Scale-up of Stirred Tank with Floating Particles

Ondrej Svacina

Tutor: Tomas Jirout

České Vysoké Učení Technické v Praze, Fakulta strojní, Ústav procesní a zpracovatelské

techniky, Technická 4, 166 07 Praha 6, email: Ondrej.Svacina@fs.cvut.cz

Abstract

The mixing and dispersing of a solid phase in liquid is a frequently used process, in many

cases vastly influencing the quality of final product. Over the last few decades many scientific

papers have been devoted describing the phenomena of mixing particles in the liquid phase,

however just a few papers pursued investigating the case when the particles were lighter than

liquids and rose to the surface. The phenomena of mixing liquids with floating particles can

be found in food processing, polymerization reactions, wastewater treatment, fermentation

processes and minerals processing, where the drawdown of floating particles is required. The

aim of this study was to explore the effect of scale on the draw-down of the floating particles

in a liquid medium. Three sizes of fully baffled vessels (0.2, 0.3 and 0.5 m diameters) mixed

with pitched blade turbine (PBT) were investigated. Pumping mode and impeller

submergence have also been studied. The ways in which floating solids are drawn down are

discussed and appropriate scale up criteria for each configuration is proposed.

Keywords

Floating particles, impeller, mixing, pitched blade turbine, scale-up, solids drawdown, solid-

liquid mixing, stirred vessel, suspension

1. Introduction

Mixing is one of the most common processing operation in a chemical, food and processing

industry. The purpose of the mixing is preparation of mixtures of required characteristics,

homogenization or intensification of heat and mass transfer. The mixing operations are being

often accompanied by chemical or biochemical reactions. The size of mixed equipment used

in industry reaches from few liter, as in case of pharmaceutical, up to thousands of cubic

meters, as in case of petrol depots.

An industrial production mixing unit is mostly not similar size or geometry to the mixer unit

used for process development in laboratory. Such differences can make scale-up from the

laboratory or pilot plant challenging. A solution to these problems is to systematically

consider, evaluate and calculate mixing characteristics for each change.

Successful scale-up of mixing equipment can rely on empirical data and experience or on

straightforward formulas; the best way is to combine both.

2. Scale-up Theory

Scaling up of mixing operation from a laboratory or pilot plant requires that the physical and

chemical properties of the product are similar at the full-scale plant level. It also requires that

the desired outcome is produced within a reasonable amount of time. Below are some items

worth considering before and during the scale-up phase of any mixing in tank operation.

Geometric similarity is often used in mixing scale-up because it greatly simplifies design

calculations. Geometric similarity means that a single ratio between small scale and large

scale applies to every length dimension. With geometric similarity, all of the length

dimensions in the large-scale equipment are set by the corresponding dimensions in the small-

scale equipment. Beside that also other parameters must be remained, like the geometrical

shape of bottom, impeller emplacement and number and baffles.

After fulfilling the geometrical similarity scale–up the only remaining variable for scale-up to

large-scale mixing is the rotational speed.

The modeling criterion for rotation speed estimation of a mechanically stirred vessel in a

turbulent regime could be written in general as follows:

(1)

This formula presents the product of impeller rotation speed (N) and impeller diameter (d)

rose to a scaling-up coefficient (γ) being constant for all scaled up vessel sizes. Value of the

scaling-up coefficient (γ) is chosen to best fit the leading phenomena in a scaled-up process,

like homogenization, mass or heat transfer etc. and also being economically sustainable.

One or more mixing characteristics, such as tip speed, rotation speed etc., can be duplicated

by the appropriate selection of a large-scale mixer speed. The most common are the three

following scale-up modeling criteria.

-Scale-up modeling criteria of constant tip speed N.d:

(2)

-Scale-up modeling criteria of constant power input per volume unit ε:

(3)

-Scale-up modeling criteria of constant Froude number Fr:

(4)

Below are mentioned some examples of which scale-up criteria to use for which process.

Scale-up coefficient γ is being chosen from range 1/2 ÷ 1 for suspendation of settling solids,

exact number depends on the size of solid particles, smaller the particles are, smaller

coefficient being chosen [20]. Exact number must be laboratory versified.

