Kinetics of Fluid-solid Reaction With an Insoluble Product_ Zinc Borate by the Reaction of Boric...

8/14/2019 Kinetics of Fluid-solid Reaction With an Insoluble Product_ Zinc Borate by the Reaction of Boric Acid and Zinc Oxide

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Journal of Chemical Technology and Biotechnology J Chem Technol Biotechnol 79:526532 (online: 2004)DOI: 10.1002/jctb.1018

Kinetics of fluidsolid reaction with aninsoluble product: zinc borate by the

reaction of boric acid and zinc oxideAparna V Shete, Sudhir B Sawant and Vishwas G PangarkarMumbai University Institute of Chemical Technology, Matunga, Mumbai400 019, India

Abstract: Mixing parameters influencing the final particle size and conversion of zinc oxide were studied

for the formation of zinc borate. Formation of zinc borate was via a fluidsolid reaction. The process was

kinetically controlled above the minimum speed for particle suspension, Ns. The reaction kinetics was

developed and the rate constant was estimated.

2004 Society of Chemical Industry

Keywords: precipitation; mixing; zinc Borate; hydrodynamics; kinetics

NOTATION

aP Particle liquid interfacial area (cm2 cm3)

cB0 Initial concentration of boric acid (kmolm3)

cBt Concentration of boric acid at time t

(kmol m3)

Dp Volume average crystal diameter (m)

dcBt/dt Rate of decomposition of boric acid (kmol

m3 s1)

dpi Diameter of crystals (m)

dpin Initial diameter of particle of zinc oxide (m)

dpt Diameter of particle of zinc oxide at time t(m)f(x) Function dependent of conversion, (1 x)1/3

(cB0 3winx/mv) (kmol m3)

kr Rate constant (cm s1)

kr Constant, kr/6dpin (s1)

m Relative molecular mass of zinc oxide

m Mass of reaction mixture

P Power dissipated, W

N Number of zinc oxide particles

t Time (s)

v Volume of boric acid solution (m3)

vi Volume fraction of crystals diameter dpi

w Mass of zinc oxide (kg)win Initial mass of zinc oxide (kg)

wt Mass of zinc oxide at time t (kg)

x Fractional conversion of zinc oxide at time t

Density (kg m3)

1 INTRODUCTION

Particle size is one of the important properties of a

material used as an additive. Also on an industrial

scale, the mean particle size of bulk solids, in some

way, governs the behavior of the particulate mass.

The hydrodynamic factors as signified by the speed of

agitation, type of agitator (high shear/low shear, higher

pumping) etc play an important role in deciding the

final size of the precipitated reaction product.1

A large body of work has been reported on the

effect of hydrodynamic conditions on the reactive

precipitation of inorganic salts. Recently, there has

been an investigation into the effect of hydrodynamic

conditions on crystal size of sodium perborate

tetrahydrate.1 It was concluded that mixing conditions

affect secondary nucleation which in turn determinesthe final crystal size.1 The influence of hydrodynamic

conditions on precipitation of calcium oxalate by

the reaction between calcium chloride and sodium

carbonate/sodium oxalate have been studied.2 Studies

on the precipitation of benzoic acid have observed that

process variables such as stirring speed and reactant

concentration may influence the products crystal size

distribution.3

The effect of mixing parameters has been studied

for the precipitation of barium sulfate produced by the

reaction of barium chloride with sodium sulfate.4 7

A new model of micro-mixing was used to evaluatethe influence of intensity of mixing on the rate of

precipitation and on the particle size of the product

obtained.4 A maximum decrease in crystal mean size

with increase in stirring rate during precipitation of

barium sulfate was observed.5 Mixing models from the

literature were combined with a precipitation model.6

The resulting model was validated using data obtained

from experiments on barium sulfate precipitation.

Almost all the studies in the published literature deal

with precipitation of a crystalline product as the result

of a homogeneous reaction between two liquid phase

Correspondence to: Vishwas G Pangarkar, Mumbai University Institute of Chemical Technology, Matunga, Mumbai400 019, India

E-mail: [email protected]

(Received 2 June 2003; revised version received 13 October 2003; accepted 8 December 2003)

2004 Society of Chemical Industry. J Chem Technol Biotechnol 02682575/2004/$30.00 526


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Formation of zinc borate

reactants. Practically no work has been published that

could adequately describe the influence of mixing on

batch reactive precipitation of a product formed by a

heterogeneous reaction between a solid and dissolved

liquid reactant producing an insoluble product.

