Heat and mass transfer from aerosol bound species, for application in the solar seeded reactor. Supervisors – Prof. Yinon Rudich, Prof. Jacob Karni A method for measuring the sherwood number of aerosols was developed, utilizing an Aerosol mass spectrometer, a thermal denuder, and a differential mobility analyzer and a condensation particle counter. The goal is to use the measured sherwood number for predicting the nusselt number through the heat to mass analogy, as described in the text.

1. Thesis for the degree *+"1' (,%1) *#& 1/"-.
Master of Science ($./#' 8#)"#
Submitted to the Scientific Council of the '! 1$./#, ,9."#' 1!&"#
Weizmann Institute of Science ./#' 7#9$" 7"6#
Rehovot, Israel '+*!$ ,1"-"4*
By 1+#
Hanan Einav-Levy $"' -2$. 724
!"#$!" %&' ($'")"*+# ,)# *-.# (/0# 1/$/#' 1$$")$2 ,3$! 4"1$5
(4, *-.# (/0# '+ ,6'!, (!' ,)# *-.#' (4 *-.# 7$- ,$&"'2+-
Development of Method for Measuring Mass Transfer Coefficients of Particles
and Use of the Mass-Heat Transfer Analogy to Obtain Heat Transfer
Coefficients
Advisors: :($42#
Jacob Karni 8$/"* 7"2$
Yinon Rudich $2*0 -0.$
January 2010 ."!1 3-! -
1

2. Abstract ..........................................................................................................................................6
Acknowledgements.........................................................................................................................7
1 Introduction...............................................................................................................................7
1.1 Solar thermal energy...........................................................................................................7
1.2 Convective heat transfer .....................................................................................................8
1.3 The heat to mass transfer analogy.......................................................................................9
1.3.1 Heat and Mass Transfer in the Continuum Regime ......................................................9
1.3.2 The dynamic transfer conditions ................................................................................10
1.3.3 The transition regime.................................................................................................13
2 Research Objectives ................................................................................................................13
3 Experimental Apparatus and Test Results................................................................................14
3.1 Experimental system ........................................................................................................14
3.1.1 Aerosol generation.....................................................................................................16
3.1.2 Coating with High Vapor Pressure Material (Benzo(a)pyrene)...................................16
3.1.3 Controlled evaporation...............................................................................................17
3.1.3.1 Increase of coating material (BaP) ambient vapor pressure..................................18
3.1.3.2 Initial design .......................................................................................................19
3.1.3.3 Final Design........................................................................................................21
3.1.4 Measurement .............................................................................................................22
3.1.5 Experimental Procedure.............................................................................................25
3.1.5.1 Data collection....................................................................................................25
3.1.5.2 Measurement of the side-center temperature correlation matrix...........................26
3.1.5.3 Data analysis procedure ......................................................................................29
3.2 Results .............................................................................................................................31
3.2.1 Mobility and vacuum aerodynamic distributions........................................................31
3.2.2 SMPS measured and AMS mass based final diameter and shape factor......................33
3.2.3 Effects of Residence time ..........................................................................................36
4 Discussion...............................................................................................................................38
4.1 Derivation of the Sherwood number .................................................................................38
4.2 Possible sources of measurement bias...............................................................................40
4.2.1 Coating thickness effect on the Sherwood number .....................................................40
4.2.2 The influence of coating thickness on the calibration ratio RM ...................................42
4.2.3 Possible uneven flow splitting effect on bias..............................................................45
4.3 Error analysis ...................................................................................................................45
4.4 Repeatability ....................................................................................................................47
4.5 Measurement of the Sherwood numbers for suspended nano-particles ..............................47
4.6 The use of the heat to mass analogy for suspended nano-particles.....................................48
4.7 Measurement of fractal soot particles................................................................................49
4.8 Correlation of heat and mass transfer vs. particle size and shape.......................................49
5 Conclusion ..............................................................................................................................50
Appendix A Calculating the Sherwood number from a non isothermal aerosol mass transfer
experiment ....................................................................................................................................51
Appendix B Theoretical estimation of the diffusion coefficient of nitrogen-PAH mixture .............52
Appendix C Measuring the desorption energy of PAHs from suspended aerosols..........................53
Bibliography .................................................................................................................................54
2

3. List of figures
Figure 1: Relevant models for describing transfer dynamics over different ranges of the Knudsen
number (Fang 2003) ..............................................................................................................11
Figure 2: Sherwood and Nusselt number prediction for the transition regime ................................12
Figure 3: Experimental system diagram ........................................................................................15
Figure 4: Coating process schematics............................................................................................16
Figure 5: Maximum BaP coating vapor density build up in the Thermal Denuder. ........................20
Figure 6: Final Thermal Denuder (TD) design...............................................................................22
Figure 7: Minimal denuded layer thickness vs. number concentration ...........................................24
Figure 8: HR-AMS mass fragments for BaP coating on PSL.........................................................24
Figure 9: Typical raw data for measurement of BaP evaporation from PSL spheres ......................25
Figure 10: TC probe configuration ................................................................................................26
Figure 11: temperature scan for fast and normal flow rates............................................................28
Figure 12: Calibrating the side thermocouples (T0-T8) versus a central probe (T9) .......................28
Figure 13: Particle size distribution for different extents of evaporation corresponding ................33
Figure 14: Comparison of vacuum aerodynamic distribution for m/z=104 and 252 .......................32
Figure 15: Change in coating thickness due to evaporation............................................................35
Figure 16: Shape factor versus coating thickness...........................................................................35
Figure 17: Effect of residence time. 200 nm PSL sphere, 15 nm thick BaP coating........................36
Figure 18: Effect of residence time. 300 nm PSL sphere 20-25 thick BaP coating .........................37
Figure 19: Effect of residence time. 400 nm PSL sphere 22-30 nm BaP coating............................37
Figure 20: Sherwood number vs. particle diameter........................................................................38
Figure 21: The effect of Coating thickness on the evaporation rate for two limiting cases. ............41
Figure 22: Partial coating scenario schematics...............................................................................42
Figure 23: Calibration ratio of AMS fragment peak mass signal vs. SMPS & CPC mass...............43
Figure 24: Median mobility diameter variations for different PSL sphere diameters......................46
List of tables
Table 1 Benzo[a]pyrene (BaP) properties......................................................................................17
Table 2: Typical side-center temperature correlation matrix ..........................................................27
3

4. Nomenclature
ai, j Temperature L [m] Typical length
correlation matrix
D [m],[nm] Particle diameter Lmin [nm] Minimum AMS detectable
coating thickness
Dva [nm] Particle vacuum Loven [m] Thermal Denuder (TD) oven
aerodynamic diameter length
Dm [nm] Particle mobility !
m '' [Kg s·m ] Mass transfer rate
2
diameter
Dm!core [nm] Particle core mobility m0 [ µ g] Residue mass of coating,
diameter obtained by Sherwood theory fit
Dm!TD [nm] Particle mobility mg [Kg] Gas molecule mass
diameter, for aerosols
passing through the TD
Dm!bypass [nm] Particle mobility mm/z [µg / m 3 ] Mass loading of a single m/z
diameter, for aerosols
bypassing the TD
Df [m 2 s] Binary diffusion mv [Kg] Particle coating molecule mass
coefficient
DAMS [nm] Equivalent diameter Mw [g / mole] Molecular weight
calculated according to
AMS and SMPS
measurement
DSh [nm] Sherwood diameter M coat [g / mole] Coating molecular weight
H [KJ / Kg] Latent heat of M AMS [ µ g] Single aerosol coating main
evaporation bypass
M AMS
fragment [m/z] mass, measured
by AMS, for aerosols (general –
TD
M AMS no superscript), or aerosols
bypassing the TD (bypass
superscript), or going through the
TD.
h !W m 2 K # Heat transfer M SMPS [ µ g] Single aerosol coating mass,
" $
coefficient measured by SMPS, for aerosols
M bypass
hm [m s] Mass transfer SMPS
(general, no superscript), or
TD
coefficient M SMPS aerosols bypassing the TD, or
going through the TD.
I [kg / m] Evaporation driving hL Nusselt number
Nu =
force k
ˆ
I [ µ g] Normalized n Analogy fit parameter
evaporation driving
force
k [W / mK ] Thermal conductivity No [#/ m 3 ] Molecule number concentration
kB [m Kg s K ] Boltzman constant
2 2
N [# m 3 ] Particle number concentration
[# cm 3 ]
kv [W / mK ] N 2 gas thermal N bypass [#/ cm 3 ] Particle number concentration,
conductivity for aerosols bypassing the TD
! Knudsen number
Kn =
L
4

