1

Thesis for the degree Master of Science

By Hanan Einav-Levy

Advisors: Jacob Karni

Yinon Rudich

January 2010

Submitted to the Scientific Council of the Weizmann Institute of Science

Rehovot, Israel

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Development of Method for Measuring Mass Transfer Coefficients of Particles

and Use of the Mass-Heat Transfer Analogy to Obtain Heat Transfer Coefficients

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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

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

4

Nomenclature ai, j Temperature

correlation matrix L [m] Typical length

D [m],[nm] Particle diameter Lmin [nm] Minimum AMS detectable coating thickness

Dva [nm] Particle vacuum aerodynamic diameter

Loven [m] Thermal Denuder (TD) oven length

Dm [nm] Particle mobility diameter

!m '' [Kg s·m2 ]

Mass transfer rate

Dm!core [nm] Particle core mobility diameter

m0 [µg] Residue mass of coating, obtained by Sherwood theory fit

Dm!TD [nm] Particle mobility diameter, for aerosols passing through the TD

mg [Kg] Gas molecule mass

Dm!bypass

[nm] Particle mobility

diameter, for aerosols bypassing the TD

mm /z [µg /m3] Mass loading of a single m/z

Df [m2 s] Binary diffusion coefficient

mv [Kg] Particle coating molecule mass

DAMS [nm] Equivalent diameter calculated according to AMS and SMPS measurement

Mw [g /mole] Molecular weight

DSh [nm] Sherwood diameter Mcoat [g /mole] Coating molecular weight H [KJ / Kg] Latent heat of

evaporation MAMS

MAMSbypass

MAMSTD

[µg] Single aerosol coating main fragment [m/z] mass, measured by AMS, for aerosols (general – no superscript), or aerosols bypassing the TD (bypass superscript), or going through the TD.

h W m2K!" #$ Heat transfer coefficient

hm [m s] Mass transfer coefficient

MSMPS

M bypassSMPS

MSMPSTD

[µg] Single aerosol coating mass, measured by SMPS, for aerosols (general, no superscript), or aerosols bypassing the TD, or going through the TD.

I [kg /m] Evaporation driving force Nu = hL

k Nusselt number

I [µg] Normalized evaporation driving force

n Analogy fit parameter

k [W /mK ] Thermal conductivity No [#/m3] Molecule number concentration kB [m2Kg s2K ]

Boltzman constant N [# m3]

[# cm3]

Particle number concentration

kv [W /mK ] N2 gas thermal conductivity

Nbypass [#/ cm3] Particle number concentration, for aerosols bypassing the TD

Kn = !L

Knudsen number

5

p [Pa] Pressure Vfrac Volume fraction of aerosol ps [Pa] Saturation vapor

pressure xo, yo, zo Normalized Cartesian

directions pd [Pa] Saturation vapor

pressure with Kelvin effect

! [m2 s] Thermal diffusivity

Pr = !"

Prandtel number ! c Energy accommodation

coefficient q '' W m2!" #$ Heat transfer rate ! Relaxation parameter for ai, j

correlation matrix calculation Q [m3 / s] Volumetric flow rate ! o Average gas adiabatic constant R [J / K ·mol] The gas constant ! coat [dyne / cm]

Coating material surface tension

ReL =UL!

Reynolds number !D[m] Coating thickness

Roven [m] Thermal Denuder (TD) oven radius

!mAMS"SMPS

[µg] Single aerosol evaporated

coating mass, measured by AMS and SMPS

RM = MSMPS

MAMS

Calibration ratio, for aerosols bypassing or passing in the TD

!mSMPS [µg] Single aerosol evaporated coating mass, measured by SMPS

RMbypass

= MbypassSMPS

M bypassAMS

Calibration ratio, for aerosols bypassing the TD oven

! [m] Mean free path

S Jayne shape factor ! [m2 s] Kinematic diffusivity

Sc = !Df

Schmidt number !coat [Kg m3]

[g cc]

Coating bulk density

Sh = hmLDf

Sherwood number !coat"vapor!coat"ambient

[Kg m3] Coating vapor density, near the particle surface, and in the free stream respectively