The purpose of this article is to present a

comprehensive set of experimental results on the

influence of process variables on the size distribution ofa product made in a batch heterogeneous reaction. The

controlling mechanism, mixing effects and reaction

kinetics were studied. The formation of zinc borate

by reaction of boric acid and zinc oxide is an

industrially important system8 and was chosen as a

model experimental chemical system. The reaction is:

6B(OH)3(aq) + 2ZnO(s)

1(2ZnO.3B2O3.3.5H2O)(s) + 5.5H2O(l) (1)

Zinc borate is (2ZnO.3B2O3.3.5H2O) and is one

of the several types of zinc borates. This compoundhas the unusual property of retaining its water of

hydration at temperatures up to 290 C. This thermal

stability makes it attractive as a fire retardant additive

for plastics and rubbers that require high processing

temperatures. It is also used as an anticorrosive

pigment in coatings. Zinc borate is produced by

reaction between aqueous boric acid and zinc oxide in

the solid state above 70 C.9

2 EXPERIMENTAL

All the experiments were conducted in a 3 dm3

cylindrical glass tank having an internal diameter of

15 cm. The flat-bottomed tank was equipped with

four glass baffles of height 17 cm. It was immersed in a

thermostatic bath to maintain the reaction temperature

throughout the experiments. A stirrer was used to

ensure proper mixing. A digital photo-type tachometer

was employed to read the stirring speed of the impeller.

A batch mode of operation was adopted, since

boric acid is soluble in water above 90 C. Initially

a known quantity of boric acid was dissolved in water

by heating the mixture to the reaction temperature.

After obtaining a clear, transparent solution, a known

amount of zinc oxide was added to this solution.Samples were collected at intervals of 30 min after the

addition of the zinc oxide. Samples were dried and

analyzed by titration for checking the conversion of

the zinc oxide. Five hours after the addition of zinc

oxide, almost complete conversion to zinc borate was

achieved. The particle size was determined for the final

product and was measured with the help of Coulter

counter particle size analyzer LS230.

The volume average crystal size was determined as:

Dp =

vidpi (2)

A standard six-bladed Rushton disc turbine (DT), a

six-bladed 45 pitched blade downflow turbine (PTD)

and a three-bladed hydrofoil impeller (HF3) were used

to study the effect of the type of impeller. To study

the suspension of zinc oxide, the impeller speed was

varied. For the DT and PTD stirrers, the speed of

agitation was maintained between 4.2 and 7.1 rev s1

while the range of speed of agitation for the HF3

system was between 8.3 and 11.7 rev s1. These ranges

spanned conditions ranging from solids partially

suspended to fully suspended. The temperature ofreaction was varied from 90 to 110C. The boric

acid to zinc oxide mole ratios employed were 3:1,

4:1 and 5:1. For the study of the effect of mean

initial particle size, three sizes of zinc oxide were used:

20.30m (50 100m), 26.29 m (100150 m) and

26.98m (150180 m). The figures 20.30 m,

26.29m, 26.98m are the average volume based

crystal sizes measured with the Coulter counter.

The corresponding screen sizes were 50 100m,

100150 m, and 150 180m, respectively. There

is a large difference between the apparent diameter

of the particles from screen analysis and the Coulter

counter analysis, caused by the irregular shapes of the

particles.

For all experiments the zinc oxide was added in

a fixed quantity, varying the quantity of boric acid.

A DT at a stirring speed of 5.8 rev s1 was used for

determining the effects of temperature of reaction,

concentration of boric acid and mean initial particle

size of zinc oxide.

3 ANALYTICAL

The progress of the reaction was followed with the

help of EDTA titration10 using the following reagents:

EDTA solution, 0.05M: 18.613g of AR disodium

dihydrogen ethylenediaminetetraacetate dihydrate dis-

solved in water and diluted to 1 dm3 with redistilled

water.

