Full text of DOI:10.1557/JMR.2000.0106

An experimental and modeling investigation of particle
production by spray pyrolysis using a laminar flow
aerosol reactor
I. Wuled Lenggoro, Takeshi Hata, and Ferry Iskandar
Department of Chemical Engineering, Hiroshima University, Kagamiyama 1-4-1,
Higashi-Hiroshima 739-8527 Japan
Melissa M. Lunden
Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory,
1 Cyclotron Road, Berkeley, California 94720
Kikuo Okuyamaa)
Department of Chemical Engineering, Hiroshima University, Kagamiyama 1-4-1,
Higashi-Hiroshima 739-8527 Japan
(Received 21 July 1999; accepted 28 December 1999)
The influence of operating parameters on the morphology of particles prepared by
spray pyrolysis was investigated using a temperature-graded laminar flow aerosol
reactor. Experimentally, zirconia particles were prepared by spray pyrolysis using an
aqueous solution of zirconyl hydroxide chloride. Hollow particles were formed if the
reactor temperature was high, the temperature gradient was too large, the flow rate
of carrier gas was high, and the initial solute concentration was low. A numerical
simulation of the pyrolysis process was developed using a combination of two
previous models. The simulation results compared well with the experimental results.
I. INTRODUCTION
continuous. These advantages are realized because the
precursor salts are mixed in solution at the molecular
level; after atomization, all particle formation processes
are integrated inside the droplet. Each droplet has the
same composition; thus multicomponent and composite
particles can be easily synthesized by controlling the
chemistry of the precursor solution. The application of
the spray pryrolysis process to industry is very promising
because the equipment is simple with short processing
times on the order of a few seconds. By comparison, the
use of conventional solid-phase or liquid-phase methods
requires the repetition of some operations, such as calci-
nation and milling, to obtain the desired particle size.
Moreover, these operations often introduce impurities
into the particles.
Using the spray-pyrolysis method, our group has been
preparing various functional fine particles such as metal
oxide superconductors,2 metal sulfides,3,4 and recently
some oxide phosphors.5 In these papers, the relationships
between physical properties of the prepared particles like
morphology and the process conditions have been ex-
perimentally investigated.
Small particles with sizes of submicron up to several
micrometers have important applications in the areas of
electronic materials, catalysis, and analytical chemistry.
It is important to develop a process which can produce
the particles having controlled characteristics such as
size, morphology, composition, and others. To be indus-
trially relevant, the process needs to be low cost with
both a continuous operation and a high production rate.
Spray pyrolysis, a method for producing particulate ma-
terials that combines both liquid and gas phase aerosol
processes, may be such a process.1
Particle synthesis by spray pyrolysis involves the at-
omization of a precursor solution into discrete droplets.
These droplets are subsequently transported through a
furnace where the solvent is evaporated from the droplets
and the dissolved species react to form the product par-
ticulate. Spray pyrolysis has a number of advantges in-
cluding the following: (i) the particles produced are
spherical; (ii) the distribution of their diameters is uni-
form and controllable from micrometer to submicron;
(iii) the purity of the product is high; (iv) the process is
Much of the work regarding spray pyrolysis had fo-
cused on the prediction and control of the final particle
morphology. A number of investigators have reported on
numerical solutions of the droplet-to-particle conversion
a)Address all correspondence to this author.
e-mail: okuyama@ipc.hiroshima-u.ac.jp
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
process. Marshall and colleagues6–12 investigated the ef-
phology. Moreover, neither their modeling results nor the
results of Jayanthi et al. are directly compared with ex-
perimental results.
fect of solvent evaporation rate on the morphology of
dried particles by deriving the diffusion equation for the
mass transfer of a dissovled solid inside a droplet. The
diffusion equations presented in Marshall’s paper6,7 were
too complicated to be solved analytically due to the mov-
ing boundary caused by the shrinkage of the droplet.
Thus, this initial work on mass transfer inside a droplet
employed several assumptions, which limited the use of
the solutions. The difficulty involved in the calculation of
the moving boundary problem was greatly simplified by
van der Lijn13 by proposing a mathematical relation for
fixing the outer boundary. This technique enables a
simple analytical relation for calculating the solute con-
centration distribution inside a droplet.
