Sidestep Mixing Missteps

Mixing eHANDBOOK

http://www.arde-barinco.com

TABLE OF CONTENTSSucceed at Mixing Scale-Up 6

Understand how best to apply and adapt simple rules

Inline Blending Offers Multiple Benefits 11

These systems offer efficiency, convenience and safety

Carefully Evaluate Blending Requirements 16

When choosing a mixer, consider these four key components

that can lead to improved mixing

Additional Resources 20

Mixing eHANDBOOK: Sidestep Mixing Missteps 3

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One question frequently asked

about mixing scale-up is whether

to use equal tip speed or equal

power per volume. While one of these cri-

teria may guide successful scale-up, you

may need to factor in some additional

limitations or qualifications to get proper

results. Scale-up using these concepts

most often involves equipment with geo-

metric similarity, i.e., length dimensions

in the large-scale mixing equipment are

in the same proportion as those in the

small-scale equipment. Because geo-

metric similarity sets all the dimensions

and impeller features in the large-scale

equipment, the only remaining variable for

scale-up is the rotational speed.

When mixer speed is the only variable in

scale-up, you can reduce the calculation

of the large-scale speed to an expression

starting with the successful small-scale

speed times the inverse scale ratio (small-

scale length/large-scale length) raised to

an exponent:

NLarge = NSmall (TSmall /TLarge )n =

NSmall (DSmall /DLarge )n

where N is the rotational speed, typically

expressed in revolutions per minute, T is

the tank diameter, and D is the impeller

diameter. (You can use either the tank or

impeller ratio because they are the same

with geometric similarity.) The exponent, n,

provides a convenient means for adjusting

the magnitude of the speed change from

the small scale to the large scale. To calcu-

late a large-scale speed for equal tip speed,

the exponent is one, i.e., n = 1. Whatever

Succeed at Mixing Scale-upUnderstand how best to apply and adapt simple rules

By David Dickey, MixTech

Mixing eHANDBOOK: Sidestep Mixing Missteps 6

www.ChemicalProcessing.com

the successful small-scale speed is, you

must reduce the large-scale speed by the

ratio of the small-scale to large-scale length

dimensions. For instance, if the effective

small-scale speed is 250 rpm and the large-

scale length dimensions are five times the

small-scale dimensions, you must set the

large-scale speed at one-fifth the small-

scale speed or 50 rpm.

Using equal power per volume for geomet-

ric scale-up usually runs into an additional

limitation for turbulent mixing conditions.

With geometric similarity in turbulent mixing,

power is proportional to speed cubed and

the impeller diameter to the fifth power.

With geometric similarity, volume is pro-

portional to the tank diameter cubed or,

alternatively, the impeller diameter cubed.

For geometric similarity, the tank diameter

and impeller diameter scale ratio are the

same. If power is defined by speed cubed

and impeller diameter to the fifth power and

volume is proportional to impeller diame-

ter cubed, then power per volume must be

proportional to speed cubed and impeller

diameter squared. So, re-arranging the pow-

er-per-volume relationships to calculate the

large-scale speed from the small-scale speed

raises the inverse scale ratio to an exponent

of two-thirds, i.e., n = 2/3.

An exponent of two-thirds reduces the

large-scale speed by less of a factor than

for equal tip speed. Again, using the suc-

cessful small-scale speed of 250 rpm and a

five-to-one length increase as an example,

the large-scale speed for equal power per

volume is 85.5 rpm. For turbulent condi-

tions, where power is proportional to speed

cubed, the large-scale power for equal

power per volume will be 4.9 times the

power for equal tip speed. This difference

in power becomes even greater with larger

scale changes and may be impractical

for some.

OTHER FACTORSBeyond the obvious differences in the

speed and power changes between equal

tip speed and equal power per volume, the

fluid dynamic reasons for choosing one or

the other set of criteria differ. With geomet-

ric similarity and turbulent conditions, the

flow pattern in a stirred tank is a constant.

In other words, the local velocity magnitude

at any point in the tank is proportional to

the impeller tip speed. Equal tip speed for

turbulent mixing and geometric similarity

will result in similar local speeds and rela-

tive velocities throughout a stirred tank.

The velocity of the impeller tip relative to

the surrounding fluid may define important

You should determine scale-up behavior in small-scale tests for best scale-up results.