For homogenization in turbulent regime scale-up coefficient γ should be equal to 0, as it

comes from theoretical analysis of the phenomena. This means that rotation speed is kept

constant for all sizes of vessels and the power input will rise with the fifth power of the

impeller diameter ratio of commerce unit to laboratory unit, as is obvious from the Formula

(5). This is economically unsustainable, so practically condition of constant power input (γ =

2/3) is being chosen and the worse homogenization efficiency is replaced by longer

homogenization time in the production unit.

Similar approach is applied for mixing processes involving heat transfer. It shows from

theoretical analysis of heat transfer in mixed vessel, that the scale-up coefficient γ should be

equal to 1/2 if the value of heat transfer coefficient is kept constant. In case the constant heat

flux from vessel volume is require, commonly for mixed chemical reaction, the scale-up

coefficient γ should be equal to -1, to withstand the requirement. This means, that the impeller

power input will rise with the eight power of the impeller diameter ratio of commerce unit to

laboratory unit. This is of course unachievable, so additional heat transfer surface like

heating/cooling coil is rather installed. For more details see publications [17, 20].

Calculation of dimensionless Power number:

(5)

Calculation of dimensionless Froude number:

(6)

3. Literature research

Drawdown of the floating solids has been investigated only in a few papers up to the present.

Most of the attention is paid to find the most efficient configuration in a sense of critical

rotation speed NJD for drawdown of the floating solids. Authors are mostly comparing

different number and length of baffles, pumping modes, types of impellers and its

submergence.

Khazam O. [11] based on his research recommends to use surface baffles rather than half or

full-baffles. Author reports that the surface baffles are able to maintain a high level of

turbulence at the surface while reducing recirculation from the bottom of the vessel which is

taking out once submerged particles back to surface. He further describes dominant

mechanisms in his next paper [12] and points out that the relationship between solids

concentration and critical just drawdown speed NJD is linear and the difference in density

between the phases increases the velocity NJD needed to pull the particle down.

Kuzmanic N. [13] investigated the impact of floating solids concentration, particle size

distribution and impeller dimension and its blade angle on the mixing time. The following

conclusions were done. The floating solids in the liquid significantly affect the mixing time

(even five times), the mixing time of the suspension increases with increase of solid

concentration and their particle size. With the increase of impeller diameter as well as with an

increase of blade angel, the value of dimensionless mixing time decreases, but the impeller

power consumption increases.

Karcz J. [8, 9] pointed out that the critical drawdown agitator speed NJD increases with the

increase of particle concentration and also baffling of the agitated vessels affects significantly

NJD required to disperse of the floating particles into a liquid. Floating particles are the best

dispersed in agitated vessel equipped with the up-pumping pitched turbine placed near the

surface and also in some configurations two half-baffles perform better than standard four-

baffles. Karcz J. [7] as well looked into an effect of particle wettability on a drawdown of

floating solids. Small amount of the surface active agent (0.5% wt.) added to the liquid phase

causes an increase of particle wettability and decreases the critical impeller speed NJD needed

for drawdown floating particles. On the other hand too high concentration of the surface-

active agent (2,5 % wt.) can cause change of liquid density, viscosity and density difference

and consequently increase the values of NJD.

Ozcan-Taskin’s [14, 16] research was interested in the effect of impeller-to-tank diameter

ration for wide range of submergences and both pumping modes. He described two types of

drawn down mechanisms, recirculation loops or air ingesting vortices. Air ingesting vortices

were observed only for downward pumping large diameter impellers, the other cases of drawn

down of solids were done by recirculation loops. Decreasing the submergence of the up-

pumping impeller results in decrease of rotation speed NJD and power requirement PJD. The

opposite was found for downward pumping impeller. Larger impeller has a stronger radial

component of flow, which is directed towards the walls, so lower rotation speed NJD is

achieved using them, but higher energy input PJD is required. Author recommends for

practical (industrial) usage an axial or a mixed flow impeller mounted close to the base,

mostly because of preventing air entrainment from surface and flexibility to liquid level

changes.

Ozcan-Taskin G. [15] is the only available author dealing with the scale-up effect for the

mixing of floating solids in classical mixing configuration. He proceeded his research in two

fully baffled vessels of diameters 0.61 m and 2.67 m with pitched blade turbine and narrow

blade hydrofoil, both pumping upward and downward varying the impeller submergence.

Author found that specific power input εJD is the best for scale-up of up-pumping impellers,

for down-pumping impellers none of the three (Froude number, specific power input and

constant tip speed) correlates data well. He ascribes this to the different mechanisms of

drawdown involved with down pumping impeller or long term flow instabilities.