Erichrome Black T indicator: 0.2 g of dyestuff dissolved

in 15 cm3 of tetraethanolamine and 5 cm3 of absolute

ethanol.

Zinc oxide solution: 2 g of dried reaction sample

which was collected during experiments dissolved in

dilute sulfuric acid and then diluted to 250 cm3 with

redistilled water.Buffer solution: AR ammonia buffer solution obtained

from E Merck (India) Ltd, Mumbai (product code no

61759205001046) was used for titration.

4 RESULTS AND DISCUSSION

Most precipitation reactions are homogeneous but

for the particular reaction which was studied in this

work, one of the reactants, boric acid, was in solution

while the other reactant, zinc oxide, was in solid

form. Therefore the reaction is heterogeneous. Some

assumptions were made, namely:

1. Both zinc oxide particles and zinc borate particles

were assumed to be spherical.

J Chem Technol Biotechnol79:526532 (online: 2004) 527


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AV Shete, SB Sawant, VE Pangarkar

2. Zinc oxide particles were assumed to be insoluble

in water.

3. Boric acid ions in boric acid solution react with zinc

oxide particles on the surface of the latter.

The reaction studied in this work is a fluid particle

forming an insoluble reaction product. It has been sug-

gested that an unreacted-core model applies in suchcircumstances.11 The successive steps visualized dur-

ing the reaction have been described by Levenspiel:11

Step1: Diffusion of borate ions from the bulk of the

boric acid solution to the surface of zinc oxide

particles (physical).

Step2: Penetration and diffusion of borate ions

through the blanket of ash layer covering the

unreacted core to the surface of unreacted core

of zinc oxide (physical).

Step3: Reaction of borate ions with zinc oxide particles

at reaction surface (chemical).

Step4: Formation of zinc borate and diffusion ofco-product water molecule through the ash layer

covering the unreacted core back to the bulk phase

(physical).

Step5 (possibility): Peeling of zinc borate layer due to

shear/collisions, etc.

The fluidsolid nature of the reaction makes it

necessary to study the effect of mixing conditions on

conversion of the zinc oxide along with the mean

particle size of zinc borate.

To determine the effects of mixing, the following

parameters were studied:

(i) Speed of agitation

(ii) Impeller type

(iii) Mean initial particle size of zinc oxide

(iv) Temperature

(v) Initial concentration of boric acid

4.1 Effect of impeller type

PTD, DT and HF3 impellers having a diameter

(0.05 m) equal to one-third of the vessels diameter

(0.15 m) were used in this study. These were located

0.05 m from the vessel bottom. This is a standard

configuration. The minimum suspension speed is animportant parameter in fluid solid reactions since only

when all the particles are suspended will the entire

particle surface be available for the reaction. Each

impeller has a minimum suspension speed,Ns. Forthe

conditions employed, theNs values were 4.92 rev s112

and 5.8rev s113 for PTD and DT, respectively. The

minimum suspension speed was 10 revs1 for the HF3

which was measured experimentally by suspending

particles in a non-reacting medium having the same

physical properties.

Conversion of zinc oxide was higher for the DT

impeller and lower for each of the PTD and HF3

impellers as shown in Fig 1. The effect of impeller

type on mean particle sizes of zinc borate is shown in

Fig 2. Mean particle sizes shown in the graph are the

0

1

0 240 300

DT

Fractiona

lconversion

1.2

0.8

0.6

0.4

0.2

Time (min)

60 120 180

PTD

HF-3

Figure 1. Effect of impeller type on conversion of zinc oxide.

Impellerdisc turbine (DT), six-bladed pitched blade turbine

downflow (PTD), three-bladed hydrofoil impeller (HF3). Temperature

of reaction 90 C. Concentration of boric acid 3:1 mole ratio. Initial

particle size of zinc oxide particles 20.3 m.

5

15

Meanparticlesizeofzincborate(m

106) 25

PTD DT HF-3

Impeller type

Figure 2. Effect of impeller type on mean particle size of zinc borate.

Impellerdisc turbine (DT), six-bladed pitched blade turbine down

flow (PTD), three-bladed hydrofoil impeller (HF3). Temperature of

reaction90 C. Concentration of boric acid 3:1 mole ratio. Initial


values obtained at Ns. As seen from Fig 2, the HF3impeller gave the lowest particle size.