T [K ] Temperature !p [Kg m3] Particle density

T o Normalized temperature

!g [Kg m3] Gas density

Tp [K ] Particle temperature !0 [Kg m3] Normalization unit density for Jayne shape factor calculation

Tg [K ] Gas temperature ! ,

!

kb [!], [K] Lennard Jones potential

parameters

Ti (t) [K ] Center of oven temperature

!"m#EV ,! I"EV

[µg] Repeatability error for !m and I respectively

Tj (t) [K ] Side of oven temperature

!(Kn) Fuchs correction for mass transfer in transition regime

U [m s] Gas velocity ! Dynamic shape factor uo,vo,wo Normalized velocity

in xo, yo, zo directions ! o Normalized mass fraction

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.

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7

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.

8

1.2 Convective heat transfer

The process of particle to gas heat transfer is best described by the heat transfer equation

q '' = h·(Tp !Tg ) (1)

h W m2K!" #$ is a heat transfer coefficient, q '' W m2!" #$ is the heat flux per particle surface area,

Tp[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

conductive heat transfer across the surface boundary -Nu = hLk

where L[m] is a typical length and

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 = !L

. In this region the heat transfer coefficient, and

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.

9

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)

uo !To

!xo+vo !T

o

!yo+wo !T o

!zo= 1ReLPr

!2T o

!xo2 +

!2T o

!yo2 +

!2T o

!zo2

"

#$%

&' (2)

Where the Reynolds number is ReL =UL!

, the Prandtl number is Pr = !"

, ![m2 s] is the

kinematic viscosity, ![m2 s] is the thermal diffusivity, U[m s] is a typical velocity, uo,vo,wo are

normalized velocities in the normalized directions xo, yo, zo respectively, and T o is the normalized

temperature.

The normalized mass transfer equation is

uo !"o

!xo+vo !"

o

!yo+wo !" o

!zo= 1ReLSc

!2" o

!xo2 +

!2" o

!yo2 +

!2" o

!zo2

#

$%&

'( (3)

Where ! o is the normalized mass fraction of the transported species in the gas stream,

Sc = !Df

is the Schmidt number and Df [m2 s] is the diffusion coefficient of the species involved in

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·m2 ] is the mass transfer per unit time and particle surface area; hm[m s] is the

mass transfer coefficient; !p[Kg /m3] 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

coefficient is related to the non-dimensional Sherwood number Sh = hmLDf

in the same manner that

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

10

Nu = Sh PrSc

!"#

$%&n

(5)

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 + 0.6Re1 2 Sc1 3 (6)

And by analogy

Nu = 2 + 0.6Re1 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 !10µm , which

corresponds to Knudsen numbers of 0.1-10. This is in the transition regime between the continuum

11

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

!qfm = ! 43

2kBmg"

#pgTg

$T$x[w m2 ] (8)

!mfm = ! 4

312"

#$g

pg

%p%x[Kg m2s] (9)

Where ![m] is the mean free path of the gas-particle system, defined as

! = 1 "No # + D2

$%&

'()2

where !"2

4[m2 ]is the effective gas molecule cross-section and D[m] is the

particle diameter, No[#/m3] is the particle number density, mg[Kg] is the gas molecule mass

(apparently, it is not specified in the article) and kB[m2Kg s2K ] 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

!qfm =pgTg

! c

2kB"mg

# o +1# o $1

%&'

()*

(Tg $Tp ) [W m2 ] (10)

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:

12

!mfm = Tg

8kB!mv

("g # "p ) [Kg m2s] (11)

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.

13

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):

ShKn = 2·!(Kn) = 2·2" + D

D + 5.33("2 D)+ 3.42" (12)

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

calculated according to ! = kT"d 2N2 p 2

[m] where p[pa] is the pressure. In the limiting cases of

molecular and continuum regimes, the Sherwood number values are therefore 45.33

· 1Kn

& 2,

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)).

14

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

15

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)

16

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.

The suspended aerosols subsequently flow through a silica gel diffusion dryer, followed by a 85Kr

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.

17

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 Co )

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 N2 flow.