Most of these earlier studies were qualitative in nature
and usually examined relatively large particles of size
100 to 1000 ␮m. Among the few studies for droplets of
size 10 to 100 ␮m, Leong9 proposed that limited control
of particle morphology could be achieved by controlling
the temperature and humidity of the carrier gas as well as
the precursor solution characteristics.
Clearly, the formation of particles by spray pyrolysis is
a complex process and is difficult to accurately model.
The task is made more difficult by the lack of data on the
chemistry and solubility of many precursors, as well as
nucleation and crystallization during precipitation. It is
essential to develop a model that considers both multiple
droplets and changes in mass concentration within the
droplets. Until now, this important problem has been left
unsolved.
In this study, we present a model of the particle
formation process that is based on the models pres-
ented by Jayanthi et al.11 and Xiong and Kodas.12 Our
model simultaneously computes the evaporation rate
from a monodisperse population of aerosol particles
and the change of the solute concentration within the
droplets. The change in droplet size and particle mor-
phology is calculated as a function of position in the
reactor and process time. For experimental comparison,
zirconia particles were prepared using the spray-
pyrolysis process at a number of operating conditions.
Zirconia was selected because the wide application in
industry due to its outstanding mechanical strength, ther-
mal stability, chemical resistance, and electrical charac-
teristics. In addition, values of the material-property data
required for the modeling study are available in the
literature.11
Jayanthi et al.11 applied van der Lijn’s technique12 to
solve the diffusion equation inside the droplet to model
the evaporation and solute precipitation of 10-␮m zirco-
nia particles. They assumed that homogeneous nuclea-
tion would occur when the solute concentration at the
surface of the droplet reached the critical supersaturation.
After nucleation of the solid, precipitation occurs only in
the part of the droplet where the solute concentration is
higher than the equilibrium saturation. Hollow particles
result if the solute concentration at the center of the drop-
let is less than the equilibrium saturation of the solute.
Using their model, they predicted the morphology result-
ing from the spray pyrolysis of ZrO2 from zirconyl hy-
droxide chloride, a precursor for which they had
previously measured the values of the critical and equi-
librium saturations.14 Their calculations considered the
effects of parameters such as process temperature and the
initial solute concentration on the morphology of single
particles. They found that lower process temperatures
and higher initial solute concentrations favored the for-
mation of dense particles.
Of all the numerical studies of the droplet to particle
conversion process, only one considered the effect of
multiple droplets.12 Their calculations were performed
using sodium chloride as a model compound. They pre-
sented calculation results for the change of solvent vapor
concentration, droplet size, and droplet temperature dur-
ing heating in a laminar flow reactor by varying values
like the initial number concentration of ambient humid-
ity. However, their model did not consider the change of
mass concentration inside the droplets due to evapora-
tion. All droplets were assumed to form solid, dense
particles; no attempt was made to model particle mor-
II. EXPERIMENTAL PROCEDURE
A schematic of the experimental apparatus used to
produce and collect the zirconia particles is shown in
Fig. 1. The main equipment consists of (i) a nebulizer
that converts the starting solution into microdroplets, (ii)
the carrier gas, (iii) a tubular, laminar flow aerosol reac-
tor, and (iv) a sampler or precipitator. The starting solu-
tion was atomized at a frequency of 1.75 MHz by an
ultrasonic nebulizer (Omron Co., Kyoto, Japan, Model
NE-U11B), which was cooled with running water. The
level of the spray solution was kept constant to ensure a
uniform generation rate of droplets. Figure 2 shows the
equivalent volume diameter distribution of the atomized
water droplets as measured by a light-scattering particle-
size analyzer (Malvern Instruments Corp., Worcester-
shire, U.K., Mastersizer DPF). The average equivalent
volume diameter of solution droplets was 4.5 ␮m. Wa-
ter was used as the solvent. The tubular furnace was
an alumina tube of 13-mm inside diameter and about
1000 mm long. The furnace consists of five indepen-
dently controlled heating zones, each 200 mm in length,
enabling flexibility in the production of the experimental
temperature distributions. The temperature of each heat-
ing zone was controlled to within 2 °C. A pre-
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
A zirconium hydroxide chloride (ZrO(OH)Cl) solution
(Nikkei-MEL, Japan-U.S.A.) was used as the precursor
for producing ZrO2 particles. All experiments were per-
formed using a molar concentration of 2.0 mol/l. The
physical properties of this solution are shown in Table I.