This was probably due to the higher absolute value

of speed of agitation for the HF3 which caused

significant secondary nucleation. Figure 3 shows a

plot of the mean particle size against power input

per unit mass, ie P/m at N/Ns = 1 for the three

different impellers used. Apparently there is no

direct correlation between mean particle size and

P/m. However, the HF3 impeller gave the lowest

mean diameter when compared at the same P/m. A

marginally higher speed than the minimum suspension

speed gave 20% lower particle size and better

conversion than that achieved at minimum suspension

speed, while the particle size was higher and conversion

was lower for speeds slightly lower than minimum

528 J Chem Technol Biotechnol 79:526532 (online: 2004)


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5

15

25

0 1

Particlediameter(m

106)

HF3DT

PTD

0.2 0.4

P/m, W kg-1

0.6 0.8

Figure 3. Plot of the mean particle size against P/m at N/Ns = 1 for

three different impellers used.

suspension speed. Aeration effects were observed for

some initial experiments carried out at very high speedsgreater than the minimum suspension speed. The ratio

of actual speed of rotation N to Ns is a significant

operating parameter which defines the degree of

suspension of the particles at the actual impeller

speed with respect to the just-suspension condition

at impeller speed Ns. The fraction of unsuspended

solids was correlated uniquely with the ratio N/Ns.14

For N/Ns < 1, some particles were settled, while at

N/Ns > 1 all particles were suspended. Therefore, a

value ofN/Ns = 1.2 proved to be the desired condition

of operation.

4.2 Effect of speed of agitation

To study the effect of speed of agitation on conversion

of zinc oxide and mean particle size of zinc borate, the

speed of agitation was varied for 0.83 < N/Ns > 1.2.

Typical results are shown in Fig 4. As the speed was

increased conversion also increased. With increasing

speed of agitation, the mass transfer of borate ions

in solution to zinc oxide particles increased. Thus

higher conversion was achieved with the increase in

speed of agitation in a shorter time. It is evident

that initially the conversion increases with speed

of agitation (N/Ns < 1). However at higher speeds(N/Ns 1) the speed of agitation has no effect on

conversion, indicating that the diffusional resistance

(Step 2 in Section 3) is eliminated.

Figure 5 shows the effect of speed of agitation on

mean particle size of zinc borate. Mean particle size

decreased with increase in speed as expected since

the higher speed of agitation caused greater secondary

nucleation due to higher strength and frequency of

collisions.

4.3 Effect of mean initial particle size of zinc

oxide

To study this effect, three different mean particle sizes

of zinc oxide were used. These are 20.30 (50 100 m),

26.29 (100150m) and 26.98 (150180 m). The

0

1

0

Fractionalconversion

1.2

0.8

0.6

0.4

0.2

4.2 RPS5.8 RPS7.1 RPS

Time (min)

60 120 180 240 300

N/Ns = 0.83

N/Ns = 1.2 and N/Ns = 1

Figure 4. Effect of impeller speed on conversion of zinc oxide.

Impellerthree-bladed hydrofoil impeller (HF3). Temperature of

reaction90 C. Concentration of boric acid 3:1 mole ratio. Initial


0

10

20

30

Me

anparticlesizeofzincborate(m

106)

DTPTD

HF-3

Speed of agitation rev s-1

200 400 600 800

Figure 5. Effect of impeller speed on mean particle size of zinc

borate for different impellers. Impellerdisc turbine (DT), six-bladed

pitched blade turbine downflow (PTD), three-bladed hydrofoil impeller

(HF3). Temperature of reaction 90 C. Concentration of boric acid

3:1 mole ratio. Initial particle size of zinc oxide particles 20.3 m.

impeller used was the DT at N/Ns = 1. Figure 6

shows that the mean initial particle size affected

the conversion of zinc oxide. The time needed forconversion of zinc oxide was longer with increase in

mean particle size of zinc oxide. This is an indication

that the process is surface reaction-controlled. The

mean particle size of zinc borate was higher for higher

mean initial particle size of zinc oxide, as shown in

Fig 7.