5. p [Pa] Pressure V frac Volume fraction of aerosol
ps [Pa] Saturation vapor x o , yo , z o Normalized Cartesian
pressure directions
pd [Pa] Saturation vapor ! [m 2 s] Thermal diffusivity
pressure with Kelvin
effect
! Prandtel number !c Energy accommodation
Pr = coefficient
"
q '' !W m 2 # Heat transfer rate ! Relaxation parameter for ai, j
" $
correlation matrix calculation
Q 3
[m / s] Volumetric flow rate ! o Average gas adiabatic constant
R [J / K·mol] The gas constant ! coat [dyne / cm] Coating material surface
tension
UL Reynolds number !D[m] Coating thickness
ReL =
!
Roven [m] Thermal Denuder !mAMS"SMPS [ µ g] Single aerosol evaporated
(TD) oven radius coating mass, measured by
AMS and SMPS
RM M SMPS Calibration ratio, for !mSMPS [ µ g] Single aerosol evaporated
= aerosols bypassing or coating mass, measured by
M AMS
passing in the TD SMPS
bypass
RM M bypass Calibration ratio, for ! [m] Mean free path
= SMPS aerosols bypassing the
M bypass
AMS
TD oven
S Jayne shape factor ! [m 2 s] Kinematic diffusivity
! Schmidt number !coat [Kg m 3 ] Coating bulk density
Sc =
Df [g cc]
hm L Sherwood number !coat "vapor [Kg m 3 ] Coating vapor density, near the
Sh = particle surface, and in the free
Df !coat "ambient
stream respectively
T [K ] Temperature !p [Kg m 3 ] Particle density
To Normalized !g [Kg m 3 ] Gas density
temperature
Tp [K ] Particle temperature !0 [Kg m 3 ] Normalization unit density for
Jayne shape factor calculation
Tg [K ] Gas temperature ! [!], [K] Lennard Jones potential
!, parameters
kb
Ti (t) [K ] Center of oven ! "m#EV , [ µ g] Repeatability error for !m and
temperature ! I "EV I respectively
T j (t) [K ] Side of oven ! (Kn) Fuchs correction for mass
temperature transfer in transition regime
U [m s] Gas velocity ! Dynamic shape factor
u o , vo , wo Normalized velocity !o Normalized mass fraction
in x o , y o , z o directions
5

6. Abstract
The use of solar energy for the production of solar fuels is currently studied throughout the
world. The first step in the process of solar thermal fuel production is to concentrate the solar flux
onto a gas stream. The gas stream used is typically transparent in the solar wavelengths. Therefore,
an absorbing medium is employed to absorb the solar flux, and transfer the heat to the gas flow.
Recently, Kogan, Kogan & Barak (2005) proposed to use nano-sized black soot particles and the
idea was tested in the solar facilities of the Weizmann Institute of Science.
The aim of this research is to develop a method for measuring mass transfer from nano-
sized particles, such as soot particles, and then obtain heat transfer coefficients through the analogy
between mass and heat transfer. The purpose of the mass transfer experiments in this research is to
examine the influence of the different experimental parameters on the mass transfer rate, and
compare the results to a known theory, thus assessing the efficacy of the measurement method for
obtaining mass and heat transfer coefficients.
A high resolution Aerodyne aerosol mass spectrometer (AMS) in conjunction with a
scanning mobility particle analyzer (SMPS) is used for measuring mass transfer rates of
Benzo(a)pyrene (BaP) from polystyrene latex (PSL) spherical particles of different sizes. The
experimental apparatus consists of a thermal denuder (TD) with a very uniform and stable
temperature profile (±0.2°C over 50 cm). The aerosols were coated by a thin layer of BaP, and then
passed through the TD at different speeds and different temperatures. The remaining mass of the
BaP was measured by the AMS and was compared to the original mass. A scan of different
residence times yields the so-called Sherwood number, which is a dimensionless mass transfer
coefficient, describing the ratio of convective to conductive transfer.
Experiments were carried out in the transition zone, between the continuum and the kinetic
regime where the Sherwood number is expected to decrease monotonically as the particles diameter
decreases in this regime.
Measurements where performed for 200,300 and 400 nm diameter core PSL spheres, coated
by 15-25 nm thick BaP. The results underestimate the theory by 5-25%, with measurement error of
±5-10%, and show the expected trend of increasing Sherwood number with particle diameter. This
implies that the proposed method can measure sublimation of thin coatings on high enough number
concentrations of aerosols, and the results are similar to pure conduction transport theory,
indicating that the process is slow enough and the mass transfer is mainly by conduction.
6

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8. Acknowledgements
I would like to acknowledge Jacob Karni and Yinon Rudich for their priceless advice and
support, walking me through the last year and a half of research and education. Yinon sent me to
learn first hand on the operation of the AMS, the main and most complicated measurement
apparatus, without which I would not have been able to conduct this research in the short time
frame I had. He followed my progress closely, making sure I know what I am after at each point.
After my first set of experiments I was perplexed by a clear difference between my results and
the theory. Jacob went with me through my experimental system step by step, trying to figure out
the error, and through his suggestions I found the mistake, and learned to take a pause, and try to
look at the problem from a different point of view. For that lesson I am deeply thankful.
I would also like to thank the Weizmann institute of science for supporting me with a generous
stipend allowing me to dedicate the last 2 years to my Ms.c. studies and research.
1 Introduction
1.1 Solar thermal energy
The use of solar energy for the production of electricity and fuels is investigated in industry
and academy with the purpose of gradual replacement of non-renewable and polluting energy
sources. Solar energy can be utilized in various ways, among them the thermo-solar method, where
the sun’s radiation flux is concentrated and used to heat a fluid, which is either used to drive a
thermodynamic cycle, which in turn drives a generator and produces electricity (Kribus et al.
1998), or to facilitate a high temperature chemical reaction to produce fuel (Kogan, Kogan, and
Barak 2005; Epstein, Ehrensberger, and Yogev 2004). A highly efficient way to facilitate high
temperature chemical reactions using particle-laden flow exposed to high concentration of solar
flux was proposed and tested (Klein et al. 2007).
In this method, a volume of gas, seeded with black soot particles is entrained in a cylinder
and exposed to a high concentration of solar flux. The soot particles absorb the flux, heat up, and
transfer the heat to the gas by conduction primarily.
The experiment conducted by Klein et al. (2007) resulted in an exhaust gas stream with
about 200 K higher temperature then the projected values of their model. The most probable reason
for this is an under estimation of the conductive heat transfer from the soot particles, since the
theory used was based on spherical particles having equivalent surface area to that of the real soot
distribution. Thus a system for measuring the real heat transfer coefficient of soot particles, or any
particle ensemble, as a function of measurable particle morphology parameters such as the mobility
and aerodynamic diameters is desired.
7