III. NUMERICAL PROCEDURE: PHYSICAL
MODEL AND BASIC EQUATIONS
A schematic of the droplet evaporation and precipita-
tion process is shown in Fig. 3. The model of this process
describes both the change of droplet diameter and the
particle morphology by simultaneously considering the
evaporation of multiple droplets along a tubular aerosol
reactor and the concurrent solute concentration distribu-
tion within the droplet. Monodispersed droplets having
diameter 2Rp0, number concentration N0, and solution
concentration C0 are introduced into the reactor with
relative humidity RH0 and ambient temperature T0, flow-
ing in either air or nitrogen at flow rate Q. The reactor
has length L and an inner diameter of 2R. The reactor
wall is maintained at a temperature Tw. During solvent
evaporation, the size of the droplets decreases and the
solution concentration inside each droplet increases as
the aerosol travels through the reactor. Eventually, the
solute concentration inside the droplet reaches the critical
supersaturation ratio at which point solute nucleation,
precipitation, decomposition, and other solid-state proc-
esses take place within the particle.
FIG. 1. Experimental apparatus.
Figure 4 shows a schematic of how the solute con-
centration within the droplet changes during solvent
evaporation, based on the formalism proposed by Jayan-
thi et al.11 The graphs in Fig. 4 show how the solute
concentration varies inside the droplet. The horizontal
axis represents the dimensionless position within the
droplet, with 0 and 1 corresponding to the center and
surface of the droplet, respectively. Initially the solute
concentration inside the droplet is uniform (C0). How-
ever, solvent evaporation causes the solute concentration
to increase at the droplet surface, forming a concentration
gradient that results in solute diffusion toward the center
of the particle. Computations are performed until the sol-
ute concentration at the droplet surface reaches the criti-
cal supersaturation (CSS). At this point, if the solute
concentration at the droplet center (r/R ס 0) is higher
than the equilibrium concentration (ES), the solid phase
will nucleate and grow throughout the entire particle,
resulting in a dense sphere. On the other hand, if the
FIG. 2. Size distribution of aqueous droplets using an ultrasonic
nebulizer.
vious numerical evaluation of the reactor15 showed that
the flow in the reactor is laminar for gas flow rates be-
tween 0.5 to 2 l/min. The Reynolds numbers of all con-
ditions performing in present study are less than 200. The
carrier gas used was nitrogen or air. Laminar flow is
necessary for comparison with the results of the numeri-
cal simulations.
TABLE I. Physical properties of the ZrO(OH)Cl solution (20 °C).
Density
(g/cm3)
Viscosity
(Pa s)
Heat capacity
(J/(g K))
ES
(mol/l)
CSS
(mol/l)
1.14
0.012
4.184
5.7
8.0
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
FIG. 3. Description of the simulation model.
FIG. 4. Change of solute concentration distribution inside the droplet. CSS is the critical supersaturation concentration, and ES is the equilibrium
concentration.
solute concentration at the center is lower than the ES, a
hollow particle will form. The CSS and the ES values of
aqueous solution of zirconium hydroxide chloride were
referred to the values which Zhang and Messing14 has
obtained experimentally (Table I).
To model this system, several assumptions were made:
(i) The temperature within a droplet is uniform; however
the temperature of both the gas and the droplets change
due to solvent evaporation and heat transfer from the
reactor walls. (ii) The effects of gravity and viscosity are
negligible. (iii) The droplet maintains spherical shape,
and the concentration fields within the droplet are spheri-
cally symmetric. (iv) Bubble formation or pressure
buildup inside the droplet is absent, and the solid crusts
formed are sufficiently permeable for solvent vapor dif-
fusion. (v) The flow is laminar and can be approximated
as one-dimensional plug flow. (vi) The only mass trans-
ports occurring in the gas phase are solvent evaporation
and vapor diffusion at steady state. (vii) The Kelvin ef-
fect is negligible because the final particle size is larger
than 0.1 ␮m.16
At pseudo-steady state, the evaporation rate from a
single droplet is given by
dm
dt
4␲RpDvMg
= −
n − n ͒
,
(1)
͑
s
g
NA
where m is mass of a droplet, Rp is the droplet radius, Dv
is the diffusion coefficient of solvent vapor, NA is the
Avogadro constant, Mg is the
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
solvent molecular weight, and ns and ng are the vapor
concentrations at the droplet surface and in the surround-
ing gas, respectively.