Next works as Joostens [5] or Hemrajani [4] used specific geometries, one or two partial

baffles at liquid surface, which encouraging central vortex formation and drawing down solids

along with the air. They recommend constant Froude number for scaling.

4. Measuring Techniques

Measurement of drawdown solid floating particles can be done by two methods. First method

concerning measurement of just drawdown impeller rotation speed NJD, when the observed

particles do not stay on the surface longer that stated time define by observer. The time

criterion is called modified Zwietering criterion, originally used for suspendation of

sedimenting particles measurements. This method is purely based on observers estimation of

the just drawdown rotation speed NJD, so it is pure subjective method. Most of the

investigators use this method. During the measurement also the power input or cloud depth is

measured. Cloud depth CD is a perpendicular distance from the liquid surface to the point

where the presence of the submerged particles decreases dramatically. Cloud depth is

measured when just drawdown rotation speed is achieved. The cloud depth CD gives the

indication of how well the particles are distributed through the volume of a vessel.

Measurement of CD can be found in a work of Khazam O. [11].

Second method is concerning measurement of mixing time tm and just completely suspended

impeller rotation speed NJS, speed at which stagnant zones of floating solids at the liquid

surface had just disappeared. Mixing time tm is measured using a conductivity method [13] or

decolourisation technique.

5. Experimental

Experimental studies for scale-up were carried out in three cylindrical vessels with flat

bottom, made of glass, which allowed visual observation from the side. The vessels were of

diameter 200, 300 and 500 mm, these are referred to as D=200, D=300 and D=500 later in the

text.

Standard 45° pitched four-blade turbine (4-PBT-45°) with diameter d=D/3 was tested, placed

at position h=0.33H and h=0.66H from bottom of the vessel (further referred as h=0.33 and

h=0.66). Impeller characterized by axial flow with also strong radial fluid flow (mixed flow

impeller) was set work in two modes, upward-pumping (-UP) and downward-pumping (-

DOWN) mode for each configuration.

Arrangement of centrically located impeller with standard four baffles was used. Baffles were

planar of the width B=0.1D and the length L=H in all cases.

Two types of particles were used, white polypropylene cylinders (WHITE P.) with the mean

diameter dP1= 3.7 mm, length lP1 = 5.3 mm and density ρP1= 894 kg/m3 and black

polypropylene cylinders (BLACK P.) with mean diameter dP2=2.9 mm, length lP1 = 3.3 mm

and density ρp2= 843 kg/m3. Mass concentrations of particles cP in range 0.5 ÷ 10 % were

tested.

Modified Zwietering criterion for just suspended condition was used for visual estimation of

critical just drawdown agitator speed NJD for the floating particles, speed at which no particles

stayed longer than 2 seconds on the surface of the liquid.

5.1 Experimental set-up

Height of liquid in a vessel

(7a)

Mixed volume

(7b)

Baffles width

(7c)

Impeller diameter

(7d)

Impeller submergence (*) (7e)

*) should be understand as the distance of an impeller from the vessel bottom

h

B d

D

H

Figure 1 – Laboratory aperture scheme

Figure 2 - Two types of experimental solid particles (White and Black particles)

5.2 Observation practice

Visual method of estimation of just drawdown speed by visual method is very easy

achievable, but suffers of considerable subjectivity and error in proper estimation of NJD for

different mixing models. Some observed particles in the vessel have been colored by reflexive

color for better visualization of the suspension motion. This helps to minimalize observation

errors in case of estimation of time spent by particles on the surface especially at higher

particle concentration.

Also each experiment was repeated 2 times and the results presented in this paper are average

of these. The fact that particles are drawn down by different ways thanks to different pumping

modes and submergences must be taken into account, so the visual observation while

determining just drawdown state NJD have to be carried out over long period of time (in our

case at least 5 minutes) to cover also long-term instabilities in flow as mentioned by Ozcan-

Taskin G. [15]. These are mostly typical for down pumping mode with deeper submergence

of the impeller.

Authors in literature mostly choose time criterion in range from 1 to 4 seconds. Time criterion

of 2 seconds for just drawdown was based on our best practice. High turbidity motion is

required to achieve short time stay of the particles on the surface which is mostly

accompanied by high rotation speed, central vortex generation and air entrapment to liquid.