9. 1.2 Convective heat transfer
The process of particle to gas heat transfer is best described by the heat transfer equation
q '' = h·(T p ! Tg ) (1)
h !W m 2 K # is a heat transfer coefficient, q '' !W m 2 # is the heat flux per particle surface area,
" $ " $
T p [K ] and Tg [K ] are the particle surface temperature and free stream gas temperature respectively.
The heat transfer coefficient relates the heat flux to the temperature difference, and is a function of
the particle morphology; fluid properties and heat transfer mechanism. The heat transfer coefficient
can be expressed in a dimensionless form, known as the Nusselt number, relating convective to
hL
conductive heat transfer across the surface boundary - Nu = where L[m] is a typical length and
k
k[W / mK ] is the thermal conductivity of the fluid. There are various theoretical and empirical
correlations between the Nusselt number and other non-dimensional parameters of the process such
as the Reynolds, Grashof and Prandtl numbers (Bird, Warren, and LightFoot 2002) describing the
heat transfer of various configurations.
Klein et al. (2007) assumed that the relative velocity between each soot particle and the gas
stream is zero, and used the pure conduction result for spheres – Nusselt = 2 (Bird, Warren, and
LightFoot 2002) ,corrected for the Knudsen number. Since in many cases the particles dimension is
relatively close to the mean free path between the gas molecules ![m] , the heat transfer occurs in
the transition regime, between continuous transfer dynamics and the kinetic regime, 0.1 < Kn < 10 ,
!
as defined by the Knudsen number Kn = . In this region the heat transfer coefficient, and
L
associated Nusselt number, are lower then the continuum solution. Several solutions for the effect
of the transition regime on the Nusselt number exist, all built upon the Fuchs boundary layer
approach (Filippov and Rosner 2000).
To simulate the heat transfer from the soot particles to the gas, Klein et al. (2007) utilized
the volume distribution of the soot particle batch used in their tests, as obtained from SEM images,
and assumed the Nusselt number relating to each volume segments diameter. The resulting
simulations underestimated the experiment by 200 K (~14%).
The main reason for this mismatch is assumed to be the heat transfer coefficient used. The
particles are not spheres, and consequently the equivalent volume approach was not accurate
enough, or may have missed a fundamental difference between the heat transfer from soot
agglomerate particles and an equivalent surface area of spheres. Even simpler, this could be the
result of the in ability to measure the exact surface area of a soot particle distribution by analyzing
2D SEM pictures.
8

10. 1.3 The heat to mass transfer analogy
1.3.1 Heat and Mass Transfer in the Continuum Regime
In the continuum regime there is a mathematical-physical equivalence between the energy
equation for convective heat transfer, and the species mass transfer equation.
The normalized energy equation is (Hong and Song 2007)
!T o o !T
o
o !T
o
1 " ! 2T o ! 2T o ! 2T o %
uo
+v +w = 2 + 2 + (2)
!z o ReL Pr $ !x o
2 '
!x o !y o # !y o !z o &
UL !
Where the Reynolds number is ReL = , the Prandtl number is Pr = , ! [m 2 s] is the
! "
kinematic viscosity, ! [m 2 s] is the thermal diffusivity, U[m s] is a typical velocity, u o , v o , w o are
normalized velocities in the normalized directions x o , y o , z o respectively, and T o is the normalized
temperature.
The normalized mass transfer equation is
!" o o !"
o
o !"
o
1 # ! 2" o ! 2" o ! 2" o &
u o
+v +w = 2 + 2 + (3)
ReL Sc % !x o
2 (
!x o !y o !z o $ !y o !z o '
Where ! o is the normalized mass fraction of the transported species in the gas stream,
!
Sc = is the Schmidt number and D f [m 2 s] is the diffusion coefficient of the species involved in
Df
the gas stream. The analogues mass transfer equation to the integral form of the heat transfer
equation, (equation (1)), is
m '' = hm ·( ! p " !g )
! (4)
!
Where m ''[Kg s·m 2 ] is the mass transfer per unit time and particle surface area; hm [m s] is the
mass transfer coefficient; ! p [Kg / m 3 ] and !g [Kg / m 3 ] are the vapor densities of the species being
transferred from the particle surface and away from the particles respectively. The mass transfer
hm L
coefficient is related to the non-dimensional Sherwood number Sh = in the same manner that
Df
the heat transfer coefficient is related to the Nusselt number.
If the Prandtl and Schmidt numbers are the same (which is not common in most fluids),
then the Sherwood and Nusselt numbers also equal, for the same flow configuration and boundary
conditions. This allows a mass transfer experiment resulting in the Sherwood number to give the
Nusselt number by analogy (Hong and Song 2007). Because the Prandtl and Schmidt numbers are
not the same in practice, the following approximate relationship is used
9

11. n
! Pr $
Nu = Sh # & (5)
" Sc %
Where n is a fit parameter obtained empirically or by calculation according to the geometry and
temperature difference sign (heating or cooling) and is typically between 0.3-0.4 (Incropera and
Dewitt 1996; Bird, Warren, and LightFoot 2002).
Many expressions for the Nusselt number have been obtained from Sherwood number
experiments. For instance, in case of forced convection on a solid sphere
Sh = 2 + 0.6 Re1 2 Sc1 3 (6)
And by analogy
Nu = 2 + 0.6 Re1 2 Pr1 3 (7)
The analogy is valid if the following conditions are met:
1. Constant physical properties
2. Small net mass transfer rates
3. No chemical reactions
4. No viscous dissipation heating
5. No absorption or emission of radiant energy
6. No pressure diffusion, thermal diffusion, or forced diffusion
7. Similar boundary conditions
In the case of pure diffusion, or pure conduction, the Sherwood and Nusselt numbers are not
dependent on the working medium properties (Schmidt or Prandtl numbers) or on flow conditions
(Reynolds number). Therefore, the analogy is expected to be even simpler (further discussion on
the analogy for suspended aerosols in the transition regime is presented in section 4.6).
1.3.2 The dynamic transfer conditions
The objective of the current research is to develop a method for measuring the mass transfer
coefficient for nano-size soot and other aerosols, at atmospheric pressure. The measured mass
transfer coefficient can be used in conjunction with the heat to mass transfer analogy to give the
heat transfer coefficient, which is necessary for further development of the solar thermal seeded
particle reactor configuration (see section 2.1 on Solar thermal energy).
In the current research, all of the conditions stated in the previous section (top of p. 10)
were taken into consideration (see Chapter 4 – Experimental Apparatus and Test Results). The
main difference between the heat-mass transfer analogy as previously used and the current one is
the dynamic transfer conditions. Soot-particles diameter is typically around 200nm ! 10 µ m , which
corresponds to Knudsen numbers of 0.1-10. This is in the transition regime between the continuum
10

12. and free molecular regimes (Figure 1). The analogy is known and holds for the continuum regime,
but has not been tested for the transition or free molecular regime.
The heat and mass transfer equations for the free molecular regime are given by Lees
(1965) for instance, for the case of no net flow perpendicular to a surface
4 2kB p $T
q fm = !
! # g [w m 2 ] (8)
3 m g" Tg $x
4 1 $ %p
m fm = !
! # g [Kg m 2 s] (9)
3 2" pg %x
Where ![m] is the mean free path of the gas-particle system, defined as
$ # + D' !" 2 2
2
! =1 "No & where [m ] is the effective gas molecule cross-section and D[m] is the
% 2 ) ( 4
particle diameter, N o [#/ m 3 ] is the particle number density, mg [Kg] is the gas molecule mass
(apparently, it is not specified in the article) and kB [m 2 Kg s 2 K ] the Boltzman constant.
Figure 1: Relevant models for describing transfer dynamics over different ranges of the Knudsen number (Fang
2003)
For spherical particles the expressions are similar, Filippov and Rosner (2000) give
pg ! c kB % # o + 1(
q fm =
! ' # o $ 1 * (Tg $ T p ) [W m ]
2
(10)
Tg 2 " mg & )
Where ! c is the energy accommodation coefficient (Burke and Hollenbach 1983), and ! o is the
average gas adiabatic constant (Filippov and Rosner 2000). Griffin and Loyalka (1994) give the
mass transfer to a spherical particle in the free molecular regime:
11

13. 8k B
m fm = Tg
! ( "g # " p ) [Kg m 2 s] (11)
! mv
Where mv [Kg] is the molecular mass of the gas phase molecule.
The driving force is similar in both heat and mass transfer expressions (Eq. (10) and (11),
respectively), the temperature difference being analogues to the partial pressure (or concentration)
difference, but there is no direct correspondence of transport properties coefficients. Instead, these
coefficients are related to the pressure, temperature and density of the gas, in different or even
opposite ways. The change of the transport properties in the continuum regime with pressure and
temperature is also not exactly similar, and this is taken into consideration through the n parameter
(Eq. (5)) relating the Schmidt and Prandtel numbers. In the transition regime however, the
deviation from the continuum model is similar for both heat and mass transfer, as can be seen in
Figure 2, reproducing results for the Nusselt number given by Klein et al. (2007), with Davies
results for the Sherwood number shown as well (Eq. (12)). The trend is the same for both non-
dimensional numbers, the deviation arising from the models themselves, as can be seen for the
large variation for the 4 Nusselt models shown. The Fuchs solution for instance, is the same for
both heat and mass transfer in the transition regime (Filippov and Rosner 2000). Analysis of the
heat and mass transfer analogy in the transition regime is provided in section 4.6.
Figure 2: Sherwood and Nusselt number prediction for the transition regime compared. Nusselt plot reproduced
from Klein et al. 2007. Only new addition is the Sherwood number theory by Davies given according to Eq. (12).
The Fuchs model (black dashed curve) applies to both mass (Sh) and heat (Nu) transfer as indicated in the
figure.
12