4.4 Effect of temperature of reaction

The temperature range selected was 90 to 110 C. The

impeller used was the DT at N/Ns = 1 From Fig 8,

it is clear that with rise in temperature, the rate of

reaction increased sharply. Complete conversion was

achieved after 3.5 h at 110C while the time needed

for complete conversion at 90 C was 4.5 h. Figure 9

shows the effect of temperature on the mean particle



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0

1

0 120 180 240 300


0.8

0.6

0.4

0.2

1.2

20.29 10-6 m

26.29 10-6 m

26.98 10-6

m

60

Time (min)

Figure 6. Effect of mean initial particle size on conversion of zinc

oxide. Impellerdisc turbine. Temperature of reaction 90 C.

Impeller speed 5.8revs1. Concentration of boric acid 3:1

mole ratio.

15

16

17

18

19

20

15 20 25 30

Me

anparticlesizeofzincborate(m

106)

Mean initial particle size of zinc oxide (m 106)

Figure 7. Effect of mean initial particle size of zinc oxide on particle

size of zinc borate. Impellerdisc turbine. Impeller speed

5.8revs1. Temperature of reaction 90 C. Concentration of boric

acid 3:1 mole ratio.

size of zinc borate. There was an approximately linear

decrease in particle size with increase in temperature.

4.5 Effect of concentration of boric acidThree different boric acid to zinc oxide mole ratios

were used, viz 3:1, 4:1 and 5:1. The impeller used was

the DT at N/Ns = 1.

Figure 10 shows the variation of conversion with

increase in concentration. When boric acid was added

in an amount in excess of the stoichiometric quantity,

there were more borate ions available to react with zinc

oxide particles. Therefore, conversion of zinc oxide

increased with increase in concentration of boric acid.

Also, complete conversion was achieved in a shorter

time.

Figure 11 gives a plot of the mean particle size of zinc

borate against the concentration of boric acid. In this

case, the reverse effect was observed for mean particle

size. The size of zinc borate particles increased with

0

1

0 120 180 240 300

Fractiona

lconversion

90C100C

110C

1.2

0.8

0.6

0.4

0.2

Time (min)

60

Figure 8. Effect of temperature of reaction on conversion of zinc

oxide. Impellerdisc turbine. Impeller speed 5.8revs1.

Concentration of boric acid 3:1 mole ratio. Initial particle size of zinc

oxide particles 20.3m.

12

14

16

18

80 90

Meanpa

rticlesizeofzincborate(m

106)

120

Temperature, C

100 110

Figure 9. Effect of temperature of reaction on mean particle size of

zinc borate. Impellerdisc turbine. Impeller speed 5.8 rev s1.

Concentration of boric acid 3:1 mole ratio. Initial particle size of zinc

oxide particles 20.3m.

increase in quantity of boric acid. This was because an

additional quantity of boric acid forms a layer aroundthe zinc borate particles. This problem can be solved

to some extent by washing the zinc borate particles

continuously with hot water for some time.

5 REACTION KINETICS

For the particular reaction of formation of zinc borate,

the majority of the experiments were conducted at the

speeds having ratios ofN/Ns greater than 1. Pangarkar

et al have presented an exhaustive discussion on the

particleliquid mass transfer coefficient, kSL, in two-

/three-phase stirred tank reactors.15 They concluded

that for N/Ns > 1, kSL is practically constant. Thus

the effect of mass transfer on the rate of this particular

reaction is negligible at N/Ns > 1.



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0

1

0


1.2

0.8

0.6

0.4

0.2

3:14:15:1

Time (min)

60 120 180 240 300

Figure 10. Effect of concentration of boric acid on conversion of zinc

oxide. Impellerdisc turbine. Impeller speed 5.8revs1.

Temperature of reaction 90 C. Initial particle size of zinc oxide

particles20.3 m.

10

15

20

25

30

Meanparticlesizeofzincborate(m

106)

Concentration of boric acid (kmol m-3)

2.5 3 3.5 4 4.5 5 5.5

Figure 11. Effect of concentration of boric acid on mean particle size

of zinc borate. Impellerdisc turbine. Impeller speed 5.8 rev s1.

Temperature of reaction 90 C. Initial particle size of zinc oxide

particles20.3 m.

