between axial (diffusive) and radial (convective) mixing rates in tumbling
blenders, which can be as high as an order of magnitude for free-flowing powders, is much less important in the case
of cohesive powders. The relative lack of influence of the loading profile on mixing performance in the case of
cohesive powders may be caused by three factors: relatively slow radial mixing, relatively fast axial mixing, or the
overriding importance of shear mixing with respect to the previous two mechanisms.
4.2.3 Effect of blender rotational speed
Unlike the free flowing powders the cohesive powders are greatly affected by the rotation rates, both in
terms of the RSD value at a given time and the asymptotic RSD value. Not only does the RSD value decrease more
quickly at high rpm, but the final RSD value is also lower than that obtained at low RPM, as expected.
4.2.4 Other factors
Cohesion effects are less dominant in the larger vessels so when scale up is done the cohesion effects keep
on decreasing. The reason is simple: Although cohesive forces are surface effects, the gravitational and convective
13
forces that drive flow in powder blenders grow proportionally to the vessel volume. Thus, as the blender’s scale
increases, gravitational and convective forces increase, thereby overwhelming cohesive forces. The characteristic
“chunk” size of a cohesive powder flow is a property of the material, and thus to a first approximation it is
independent of the blender size. The dependence of the chunk size on properties of powder is already discussed in
the cohesive materials section. As the blender size increases, the chunk-to-blender size ratio shrinks, thus reducing
the effect of cohesion. Pre blend composition has seen to greatly affect the mixing performance so the order in
which the components are added in the blender also affect the mixing quality.
6.
Scale-Up
Scale up of V-blenders is still not understood theoretically but there are some observations and empirical
relations which should be used. For Scaling the V-Blenders the approach for the cohesive powders and non-cohesive
powders are different. For each of them first of all the optimum point is to be determined experimentally. So based
on the product requirements and the dependence of mixing on various variables (as discussed above) the
experimental procedure should be designed. While designing the experimental procedure the following guidelines
should be followed –
The rotation speed of vessel should be kept between 40% to 80% of the critical speed which can be calculated by
𝑔
Critical Speed (ω) = √
𝑅
(4)
Where ‘g’ is acceleration due to gravity and R is vessel radius. Vessel radius is half of the height of the blender. For
non-cohesive or free flowing mixtures the rotation rate does not affect the blending rate or blend quality, for these
the number of rotations is the parameter is the deciding factor. Segregation pattern for free flowing mixtures is
highly dependent on the rotation rates. Mixing flow mechanism of segregating mixtures changes with changing the
RPM. In case of the cohesive mixtures the asymptotic variance value decreases with the increasing the rotation rate
but as we come near to the critical speed the mixing performance deteriorates. On increasing the rotation rate the
rate of the mixing in cohesive powders also increases.
When deciding the loading pattern convective mixing should be prompted so that the rate is fast. Hence
top-bottom or front–back loading should be promoted over the right–left loading. Major components (components
having the highest percentages) should be loaded first. The components which have a very low percentage (<10 %)
should be added carefully and in 2-3 steps not at once. All material should be loaded when the V-blender is inverted
to ensure equal loading into both shells. The best method for loading is the front-back loading which is slightly better
than the top-bottom loading, left-right loading should be avoided. For cohesive powders the loading profile is not
significant and seen to have no effect on the mixing performance. All experiments should be performed between
the 40-80 % of blender volume. In case of the non-cohesive or the free flowing mixture the fill level nearby of 50%
should be avoided as at this fill level there is change in the flow pattern and the convective mixing is minimum and
so is the rate. When convective mixing is minimum at the 50% fill level the circulation intensity is minimum.
Segregation pattern is very sensitive to the fill level (1% change of fill level can change segregating pattern) and RPM
so experiment should be done carefully. Rate of mixing decreases with increase in the fill level. Asymptotic value of
the standard deviation increases with the increasing the fill level. Industrial suggested fill level for v-blender is 60 %.
Now we know the optimum point for the system and also the flowing property of the system. So if the
system is free flowing we can use Froude Number (Fr) approach or Rayleigh method.
𝐹𝑟 =
𝑤2𝑅
𝑔
(5)
Where (w is the rotation rate, R is the vessel radius, and g is the acceleration from gravity) is often suggested for
tumbling blender scale-up. While scaling the Froude number should be kept constant. This relationship balances
14
gravitational and inertial forces and can be derived from the general equations of motion for a general fluid. Rayleigh
method is based on the particle surface velocities and is seen to be more reliable than the Froude number method.
V=KR Ω2/3(g/d)1/6
Ω<30 RPM
(6)
V=KR Ω1/2(g/d)1/4
Ω>30 RPM
(7)
Where ‘V’ is particle surface velocity, ‘d’ is diameter of the particle, ‘Ω’ is rotation rate and ‘R’ is vessel radius. In
Rayleigh method the particle velocity is kept constant. For the cohesive system the rates are not affected by the
vessel size and time obtained from experimental optimum is also the optimum for the scaled case.
7.
References
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Cleary, P. W. (2009). Industrial particle flow modelling using discrete element method. Engineering
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Cleary, P. W., & Sinnott, M. D. (2008). Assessing mixing characteristics of particle-mixing and granulation
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Adam, S., Suzzi, D., Radeke, C., & Khinast, J. G. (2011). An integrated Quality by Design (QbD) approach towards
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Technology, 266, 240-248.
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