The rise in temperature of the droplet is given by the
following equation derived from the heat transfer into the
droplet gained from surrounding gas and the latent heat
of solvent evaporation:
where C(Rp0) is the solute concentration, m0 is droplet
mass, Rp0 is droplet radius, and T0 is the temperature of
the droplet. Subscript 0 denotes the initial value. We
assume that the initial droplet temperature is equal to the
temperature of the carrier gas at the inlet.
The boundary conditions are as follows:
Ѩu
= 0 at y = 0
,
(7)
(8)
dTs
1
dm
dt
Ѩy
=
4␲R K T − T ͒ + ␭
,
(2)
͓
͑
͔
p
g
s
dt mCp
4␲Rp ␳ 2Ds Ѩu dm
1
2
l
=
at y = 1
.
where Ts is the droplet temperature, Tg is the surrounding
gas temperature, Cp is the droplet heat capacity, K is the
thermal conductivity of the surrounding gas, and ␭ is the
latent heat of solvent evaporation.
2
2
Ѩy dt
z 1 + u͒
4␲Rp
͑
0
By using the variables u and y, the droplet radius can
be expressed as follows:
The transport equation describing the mass transfer/
diffusion in the droplet was presented by Charlesworth
and Marshall.7 As discussed previously, their formula-
tion was difficult to solve numerically because of the
moving boundary (solvent evaporation). Van der Lijn13
simplified the calculation by using dimensionless vari-
able y as follows:
3z0
4␲
1
1 + u
3
Rp
=
dy
.
(9)
ͫ
ͬ
͐
0
␳
l
As solvent evaporates from the droplets in the reactor,
the vapor concentration of the carrier gas will increase.
This increase is governed by (i) the solvent vapor intro-
duced into the gas by droplet evaporation and (ii) vapor
loss by diffusion from the gas to the reactor wall. The
change in vapor concentration can be written as
r4␲r2M C r͒ dr
͑
͐
s
0
y =
,
(3)
R4␲r2M C r͒ dr
dng
dt
2Km n − n ͒
͑
w
͑
͐
s
= −4␲R D N n − n ͒ −
,
͑
0
0
p
v
g
s
R
(10)
where Ms is the solute molecular weight and C(r) is the
solute concentration at a radius r. The denominator is the
total mass of solute in the droplet, and the numerator is
the mass of solute within a radius r. When r ס 0, y ס 0,
and when r = Rp, y ס 1. Therefore, even though Rp
decreases with time due to droplet shrinkage, the value of
y stays between 0 and 1.
In order to further simplify the diffusion equation,
Jayanthi et al.11 suggested that the dependent variable be
changed from mass fraction of solute to u, which is the
ratio of mass fraction of solvent WA1 to the mass fraction
of solute,
where ng, ns, and nw are the vapor concentration in the
surrounding gas, at the droplet surface, and at the reactor
wall, respectively. R is the radius of the reactor tube, N0
is the droplet number concentration, and Km is the vapor
mass transfer coefficient for laminar tube flow.
The temperature of the surrounding gas results from a
balance between the heat transfer to droplets and from
the reactor wall,
dTg
1
2
=
−4␲2R2R N h T − T ͒
͑
p 0 s g s
͓
dx FCpa
dt
1000␳ − M C r͒
͑
s
+ 2␲Rh T − T ͒
,
(11)
͑
w
͔
g
ͩ ͪ
w
u =
.
(4)
dx
M C r͒
͑
s
where x is the reactor axial coordinate, Qm is the carrier
gas molar flow rate, and Cpa is the heat capacity of the
wet air. hs and hw are the heat-transfer coefficients at the
droplet surface and at the reactor wall, respectively.
