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Continuous processing iswidely used in bulk solidsmanufacturing, especially

for processing large materialvolumes in industries such asminerals, foods, detergents, andconstruction materials. Few studieshave been published on continuousbulk solids mixing,1-4 but in recentyears, continuous mixing hasattracted increasing interest,particularly in pharmaceuticalsolid oral dose manufacturing,t rad i t iona l ly a batch-basedindustry.

The most common type o fcontinuous blender is the convectivetubular blender, as shown in Figure1. The convective tubular blenderconsists of a stationary horizontal

mixing cylinder with a materialinlet at one end and a materialoutlet at the other end. An overflowweir is typically mounted inside thecylinder before the material outletto control material flow. Thecylinder contains a rotating shaftwith impellers (such as blades,paddles, or ribbons) that mix thematerial by convection (moving theparticles within the cylinder relativeto each other). For applicationsrequiring gentle material handling,twin screws are sometimes used tomix the ingredients.

In operation, unmixed ingredientsenter the blender’s inlet and arelifted, tumbled, sheared, andconveyed by the rotating impellersto the blender’s outlet, where thematerial exits the blender as ahomogeneous stream. Duringsteady-state operation, the massflowrate into the blender equals themass flowrate out of the blender,and the mass of material inside theblender (called the mass holdup)remains constant.

Continuous mixing modesMaterial mixing in a continuoustubular blender can be divided intotwo modes: cross-sectional (orradial) mixing and axial mixing. InFigure 1 , for example , twoingredients (Ingredient A andIngredient B) are being fed into theblender. We can consider them tobe completely unmixed at theblender inlet, as shown in the cross

Using residence time distributionto understand continuous

blending

Fernando Muzzio Sarang Oka

PBEAs appeared in April 2017

Figure 1

Cross-sectional mixing in acontinuous tubular blender

Ingredient B Blendedmaterial

Ingredient A

Weir

Impellers

Rotatingshaft

Materialoutlet

Materialinlet

Feeder BFeeder A

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section on the left in the figure. Asthe blender’s impellers rotate, theylift and tumble the ingredients,mixing the material in the cross-sectional plane. At steady state,cross-sectional mixing can belargely time independent, whichmeans that each cross section in theb lender exh ib i t s the samearrangement of ingredients overtime. As the figure shows, however,subsequent cross sections exhibitdifferent ingredient arrangements.This is because when the impellerslift and tumble the material in thecross - sec t ional p lane , someparticles are pushed forward (andto a lesser extent, backward) in thecylinder, resulting in axial mixing asthe material is transported andmixed along the cylinder’s axis.

Residence time distributionWhen material enters the blenderduring steady-state operation,most particles remain in the blenderfor a time close to a certain meanvalue, defined as the mean residencetime, which is determined bydividing the mass holdup by themass flowrate. However, somepar t i c l e s exper i ence fas te rconvection in the forward axialdirection, while other particlesexperience an unusual amount ofbackward pushing or occupy a“dead” volume within the blenderfor some time. This causes someparticles to exit the blender veryquickly, while other particles spendan unusually long time in thecylinder. As a result, a represent -ative group of particles passingthrough a blender operating atsteady state will have a range ofresidence times, called a residencetime distribution (RTD).

There are two idealizations ofresidence time behavior: plug flowand continuous stirred tank flow. Inplug flow, all particles move at thesame speed along the cylinder’saxis, so particles entering theblender together exit the blendertogether and only cross-sectionalmixing occurs. Continuous stirredtank flow, on the other hand,

assumes that particles entering theblender inlet are instantly andcompletely mixed into the rest ofthe material in the blender, so someparticles exit instantaneously, whileother particles take a very long timeto exit. In reality, all blendersoperate somewhere between thesetwo idealized states.

As will be discussed shortly, it’spossible to tune a blender’s RTDby changing certain operating anddesign parameters. The question is:what is a desirable RTD? For puremixing applications, plug flowtends to be undesirable becauseaccurately feeding bulk solidmaterials can be challenging.Feeders often directly precedeblenders in the process train, and allfeeders introduce a certain degreeof variability. Feeders must also beperiodically refilled, which canintroduce sizable perturbations(a l so ca l l ed no i se ) in to theingredient blend.5 This noise willpass unfiltered through a blenderoperating in complete plug flow,which can affect the quality of thefinal product.

For example, Figure 2a shows theconcentration profile for oneingredient in a blend over time, aftereach unit operation in a tabletingprocess train. The process trainincludes the ingredient feeders, amill, a blender, and a tablet press inthat order . The ingred ientconcentration in the feed stream isindicated by the dark blue line, andthe appl icat ion’s maximumacceptable concentration for theingredient is indicated by thehorizontal purple line. The greenline indicates a perturbation (a 0.25-gram pulse) in the ingredientconcentration introduced into thefeed stream that passed unfilteredthrough the mill. As indicated bythe red l ine , the mix ing thatoccurred in the blender dampenedthe effects of the perturbationenough that the ingred ientconcentrat ion in the table ts(indicated by the turquoise line)remained below the maximumacceptable value.