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Mixing eHANDBOOK: Sidestep Mixing Missteps 7

velocity gradients, which can affect certain

types of dispersion. Drop size in two-phase

liquid/liquid systems and agglomerate

breakup size in solid/liquid systems may

be closely related to impeller tip speed in

scale-up. Power per volume, which also is

power per mass, can be related to turbu-

lence factors, such as micro-scale length

and time or energy dissipation. These

power-per-volume effects may influence

certain types of chemical reactions and

product distributions.

Although some process generalizations

may point in favor of tip speed or power

per volume, you should determine scale-up

behavior in small-scale tests for best

scale-up results. Varying the impeller size as

well as the speed in these tests often may

help better differentiate between scale-up

by tip speed or power per volume.

NON-GEOMETRIC SCALE-UPGeometric similarity, while reducing the

number of variables, isn’t essential for

successful scale-up. One of the most

common geometry changes is the impel-

ler-to-tank-diameter ratio. By simple logic,

a small impeller operating at a high speed

should provide similar results to a large

impeller running as a low speed. What

“similar results” means depends on the

process. Because impeller pumping capac-

ity and power input don’t have the same

functionality with respect to impeller diam-

eter and rotational speed, the tip speeds

or power requirements likely will differ

depending on the impeller-to-tank-diam-

eter ratio. Small impellers tend to operate

at higher tip speeds and power inputs than

large impellers.

Sometimes geometric similarity isn’t prac-

tical or even advisable. Unfortunately,

non-geometric scale-up is a more difficult

process. It may involve several different

combinations of constant or changing

mixing parameters. A step-by-step scale-up

process may begin with a geometric sim-

ilarity scale-up to the large-scale tank

diameter. Once some conditions have been

established in the large scale, you can

adjust liquid level to alter the volume. Then,

you can make further changes to impeller

diameter or type with assumptions about

equal tip speed, equal power per volume, or

other factors (such as torque per volume,

mixing intensity, surface motion, blend

time, and heat or mass transfer rates) being

kept constant or changed. The combina-

tion of factors best suited for successful

non-geometric scale-up will depend on

the particular aim of the mixing.

Perhaps the most difficult scale-up occurs

when viscosity is a significant factor in

mixer performance. High viscosity almost

always makes mixing tougher. However, the

effect of viscosity on mixing isn’t measured

just by the magnitude of the viscosity.

Instead, the impeller Reynolds number, Re,

typically is used. It includes the effect of

www.ChemicalProcessing.com

Mixing eHANDBOOK: Sidestep Mixing Missteps 8

impeller size, rotational speed, fluid den-

sity and apparent viscosity. The Re is the

best way to judge whether fluid motion is

turbulent, transitional or laminar. Because

the impeller diameter appears as a squared

factor in the Re numerator with viscosity

in the denominator, scale-up from a small

mixer to a large mixer increases the Re and

decreases the effect of viscosity magnitude.

This rise in Re with size means that viscos-

ity will have less impact in the large-scale

mixer — and that mixing may get easier as

the scale of the process goes up.

GO BEYOND SIMPLE RULESThe real problem with mixing scale-up is

that the simple rules like tip speed and

power per volume are only part of the

answer. Other factors may help or hurt the

results of using the simple rules. You can

successfully use scale-up to design a mixer

for a process — if you understand the pro-

cess needs and keep the essential features

the same with scale-up. Take advantage

of the many studies of mixing scale-up

reported in books and technical literature.

Scale-up requires some process knowledge

and background information.

DAVID S. DICKEY is a senior consultant at MixTech, Inc.,

Coppell, Texas. E-mail him at d.dickey@mixtech.com.

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Sometimes geometric similarity isn’t practical or

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Mixing eHANDBOOK: Sidestep Mixing Missteps 9

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Inline Blending Offers Multiple BenefitsThese systems offer efficiency, convenience and safety

Robert Brakeman, Sonic Mixing

For ages, factory workers have been

handling drums, totes and pails to

dump numerous ingredients into large

batch tanks manually on load cells with large

horsepower agitators on top. Drum pumps

might be used to transfer liquid material to

the tank based on weight addition. Smaller

pails of material will be trudged up to the top

of the tank and dumped in by hand. A centrif-

ugal or positive displacement (PD) transfer

pump might be wheeled over and connected

to a tote or raw material storage bulk tank as

larger-quantity materials are transferred again

by weight addition.