14. 1.3.3 The transition regime
The experiments presented in Chapter 3.2 were conducted in the transition regime;
0.2 < Kn < 0.7 where the dynamics are best described as a combination of a continuum and free
molecular dynamics, such as the Fuchs 2-layer approach (Filippov and Rosner 2000): The theory is
based on a boundary layer approach. Since there is no general analytical solution of the Boltzmann
equation describing gas behavior in the intermediate regime of moderate Knudsen numbers, an
interpolation formula is used which is based on the separation of the space outside the particle
surface into two parts: Close enough to the surface of the particle (the boundary layer), the
conditions are assumed to be collision-less – no collisions between gas molecules, only gas-aerosol
interactions are assumed. The boundary layer thickness is typically set to be the same as the gas
mean free path. Outside of the boundary layer, the conditions are described by the continuum
dynamics. A consistent solution is found for both regimes by ascribing the same heat (or mass)
transfer rate at the boundary.
Different interpolation formulas exist for mass transfer in the transition regime, as discussed
above. Our results are compared to the derivation of Davies (1978) from ((Hinds 1999) p. 288):
2" + D
ShKn = 2·! (Kn) = 2· (12)
D + 5.33(" 2 D) + 3.42 "
Where ! (Kn) is referred to as the Knudsen correction. Multiplying the Knudsen correction by 2,
gives the pure diffusion result for Re = 0 (as also predicted by equation (6)). The mean free path is
kT
calculated according to ! = [m] where p[ pa] is the pressure. In the limiting cases of
"d p 2
2
N2
4 1
molecular and continuum regimes, the Sherwood number values are therefore · & 2,
5.33 Kn
respectively.
Although this derivation is for the case of a light molecule evaporating through a bath gas made out
of heavier molecules, which is not our case, using more apparently appropriate derivation, such as
Sitarski and Nowakowski (1979) (see Davis 1983) gives very similar results, and so we settled for
this simpler derivation.
2 Research Objectives
The research objectives are:
• Development of an experimental method to measure the evaporative mass transfer from
nano aerosol particles in the transition regime
• Use the analogy between heat and mass transfer to relate the mass transfer coefficient to
the heat transfer coefficient (Eq. (5)).
13

15. An important additional objective is the validation of the proposed method – using spherical
particles suspended in nitrogen – by experimentally obtaining the theoretically predicted rate of
mass transfer, corresponding to each particles size, in the transition regime.
3 Experimental Apparatus and Test Results
3.1 Experimental system
A system was designed and built to measure the mass transfer rate from aerosol particles. It is
composed of the following components (Figure 3: Experimental system diagram):
1. Aerosol Generation:
Create a suspension of monodisperse aerosol – polystyrene latex (PSL) spheres – in
nitrogen at atmospheric pressure.
2. Coating of Aerosol with a thin layer of a high vapor pressure material – Benzo(a)pyrene
(BaP)
3. Evaporation step: Allows the aerosols to flow through one of two paths:
a. A thermal denuder (TD) with precisely controlled temperature and flow rate.
b. Bypass at room temperature
4. Measurement of aerosol mass and composition: the aerosol flow is split into a measuring
system consisting of a scanning mobility particle sizer (SMPS), Aerodyne high-resolution
aerosol mass spectrometer (AMS), and a condensation particle counter (CPC).
The flow is continuously split into these three measurement devices, and measurements are
acquired (>10 Hz), averaged and saved on intervals of 1 second (CPC), 0.5 minute (AMS)
and 1 minute (SMPS). All instruments are controlled through a PC computer. These
instruments are discussed in more detail in section 3.1.5.1
14

16. Figure 3: Experimental system diagram
PSL: polystyrene latex, DMA: differential mobility analyzer
HR-AMS: high resolution aerosol mass spectrometer, CPC: condensation particle counter
SMPS: scanning mobility particle sizer (combination of CPC and DMA)
15

17. 3.1.1 Aerosol generation
A standard atomizer (TSI 3076) was used to atomize a solution of nanopure water and
polystyrene latex (PSL) spheres. A magnetic stirrer was used to ensure homogenous suspension.
85
The suspended aerosols subsequently flow through a silica gel diffusion dryer, followed by a Kr
radioactive source that creates a symmetrical Boltzman charge distribution. In all of the
experiments the particles’ number concentration increased gradually from about 500[#/cc] to about
800[#/cc] (example for 300 nm PSL spheres), due to increased solution concentration caused by
evaporation of water from the solution. The dried and charged aerosols then passed through the
electrostatic classifier (differential mobility analyzer, DMA), set at the PSL spheres nominal
diameter, to remove all other particles, except the PSL-sphere aerosols with the designated
diameter.
3.1.2 Coating with High Vapor Pressure Material (Benzo(a)pyrene)
Figure 4: Coating process schematics
The nearly mono-disperse PSL aerosol (Duke scientific corp., normally D±1-3%) is injected
into an oven containing a batch of the organic material (Figure 4), in which a type T thermocouple
is attached and used to control an electrical heating tape surrounding the glass oven. The glass
vessel has a central input tube, which impinges the aerosols towards the bottom, and an annular
exit. The suspended aerosols typically stay in the oven for 1-7.5 seconds. Another outlet allows for
the insertion of a thermocouple.
The coating materials used is the polycyclic aromatic hydrocarbon (PAH) benzo[a]pyrene
(BaP). A PAH was chosen for three reasons:
1. Stable materials, which do not react with PSL or any other material in the system.
16

18. 2. High molecular mass. The HR-AMS fragmentation pattern of BaP has its major peak well
above the 104 m/z (ion mass over charge) peak associated with PSL (see Figure 8)
allowing for simple mass calibration of the main fragment peak and the real coating mass.
3. Vapor pressures are low enough to have very small evaporation rate at room temperature,
but high enough to enable measurements at not too high oven temperatures (oven
temperatures were 80-160 C o )
The coating material chosen for this research is Benzo[a]pyrene (BaP) (see Table 1). There are
tabulated physical-chemical data for this material at the relevant temperature and pressure ranges of
this research, except for the binary diffusion coefficients in nitrogen or air. Values of these
coefficients do not exist for any PAH of relevance to this study, and it was calculated according to
the Chapman-Enskog relationship (see appendix B) according to the LJ parameters (see Table 1).
The residence time in the coating oven was controlled by an additional N 2 flow.
Table 1.A Benzo[a]pyrene (BaP) physical properties
Molecular weight Bulk density Surface tension Melting point
Formula !coat [g / cc] ! coat [dyne / cm]
M coat [g / mol] [ o C]
C20H12 252.3093 1.286 64.7 179
Source: (chemspider.com)
Table 1.B Benzo[a]pyrene (BaP) Lennard-Jones parameters
!
" (!) [K ]
kb
7.66 918.15
!
Source: Using PAH derived fit = 37.15·Mw 0.58 and ! = 1.234·Mw 0.33 from (Wang and
kb
Frenklach 1994)
Table 1.C Benzo[a]pyrene (BaP) vapor pressure parameters
Expression A B
A
B!
P = 101325·10 [Pa]T 6181±32 9.601±0.083
Source: (John James Murray, Roswell Francis Pottie, and Pupp 1974)
3.1.3 Controlled evaporation
Either controlled coating or controlled evaporation of the particles, driven by a vapor pressure
gradient, could have achieved the goals of this investigation. The choice of controlled evaporation
is a natural one, since creating a known vapor pressure difference is much simpler when far away
from the particle the desired partial vapor pressure is zero, rather than a finite number. Activated
17