Table 1.A Benzo[a]pyrene (BaP) physical properties

Formula Molecular weight Mcoat[g /mol]

Bulk density !coat[g / cc]

Surface tension ! coat[dyne / cm]

Melting point [oC]

C20H12 252.3093 1.286 64.7 179

Source: (chemspider.com) Table 1.B Benzo[a]pyrene (BaP) Lennard-Jones parameters

" (!)

!

kb[K ]

7.66 918.15

Source: Using PAH derived fit

!

kb= 37.15·Mw0.58

and

! = 1.234·Mw0.33

from (Wang and

Frenklach 1994) Table 1.C Benzo[a]pyrene (BaP) vapor pressure parameters

Expression A B

P = 101325·10B! A

T [Pa] 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

18

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:

!coat"ambient = !coat ·Vfrac[

Kgm3 ];Vfrac = N

#6

((D + $D)3 " D3) !1 (13)

Where N[# m3] is the particle number concentration, !coat[Kg m3] is the coating material

bulk density, !D[m] is the evaporated coating thickness, and Vfrac 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])

ps = 101325·10B!

ATp [Pa], pd = ps ·e

4" coatMcoat#coat R·Tp ·D [Pa] (14)

Where A & B are taken from Table 1,Mcoat is the molecular mass, R is the gas constant,

Tp[K ] is the coating (particle surface) temperature and ! coat[N /m] is the coating surface

tension.

Finally, according to the ideal gas law –

!coat"vapor = Mcoat ·pdR·Tp

Kgm3

#$%

&'(

(15)

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

19

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 oC 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] .

20

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 /m3)] ) 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 oC .

dDdt

= - 4DfTp ·Mcoat

!coatR·Td ·D·pd ·"(Kn) for Kn #1

"= 2$+D

D+5.33$2

D+3.42$

(16)

Where ! = kT

2p"!dN22 m[ ] is the mean free path, Kn =

D!

is the Knudsen number, ! is the Fuchs

slip correction and Df is the binary diffusion coefficient, estimated by the Chapman Enskog theory

(See Appendix B). Tp 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

Td =T! +DABMHpdRkvTd

(17)

21

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 ! Tp . This

assumption was validated by calculating Eq. (16) for the temperature ranges used in the

experiments (100-200 oC ). The resulting difference between Td and Tp 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 oC showed that a residence time

between 1-5 seconds is appropriate, and translates to an oven length of 60 cm according to

t = !R2ovenLovenQ

where Roven is the oven inner diameter and Q[m3 s] is the volumetric flow rate.

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.

22

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

23

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[µg m3] . 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[µg m3] . Combined with the bulk density of BaP this gives the estimated

minimal denuded coating thickness detected by the AMS:

Lmin =6s

N!coat"+ D3#

$%&'(

13) D[nm] (18)

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[#/ m3 ] 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.

24

Figure 7: Minimal denuded layer thickness vs. number concentration, for AMS sensitivity of 0.04 µg / m 3 and

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 = [# cm3] , combined with the AMS

measurement of the mass loading of the coating material main fragment m/z m252bypass[µg /m3] gives

the coating mass for each aerosol (Eq. (20)).

25

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 oC ) 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

nm diameter PSL spheres where coated by 25 nm thick BaP, in a 80 oC oven and a flow rate of 120 cc·min!1

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.

26

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 Tj (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 ·Tj = 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:

ai0 , j0= 1!Ti0Tj0

,ai0 , j0 "1 = ai0 , j0 +1 =Ti0 1" 1

!#$%

&'(

Tj0 "1 "Tj0 +1

where 1) ! ) 2 (19)

27

For the end points ai0, j0 =Ti0Tj0

. All other ai0, j in the row are set to 0. This equation is the result of

satisfying ai, j ·Tj = 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.

Table 2: Side-center temperature correlation matrix ai, j =TiTj

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

28

Figure 11: Top: temperature scan for fast flow rate of 1400[cm!3 ·min!1 ] 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)

Bottom: Typical oven temperature profile for I (see Eq. (24)) at flow rate of 400[cm!3 ·min!1 ] 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.