All of these effects are unwanted for real industry process. For instance Karcz J.[6, 8] also use

the time criteria of 2 seconds.

Subjective mistake in correct estimation of NJD is estimated up to speed +/- 20min

-1.

6. Data evaluation

Just drawdown rotation speed NJD was measured in 3 vessels of different sizes, in 2

configurations and 2 modes of pumping in range from 0,5 to 10% mass particle concentration.

Obtained data for white particles can be seen in Figure 3, data for black particles can be seen

in Figure 4.

Figure 3 - Effect of solid particle concentration cP on just drawdown speed NJD (White

particles)

Afterwards data of just drawdown rotation speed NJD for all three vessel sizes and each

particle concentration and corresponding mixing configuration were put in a ration each to

another according to Formula 8.

(

) (

)

(8)

This way, the scale-up index γ for each configuration and particle concentration was obtained.

Practically this was done by using logarithmic graph with represented data of rotation speed

in all three vessels for each inspected configuration. An example can be seen in Figure 5.

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6 7 8 9 10

Just

dra

wd

ow

n r

oat

ion

sp

ee

d N

JD [

1/m

in]

Solids mass concentration cP [% ms.]

DOWN h=0,33 D=200 UP h=0,33 D=200 DOWN h=0,66 D=200

UP h=0,66 D=200 DOWN h=0,33 D=300 UP h=0,33 D=300

DOWN h=0,66 D=300 UP h=0,66 D=300 DOWN h=0,33 D=500

UP h=0,33 D=500 DOWN h=0,66 D=500 UP h=0,66 D=500

Figure 4- Effect of solid particle concentration cP on just drawdown speed NJD (Black

particles)

Figure 5- Estimation of Scale-up coefficient γ from logarithmic graph

Summarized results are presented in Table 1, 2 and Figure 6, 7. Numbers in italics were

excluded from average evaluation.

0

200

400

600

800

1000

1200

1400

0 1 2 3 4 5 6 7 8 9 10

Just

dra

wd

ow

n r

oat

ion

sp

ee

d N

JD [

1/m

in]

Solids mass concentration cP [% ms.]

DOWN h=0,33 D=200 UP h=0,33 D=200 DOWN h=0,66 D=200

UP h=0,66 D=200 DOWN h=0,33 D=300 UP h=0,33 D=300

DOWN h=0,66 D=300 UP h=0,66 D=300 DOWN h=0,33 D=500

UP h=0,33 D=500 DOWN h=0,66 D=500 UP h=0,66 D=500

y = 0,9922x0,8811 R² = 0,9947

y = 1,006x0,7629 R² = 0,9958

y = 0,9478x0,7566 R² = 0,7468

y = 0,946x0,9143 R² = 0,8006

1

1,4 2,8

Log

(ni/

nj)

Log (dj/di)

DOWN h=0,33 UP h=0,33 DOWN h=0,66 UP h=0,66

Table 1 - Scale-up coefficients for inspected geometries (White particles)

Table 2- Scale-up coefficients for inspected geometries (Black particles)

Figure 6 - Effect of solid particle concentration cP on Scale-up coefficient γ (White particles)

Pumping mode: Off-bottom clearance: 0.5 1 2.5 5 7.5 10 Average: Error (+/-):

DOWN h=0,33 0,84 0,92 1,09 1,07 1,09 1,05 1,04 0,10

UP h=0,33 0,50 0,63 0,84 0,90 0,85 0,83 0,81 0,15

DOWN h=0,66 0,22 0,50 0,62 0,64 0,68 0,76 0,67 0,13

UP h=0,66 0,55 0,64 0,80 0,81 0,85 0,84 0,82 0,05

Scale-up coefficiet γ [-] White particles

Particle Concentration [% ms.]Geometry:

Pumping mode: Off-bottom clearance: 0.5 1 2.5 5 7.5 10 Average: Error (+/-):

DOWN h=0,33 0,87 0,88 0,97 0,87 0,88 0,75 0,87 0,08

UP h=0,33 0,53 0,67 0,76 0,79 0,76 0,66 0,70 0,11

DOWN h=0,66 0,64 0,64 0,69 0,70 0,76 0,60 0,67 0,06

UP h=0,66 0,75 0,80 0,87 0,95 0,91 0,79 0,84 0,09

Scale-up coefficiet γ [-] Black particles

Particle Concentration [% ms.]Geometry:

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1,1

0 1 2 3 4 5 6 7 8 9 10 11

Scal

e-u

p C

oe

ffic

ien

t γ

Particle concentration CP (% ms.]