19. charcoal (Aldrich, granules, 4-14 mesh) is used to absorb BaP vapor and create a zero vapor
pressure environment immediately after the oven section.
3.1.3.1 Increase of coating material (BaP) ambient vapor pressure
Concern related to this experimental design was that the denuded BaP coating might,
a. Change the coating vapor pressure in the vessel’s ambience (which starts as zero)
b. Condense back on the particles as they cool down between the oven and the denuder
The following approach was taken to deal with these issues:
a. The initial vapor pressure of the coating material in the surrounding ambience is zero. The
vapor pressure of the BaP coating in the ambience, after denuding an L[m] layer from a
D + L diameter sphere is calculated according to:
Kg #
!coat "ambient = !coat ·V frac [ 3
];V frac = N ((D + $D)3 " D 3 ) ! 1 (13)
m 6
Where N[# m 3 ] is the particle number concentration, !coat [Kg m 3 ] is the coating material
bulk density, !D[m] is the evaporated coating thickness, and V frac is the volume fraction of
aerosol coating in a unit volume and is smaller then 1, so that the resulting
!coat "ambient ! !coat . Thus, !coat "ambient is the resulting coating material vapor concentration in
the end of the tube after all the coating ( !D[m] ) evaporated. Eq. (13) holds whenever L is
smaller that the initial coating layer.
The surface vapor density is calculated according to the vapor pressure correlation listed in
Table 1 ( ps [Pa] ), and corrected according to Kelvin Law (to give pd [Pa] )
A 4 " coat M coat
B!
#coat R·T p ·D
ps = 101325·10 [Pa], pd = ps ·e
Tp
[Pa] (14)
Where A & B are taken from Table 1, M coat is the molecular mass, R is the gas constant,
T p [K ] is the coating (particle surface) temperature and ! coat [N / m] is the coating surface
tension.
Finally, according to the ideal gas law –
M coat ·pd # Kg &
!coat "vapor = (15)
R·T p % m 3 (
$ '
Where !coat-vapor is the vapor density of the evaporated coating, and pd is the vapor pressure
of the evaporating layer corrected for the Kelvin effect.
Figure 5 shows the relation between Equations(13) and (15). The black lines are !coat "ambient
for two limiting cases, of 20 nm coating completely denuded, with BaP as the coating
material, and the color indicates log( !coat "vapor ) and is shown for different temperatures, and
18

20. particle diameters. The particle diameter influences the vapor pressure through the Kelvin
effect, which, as can be seen, is not large for these diameters.
A temperature of at least 75 o C is needed for the two limiting cases to get a one order of
magnitude difference between the surface vapor pressure and the ambient vapor pressure of
BaP at the end of the Thermal Denuder (TD) oven, which ensures that the difference
between vapor densities will be larger then one order of magnitude in the interior of the
oven. Under these conditions the assumption !coat "ambient # 0 is valid.
b. According to Huffman et al. (2008), who designed and built a fast stepping thermo-denuder
for the measurement of ambient aerosols in conjunction with the Aerosol Mass
Spectrometer (AMS) measurements, and dealt with a similar issue, the condensation of the
coating material vapor on the particle is not a problem. In their configuration the denuder
follows the oven section without any overlap, and the denuder section starts only when the
temperature drops below 10% above the room temperature. During our experiments no back
condensation was detected in cases where only part of the BaP coating evaporated.
3.1.3.2 Initial design
The initial design of the Thermal Denuder (TD) oven, and the activated charcoal tube length
were done according to Huffman et al. (2008), Jonsson, Hallquist, and Saathoff (2007) and Orsini
et al. (1999). The general dimensions of activated charcoal section, and oven diameter, length and
resident times where referenced from Orsini et al. (1999) and Jonsson et al. (2007), and the
possibility of separating the oven (evaporation) and the activated charcoal (absorption of
evaporated coating) was verified by all three papers. The following describes the initial design
verification. A description of the final TD is given in section 3.1.3.
For verifying the flow rates and oven length, the evaporation rate for the initial design diameter
(4.3 mm) was calculated for the aerosols of interest and various oven lengths and flow rates. Klein
et al. (2007) found that in their solar reactor, the most effective soot agglomerates for radiation
absorption and conductive heat transfer to the gas were in the size range of 200 < D < 2000[nm] .
The aerodyne HR-AMS used in the present study (described briefly described briefly in section
3.1.4; for a full description see DeCarlo et al. (2006)) can measure only particles in the size range
of 50 < D < 750[nm] . Therefore the particles tested in the present study were in the size range of
200 < D < 500[nm] .
19

21. Figure 5: Maximum BaP coating vapor density build up in the Thermal Denuder. The Y axis is the diameter of
the denuded particle, showing the negligible effect of the Kelvin effect on the vapor density for particles of 200-
500 nm diameter. The X axis is the temperature of the oven, and the color is negative orders of magnitude
( log( ! )[log(Kg / m
3
)] ) of saturation vapor density of the coating material (BaP). The black line shows the
developed vapor density for the complete evaporation of the coating for two limiting cases as discussed in the
text, and the dashed rectangle shows the experimental conditions, of nominal TD temperature and particle
diameter.
The evaporation rate was calculated by solving the continuum-based differential diffusion
equation (16), including the Fuchs correction for the transition regime (Hinds 1999). The Kn
number equals 0.2-0.7 for particles in the range of 200-500 nm, in nitrogen flow at 1 bar pressure,
at temperatures of 100-200 o C .
dD 4D f T p ·M coat
=- ·p ·"(Kn) for Kn # 1
dt !coat R·Td ·D d
2$ + D (16)
"=
$2
D +5.33 +3.42$
D
kT D
Where ! = [m] is the mean free path, Kn = is the Knudsen number, ! is the Fuchs
2 p" !d 22 !
N
slip correction and D f is the binary diffusion coefficient, estimated by the Chapman Enskog theory
(See Appendix B). T p is the particle surface temperature, assumed to be equal to the average
surrounding temperature at a given flow-wise oven cross section, and Td is the aerosol surface
temperature after the latent heat release due to the evaporation process, according to
DAB MHpd
Td = T! + (17)
RkvTd
20

22. Where H is the latent heat of evaporation and kv is the nitrogen thermal conductivity. It was
assumed that the rate of evaporation during the experiments is slow enough for Td ! T p . This
assumption was validated by calculating Eq. (16) for the temperature ranges used in the
experiments (100-200 o C ). The resulting difference between Td and T p was less then 10 !4 [K ]
indicating this assumption is valid.
The initial design of the TD system was based on the following assumptions:
1. 100% Nitrogen flow
2. Constant temperature profile in the Thermal Denuder
3. Average flow rate used to calculate resident time
4. The times of temperature increase and decrease near the oven inlet and outlet, respectively,
is negligible in comparison to the residence time in the oven.
5. The partial pressure of the coating material far away from the particle surface is zero (this
assumption has been used throughout the prior analysis (see p. (18)), and validated above
(See discussion following Eq. (16)).
An oven tube inner diameter of 4.3 mm was chosen, based on prior designs (Orsini et al. 1999).
A flow rate range of 100-400 cm3 min-1 was used, according to the flow rate requirements of the
other instruments attached (AMS, DMA) and the particle concentration number needed. The
solution of equation (17) for PSL spheres of 200 nm coated with 10 nm of Coronene (the initial
choice for the coating material), at a temperature range of 100-180 o C showed that a residence time
between 1-5 seconds is appropriate, and translates to an oven length of 60 cm according to
Loven
t = !R 2
oven where Roven is the oven inner diameter and Q[m 3 s] is the volumetric flow rate.
Q
3.1.3.3 Final Design
3 different TDs were built. The two earlier designs used heating coils in one and two separately
controlled sections, respectively. The 3rd and final design used a silicon oil heat bath circulating
around the aerosol tube, which yielded the most uniform temperature distribution along the oven.
21