29

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)):

MAMSbypass = m252

bypass

N bypass1

1003[µg] (20)

MSMPSbypass = !

6(Dm"bypass

3 " Dm"core3 )·#coat ·10

"18[µg] (21)

RMbypass = MSMPS

bypass

MAMSbypass (22)

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 = MSMPSbypass " RMMAMS

TD (23)

Where MAMSTD 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

30

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

RM = RbypassM : !mAMS"SMPS = MSMPS

bypass · 1" MAMSTD

MAMSbypass

#$%

&'(

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

mass), according to Ui =Uref ·!ref!(Ti )

where !ref is calculated at room temperature.

4. Evaporation driving force: The integrated evaporation driving force I[Kg m] defined

below is calculated and integrated for each data point -

I = !satDf dt[Kg /m]0

t f

" (24)

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

Sh = 1!D

"m # m0

I (25)

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

!mSMPS ="6(Dm#bypass

3 # Dm#TD3 )·$coat ·10

#18[µg] (26)

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

31

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

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 109µg , 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.

32

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 Dm 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

40-50 nm BaP, Oven average temperature = 85-130 oC Flow rate = 400-1400 cc/min. The shape factor (Figure 16)

was calculated according to these measurements.

33

Figure 14: comparison of vacuum aerodynamic diameter distribution for 104 m/z (PSL peak) and 252 m/z (BaP

peak) for 300 nm PSL spheres coated with 50 nm thick BaP. Oven average temperature = 115 oC 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

34

the SMPS measured diameter after evaporation in the TD, and the AMS based diameter, calculated

according to a mass balance

DAMS = Dcore + RMMAMS6

!"coat

#$%

&'(

13 (27)

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.

2004) S = Dva

Dm

!0!p

where !0[Kg /m3] , which is a normalization factor – in the same units as the

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

limit S ! 1" 2 and the kinetic limit S ! 1

" 3 2 , assuming the particle has no internal voids (DeCarlo et

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.

35

Figure 15: Change in coating thickness due to evaporation. PSL spheres of 300 nm diameter, coated by 40-50 nm

BaP, Oven average temperature = 85-130 oC Flow rate = 400-1400 cc/min.

Figure 16: Shape factor versus coating thickness for (a) 50 nm BaP coating (from distributions shown in Figure 13) and (b) 5 nm BaP coating, both on 300 nm PSL sphere. Oven average temperature = 85-130 oC Flow rate = 400-1400 cc/min.

36

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.

Sbypass STD 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 85o (upper red fit line), TD flow rate sweep 200-450 cc/min at 80o (lower red fit line). Associated table

displays minimum, maximum and average values for the Jayne shape factor (see page 33) of the coated particles

Sbypass , evaporated particles STD , number concentration N[#/ cc] and calibration ratio RbypassM

37

(a) (c)

Sbypass STD N RbypassM Sbypass STD 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 85o (b) 20 nm BaP coating, size selected by second DMA, TD flow sweep 380-1240 cc/min at 85o

(a) (b) (c)

Sbypass STD N RbypassM Sbypass STD N Rbypass

M Sbypass STD N RbypassM

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 95o (b) 25-30 nm BaP coating, TD flow rate sweep 380-500 cc/min at 90o (upper 3 points), TD flow rate

sweep 115-500 cc/min at 85o (rest of points) (c) 22-30 nm BaP coating, TD flow rate sweep 290-470 cc/min at 85o .

Associated table displays minimum, maximum and average values for the Jayne shape factor (see page 33) of the

coated particles Sbypass , evaporated particles STD , number concentration N[#/ cc] and calibration ratio RbypassM

38

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)

ShKn = 2·!(Kn) = 2·2" + D

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

mean path ! was calculated according to ! = kT"d 2N2 p 2

[m] where p = 101325[Pa] and T is the

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 .

39

The derived Sherwood number, by !mAMS"SMPS measurements (solid circles),

underestimates the theoretical value by ~5-25%, whereas the Sherwood number based on !mSMPS is

overestimated the theoretical prediction by 0-15% for 300 and 400 nm PSL spheres, and

considerably overestimates the theoretical result for the 200 nm PSL measurement. The difference

for the 200 nm core particle measurements is due to partial thin coating and will be further

discussed in section 4.2.2.