Note that this example’s RTDstandard deviation value (a measureof the blender’s noise-filteringability) is 12 seconds. If a 1-grampulse of the same ingredient isintroduced into the feed stream, asshown in Figure 2b, a blenderoperating at the same RTD andstandard deviation value won’t beable to dampen the effects of theperturbation enough to keep theingredient concentration in thetab le t s be low the max imumacceptable value.

However, if the RTD is widened toa standard deviation value of 24.9seconds, as shown in Figure 2c, theblender can successfully dampenthe la rger ingred ient pu l se .Widening the RTD means that theblender is operating closer tocontinuous stirred tank flow, whichallows the blender to filter the noisein the ingredient feed and maintainthe quality of the final product.

Measuring a blender’sresidence time distributionDetermining a blender’s RTD iscritical to understanding andcharacter iz ing the blender’soperation. The RTD helps youunderstand how material flowsthrough the blender as well as howeffectively the blender will filterincoming noise from the unitoperation immediately upstream.Determining the blender’s RTDalso enables you to develop feed-forward (downstream) and feed-back (upstream) control strategiesto ensure the f inal product’squality. If you have incoming noisefrom a feeder or unit operationdirectly upstream, you can use theblender’s RTD to predict thecomposition of the blender’soutput stream. You can then takefeed-forward action to either rejectout-of - spec product or takecorrective action in downstreamunit operat ions to br ing theproduct back within specifications.You can also take feed-back actionto eliminate the source of the noise.

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A blender’s RTD can be measuredby introducing an instantaneouspulse of a tracer material into thematerial stream and measuring thet racer concentra t ion a t theblender’s outlet as a function oftime, as shown in Figure 3. As thefigure shows, the sharp pulse at thefeeder inlet is broadened at theoutlet due to axial convection as thetracer moves through the blender.

The RTD function [E(t)] is definedby the equation:

Where t is time and c(t) is the tracerconcentration as a function of time.The mean residence time (τ) isdefined by the equation:

Lastly, the mean centered variance(σ2

τ) is defined by the equation:

The mean centered var iance(MCV) is the variance (square ofthe standard deviation) normalizedby the square of the mean value ofthe distribution. In this case, themean value of the distribution is theresidence time. Standard deviationand MCV are qualitatively similar;both are a measure of the width ofthe RTD.

E(t) =c(t)

∫∞

ο c(t).dt

∫∞

ο τ = t.E(t).dt

σ 2τ =

∫∞

ο (t – τ)2 .E(t).dt

τ2

Figure 2

Ingredient concentration profiles in a tableting process train

a. Small (0.25-gram) pulse sufficiently dampened by blenderat 12-second RTD standard deviation

b. Large (1-gram) pulse not sufficiently dampened by blenderat 12-second RTD standard deviation

b. Large (1-gram) pulse not sufficiently dampened by blenderat 12-second RTD standard deviation

Feed streamMill exitBlender exitTablets

Concentra

tion

(percentage by mass)

0.090

0.085

0.080

0.075

0.070

0.065

0.060

200 400 600 800 1,000 1,200 1,400

Concentra

tion

(percentage by mass)

0.090

0.085

0.080

0.075

0.070

0.065

0.060

200 400 600 800 1,000 1,200 1,400

Concentra

tion

(percentage by mass)

0.090

0.085

0.080

0.075

0.070

0.065

0.060

200 400 600 800 1,000 1,200 1,400

0.25-gram pulseBlender MRT: 41.6 secondsRTD standard deviation: 12 seconds

1-gram pulseBlender MRT: 41.6 secondsRTD standard deviation: 12 seconds

1-gram pulseBlender MRT: 71.7 secondsRTD standard deviation: 24.9 seconds

Time (seconds)

Time (seconds)

Time (seconds)

Figure 3

Blender inlet and outlet profileof a tracer material

Tracer concentration

Time

Monitoringoutlet

Achievedsteady-stateoperation

Tracer pulseat blender inlet

Tracer measuredat blender outlet

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Alternately, the tracer can also beintroduced as a step function (aninstantaneous change in the tracerconcentration at the blender inlet).The system response (the tracerconcentration at the blender outlet)would then be measured as afunction of time and would dependon the blender’s RTD.

Tracer selectionUsing a tracer to measure a unit op-eration’s RTD is widely practiced,but the importance of selecting anappropriate tracer material is oftenoverlooked. The tracer must haveflow properties as similar as possi-ble to the overall blend but mustalso be chemically distinguishablefrom the rest of the material. Thetracer must not disturb the materialstream’s flow behavior and shouldtravel through the blender at thesame rate as the rest of the material.