WHITE P. DOWN h=0,33 WHITE P. UP h=0,33 WHITE P. DOWN h=0,66 WHITE UP h=0,66

Figure 7 - Effect of solid particle concentration cP on Scale-up coefficient γ (Black particles)

As can be seen from average values of scale-up coefficient in Table 3, values of scale-up

coefficient are different for various configurations but do not differ for of particle type.

Table 3 - Average scale-up coefficient γ values for each investigated configuration

Based on obtained results it can be concluded, that scale-up coefficient for down-pumping

impeller (4-PBT-45°) nearer to the vessel bottom is in range of 0.87 to 1.04. The analogy with

constant tip speed scale-up criteria can be applied, see Formula 2.

In case of down-pumping impeller placed near to the surface the value of scale up coefficient

γ equal to 0.67 was measured. This corresponds to scale-up criteria of constant power per unit

volume (Formula 3).

If the impeller is pumping upwards, the influence of submergence is not essential for scale-up

coefficient estimation. The scale-up coefficient values range in-between 0.70 ÷ 0.84. None of

the three previously mentioned scale-up criteria can be directly applied.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 1 2 3 4 5 6 7 8 9 10 11

Scal

e-u

p C

oe

ffic

ien

t γ

Particle concentration CP (% ms.]

BLACK P. DOWN h=0,33 BLACK P. UP h=0,33 BLACK P. DOWN h=0,66 BLACK UP h=0,66

Pumping mode: Off-bottom clearance: Black p. White p. Average: Error (+/-):

DOWN h=0,33 1,04 0,87 0,96 0,09

UP h=0,33 0,81 0,70 0,75 0,13

DOWN h=0,66 0,67 0,67 0,67 0,10

UP h=0,66 0,82 0,84 0,83 0,07

Scale-up coefficiet γ [-]

Geometry:

Only one study concerning scaling up of floating particles was found [15] to compare

obtained results. Ozcan-Taskin G. [15] found that the constant power per volume εJD (specific

power input) is the most appropriate criterion for scaling upward impeller mixing of floating

particles. None of three tested criteria (Fr, P/V, N.d) correlated data well for downward

pumping impeller. This is different from results presented in this paper. Discrepancy can be

caused by following influences.

Ozcan-Taskin G. [15] carried out his measurements only in two vessel sizes and he was able

to measure only four values of submergence in a bigger vessel (T267). In this case one

measurement error can easily influence obtained results. On the other hand Ozcan-Taskin G.

was measuring in vessel of larger size difference (D = 0.61 m and D = 2.67 m), where the

influence of scaling of size can be better noticed. Author also used the vessels with

torispherical base, but this is not expected to have important influence. Other parameters are

almost same, fully baffled vessels, impeller type (4-PBT-45°) time criterion (2 seconds)

particle size (5 x 3 x 2 mm). Particle properties like shape or surface tension should also be

taken into account.

The difference can be caused by inaccuracy and subjectivity of the visual measuring method

and accumulation of (slight) differences in a measurement set up.

Based on research results following recommendation are given. For downward pumping

impeller placed near to the bottom usage of scale-up coefficient equal to 1 is recommended

for model enlargement. In case an impeller is placed near to the surface, usage of scale-up

coefficient equal to 2/3 is recommended.

For upward pumping impeller usage of scale-up coefficient equal to 0.8 is recommended for

model enlargement. This is recommendation for upward pumping impeller is independent on

impeller submergence

All the recommended and measured scale-up coefficients are in range of 2/3 ÷ 1 which causes

that the power per volume (εJD) will stay constant (γ = 2/3) or will slightly decrease (γ > 2/3)

when scaling up laboratory model to industry unit, which is favorable.

This effect can be seen in Figure 8, comparing power input per volume for vessels of

diameter D=200 mm and D=500 mm. This figure also illustrates, that the upward pumping

impeller placed near the liquid surface is the most favorable from point of view of power

consumption, opposite to this the configuration of downward pumping impeller placed near

the bottom is the most energetically demanding.

Data for power input were calculated based on formula for power number, see Formula 5.