These results suggest that at the size ranges of 200-500 nm and coating thicknesses that are

sufficient to keep a complete coating after evaporation, only SMPS measurements are needed

(tandem DMA), as has been done before by Rader and McMurry (1986) for spherical particles,

although they seem to be more dependent on complete coating (see discussion in section 4.2.2).

However, for non-spherical particles, this approach cannot work since the mass is not a simple

function of diameter, and instead a method based on the use of both the AMS and SMPS will be

used here (as discussed below, in section 4.7).

The flow rate used to calculate residence times was based on plug flow calculations,

dividing the volume flow rate by the TD cross section resulting in a mean flow rate. Since the

actual velocity profile in the oven is non uniform, and the aerosols tend to concentrate at the center

due to the thermophoretic force in the oven’s entrance (Orsini et al. 1999), the actual residence time

may be slightly shorter than that calculated by the plug flow assumption. A correction based on

Luo and Yu (2008) and the measured axial temperature profile gives a velocity correction of 9-

15%. Applying this correction would increase the AMS-derived Sherwood number by

approximately the same ratio (not exactly the same due to m0 mass bias, Eq. (25)), which would

bring it closer to the theoretical value. However, it will result in a similar increase in the Sherwood

number derived from SMPS.

The trend in !mAMS"SMPS and the trend in !mSMPS versus evaporation driving force typically

yield parallel slopes (Figure 18 (a), and Figure 19(a-c)), implying the same Sherwood number, but

different bias in the measurements.

In some cases it was found that the measurement of !mAMS"SMPS can suggest two or more

groups of parallel lines, reflecting the same Sherwood number but biased differently (Figure 18 (b)

and Figure 19 (b)).

Looking at Figure 19 (b), the upper points, above the top trend line, where measured for a

nominal TD temperature higher then the rest of the points (the points which the bottom two trend

lines go through). This means faster flow rates where used, with higher temperature, to maintain the

same evaporation driving force range, but different mass loss was measured. On the other hand, the

bottom 2 parallel lines go through measurements done in different flow rates and with the same

nominal oven temperature. So the temperature profile cannot be the only cause for the different

40

mass measurement bias. The possible reasons for flow bias, that can change in between

measurements, are discussed below (section 4.2). For Figure 19 (b), the bottom points where fitted

and the resulting line slope was duplicated and translated. That is how the two additional lines were

created. It can be seen that they fit very closely to the measurements. This suggests that the same

evaporation trend is exhibited (i.e. Sherwood number) but the coating is measured with different

degrees of efficiency.

4.2 Possible sources of measurement bias Differences in measured mass between !mAMS"SMPS and !mSMPS possibly arise from several

sources

• Coating: Non-spherical particles due to uneven coatings can affect the SMPS derived

mobility diameter, which is calculated by assuming a spherical shell volume, multiplied by

the BaP density.

• Measurement Bias between the AMS and the SMPS measurement caused by calibration

differences, in SMPS diameter and RM .

• Flow: Biased flow splitting into the AMS and CPC, could possibly affect the concentration

of particles in one of the flows.

Bias always resides to some extent in any measuring apparatus, and so measurement bias could

explain the shift between the measurement of the SMPS and AMS-SMPS combination. These

different sources are discussed in the next sections:

4.2.1 Coating thickness effect on the Sherwood number We tested the effects of different BaP coating thicknesses for the same diameter core

particle. The coating thickness had a large effect on the evaporation rate as can be seen in Figure 21

for two limiting cases, of 5 nm and 50 nm thick coating. In the case of the thinner coatings, the

evaporation rate decreased, resulting in a lower Sherwood number then that obtained with the

thicker coatings. Such behavior could possibly result from partial coating. When the coating is

sufficiently thick, the evaporation process over a coated particle with spherical shape and smooth

surface, will tend to keep the particle spherical. When the coating is not smooth and contains

“valleys” and “hills” the vapor densities in these locations are different, and the “hills” will

evaporate faster than the valleys, leading to a smoother, more spherical particle as the evaporation

continues.