Large manufacturing sites with larger bud-

gets might be more sophisticated with their

approach by automating these transfers

and will draw from bulk storage versus

totes, drums, etc., when possible. These

ingredient additions still are dumped one

at a time by weight addition. The load cells

or floor scales have to consider the tank’s

weight, so their resolution typically is poor

when it comes to smaller-ingredient dump

amounts, thereby providing poor ratio con-

trol among ingredients.

More advanced factories may use expensive

mass flow meters to “fly in” liquid ingredients

simultaneously but with no guarantee that

the proper amount was dumped as the flow

meters won’t consider material left in piping,

drain amounts, etc. Typically, manufactur-

ers’ recipes include large quantities of either

water or some bulk ingredient. Transferring

water to a batch tank is a wasteful practice,

but we’ll get to that later.

INLINE BLENDING BASICSBatch mixing is confined to a single tank

where all the materials typically are added

Mixing eHANDBOOK: Sidestep Mixing Missteps 11

www.ChemicalProcessing.com

one at a time. This approach has many

inherent drawbacks:

• A large costly tank is required.

• Tanks consume valuable floor space.

• Ingredients usually are added one at

a time.

• Large bulk materials or water are

transferred to this tank, consuming valu-

able space.

• Agitation at large horsepower is

required in the tank.

• Ratio control is not accurate due to

low-resolution flow scales or load cells.

• More tanks are added and more floor

space is consumed as demand for more

capacity grows.

Inline blending systems are used to eliminate

these restrictions and flaws. A typical system

uses multiple PD pumps with various types

of flow meter technologies to meter liquid

ingredients simultaneously into a common

pipeline with static mixers or an alternate

inline shearing device. These PD pumps get

connected to bulk storage tanks, totes, drums

or the factory water supply. Programmable

INLINE BLENDING SYSTEMFigure 1. This diagram shows the mechanics of an inline blending system. Image courtesy of Sonic Corp.

www.ChemicalProcessing.com

Mixing eHANDBOOK: Sidestep Mixing Missteps 12

logic control (PLC) automation onboard the

skid will start and stop these pumps together

and provide PID ratio control for each. Figure 1

illustrates the mechanical concept nicely.

Inline blending systems typically fea-

ture their own onboard controls, which

can be as simple as a PLC by Allen-Brad-

ley or Siemens, for example; an operator

human-machine interface (HMI) panel; and a

variable frequency drive (VFD) inverter cab-

inet. The VFD inverters communicate with

the motors connected to each PD pump to

drive the pump to specific speeds.

The flow meters read the resulting flow from

the PD pumps, and the PLC PID control

block compares the actual flow to a target

flow and adjusts the motor speed (pump

flow rate) automatically via the VFD to track

the flow setpoint accurately. Depending on

the type of flow meters used — Coriolis

mass flow meters by Endress+Hauser and

Micro Motion being the most accurate —

ratio control can be within 0.25 to 0.35%

across two or more feeds.

To keep the inline blending system operating

at a steady state, a buffer tank sometimes

is used that feeds directly to a filling line.

This also eliminates need for large storage

holding tanks, thereby consuming yet less

factory space.

In the most simplistic sense, manufacturers

should avoid transferring water to a batch

tank. Making a concentrate where possible and

using a two-feed inline blend system to meter

the water and the concentrate at ratio is a far

better approach. You do still have to contend

with some level of batch making vis-à-vis the

concentrated premix, but the process is sim-

plified. It ultimately reduces the amount

of water, or other bulk fluid, placed in

a tank, allowing more product yield for

that given tank size.

The idea is to expand from there

and meter all or as many ingredients

as possible. In the case of chemical

cleaning solution, for example, there

are a finite or low number of liquids

to meter from bulk storage and

totes, so zero concentrates or pre-

mixes are required, and everything

is metered from source

such as totes, drums and

bulk storage (Figure 2).

MULTI-FEED INLINE BLENDING SYSTEMFigure 2. This multi-feed inline blending system can be used safely to produce cleaning chemical solutions. Image courtesy of Sonic Corp.

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Mixing eHANDBOOK: Sidestep Mixing Missteps 13

In other processes you might not be so lucky

as to meter everything because you’ll have

powders to deal with, and a premix becomes

unavoidable. Again, the focus is on increased

product yield for given tank and floor space

while reducing tank sizes overall.

