Evaporation of Solution Droplets in Low Pressures,
for Nanopowder Production by Spray Pyrolysis
August 2004
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Outline






Introduction
Objective
Experimental set-up
Future Work
Theoretical Model
Timetable
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Introduction: Spray Pyrolysis
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Crust Formation
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Zirconia Production
Zirconium nitrate

ZrO(NO3)2.xH2O

ZrO2 + NO2+H2O
Decomposition temperature: 270 0C
Zirconium chloride

ZrOCl2.8H2O

ZrO2 + HCL + H2O
Decomposition temperature: 380 0C
Zirconium acetate

Zr(CH3COO)4 +H2O
ZrO2 + CO2 + HCL
Decomposition temperature: 320 0C
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Modeling Nanopowder Production

Nanopowder production in the atmospheric pressure occurs
in the Transition Regime: Kn~1
Actual case
P=101 kPa
d=100 nm
Kn=1.8
Kn 
2
d
Modeled case
P=0.05 kPa
d=200,000 nm
Kn=1.8
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Evaporation in low pressures

Continuum assumption is no longer valid when the
pressure is relatively low.

For low density gases in equilibrium the kinetic theory
applies.

Nanopowder production occurs in the transition
regime and in this region the Boltzmann equation
should be solved for the velocity distribution.

Evaporation data of solution droplets for low
pressures is very sparse in the literature.
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Objectives

Experimental investigation on the effect of
operating conditions (Chamber P, T, φ, and droplet
D and Cin) on the morphology of nanopowders of
ZrO2.

Experimental investigation on the single droplet
evaporation in low pressures.
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Important Issues

Chamber heating in low pressures

Adequate chamber height

Uniform droplet generation

Accurate imaging
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Droplet Evaporation Characteristics
Evaporation Time
Terminal Velocity
Evaporation Length
Water
Methanol
Pentane
Water
Methanol
Pentane
Water
Methanol
Pentane
30
micron
0.35 s
0.056 s
0.011 s
0.021
m/s
0.017 m/s
0.013 m/s
0.73 cm
0.095 cm
0.014 cm
200
micron
8s
1.38 s
0.28 s
0.93
m/s
0.74 m/s
0.59 m/s
700 cm
102 cm
18 cm
300
micron
13 s
2.22 s
0.47 s
1.95
m/s
1.6 m/s
1.33 m/s
2500
cm
350 cm
60 cm
400
micron
17 s
2.95 s
0.63 s
3.15
m/s
2.6 m/s
2.3 s
5300
cm
7670 cm
150 cm
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Evaporation of Pentane Droplets: Effect of
Pressure
Pressure
(kPa)
Kn
ReD
U terminal
Evaporation
Time
(symmetric)
Evaporation
Time
Convective
Evaporation
Time
Kinetic theory
101
0.0009
4.5
0.59
0.51
0.28
-
53
0.0017
2.38
0.59
0.44
0.27
-
34
0.0021
1.5
0.59
0.40
0.27
-
10
0.0093
0.44
0.59
0.34
0.27
-
4
0.0232
0.18
0.6
0.31
0.26
-
2.5
0.0374
0.11
0.61
0.29
0.26
-
1
0.0928
0.048
0.64
0.28
0.25
-
0.65
0.14
0.032
0.65
0.27
0.25
-
0.13
0.69
0.007
0.76
0.25
0.24
-
0.07
1.32
0.004
0.8
0.24
0.24
0.000045
T of ambient=400 K,
T of droplet=300 K,
Humidity=0,
Droplet initial diameter= 200 μm
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Experimental Set-up
Liquid and power feedthrous
Droplet
generator
Heaters
Grooved plate
View ports
thermocouples
Laser Source
photodiode
Light
Data acquisition
system
Camera
Support frame
Powders
To the vacuum pump
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Vacuum System
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Chamber Accessories
• Thermocouple feedthroughs
• Power feedthroughs
• Liquid feedthroughs
• Signal feedthroughs
• Pressure gauge
• Discharge Valve
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Droplet Generator Requirements
• Repeatable droplet generation (equal size)
• Capable to operate in hot and low pressure environments
• Easy to operate
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Droplet Generator
Piezoelectric droplet generator
Pneumatic droplet generator
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Pneumatic droplet generator