When the coating evaporates such that areas with no coating begin to appear (see the Figure

22), the vapor pressure immediately above these areas is zero. Consequently, the vapor density

directly over this zero coating spot is below the original vapor density. Such process will result in a

41

reduced rate of mass transfer, since it is driven by the vapor density difference between the

“boundary layer” surrounding the particle, and the ambient zero vapor density.

This is illustrated in Figure 22, where the orange layer symbolizes the coating, and the

green core is the PSL sphere core particle. Partial coating was observed in measurements with low

coating thickness using the same coating oven by Lang-Yona et al. (2008), measuring extinction

coefficient with cavity ring down spectroscopy.

Figure 21: The effect of Coating thickness on the evaporation rate for two limiting cases. Core particles 300 nm,

with 50 nm thick BaP coating and 5 nm thick BaP coating respectively. Oven average temperature = 85-130 oC

Flow rate = 400-1400 cc/min.

As a result of these considerations all experiments were conducted with thick coatings,

above 15 nm.

42

Figure 22: Schematic illustration of Partial coating scenario

Rough coating effect: The measured evaporation rate shown in Figure 19 (c) is higher than

the expected evaporation rate according to Eq. (12). Both, the dmAMS!SMPS and dmSMPS based

Sherwood number fit give the same slope within the error estimate,

ShSMPS = 4.99 ± 0.45, ShAMS!SMPS = 4.72 ± 0.97 . These results suggest that this is a real process and

not the result of systematic measurement or flow bias. The shape factor was similar to other

measurements of similar coated particles. This suggests that the coating was rough, for the duration

of that experiment, resulting in a larger than spherical surface area and consequently higher

evaporation rate than expected for a sphere of the same diameter. Most importantly, this is the

expected behavior for non-spherical particles. The preparation for this experiment (water filtration,

PSL concentration, flow rates) was no different then for any other. The evaporation trend with

increased driving force returned to the expected slope (Figure 19 (a) shows the same experiment

day for higher evaporation driving forces) after a threshold of driving force, which could further

indicate that the initial coating was rough and only after a threshold of evaporation did the surface

become smooth (as explained in section 4.2.1)

High evaporation driving force effect: For all measurements, the linear trend of

evaporation with increase in driving force diverges from a straight line for high enough evaporation

driving force. This is due to the evaporation of most of the coating, causing a decrease in the vapor

density and the evaporation rate (as explained in section 4.2.1 and Figure 22). Thus we avoid in our

discussion high evaporation driving force conditions.

4.2.2 The influence of coating thickness on the calibration ratio RM Initially the calibration ratio of particles at the AMS heater ( RM ,Eq. (22)) was derived by

measuring the PAH main fragment signal at m/z=252 as a function of particle number. This

calibration ratio corresponds to the collection efficiency multiplied by the ratio between the main

fragment of the coating material (Figure 8) and the sum of the fragments. The resulting calibration

43

curve was linear, as expected (see the collection efficiency curve in Jayne et al. (2000) for

example). However, it was found that the calibration factor depended on the coating thickness, and

it also changed significantly for the same coating thickness but in different days. This was taken

into account in each experiment by calculating the relevant RM for the experiment (Eq. (22), for

data acquired as shown in Figure 9). Figure 23 shows the dependence of RM (Eq. (22)) on the

coating diameter (twice the coating thickness) to core diameter ratio, for all the performed

experiment.

Figure 23: Calibration ratio of AMS fragment peak mass signal vs. SMPS & CPC mass calculation (Eq. (22) ) vs.

coating diameter to core diameter ratio

Initially no SMPS was employed, and a 2nd DMA was used to size-select coated aerosols.

This experiment is shown in the vertical line (light blue full circles) depicting RM for 20 nm

coating on 300 nm diameter PSL, for the same estimated coat to core ratio. For all other

experiments the actual mobility diameter distribution is constantly measured (Figure 13), and since

the coating process changes slightly with time, meaning the coating thickness is reduced constantly

for the same coating oven temperature, in a rate of ~4 nm per hour, the result is a scan over a small

interval (~0.05) of coating to core ratio for each experiment.