Assuming the carrier gas is ideal, the droplet residence
time along the reactor can be found as follows:
Then using Eqs. (3) and (4), the diffusion equation
becomes
2
2
l
Ѩu 16␲
Ѩ
␳
Ѩu
Ѩy
=
D
r4
,
(5)
ͫ
ͭ ͮ
ͬ
s
z02
1 + u͒
2
Ѩt
Ѩy
͑
where ␳ is the droplet density and Ds is the solute dif-
1
dt 0.06␲R2 T0 1 − y ͒
͑
fusion coefficient.
w
=
,
(12)
ͩ ͪ
0
The initial conditions for the diffusion equation are as
follows:
dx
Q
Tg
1 − y
)
͑
w
where t is the residence time, x is the reactor axial
coordinate/length, Q is the carrier gas flow rate, Tg and
T0 are the temperature of carrier gas at the current posi-
tion, x, and at the reactor inlet, x ס 0, respectively, and
1000␳ − M C R ͒
͑
l
s
p0
u =
m
M C R ͒
͑
s
p0
= m0 R = Rp0 Ts = T0
,
(6)
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
yw and yw0 are the solvent mole fraction in the carrier gas
at x and x ס 0, respectively. The correction factor (1 −
yw)/(1 − yw0) accounts for the change in the vapor content
of the carrier gas as a result of droplet evaporation.
The temperature gradient along the hot wall reactor,
dTw/dx, was measured for the reactor used in the experi-
ments, and Tw was expressed as a function of x-axis
length, x. The wall of the reactor does not interact with
the solvent, which corresponds to a no-flux condition at
the wall. For more detailed information regarding the
parameters and properties mentioned above, see Jayanthi
et al.11 and the appendix of Xiong and Kodas.12
The model allows the exploration of the influence of
parameters such as the reactor temperature, the wall tem-
perature gradient, the initial solution concentration, the
initial droplet size, and the droplet number concentration
on the final particle morphology. In addition, variables
such as the droplet temperature and the solute concen-
tration distribution within the droplet can be investigated
as a function of distance along the reactor. The calcula-
tion procedure is as follows: (i) The values of m, Ts, u,
Rp, ng, Tg, and x are calculated at an interval of 10−3 s.
New values of these variables are calculated from the
previous values. These new values are used to calculate
the time derivative. The calculations are stopped when
the solute concentration at the droplet surface reaches the
critical supersaturation concentration as determined in
Eq. (5). (ii) Changes in mass, temperature, and radius for
a single droplet are are calculated using Eqs. (1), (2), and
(9). The interior of the droplet is divided into 50 sections.
The solute concentrations in each section are calculated
using Eq. (5), and then the contribution from each section
is summed to obtain the total solute concentration distri-
bution inside the droplet. (iii) The changes in the vapor
concentration and the temperature in the carrier gas due
to interactions with the droplet population are calculated
using Eqs. (10) and (11). The axial positions of droplets
in reactor tube are calculated from Eq. (12).
FIG. 5. XRD spectra of zirconia particles at different furnace tem-
peratures (200, 500 °C). Other experiment conditions: C0 ס 2 mol/l;
Q ס 2 l/min.
the zirconia phase to be formed by thermal decomposi-
tion of the precursors. The XRD patterns of the particles
prepared at 500 °C show excellent agreement with the
reference spectrum (Powder Diffraction File JCPDS No.
27-0997) of ZrO2 (tetragonal phase, metastable). When
the process temperature is increased further (1000 °C),
the ZrO2 phase grew and the peaks become sharper. In
this temperature, the XRD pattern included few peaks
corresponding to monoclinic phase of zirconia.
Figure 6 shows pictures of the zirconia particles
obtained by scanning electron microscopy (SEM). The
figure shows that the particles formed at reactor tempera-
tures of 100 and 200 °C were spherical and appear solid.
However, at the higher temperatures of 300 and 500 °C,
many of the particles were disrupted. This is particularly
the case at 500 °C. This result indicates that at high tem-
peratures, precipitation occurs only in the region around
the particle surface, due to rapid solvent evaporation and
slow solute diffusion.7 As solvent is depleted from the
droplet surface, the temperature will rise substantially.
Thermal diffusion is much larger than mass diffusion.
Hence, the solvent could be trapped in the core of the
droplet and heated to temperatures much above the nor-
mal boiling point. In fact, it is known that temperatures in
multicomponent droplet vaporation can exceed the limit
of superheat. In that case, nucleation of the liquid solvent
Equations (1), (2), (5), and (10)–(12) are coupled or-
dinary differential equations and were solved simulta-
neously using an integration tool package EPISODE.17
IV. RESULTS AND DISCUSSION
Initial experiments were performed to investigate the
influence of the reactor temperature on the crystalline
phase and morphology of the zirconia particles. The par-
ticles were produced from a solution concentration of
2.0 mol/l and a flow rate of 2.0 l/min, at a number of
isothermal reactor temperatures. Figure 5 shows the x-
ray diffraction (XRD) patterns of the resulting particles.