23. Figure 6: Final Thermal Denuder (TD) design. The T’s are thermocouple locations. Flow direction is from left to
right, as indicated by the black arrows. Activated charcoal was used downstream of the oven section, for
absorbing the evaporated coating and preventing re-adsorption to the particles.
Gas flow (Q) is measured before the oven with a differential pressure transducer. 9 type-T
thermocouples (TC) are attached to the outer side of the flow tube (T0 - T8), in the circulating oil
bath volume, and measure the temperature along the 60 cm oven length. Another TC is located
between the oven and the activated charcoal (T9 in Figure 6). A circulation of flow was maintained
in the TD, running through a HEPA (high efficiency particulate air) filter, when the aerosol-laden
flow was diverted to the bypass. This was used to insure that no residue-coating vapor remained in
the TD.
3.1.4 Measurement
The coated aerosols were measured with a combination of instruments. The main flow was
split iso-kineticly (maintaining the same direction and magnitude of flow velocity across the split
cross-section) to 3 streams, flowing into the Aerodyne high-resolution aerosol mass spectrometer
(AMS), condensation particle counter (CPC) and the scanning mobility particle sizer (SMPS).
The coating’s mass and the aerosols’ aerodynamic diameter were measured with a high
resolution AMS, thoroughly described by DeCarlo et al. (2006). Briefly, The AMS samples 85
[cm3 min-1] of gas through a critical orifice, followed by an aerodynamic lens, which focuses the
aerosols into a tight beam. The aerosols expand out of the outlet into a vacuum of 10 !4 [Pa] where
the beams encounter a chopper – a rotating disk with two opposite thin slits – positioned by a servo
in one of three options – open, closed or chopped. In the open mode the aerosol beam does not
impact the chopper, in the closed mode the aerosol beam is completely blocked by the chopper, and
in the chopped mode the aerosols are focused onto the slit in the rotating chopper, and pass through
a close/open cycle at the rate of ~120 Hz. After passing through the chopper the aerosol beam
impacts a cup-shaped tungsten oven at 600-900°C, named the vaporizer, which flash-vaporizes the
22

24. aerosols. The resulting vapor is ionized by electron impact at 70 eV. The resulting ions are
extracted into a time of flight (TOF) high-resolution time of flight mass spectrometer (TofWerk).
The AMS is operating in one of two modes – the average mass mode, in which the open and
closed positions of the chopper are used. The open mode measures the average mass spectrum of
the aerosol and gas stream, while the closed position measurement reflects the gas background
only. The subtraction of the “closed” mass spectrum from the “open” one gives the average aerosol
mass spectrum mm/z [ µ g m 3 ] . In the second mode, the chopper stays in the chopped position. The
chopper is used as the starting signal for a particle time of flight measurement through the 39.5 cm
section following the chopper, and the mass measurement signal is the final measurement thus
giving a measurement of the vacuum aerodynamic time of flight related to each mass spectrum,
which allows to calculate the vacuum aerodynamic diameter dva [nm] .
The AMS detection limit in V-mode (the path of the ions. see DeCarlo et al. (2006)) is
estimated as s < 0.04[ µ g m 3 ] . Combined with the bulk density of BaP this gives the estimated
minimal denuded coating thickness detected by the AMS:
1
# 6s 3 &
Lmin = % + D 3 ( ) D[nm] (18)
$ N !coat " '
Where s is the detection limit, D is the core PSL diameter, !coat is the BaP bulk density (BaP was
the chosen material for all experiments shown here. For the initial design, coronene was used as
well, and so it appears in previous calculations), N[#/ m 3 ] is the aerosol number density, and
Lmin is the minimum detectable BaP layer thickness.
Figure 7 shows a plot of Eq. (18), for relevant core diameters and number concentrations.
As can be seen, the AMS can detect nanometer size coatings, which are small enough to have a
negligible affect the morphology of non-spherical aerosols with a characteristic length bigger then
~30 nm.
23

25. Figure 7: Minimal denuded layer thickness vs. number concentration, for AMS sensitivity of 0.04 µ g / m and
3
BaP as the coating material.
Figure 8: HR-AMS mass fragments for BaP coating on PSL
300 m/z (mass over charge) intensity was used to calculate the mass of the coronene
coating, and 252 m/z was used for the BaP coating (Figure 8). These were based on SMPS, CPC
and differential mobility analyzer (DMA) combination as will be described in the experimental
section 3.1.5.1 below.
In addition, the vacuum aerodynamic diameter measurement (from the AMS) was used to
assess the sphericity of the coating (see section 3.2.1).
The CPC measures particle number concentration N = [# cm 3 ] , combined with the AMS
measurement of the mass loading of the coating material main fragment m/z m252 [ µ g / m 3 ] gives
bypass
the coating mass for each aerosol (Eq. (20)).
24

26. The SMPS measures the mobility diameter distribution of the aerosols, by combining a CPC and a
DMA. The DMA’s voltage is scanned between low and high voltages, set according to the desired
size range, and the CPC counts the number concentration for each voltage. The result can be
inverted to give a mobility diameter distribution (for more detailed description see Rader and
McMurry (1986)).
3.1.5 Experimental Procedure
This section gives a step-by-step description of a typical experiment:
3.1.5.1 Data collection
Different sizes of PSL spheres (200-400 nm diameter) were coated and denuded, in
different oven temperature fields (75<T<130 o C ) and flow rates (80<Q<1400 cm !3 ·min !1 ). Each
experiment consisted of 3 stages – bypass (un-denuded particles), oven (denuded particles) and
bypass again. A typical experiment’s raw data is presented in Figure 9.
Figure 9: Typical raw data for measurement of BaP evaporation from PSL spheres. In this measurement 300
o !1
nm diameter PSL spheres where coated by 25 nm thick BaP, in a 80 C oven and a flow rate of 120 cc·min
Dm [nm] is the peak of a Gaussian fit around the mode of the monodisperse aerosol mobility
diameter distribution measured by the SMPS (the mode diameter is the diameter corresponding to
the highest particle number concentration). Dm!bypass [nm] is the average of Dm [nm] in the bypass
section, and Dm!TD [nm] is the average in the TD section.
25

27. Dm!core [nm] was obtained by measuring the size distributions of the core particles of each PSL
sphere diameter used in the tests.
In addition to these measurements, a correlation was established between the sidewall
temperature measurements of the oven and the temperature at the center of the oven cross section at
each point along the oven’s tube.
3.1.5.2 Measurement of the side-center temperature correlation matrix
The oven temperature distribution, Twall (x j ,t) , which is also referred to as T j (t) , is
continuously measured by thermocouples connected to the outer side of the oven’s tube, evenly
spaced along its axis (Figure 6). This measurement is calibrated against a separated experiment,
where a stiff, thin (1.6 mm diameter) type T thermocouple probe is moved along the oven axis,
measuring the temperatures Tcenter (xi ,t) – also referred to as Ti (t) – at the center-line of the oven
cross section, while the side-wall temperature is also measured. As shown in Figure 9, a small
triangular Teflon holder, with holes at each side, holds the thermocouple probe, allowing the flow
to pass while maintaining the TC tip at the middle of the cross section.
Figure 10: TC probe configuration
The correlation between the center temperature and the wall temperature at close locations
is obtained and averaged over time. A calibration matrix ai, j is then calculated such that
ai, j ·T j = Ti . Since x j points are fewer then xi points, the sparse wall temperature measurements,
which are the only temperature measurements taken during the aerosol denuding experiment, are
each related to a large oven length interval by the last expression.
The 3 closest j points are used with each i point to calculate ai, j according to the following
relations:
# 1&
Ti0 % 1 " (
1 Ti0 $ !'
ai0 , j0 = , ai0 , j0 "1 = ai0 , j0 +1 = where 1 ) ! ) 2 (19)
! T j0 T j0 "1 " T j0 +1
26

28. Ti 0
For the end points ai 0, j 0 = . All other ai 0, j in the row are set to 0. This equation is the result of
Tj0
satisfying ai, j ·T j = Ti with the closest 3 points.
A typical calibration matrix is shown in Table 2, for the temperature profile shown at the
lower part of Figure 11, obtained for 50 mm steps of the probe along the oven center-line (shown in
Figure 12). The steadiness of the oven temperature can be appreciated from this measurement
(Figure 12). The I parameter (see Equation 23) is the vapor density of BaP, multiplied by its
diffusion coefficient of BaP in nitrogen.
Ti
Table 2: Side-center temperature correlation matrix ai, j =
Tj
j0 j1 j2 j3 j4 j5 j6 j7 j8
i0 0.2690 0 0 0 0 0 0 0 0
i1 0.4700 0 0 0 0 0 0 0 0
i2 0.2320 0.4530 0.2320 0 0 0 0 0 0
i3 0.2520 0.4940 0.2520 0 0 0 0 0 0
i4 0 0.2490 0.4980 0.2491 0 0 0 0 0
i5 0 0 0.2490 0.4980 0.2492 0 0 0 0
i6 0 0 0.2490 0.4980 0.2493 0 0 0 0
i7 0 0 0 0.2492 0.4989 0.2492 0 0 0
i8 0 0 0 0 0.2493 0.4982 0.2493 0 0
i9 0 0 0 0 0.2492 0.4980 0.2492 0 0
i10 0 0 0 0 0 0.2492 0.4983 0.2492 0
i11 0 0 0 0 0 0 0.2539 0.4984 0.2539
i12 0 0 0 0 0 0 0.2542 0.4986 0.2542
i13 0 0 0 0 0 0 0 0 1.0351
i14 0 0 0 0 0 0 0 0 0.9770
i15 0 0 0 0 0 0 0 0 0.8000
i16 0 0 0 0 0 0 0 0 0.5925
i17 0 0 0 0 0 0 0 0 0.5430
27