The various kinetic expressions considered for

fitting the experiments were:

1. Reaction between dissolved zinc oxide and boric

acid. However, this possibility is very remote due

to the very low solubility of zinc oxide in water

(assumption 2 in Section 4).

2. First/second order surface reaction between boric

acid and zinc oxide. However, the data showed a

very poor fit for the second order surface reaction.

The first order kinetics on the other hand gave an

excellent fit of the data (R2 = 0.96), indicating that

this represents the intrinsic kinetics of the surface

reaction.

From Fig 12, it is seen that ln (rate of consumption

of boric acid), ln r, is a linear function of 1/T.

The slope of this line yields an activation energy

-7

-6

-5

-4

-3

lnr

0.00280.0026 0.0027

1/T (K-1)

y = -7214.3x + 14.266

Figure 12. Plot of ln r vs 1/T for calculation of activation energy.

value of 6.1 104 J mol1 and is sufficiently high to

ensure that the process is kinetically controlled. Thus,the controlling regime is likely to be the reaction

between boric acid and zinc oxide on the surface of

zinc oxide particles.

5.1 Estimation of rate constant

The general rate expression for a first order surface

reaction is:

dcBt

dt= krapcBt (3)

ap = 6dpt (4)Where dpt is diameter of zinc oxide particle at

time t (which is an unknown quantity). This can

be eliminated with the help of weight of zinc oxide and

fractional conversion of zinc oxide.

The weight of zinc oxide is given by:

w =

6d3ptN (5)

while the fractional conversion of zinc oxide in terms

of weight of zinc oxide is:

x =weight of zinc oxide reacted

initial weight(6)

x =(win wt)

win(7)

This can be written in terms of the diameter of the

particle of zinc oxide:

x =

d3pin d

3pt

d3pin

(8)

From eqn (8) the diameter of the particle of zinc oxide

at time t is:

dpt = dpin (1 x)1/3 (9)



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Substituting this value of dpt, eqn (3) becomes:

dcBt

dt= kr

6

dpin (1 x)1/3

cBt (10)

cBt, the concentration of boric acid at time t, can be

written as:

cBt = cB0

3(win wt)

mv (11)

Also wt, the remaining weight of zinc oxide at time t is:

wt = win(1 x) (12)

Substituting wt in eqn (10) gives:

cBt = cB0 3(win (1 x)win)

mv(13)

Therefore,

cBt = cB0 3winx

mv

(14)

Substituting the value of cBt in eqn (9):

dcBt

dt= kr

6

dpin(1 x)1/3

cB0

3winx

mv

(15)

The above equation can be rearranged as:

dcBt

dt= krf(x) (16)

where

kr = kr 6dpin(17)

f(x) = (1 x)1/3

cB0 3winx

mv

(18)

In eqn (16), the values of dcBt/dt and f(x) can

be obtained from experimental data. Therefore,

dcBt/dt was plotted against f(x). The straight line

plot obtained further supported the assumption that

the reaction is first order with respect to boric

acid. The slope of this line gives the value of kr.

As the initial particle size of zinc oxide was a

measured quantity, it was substituted in eqn (17)and kr was calculated. According to the first order

surface reaction kinetic expression given by eqn (3),

the dimensions of kr are LT1. The value of rate

constant for the experiments using DT is 3.83

105 cm s1.

The corresponding values of kr for the PTD and

HF3 are 2.7 105 cm s1 and 1.61 105 cm s1

respectively. The difference in the values is most likely

due to the variation in dpin , dpt and the shape factor

which vary with the type of the impeller. However, the

differences are less than an order of magnitude and

are explainable on the basis of different dpin , dpt and

shape factors given above.

6 CONCLUSION

The effect of hydrodynamic and operating conditions

was studied for the formation of zinc borate in a batch

stirred reactor. From the results, it was observed that

mixing parameters show an influence on the particle

size of the zinc borate. It was also observed that the

rate controlling step is a surface reaction between

dissolved boric acid and zinc oxide. To achieve rapidconversion and lower crystal size of the zinc borate, a

speed marginally higher than the minimum suspension

speed of the impeller should be used. Also, higher

temperatures and low mean initial particle size of zinc

oxide were beneficial in obtaining a lower final product

size.

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