The peaks from the particles obtained at 200 °C show
only a slight similarity to those in the zirconia phase,
indicating that the reaction temperature was too low for
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
FIG. 6. Effect of furnace temperature on the morphology of zirconia
particles: (a) 100 °C, (b) 200 °C, (c) 300 °C, and (d) 500 °C. Other
experiment conditions: C0 ס 2 mol/l; Q ס 2 l/min.
occurs with the formation of a gas bubble and subsequent
disruption of the droplet. It is necessary to investigate
further on these mechanisms.
Figure 7 shows results of model calculations for initial
conditions of 2Rp0 ס 4.5 ␮m, N0 ס 5 × 106 cm−3, C0 ס
2.0 mol/l, RH0 ס 0%, and constant temperature distri-
bution (see Fig. 8). Figure 7(a) shows the change of
droplet diameter along the reactor axis at different reactor
temperatures. Clearly solute precipitation occurred faster
at higher reactor wall temperatures due to faster evapo-
ration rates. Figure 7(b) shows the solute concentration
distribution inside the droplet at the time of precipitation
(i.e., when the solute concentration at the surface reaches
the CSS). At reactor wall temperatures, Tw, of 100 and
200 °C, the solute concentration at the center is higher
than the ES when the surface reaches the CSS. Thus, at
these conditions the formation of solid particles is pre-
dicted. Conversely, at temperatures of 300 and 500 °C,
C(rס0) is lower than the ES when C(rס1) reaches the CSS
predicting hollow particle formation. This prediction
agrees with the experimental results shown in Figs. 6(c)
and 6(d), indicating good correlation between the nu-
merical and experimental results.
To further explore the spray pyrolysis process, the ef-
fect of the temperature profile within the reactor on drop-
let evaporation and ultimate particle morphology was
investigated. Figure 8 shows two different temperature
profiles, constant and increasing, used in the present
study. The temperature profiles were produced by adjust-
ing the five heating zones. It is evident from the figure
that the linearly increasing temperature profile will result
in a lower heating rate along the reactor. Particles were
FIG. 7. Effect of furnace temperature on (a) the droplet/particle size
and (b) the solute concentration distribution inside the droplet at the
time of precipitation. Conditions: Dp0 ס 4.5 ␮m; C0 ס 2.0 mol/l;
Q ס 2.0 l/min; RH0 ס 0%.
produced using the two different profiles for several car-
rier gas flow rates resulting in a number of particle resi-
dence times and heating rates. SEM photographs of the
resulting particles are shown in Fig. 9. The ZrO2 particles
produced at 500 °C and a flow rate of 2.0 l/min are dis-
rupted and hollow. Changing to either an increasing tem-
perature profile or a longer residence time has little effect
on the final particle morphology. As seen in Fig. 9, both
changes in the process are necessary to shift the mor-
phology toward the production of more spherical par-
ticles with fewer disrupted particles.
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
FIG. 8. Furnace wall temperature distribution.
FIG. 9. Effect of temperature distribution and the residence time on
morphology of zirconia particles. C0 ס 2.0 mol/l.
FIG. 10. Effect of furnace temperature distribution and the carrier gas
flow rate on (a) the droplet/particle size and (b) the solute concentra-
tion distribution inside the droplet at the time of precipitation. Condi-
tions: Dp0 ס 4.5 ␮m; C0 ס 2.0 mol/l; RH0 ס 0%.
Figure 10 presents simulation results for the experi-
mental conditions shown in Fig. 9. The use of the slowly
increasing temperature profile gives lower evaporation
rates than a constant profile for both flow rates. As a
result, this operation decelerates the onset of solute pre-
cipitation [Fig. 10(a)] and reduces the formation of hol-
low, disrupted particles [Fig. 10(b)]. However, as seen in
Fig. 9, it is necessary to both change the temperature
profile and residence time to obtain solid particles at
500 °C. Neither change on its own slows evaporation
rates enough for the center of the particle to reach the
equilibrium saturation at the point at which solute nu-
cleation occurs on the surface. A numerical simulation
with an exceedingly low flow rate of 0.1 l/min at a con-
stant temperature profile (500 °C) was also performed.