29. !3 !1
Figure 11: Top: temperature scan for fast flow rate of 1400[cm ·min ] and nominal oven temperature of
115°C. The “center of cross section evaporation driving force” is the evaporation driving force (equation (24))
calculated according to the center of cross section temperature profile along the oven (in red)
!3 !1
Bottom: Typical oven temperature profile for I (see Eq. (24)) at flow rate of 400[cm ·min ] and nominal oven
temperature of 85°C
Figure 12: Calibrating the side thermocouples (T0-T8) versus a central probe (T9)
The top of Figure 11 shows the temperature profile during fast flow (Q=1400 cm !3 ·min !1 ) through
the oven. The temperature increase is slower than for 400 cm3 min-1, as expected, and the
evaporation driving force increase is even slower then the temperature increase. Most of the
experiments where conducted in flow rates lower than 700 cm3 min-1, where the flow pattern is
almost as flat as that shown in the lower part of Figure 11. The flow pattern was measured for
several flow rates, and then used to calculate the correlation matrix for these flow rates. The
temperature profile was linearly interpolated for all other flow rates in between.
28

30. 3.1.5.3 Data analysis procedure
1. Defining a “mass calibration ratio” RM : The AMS does not have a 100% collection
efficiency due to bouncing of particles from the hot place without evaporation.
Additionally, only the main fragment was used to calculate the mass of the coating material.
To provide a real mass determination by AMS, a “mass calibration ratio” is defined. The
mobility diameter of coated particles is calculated by fitting the SMPS distribution to a
Gaussian curve around the coarser mode as measured by the SMPS (See Figure 13 in
section 3.2.1). Using this diameter and the known coating mass density, the calibration ratio
RM is calculated between the AMS’s BaP main fragment peak mass (see Figure 8) and the
mass calculated using the SMPS diameter (Eq. (21)):
bypass
m252 1
M AMS =
bypass
bypass
[ µ g] (20)
N 100 3
! 3
M SMPS =
bypass
(Dm"bypass " Dm"core )·#coat ·10 "18 [ µ g]
3
(21)
6
bypass
M SMPS
RM =
bypass
bypass
(22)
M AMS
This value changed with the coating thickness (For the same core particle diameter).
Changing the coating thickness changed the calibration ratio, possibly due to different
bouncing probabilities in the AMS vaporizer (Matthew, Middlebrook, and Onasch 2008).
This is further discussed in section 4.2.2. Also, a slight drift was noticed in this ratio during
experiments, perhaps due to contamination of the vaporizer. Bypassing the oven before and
after TD experiments allows calculation of RM for the segments immediately before, and
immediately after the oven. It was then possible to interpolate RM linearly and obtain a more
accurate RM for each evaporation measurement in the oven.
2. Calculating the mass loss: The mass loss in the oven is calculated for each data point, as
!mAMS"SMPS = M SMPS " RM M AMS
bypass TD
(23)
TD
Where M AMS is calculated according to Eq.(20). The effect of a thin layer on the mobility
diameter of non-spherical particles is not necessarily linear. Therefore, using the SMPS to
calculate the mass will provide correct results for spherical particles only. The SMPS is
used primarily for calibration of the coating mass, and for checking the sphericity of the
coating before and after the evaporation stage, by comparing it to the aerodynamic diameter
as measured with the AMS (see Results section, page 31). A different approach must be
29

31. used to calculate RM in measurements of non-spherical particles. This is further discussed
in section 4.7.
Finally, Eq. (22) and (23) can be written in a more compact form, assuming that
bypass # M AMS &
TD
RM = Rbypass : !mAMS"SMPS = M SMPS ·% 1 " bypass (
$ M AMS '
M
3. Flow velocity correction: The flow velocity measurement is corrected for nitrogen density
decrease due to temperature increase in the oven and constant pressure (conservation of
!ref
mass), according to U i = U ref · where !ref is calculated at room temperature.
!(Ti )
4. Evaporation driving force: The integrated evaporation driving force I[Kg m] defined
below is calculated and integrated for each data point -
tf
I = " !sat D f dt[Kg / m] (24)
0
Where Df is the diffusion coefficient (for further details see Appendix B), and t f is the time
from at least 1% increase in ambient vapor pressure of the coating material until the vapor
pressure returns to at least 1% above the ambient vapor pressure (see Figure 11). 1% was
chosen as a low enough value so the error will be negligible. The use of this integral term in
calculating the Sherwood number is based on a simple derivation shown in Appendix B.
5. Deriving the Sherwood number: !m is measured for the same particle at different
evaporation driving forces, by either increasing oven resident time, or the temperature. A fit
line is calculated on a !m vs. I plot, and the Sherwood number is calculated as the best fit
of
1 "m # m0
Sh = (25)
!D I
Where m0 is the residue mass, obtained by the linear orthogonal distance least square fit.
This method is based on the relationship between the mass transfer coefficient and the Sherwood
number, as derived in Appendix A. m0 accounts a measurement bias Eq. (23) or (26)
Mass loss can alternatively be calculated for spherical particles with the SMPS
measurement alone, according to
" 3
!mSMPS = (Dm#bypass # Dm#TD )·$coat ·10 #18 [ µ g]
3
(26)
6
And the Sherwood number is calculated in the same manner (Eq. (25)).
In all experiments where an SMPS was used along side the AMS and CPC (as illustrated in
Figure 3), !mAMS"SMPS and the resulting Sherwood numbers are shown as well as !mSMPS and the
30

32. resulting Sherwood numbers (see Figure 17, Figure 18 and Figure 19). In initial experiments the
second DMA was used to size-select coated aerosols to a specific size. No SMPS scans were done
for the evaporated particles.
!mSMPS cannot be used for non-spherical particles and is only used here as an independent
comparison for the mass loss. For non spherical particles !mAMS"SMPS will also have to be calculated
in a different manner, this is discussed in section 4.7.
3.2 Results
The main objective of the study is to evaluate the influence of different temperatures and
residence times in the thermal denuder (TD) on the evaporation rate of a coating material for
different PSL particle sizes.
We defined a normalized-driving-force-integral in which both the temperature profile and
ˆ
the residence time are taken into account: I = I·! D[Kg] (Eq. (25), Further discussion in appendix
A). Since the entire oven temperature profile is taken into account through the integration (Eq. (24)
), different temperatures and different residence times can both be shown on a normalized driving
force scale ((see Figure 17, Figure 18 and Figure 19)). An adequate unit for designating the coating
mass of a single aerosol and normalized driving force is 10 9 µ g , since the mass of typical single
aerosol coating is 10-15 to 10-14 gr.
The pressure of the nitrogen in which the particles are suspended is 1 Bar (the system is
open to the atmosphere) in all the measurements presented here.
3.2.1 Mobility and vacuum aerodynamic distributions
A typical mobility and vacuum aerodynamic distributions, measured by the SMPS and
AMS respectively are shown in Figure 13. The right column is based on the 104 m/z peak, which is
the main fragment peak for the PSL particles. The same distribution can be seen in the BaP main
peak, m/z 252 (see Figure 8), but the error is larger, especially for the evaporated particles, due to
the lower amount of material. This is shown for one example measurement in Figure 14.
31