Dimensionless values of power numbers for the researched configurations were obtained in

previous research [19].

Figure 8- Power per volume needed for drawdown effect for different configuration (D=500,

Black particles)

Above proposed values for scale up coefficient for each configuration were used to predict

just drawdown rotation speed NJD in the biggest vessel (D=500) from data obtained by

measurement in two smaller ones (D=200 and D=300).Comparison of predicted and measured

rotation speed can be seen in Figures 9 ÷ 12 within ±30 % error.

Figure 9 - Scale-up based on constant tip speed criterion (γ = 1); Left-White particles. Right -

Black particles.

0

500

1000

1500

2000

2500

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0

Just

dra

wd

ow

n p

ow

er

pe

r vo

lum

e P

JD /

V [

W/m

3 ]

Solids mass concentration cP [% ms.]

DOWN h=0,33 D=300 UP h=0,33 D=300 DOWN h=0,66 D=300

UP h=0,66 D=300 DOWN h=0,33 D=500 UP h=0,33 D=500

DOWN h=0,66 D=500 UP h=0,66 D=500

Figure 10 - Scale-up based on scale up coefficient equal to 0.8 (γ = 0.8); Left-White particles.

Right - Black particles.

Figure 11 - Scale-up based on constant power per unit volume (γ = 2/3); Left-White particles.

Right - Black particles

Figure 12 - Scale-up based on scale up coefficient equal to 0.8 (γ=0.8); Left-White particles.

Right - Black particles.

7. Observed effects

When the impeller is set to down-pumping mode and placed close to the bottom, solids are

drawn down from the surface close to the vessel walls or central shaft through recirculation

loops.

During this process the submerged particles are almost equally distributed in the volume,

which can be more important for some industrial processes than lower power efficiency of

this configuration.

Attention needs to be pay to the “dead zones” emerging in the occultation of the baffles,

which were spotted for this configuration in fully baffled tank. Particles “hidden” in the

occultation of the baffles are not so much exposed to the surface turbidity than then rest on the

surface and tend to stay for longer time on the surface, higher rotation speed is needed to be

set to submerge them.

In case the impeller is placed closer to the surface, particles are drawn down by vortexes

emerging on the surface. If the higher concentration of particles is mixed or if the shorted

residence time of the particles on the surface is required, higher rotation is necessary to be set

and central vortex near shaft is formed and the particles are entrained along with the air.

When the impeller is set to up-pumping mode and placed close to the surface, flow from the

impeller can directly act on the surface, solids are drawn down from the surface by main

circulation loop producing wavy surface trapping the floating particles. This causes the

decrease of rotation speed and power input. Up-pumping impeller placed near to the surface is

the most efficient configuration for fully baffled vessel [19].

When the submergence of the up-pumping impeller increases, the mixer’s direct impact on

the surface decreases and particles are drawn down thanks to recirculation loops and vortexes.

8. Conclusions

Linear dependence of just draw down rotation speed NJD on floating solids concentration was

verified.

From all investigated configuration, the lowest impeller rotation speed needed for particle

drawdown in a fully baffled vessel is achieved by upward pumping impeller placed near to a

liquid surface (h=0.66). This configuration also requires the lowest power per volume

(specific power input) εJD. The most energetically demanding configuration is downward

pumping impeller placed near to a vessel bottom (h=0.33). On the other hand, this

configuration proves the best redistribution of submerged particles in the vessel volume.

For scale-up, constant tip speed (N.d const.) was found to be the best appropriate criterion to

model scaling of downward pumping impeller (4-PBT-45°) placed near to a bottom in a fully

baffled tank.

For downward pumping impeller placed near to a liquid surface, criterion of constant power

per unit volume correlates this geometry the best.

In case of upward pumping impeller, the factor of impeller submergence seems does not play

an important role. Scale-up coefficients (γ) should be chosen in range of 0.7 to 0.84.