The morphology of final particles is predicted to be solid.
However, it is difficult to carry out an experiment with
such a low flow rate of 0.1 l/min because the sprayed
droplets cannot be transported well.
Figure 11 shows the simulation results of several dif-
ferent droplet number concentrations (N0). It is clear
from Fig. 11(a) that the smaller the number concentration
of droplets, the faster the onset of precipitation, increas-
ing the likelihood that hollow particles will form. For the
conditions represented in Fig. 11, a droplet number con-
centration of 7.5 × 106 cm−3 should result in solid par-
ticles. However, when further increasing the number
concentration to N0 ס 2.0 × 107 cm−3, the solution con-
740
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
FIG. 12. Effect of initial droplet diameter on (a) the particle size and
(b) the solute concentration distribution inside the droplet at the time
of precipitation at the constant temperature distribution with Tw
ס
300 °C. Conditions: C0 ס 2.0 mol/l; Q ס 2.0 l/min; RH0 ס 0%.
FIG. 11. Effect of droplet number concentration on (a) the particle
size and (b) the solute concentration distribution inside the droplet.
Conditions: Dp0 ס 4.5 ␮m; Tw ס 300 °C; Q ס 2.0 l/min; RH0 ס 0%.
Figure 12 shows simulation results for different initial
droplet diameters at a wall temperature of 300 °C with a
solution molality of 2.0 mol/l and a flow rate 2.0 l/min.
The temperature distribution of the reactor is superim-
posed over the evolution of droplet diameters along the
length of the reactor. As expected, the final particle diam-
eter decreases as the diameter of the initial droplet de-
creases. It has been generally proposed that the use of
smaller droplets in spray pyrolysis will produce solid
particles because the diffusion distance for the solute is
shorter, resulting in a more uniform concentration distri-
bution within the particle. A previous theoretical study
concluded that the initial droplet diameter does not affect
the concentration profile inside the droplet at the time of
centration at the surface does not reach the ES by the
time the droplets exit the reactor, and precipitation will
not occur. Clearly, an increase in the number concentra-
tion of droplets will result in more evaporation and a
larger solvent vapor concentration in the carrier gas. As
a result, the evaporation rate will decrease, delaying pre-
cipitation. Figure 11(a) also predicts that the final par-
ticle diameter will increase as the droplet number
concentrations decrease. This increase is due to the fact
that the hollow particles that form under the lower num-
ber concentration conditions have larger outer diameters.
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
precipitation because the characteristic times for diffu-
sion and evaporation depend in the same way on the
particle radius.11 However, contrary to these arguments,
it is interesting to note that the formation of solid par-
ticles is predicted for dp0 ס 2 and 6 ␮m and the hollow
particles for dp0 ס 3, 4, or 5 ␮m [Fig. 12(b)]. As shown
in Fig. 12(a), the reactor temperature increases rapidly
from its initial temperature to the reactor wall tempera-
ture in the first 20 cm of the reactor. For small initial
sizes, the majority of the evaporation and precipitation of
the droplet are completed during this initial high-
temperature gradient. The ultimate morphology of these
particles is predicted to be hollow. On the other hand, for
larger initial droplet sizes (e.g., dp0 ס 6 ␮m), the major-
ity of the particle evolution occurs during the isothermal
region of the furnace, and the resulting particles are solid.
In comparison to the smaller droplet, for dp0 ס 6 ␮m the
heating rate is reduced and as a result the formed par-
ticles are solid. For dp0 ס 2 ␮m, the temperature gradi-
ent is not as high as in the cases of dp0 ס 3 or 4 ␮m, so
the final formed particles are solid. In the case of droplets
having diameter larger than 6 ␮m, the droplets exit 1-m
length reactor without precipitation, because the solution
concentration at the surface does not reach ES.
In order to confirm the relationship between tempera-
ture distribution along the reactor and the initial droplet
diameter, the experiment was repeated using a linearly
increasing temperature profile with a maximum tempera-
ture of 300 °C. Figure 13 shows the simulation results for
this profile, with the other parameters the same as
Fig. 12. In the increasing temperature profile, the tem-
perature of the reactor just reaches 300 °C before the exit
of the reactor. A reduction in starting droplet diameter
allows the formation of solid particles. From these re-
sults, it is clearly necessary to design a reactor to give an
appropriate temperature distribution and residence time
in order to produce particles with desirable morphology.
