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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: vgp@udct.org
(Received 2 June 2003; revised version received 13 October 2003; accepted 8 December 2003)
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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.
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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
particle size of zinc oxide particles 20.3 m.
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
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Formation of zinc borate
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
particle size of zinc oxide particles 20.3 m.
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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AV Shete, SB Sawant, VE Pangarkar
0
1
0 120 180 240 300
Fractionalconversion
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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Formation of zinc borate
0
1
0
Fractionalconversion
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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