Figure 4a shows a blender’s RTDwhen the physical properties of thetracer and the blend were similar.The overall throughput was 20 kg/hand the impeller speed was 350rpm. As the figure shows, the tracermaterial was fully flushed from thesystem within 10 minutes. How-ever, the same blender under identi-cal processing conditions exhibited

a very different RTD when using atracer material with a much higherbulk density than the blend. Asshown in Figure 4b, the tracer hadnot fully exited the blender after 30minutes of operation, resulting inincorrect RTD characterization.

Adjusting a blender’sresidence time distributionAs previously mentioned, you canoften adjust or tune a blender toachieve the desired RTD for yourappl i ca t ion . Chang ing theblender’s impel ler speed is acommon way to manipulate theRTD. Increasing the impeller speeddecreases the mass holdup but alsoresults in an increased MCV. Forexample, two RTD values for puresemi-fine acetaminophen runningthrough a blender at 18 kg/h insteady state are shown in Figure 5.The tracer material was caffeine,introduced as a pulse at the blenderinlet. The RTD on the left in thef igure was obtained with theimpeller speed at 350 rpm, while theRTD on the right was obtainedwith the impeller speed at 400 rpm.The disparity between the RTDshapes is discernible in the figure;operating at higher rpm results in alarger MCV value (0.406 at 350rpm and 0.483 at 400 rpm).

Figure 5

Blender RTD profiles at 350 and 400 rpm

Tracer concentration (percentage by mass)

7.00

6.00

5.00

4.00

3.00

2.00

1.00

0.00

-1.000 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

Time (minutes)

Start at 350 rpm

Tracer added (3:53)

Increase to 40

0 rpm

(21:57)

Tracer added (27:33)

Figure 4

Effect of tracer properties onRTD profile

Tracer concentration (percentage by mass)

a. Tracer properties similar tomaterial properties

b. Tracer bulk density much higherthan material bulk density

4.003.503.00

2.50

2.00

1.50

1.00

0.500.00

0.00 5.00 10.00 15.00Time (minutes)

Tracer added

Tracer concentration

(percentage by mass)

181614121086420-20.00 10.00 20.00 30.00

Time (minutes)

Tracer added

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An alternate strategy for changinga material’s RTD is to manipulateblender design variables. This canbe ach ieved by a l t e r ing theblender’s incline angle or the angleof the weir at the blender’s outletbut is most commonly done byadjust ing the impel ler bladeorientation.6 Many blenders areavailable with adjustable impellerblades that you can orient to eitherpush the material fully forward orbackward or at an intermediateangle to increase cross-sectionalmixing. Increasing the number ofblades pushing material backwardwill generate an RTD with a largerMCV.

The total mass flowrate through theblender also affects the material’sRTD. Changing the overall massflowrate to manipulate the RTD isuncommon, however, since massflowrate changes imply an unsteadycontinuous process, and the massflowrate of a process is generallypredetermined based on productionrequirements and other non -technical considerations.

A blender’s RTD is a crit icalmeasurable attribute that aids inthe understanding and design of ablending operation. While theeffects of process and designparameter s and opera t ingconditions on a blender’s RTDhave been well examined, theeffects of material properties on acontinuous blender’s RTD remainlargely unexplored. PBE

References1. Colin F. Harwood, Kenneth Walanski,

Erdmann Luebcke, and Carl Swanstrom,“The performance of continuous mixersfor dry powders,” Powder Technology,Vol. 11, No. 3, pages 289-296.

2. Ralf Weinekötter and Lothar Reh,“Continuous mixing of fine particles,”Particle & Particle Systems Character -ization, Vol. 12, No. 1, pages 46-53.

3. B. Laurent and J. Bridgwater,“Continuous mixing of solids,” ChemicalEngineering & Technology, Vol. 23, No.1, pages 16-18.

4. Sarang Oka, Abhishek Sahay, WeiMeng, and Fernando J. Muzzio,“Diminished segregation in continuouspowder mixing,” Powder Technology,Vol. 309, pages 79-88.

5. William E. Engisch and Fernando J.Muzzio, “Feedrate deviations caused byhopper refill of loss-in-weight feeders,”Powder Technology, Vol. 283, pages 389-400.

6. Aditya U. Vanarase and Fernando J.Muzzio, “Effect of operating conditionsand design parameters in a continuouspowder mixer,” Powder Technology, Vol.208, No. 1, pages 26-36.

Fernando J. Muzzio is director of theNational Science Foundation’sEngineering Research Center onStructured Organic ParticulateSystems (ERCSOPS) (http://ercforsops.org/) and distinguishedprofessor, chemical and biochemicalengineering, Rutgers University,Piscataway, NJ. He can be reachedat 848-445-3357 (fjmuzzio@yahoo.com). Sarang Oka is a postdoctoralas soc ia te in chemica l andbiochemical engineering at Rutgers.He can be reached at 848-445-5057(soka@rutgers.edu).

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