33. Figure 13: Particle size distribution for different extents of evaporation.
Typical SMPS mobility diameter distribution (left column) and AMS-PToF aerodynamic vacuum diameter
distribution (right column) measurement for evaporation of BaP coated PSL particles. As indicated by the gradual
decrease of D m and Dva of the particles flown through the TD, the extent of evaporation increased from 1 to 6, with
a1 and b1 showing the same evaporated particle ensemble, a1 is the mobility diameter distribution, and b1 is the
vacuum aerodynamic distribution. A Gaussian fit is used to calculate a higher resolution mode (diameter
corresponding to maximum particle counts) diameter. Core particles are 300 nm diameter PSL spheres, coated by
o
40-50 nm BaP, Oven average temperature = 85-130 C Flow rate = 400-1400 cc/min. The shape factor (Figure 16)
was calculated according to these measurements.
32

34. Figure 14: comparison of vacuum aerodynamic diameter distribution for 104 m/z (PSL peak) and 252 m/z (BaP
o
peak) for 300 nm PSL spheres coated with 50 nm thick BaP. Oven average temperature = 115 C Flow rate = 700
cc/min.
The distribution is nearly monodisperse. A normal Gaussian fit around 4-8 point
surrounding the SMPS mode and 8-16 points surrounding the m/z 104 PToF mode was used to
calculate the more refined mode diameter for all shape factor calculations.
3.2.2 SMPS measured and AMS mass based final diameter and shape factor
Figure 15 shows the initial aerosol diameter (peak of Gaussian fit around the mode
diameter, shown in Figure 13) as measured by SMPS, for a typical experiment. The Figure shows
33

35. the SMPS measured diameter after evaporation in the TD, and the AMS based diameter, calculated
according to a mass balance
1
# 6 &3
DAMS = % Dcore + RM M AMS (27)
$ !"coat (
'
There is a close agreement between the two.
The difference in sphericity can be calculated by comparing the aerodynamic vacuum
mode diameter and mobility mode diameter. This yields the “Jayne shape factor” (DeCarlo et al.
Dva !0
2004) S = where !0 [Kg / m 3 ] , which is a normalization factor – in the same units as the
Dm ! p
particles density which is calculated according to the combined mass of the PSL core, and BaP
coating, divided by the volume of the coated sphere. The relation between the Jayne shape factor
and the dynamic shape factor can be explained by looking at two limiting cases – the continuum
1 1
limit S ! and the kinetic limit S ! 3 2 , assuming the particle has no internal voids (DeCarlo et
" 2
"
al. 2004). The different shape factors are displayed in Figure 16, for a thick initial coating (50 nm)
of BaP, and thin initial coating of BaP (5 nm), on 300 nm diameter PSL spheres, For a spherical
particle the Jayne shape factor = 1, and for semi-spherical it is ! 1. The dynamic shape factor
approached 1 from above as the particle becomes more spherical. In all the experiments the Jayne
shape factor was above 0.8, and converged towards 1 with the evaporation. This behavior is
expected, since the evaporation tends to make particles more spherical: The vapor density
difference, which is the driving force for evaporation, diminishes at a point inside a “valley” on the
surface of a coated particle, and so the “hills” tend to evaporate faster then the “valleys” leading to
a more spherical particle as the evaporation time increases. The initial coating is therefore mildly
non spherical, and becomes more spherical as the particle outer surface evaporates (annealing).
Further discussion of coating and partial coating effect on evaporation rate is given below in
section 5.2.1.
The Jayne shape factor measured with thick coatings (Figure 14(a)) after most of the
coating evaporated (coating thickness = 10 nm) is higher than one, which is unphysical (DeCarlo et
al. 2004). This is in the range of error of the mobility and vacuum aerodynamic diameter, and
therefore associated with measurement error.
34

36. Figure 15: Change in coating thickness due to evaporation. PSL spheres of 300 nm diameter, coated by 40-50 nm
o
BaP, Oven average temperature = 85-130 C Flow rate = 400-1400 cc/min.
Figure 16: Shape factor versus coating thickness for (a) 50 nm BaP coating (from distributions shown in Figure
o
13) and (b) 5 nm BaP coating, both on 300 nm PSL sphere. Oven average temperature = 85-130 C Flow rate =
400-1400 cc/min.
35

37. 3.2.3 Effects of Residence time
Figure 17 - Figure 19 show the effect of residence time on the evaporation. In this
configuration the oven nominal temperature is held constant, while changing the residence time in
the oven by changing the gas flow velocity. Two trends are observed in Figure 18 (a) and Figure 19
(b): A linear trend, following Eq. (25), and a decaying trend, caused by the lower vapor density of
an incomplete coating, remaining over the particles when the evaporation period is too long. The
flow rates during the experiments were normally set to avoid this decaying trend, and make sure
only part of the coating is evaporated.
S bypass S TD N Rbypass
M
Minimum 0.796 0.815 260 1.76
Average 0.806 0.877 725 1.98
Maximum 0.816 0.936 1600 2.24
Figure 17: Effect of residence time. 200 nm PSL sphere, 15 nm thick BaP coating. TD flow rate sweep 350-780
cc/min at 85 o (upper red fit line), TD flow rate sweep 200-450 cc/min at 80 o (lower red fit line). Associated table
displays minimum, maximum and average values for the Jayne shape factor (see page 33) of the coated particles
S bypass , evaporated particles S TD , number concentration N[#/ cc] and calibration ratio Rbypass
M
36

38. (a) (c)
bypass
S bypass
S TD
N R M S bypass S TD N Rbypass
M
Minimum 0.805 0.88 260 1.6 - - 200 2.2
Average 0.81 0.92 310 2.1 - - 430 2.8
Maximum 0.815 0.94 360 2.7 - - 660 3.6
Figure 18: Effect of residence time. 300 nm PSL sphere (a) 25-30 nm BaP coating, TD flow rate sweep 80-260
cc/min at 85 o (b) 20 nm BaP coating, size selected by second DMA, TD flow sweep 380-1240 cc/min at 85 o
(a) (b) (c)
bypass bypass
S bypass S TD N R M S bypass S TD N R M S bypass S TD N Rbypass
M
Minimum 0.85 0.91 200 2.5 0.77 0.8 75 3.44 0.84 0.87 190 2.1
Average 0.87 0.94 380 2.85 0.81 0.84 500 4.3 0.85 0.89 320 2.4
Maximum 0.88 0.97 570 3.1 0.85 0.88 1550 7.07 0.86 0.91 440 2.7
Figure 19: Effect of residence time. 400 nm PSL sphere (a) 22-30 nm BaP coating, TD flow rate sweep 300-1100
cc/min at 95 o (b) 25-30 nm BaP coating, TD flow rate sweep 380-500 cc/min at 90 o (upper 3 points), TD flow rate
sweep 115-500 cc/min at 85 o (rest of points) (c) 22-30 nm BaP coating, TD flow rate sweep 290-470 cc/min at 85 o .
Associated table displays minimum, maximum and average values for the Jayne shape factor (see page 33) of the
coated particles S bypass , evaporated particles S TD , number concentration N[#/ cc] and calibration ratio Rbypass
M
37

39. 4 Discussion
4.1 Derivation of the Sherwood number
Figure 20: Sherwood number vs. particle diameter for experiments shown in figures 17-19
The Sherwood number (Sh) was derived for different nominal PSL sphere diameters
according to Equation (25), and is compared to the theoretical diffusive mass transfer case in the
transition regime, using Eq (12) (Davies (1978) from Hinds (1999) p. 288)
2" + D
ShKn = 2·! (Kn) = 2·
D + 5.33(" 2 D) + 3.42 "
Theoretically, for a spherical particle, in the continuum regime, where no convective mass
transfer occurs, Sh should equal 2. This is corrected for the transition regime using Eq (12), which
leads to lower Sh. Figure 20 presents the derived Sherwood number for different PSL diameters and
driving force. The dotted line represents the calculated ShKn numbers for these conditions. It can be
seen that most of the measurements fall close to this line, within the measurement errors. The free
kT
mean path ! was calculated according to ! = [m] where p = 101325[Pa] and T is the
"d p 2
2
N2
average of the flat part of the oven, as seen in the bottom of Figure 11. The mass loss calculation,
based on AMS and SMPS, or only on SMPS, are shown in section 3.1.5.3 .
38