Symbols

B baffle width [m]

CD cloud depth (of submerged solid particles) [-]

d impeller diameter [m]

dP solid particle diameter [m]

D vessel diameter [m]

Fr Froude number [-]

Fr´ modified Froude number [-]

h impellers height from the vessel bottom [m]

H liquid height in the vessel [m]

N impeller rotation speed [s-1

]

NJD just draw down impeller rotation speed [s-1

]

P power input [W]

PJD power input at NJD [W]

Po dimensionless power number [-]

Re Reynolds number [-]

V liquid volume [m3]

γ Scale-up coefficient [-]

εJD power input at NJD [W/m3]

ρL liquid density [kg/m3]

ρP solid particle density [kg/m3]

μ dynamic viscosity [Pa.s]

4-PBT-45° standard 45° pitched four-blade turbine [-]

References

[1] Bakker, A., & Frijlink, J. J., The drawn down and dispersion of floating solids in aerated

and unaerated vessel. 1989, Chemical Engineering Research & Design, 67, 208–210.

[2] Edward, L. P., Handbook of industrial mixing, 2004 John Wiley & Sons, ISBN 0-471-

26919-0

[3] Harnby N., Edwards M. F., Mixing in the process industries- (Chapter 6), 2008

Butterworth-Heinemann, ISBN: 978-0-7506-3760-2.

[4] Hemrajani, R.R., Smith D.L., Suspending floating solids in stirred tanks: mixer design,

scale-up and optimization. 1988Sixth European conference on Mixing , 24-26 May Pavia,

Italy

[5] Joosten, G. E. H., Smith, J. G. M., & Broere, A. M. (1977). The suspension of floating

solids in stirred vessel. Transactions of the Institution of Chemical Engineers, 55, 220–222.

[6] Karcz, J., & Mackiewicz, B. (2006). Suspending of floating solids in an agitated vessel.

Inzynieria Chemiczna i Procesowa, 27, 1517–1533.

[7] Karcz, J., Mackiewicz, B., An effect of particles wettability on the drawdown of floating

solids in a baffled agitated vessel equipped with a high-speed impeller.2007, Inzynieria

Chemiczna i Procesowa, 28, 661–672.

[8] Karcz, J., Mackiewicz B., Effects of vessel baffling on the drawdown of floating solids.

2009, Chemical Papers, Vol. 63(2), p. 164-171.

[9] Karcz, J., Mackiewicz B., Suspension of floating solids in an agitated vessel. 2006,

Chemical and Process Engineering, Vol. 27. p. 1517-1533.

[10] Karcz, J., Major M., An effect of baffling on the power consumption in an agitated

vessel. 1998, Chemical Engineering and Processing, Vol. 37, p. 249-256.

[11] Khazam, O., Kresta M.S., A novel geometry for solids drawdown in stirred tanks. 2009,

Chemical Engineering Research and Design, Vol. 87, p. 280-290.

[12] Khazam, O., Kresta M.S., Mechanism of solids drawdown in stirred tanks. 2008, The

Canadian Journal of Chemical Engineering, Vol. 86, p. 622-634.

[13] Kuzmanic, N., Ljubičic B., Suspension of floating solids with up-pumping pitched blade

impellers, mixing time and power characteristics. 2001, Chemical Engineering Journal Vol.

84 p. 325-333

[14] Ozcan-Taskin, G., McGrath, G., Draw down of light particles in stirred tanks. 2001,

Trans. IChemE, Vol. 79, Part A

[15] Ozcan-Taskin, G., Effect of scale on the drawdown of floating solids. 2006, Chemical

Engineering Science, 60, 2871–2879.

[16] Ozcan-Taskin, G., Wei, H., The effect of impeller to-tank diameter ratio on draw down

of solids. 2003, Chemical Engineering Science, Vol. 58, p.2011–2022.

[17] Perry, R., Perry's Chemical Engineers' Handbook- Eighth Edition, 2008 McGraw-Hill,

ISBN 0-07-142294-3

[18] Svačina. O., Jirout, T., Míchaní suspenzí částic lehčích než kapalina. 2012, presented at

the conference Procecesní technika 2011, collection book ISBN 978-80-01-04858-0.

[19] Svačina. O., Jirout, T., The effect of the stirred vessel geometry arrangement on the

drawdown of floating solids. 2012, presented at the conference Procecesní technika 2012,

collection book ISBN 978-80-01-05109-2.

[20] Šulc, R., Zvětšování měřítka v mechanicky míchaných nádobách. Habilitační přednáška,

ČVUT Praha, 2012.

[21] Takahashi, K., & Sasaki, S. J., Complete drawn down and dispersion of floating solids in

agitated vessel equipped with ordinary impellers. 1999, Journal of Chemical Engineering of

Japan, 32(1), 40–44.