THE BENEFITS OF INLINE BLENDINGInline blending can have advantages

over conventional batch mixing meth-

ods. Moving water or other bulk materials

around frequently is wasteful, so moving

from bulk to batch tank and then from

batch tank to hold tank or fillers is waste-

ful. Inline blending systems move finished

product while mixing on the go, in essence

eliminating the middle-man batch mixing

tank. This saves process time by reducing

transfers and eliminating batch tank agita-

tion times. The larger the batch tanks, the

larger the agitator motors. Inline blending

systems can meter as many as four fluids

at 100 gpm total flow at less than 10 hp in

some cases.

Other considerations exist as well. In dealing

with flammable fluids, as discussed, drawing

from bulk tanks located safely outside the

building keeps the building interior safe and

reduces costly fire code issues.

In the case of ethanol or methanol, in the

manufacture of hand sanitizer or windshield

washer fluid, the bulk of the material that

releases larger quantities of flammable

vapors is kept outside.

With batch mixing those materials get trans-

ferred inside in large quantities that render an

XP hazard rating inside the building. An inline

blending system is a closed system that con-

tains only minor volumes of vapor-releasing

liquids inside pumps and piping, insufficient

to require an XP rating (Figure 3).

In summary, inline blending offers:

• elimination of batch mixing tanks

• elimination of multiple transfers

• increased product yield for any premix

tanks used

• increased accuracy of ingredient ratio –

0.25 to 0.35% (flow meter dependent)

• reduced process cycle times

• reduced energy consumption

ROBERT BRAKEMAN is president of Sonic Mixing Corp.

E-mail him at rob.brakeman@sonicmixing.com.

HAZARDOUS CHEMICALS HANDLINGThis multiple-feed inline blend system can be used when working with hazardous chemicals. Image courtesy of Sonic Corp.

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Mixing eHANDBOOK: Sidestep Mixing Missteps 14

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Carefully Evaluate Blending RequirementsWhen choosing a mixer, consider these four key components that can lead to improved mixing

By Roy R. Scott, Arde Barinco

It is not unusual for mixing suppliers to

receive the following request, or simi-

lar: “I need a mixer for a 500-gal. tank.”

The requestor then may expect a product

suggestion to satisfy all requirements. The

supplier’s typical response is, “What is

your mixture’s viscosity?” Many times, this

is the entire conversation, and a mixer’s

specification and pricing proceed from

there. This often can lead to dissatisfying

results. Here are four things to consider

for successful mixing.

1. MAKE SURE IMPELLER IS IMMERSEDAll batch mixers use some type of impel-

ling device that typically is connected to

a shaft driven by an electric motor. That

impeller, sometimes known as a rotor or

a propeller and other times as a turbine,

must be in sufficient contact with the

mixture if it is going to have any success

impelling that mixture (Figure 1).

IMPELLER LENGTHFigure 1. Impeller shaft must be long enough to reach liquid mixture.

Mixing eHANDBOOK: Sidestep Mixing Missteps 16

www.ChemicalProcessing.com

This may seem obvious, but the details of

the process vessel’s shape determine the

details of the mechanical design of the

shaft connected to the mixing impeller. In

short, the impeller’s drive shaft has to be

long enough to reach down into the liquid

at all times if mixing is to proceed. If the

mixing vessel usually is close to full, then

the mixing impeller will make good contact

with the mixture in almost any circumstance

(Figure 2).

If the batch begins with the vessel half-

filled and the other half of the mixture

must be added while mixing, then the mix-

ing impeller must make good contact with

the liquid even when the tank is half-full.

This result is even more difficult to achieve

if the vessel needs to be stirred at a less-

than-half-filled level (Figure 3).

The mixing vessel’s diameter and depth

will determine how much volume exists

at a given fill level. These dimensions are

required to calculate the fill levels to make

sure that the impeller can impel the mix-

ture. Most impellers require some minimum

immersion, such as 6 or 12 in. of mixture

over top of the impeller, to do the job.

After the mixing impeller is configured

and located so that it can start doing its

job of pumping and moving the mixture

throughout the mixing vessel, the pump-

ing and circulation must be strong enough

to mix all areas in the mixing vessel. No

stagnant locations can exist because, if

any of the mixture’s components enter an

area with no flow, they will, by definition,

stay there and not get mixed with the other

components (Figure 4).