Collection efficiency: The calibration of the fragmentation pattern main signal with total

PAH mass depends on the ionization efficiency and the collection efficiency (Huffman et al. 2005).

The collection efficiency is made up of three terms - CE(dva ) = EL (dva )·ES (dva )·EB (dva ) . The

transmission efficiency EL (dva ) is the ratio of particles passing through the aerodynamic lens,

focused onto the vaporizer. The collection efficiency due to irregular shape ES (dva ) is the amount

44

of same-size particles hitting the vaporizer versus spheres. Finally, the collection efficiency due to

particle bounce efficiency EB (dva ) is the amount of particles that stick to the surface of the

vaporizer long enough to flash vaporize, divided by the number of particles that made it to the

vaporizer plate and were not accounted by the two prior measures. The particle bounce efficiency is

the only part which has been shown to be affected by the particle coating, and it is directly related

to RM .

Bounce efficiency: Hard particles with high vaporization temperature tend to bounce off

the vaporizer, before actually evaporating. Softer particles (fluid or soft solid) have close to 100%

collection efficiency. The BaP coating was used in all of the measurements shown in Figure 23. No

information was found in the literature on the hardness of either PAH core, or BaP coating, so it is

unknown whether the coating material used is softer or harder than the PSL sphere. The melting

points of polystyrene and BaP are 240oC and 179oC respectively, and the densities are

1.05[gr·cm!3] and 1.286[gr·cm!3] respectively.

Figure 23 shows large variations in RM for the same coating thickness to core diameter.

Additionally, there are different RM values for the same coating to core ratio and different

experiments, for instance the 400 nm blue and green full circles.

Consistency of RM in a single experiment: The difference in RM calculated for particles

bypassing the TD before directed into the TD (first segment of experiment - Figure 9) and

afterwards (last segment of experiment - Figure 9) is below 3% for all experiments. RM for the

particles passing through the TD (open circles in Figure 23) were only calculated for this

presentation, and were not used in calculating !mAMS"SMPS (Eq. (23)). These differences are the

cause of the different measurement in the 400 nm PSL’s of !mSMPS and !mAMS"SMPS , and the

resulting difference between the Sherwood numbers.

Very low evaporation driving force: For low evaporation driving force, RM changed

substantially with the extent of evaporation. This lead to a difference between the !mAMS"SMPS and

!mSMPS slope in some of the measurements, and therefore these points were not used for

calculating the Sherwood number. We attribute the discrepancy to the thin coating, which results in

higher RM value for these measurements then measured in the bypass conditions when the coating

was thicker. This suggests that AMS measurements are highly sensitive to the phase and coatings

of particles, and that these can limit the quantitative nature of AMS under some conditions.

Different trends in Figure 17 for 200 nm core PSLs: The measurements of 200 nm PSL

core particles (Figure 17) is the only measurement showing large discrepancies between

!mAMS"SMPS and !mSMPS , resulting in different slopes and therefore Sherwood numbers. This is

possibly because of the thin coating applied in these measurements. If the evaporated particles

45

coating became partial, then the SMPS derived evaporated mass would not be correct, since the

spherical shell volume is not the real coating volume. The full orange circles in Figure 23 show the

RM value used for calculating !mAMS"SMPS , and the open orange circles show the RM calculated for

the evaporated particles. There is a large and systematic variation in the evaporated RM . As the

coating to core ratio decreases, RM decreases. This could be the result of partial coating, as

explained above, and therefore suggests !mSMPS is wrong.

4.2.3 Possible uneven flow splitting effect on bias The different bias between !mAMS"SMPS and !mSMPS measurements, most apparent in Figure

19 (b) and also Figure 18 (b) could also arise from unequal splitting of the flow into the CPC and

AMS. Since the aerosol coated mass is calculated according to MAMS =m252

N1

1003[µg] , a bias in the

aerosol concentration N # cc[ ]versus the mass concentration of the BaP main peak m252 µg m3!" #$

would alter the single aerosol coated mass, and also the ratio between m252 µg m3!" #$ and the total

BaP derived mass (Eq. (22)) as observed in the experiments. The split was designed according to

iso-kinetic conditions at the split cross section, so this is highly unlikely.