Air flow rate
Air pressure
Pulse width
Liquid level
Liquid properties
Orifice size
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Droplet Generator Operation
• Single Droplet Generation
• Multiple Droplet Generation: A droplet with several satellites
• Difficult to produce, but relatively repeatable
• Droplets wander during their fall. To reduce droplet drift, a glass tube will be used
around the flow path.
t=10 x 10-4
t=25 x 10-4
t=40 x 10-4
t=55 x 10-4
t=70 x 10-4
t=85 x 10-4
t=100 x 10-4
t=115 x 10-4
t=130 x 10-4
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Droplet Generator Operation
• Stream of droplets: Smaller droplets are produced, but not repeatable
t=0
t=15 x 10-4
t=30 x 10-4
t=45 x 10-4
t=60 x 10-4
t=75 x 10-4
t=90 x 10-4
t=105 x 10-4
t=120 x 10-4
t=135 x 10-4
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Data Acquisition System





IEEE 488 GPIB Interface
Temperature module
Non-conditioning module
SCXI 1000 Chassis
LabView software:




Temperature measurement
Pulse generation
Trigger system
Pressure recording
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Trigger System
Photodiode: a semiconductor sensor
Light Source: Laser
DAQ
Laser
Camera
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Heating Elements
Four 1800 Watts Convective Heaters
 Maximum Surface Temperature: 325 0C

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Imaging
• FASTCAM-Ultima 1024 model 16K
16000 fps
• One camera will be moved to take several images at different locations
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Future Work
XRD TEST


Reflection of x-ray beams from parallel atomic planes

Identifying crystalline phases
Crystallite size

2



TEM or SEM TEST
Examine microstructure
Identifying Hollow or dense particles
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Theoretical Model

Inviscid free stream of gas outside its wake and
flowing over the droplet

Gas-phase viscous boundary layer and near
wake.

Core region within the droplet, that is rotational but
nearly shear free and can be approximated as a
Hill’s spherical vortex.
8
 ~ 4
AR
s
r
R
  1  4s 2 (1  s 2 ) sin 2 
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df
(0)  0
d
df
( )  1
d
Gas Phase Analysis
• Boundary Layer Equations of Momentum, Energy and Mass is applied to the
boundary layer around the droplet.
• For the stagnation point and the shoulder region (θ=π/2), where the pressure
gradient is zero and the flow locally behaves like a flat-plate flow, local similarity is
believed to be a very good approximation
d3 f
d2 f
f
0
3
2
d
d
df
(0)  0
d
df
( )  1
d
f (0)  
f (0)
B
( v) s   Af (0)
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Heat Transfer in the Droplet
 With a certain coordinate transformation, the large Peclet
number problem can be cast as a one-dimensional, unsteady
problem (Tong and Sirignano ).
 In axisymmetric form of the energy equation, and in a large
Peclet number situation, heat and mass transport within the droplet
involve a strong convective transfer along the streamline with
conduction primarily normal to the stream surface
(i )
Tl
 Tl
Tl


(
1

C

)


 2
2
at
(ii )
at
(iii )
 R0 
C  C ( )  2

 R 
ql 
T

3
2
at
  0,
  0,
  1,
Tl  0
Tl
Tl



Tl
 ql

3
d  R 2



d 
R
 0 
1
2

Re   (T  TS ) L 
  k[ f (0)]
 

8

l
B
cp 

S
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Concentration Equation in the Droplet
Yl
  2Yl
1
Yl


(

C

)

Le  2
Le

  0,
(i )
at
(ii )
at
  0,
(iii )
at
  1,
Yl  Yl 0
Yl
Yl
 Le


Yl
 fl

Yl , m 
k [  f (0)] Re1 / 2 D
 
fm 
(Yl , ms  1)
  S

lD l
8
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Algorithm
• At any given time instant with known droplet surface temperature Ts and solvent phase
species mass fraction Yls, ,the gas phase species mass fractions at the droplet surface Ygs
can be obtained by means of Raoult’s and Clausius-Clapyron laws.
• Therefore, boundary conditions of the gas phase equation will be determined.
• From the solution of the gas phase, the boundary conditions of the liquid phase will be
determined.
• Enegy and concentration equations will be solved. The new droplet surface temperature
and the new liquid phase mass fractions at the droplet surface are used for the gas phase
solution for the next time step.
• When the surface concentration reaches the critical super saturation (CSS), precipitation
starts from the surface of the droplet
• If at this moment, the concentration of the droplet center is higher than the equilibrium
saturation (ES) of the solution, a solid particle will form, otherwise, the particle will be
hollow.
• This new model predicts that the dried particle will have two not necessarily spherical
pores on account of the fluid circulation within the droplets
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