PROPER CONTACTFigure 2. This impeller is well covered and in contact with mixture.

FILL LEVELFigure 3. Here, the fill level is too low to cover the impeller and the mix vessel is too wide and shallow.

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Mixing eHANDBOOK: Sidestep Mixing Missteps 17

2. MAKE SURE IMPELLER IMPARTS FLOW TO ALL AREAS OF MIX VESSELThe mixer supplier must offer an impeller

capable of moving the mixture throughout

the vessel, and that impeller will require

a certain amount of mechanical power.

The mixer manufacturer must configure a

power source (motor) along with its shaft

and impeller that can pump the mixture’s

viscosity and density. However, just causing

good flow from top to bottom and round

and round may not produce any mixing at

all. The impeller must produce a pattern of

flow that causes swirls and eddies that can

intermingle the various components.

Sometimes the impeller-produced flow

needs to be baffled by installing station-

ary vertical obstacles in the mixing vessel.

Other mixers operate at very high flow rates

that cause natural flow patterns to produce

good mixing without the installation of

baffles (Figure 5). Once there is sufficient

flow to produce different velocities within

a mixing vessel, these shearing zones then

can produce the desired result (Figure 6).

That is, all of the various components must

exist in the correct percentage for whatever

sample size is taken from the mixing vessel.

This is the definition of successful mixing.

3. MAKE SURE MIXING QUALITY GOALS ARE METEven if the mixer has impelled all of the

various components into the correct per-

centages, additional quality requirements

may exist, such as a desired particle size

distribution of a solid dispersed into a liq-

uid or an emulsion droplet size distribution.

POOR FLOWFigure 4. Impeller is well covered but good flow doesn’t reach lower areas of vessel, allowing set-tling to occur.

FLOW PATTERNSFigure 5. These mixers operate at very high flow rates that cause natural high shear flow patterns to produce good mixing.

Upward “umbrella” flow

Downward “vortex” flow

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Mixing eHANDBOOK: Sidestep Mixing Missteps 18

Perhaps solids need be dissolved into the

liquid at a given concentration.

Mixing quality can be measured in differ-

ent ways. Different desired process results

often will require different types of mixing

equipment. For fine-particle-size dispersion,

mixing equipment generically described as

“high shear” may be required. However, “high

shear” can refer to thousands of mixer types.

In short, the mixing impeller not only must

mix the components to the right ratio but

also may be required to achieve some other

physical or chemical result.

4. MATCH BATCH COMPLETION TIME TO REQUIRED OUTPUTOne more requirement for a mixer to be suc-

cessful is that it must do everything described

above and also do it in the right amount of

time. For a 500-gal. batch, it has been as-

sumed the mixer will produce the volumes

required for the mixer’s owner. How much of

the mixture needs to be made, and how much

per day and how much per year?

Suppose the annual requirements are 100,000

gal. Mixing time for a 500-gal. mixer includes

filling the vessel, adding the other required

components, mixing, dispensing and cleaning

the vessel to make it ready for the next batch.

If these steps take an 8-hr. shift, then it would

take 200 days on a one-shift basis to make

the required 100,000 gal. Because a typical

work year is 200 days, the mixer is successful.

However, if 200,000 gal. are required annual-

ly, the facility would have to go on a two-shift

basis or install two 500-gal. tanks.

Another alternative would be to specify a

faster mixer that might complete the mixing

process twice in one shift. The decision to

use the 500-gal. mixing vessel size might be

reconsidered. Perhaps a larger batch with

a larger, faster mixer would cost less than

starting a second shift.

Extensive research for blending applica-

tions is available in a number of textbooks.

However, for many processes, no substitute

exists for doing experimental trials on a

small scale and then scaling up.

ROY R. SCOTT is sales engineering manager at Carlstadt,

N.J.-based Arde Barinco. Email him at r.scott@ardeinc.com.

SUFFICIENT FLOWFigure 6. Impeller is well covered and close enough to the vessel bottom to reach lower areas of vessel to prevent settling.

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Mixing eHANDBOOK: Sidestep Mixing Missteps 19

Mixing eHANDBOOK: Sidestep Mixing Missteps 20

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