FIG. 13. Effect of the increasing temperature distribution on param-
eters that are the same as Fig. 12.
V. CONCLUSION
The simulation also indicates that the hollow particles in
spray pyrolysis is formed if the initial droplets are large
and the droplet number concentration is low. The model
should be useful is solving some problems on the spray
pyrolysis process; however, it is necessary to investigate
further the determinaton of critical solution concentration
and its temperature-dependent nucleation or crystal
growth of the related materials.
A spray pyrolysis model for fine particle preparation
has been developed from a combination of two previous
models. The model, for the first time, simultaneously
considered the comparison of results obtained from ex-
periment and numerical simulation. The results include
the influence of operation parameters on the following:
(i) changes of size and temperature of multiple droplets
along a laminar reactor (ii) the solute concentration gra-
dient inside the droplets (iii) the final morphology of pre-
pared particles.
In general, the predicted simulation results are in good
agreement with those obtained from the experiment. The
solid particles can be formed if the reactor temperature is
low or has a gradual distribution, the initial solute con-
centration is high, and the flow rate of carrier gas is low.
ACKNOWLEDGMENTS
T. Komiya was very helpful in the experimental work.
Support from the Ministry of Education, Culture, and
Science of Japan (Grant No. 10650745) and the Hiro-
shima Industrial Technology Organization is gratefully
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I.W. Lenggoro et al.: An experimental and modeling investigation of particle production by spray pyrolysis
t
time
(s)
ackowledged. Nikkei-MEL (a joint venture between Nip-
pon Light Metal Co. Ltd., Tokyo, Japan, and MEL
Chemicals, Flemington, NJ) provided the precursor.
T0
Tg
Ts
Tw
u
initial temperature of reactor inlet
temperature of surrounding gas
temperature at the droplet surface
temperature at the reactor wall
ratio of mass fraction of solvent to
mass fraction of solute
(K)
(K)
(K)
(K)
(-)
NOMENCLATURE
C0
initial solution concentration
heat capacity of surrounding gas
heat capacity of droplet
(mol/l)
x
reactor axial coordinate
ratio z to z0
(cm)
(-)
Cpa
Cpd
(J/(mol K))
(J/(mol K))
(mol/l)
y
yw
vapor mole fraction in surrounding
gas
(-)
CSS critical supersaturation concentration
C(r) solute concentration at a radius r
(mol/l)
0
yw
z
vapor mole fraction in surrounding
gas at the reactor inlet
(-)
dp0
Ds
Dv
ES
hs
initial droplet diameter
solute diffusion coefficient
solvent vapor diffusion coefficients
equilibrium saturation concentration
heat-transfer coefficient at the droplet
surface
(cm)
(cm2/s)
mass of solute present from the
droplet center to a radius r
total mass of solute in the droplet
latent heat of vaporization
density of the droplet
(g)
(cm2/s)
(mol/l)
(J/cm2 s K)
z0
(g)
␭
(J/g)
(g/cm3)
␳
(J/cm2 s K)
(J/cm s K)
(cm/s)
1
hw
K
heat-transfer coefficient at the reactor
wall
thermal conductivity of surrounding
gas
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Km
vapor mass transfer coefficient for
laminar tube flow
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nol. 19, 478 (1993).
L
reactor length
(cm)
Mg
Ms
m
solvent molecular weight
solute molecular weight
droplet mass
(g/mol)
(g/mol)
(g)
m0
N0
initial droplet mass
(g)
(no./cm3)
vapor concentration at the droplet
surface
NA
Avogadro constant
(No./mol)
(molecules/cm3)
ng
vapor concentration in surrounding
gas
ns
vapor concentration at the droplet
surface
vapor concentration at the reactor wall (molecules/cm3)
(molecules/cm3)
nw
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Laboratory Report, UCID-30112 (1977).
Q
Qm
R
carrier gas flow rate
carrier gas molar flow rate
reactor tube radius
(l/min)
(mol/s)
(cm)
(cm)
(-)
r
radial coordinate
RH0 relative humidity in surrounding gas
Rp
droplet radius
(cm)
(cm)
Rp0
initial droplet radius
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