Bias summary: To conclude these three possible effects (measurement bias, non spherical

coating and flow splitting), the parallel lines shown in Figure 18 (b) and Figure 19 (b) (the 4 lower

measurements shown in Figure 19 (b) were fitted and the line shifted to create the two upper dotted

red lines) indicate that there is constant bias in the measurement, since constant slope indicates that

the evaporation process does take place in the same mass transfer rate (thus the same Sherwood

number). This bias therefore does not affect the derived Sherwood number.

4.3 Error analysis

The Sherwood number was calculated according to a linear fit to several !m[Kg]

measurements, vs. different I = I ·!D[Kg] (Eq. (23) to (25)). According to the theory of

propagation of errors, a general expression for the error in each term can be associated to the errors

in each measurement, for instance:

! I = ("Sh"D

! D )2 + ("Sh

"I! I )

2 where ! D ,! I are the standard deviations, or errors, associated with

D and I respectively. The random errors taken for the various parameters are as follows:

• The DMA error is taken as ! D (dm ) = -0.07+ 0.00165·dm[nm] .

46

The calculation of the calibration ratio is very sensitive to small changes in the DMA

measurement. An experimental verification was made to measure the actual standard

deviation in the median diameter for monodisperse PSL spheres of different sizes, for more

than half an hour (this is shown in Figure 24). The results gave a very low standard

deviation; lower than 0.8 nm for the 500 nm PSL spheres, and about 0.16% relative to the

diameter. This low error is in agreement with Rader and McMurry (1986), who showed

mathematically, and verified experimentally, that mobility diameters can be measured with

an error of 0.24%. The equation used is a fit to the experimental median error measurement

(Figure 24).

• The mass measurement error ! dm is taken as the standard deviation of the actual

measurements of the coating mass marker m252[µg m3]divided by the particle number

concentration N[# m3] .

• The driving force integral error ! I [Kg m] depends on the oven temperature measurements,

their calibration to the center of oven temperatures (Eq. (19)), the flow rate measurement,

and the diffusion coefficient calculation. A 10% error is taken for the diffusion coefficient,

according to Wang and Frenklach (1994). The intrinsic vapor pressure parameterization

error was also taken into account ( A,B errors, Eq. (14)), and is the cause for 50-70% of the

error in ! I [Kg] . The averaging over X measurements for each data set is introduced

through the relation ! x =1X! x .

After evaluating each experiment, for a specific aerosol with the approximate same coating

thickness, the data with its associated error bars was fitted according to minimal orthogonal

distance regression (Boggs et al. 1989), to obtain Sh and m0 .

For !mSMPS the only error results from the SMPS median diameter error, which was taken as

specified above.

Figure 24: Median mobility diameter variations for different PSL sphere diameters

47

The results show that the errors in !mSMPS are equal in magnitude to the !mAMS"SMPS errors for

300 nm and 400 nm diameter particles, and lower for the 200 nm diameter. This is because the

SMPS based error is derived from the median SMPS error, which decreases with diameter (Figure

24).

4.4 Repeatability The repeatability of !mSMPS , !mAMS"SMPS and I measurements was estimated by repeating

the same experiment under the same conditions. We found that the standard deviation for mass loss

measurements (both !mSMPS and !mAMS"SMPS ) !"m#EV is

!"m#EV = 0.17[109µg],!"I#EV = 0.0175[109µg] where EV stands for equipment variation (Crossley

2000), and !"I#EV is the repetition standard deviation for the evaporation driving force. The

associated repeatability of the average Sherwood number is ±5% of the average Sherwood

number.

4.5 Measurement of the Sherwood numbers for suspended nano-

particles

The main result from our measurements of nearly spherically coated PSL core particles

(Figure 20) indicate that the proposed method is adequate and gives the expected theoretical value

for the Sherwood number of slowly evaporating spheres. The derived Sherwood numbers are close

to the values predicted by theory.

Measurement errors between 10-6% for the AMS-SMPS based mass loss, and 8-25% for

the SMPS based mass loss were estimated. The errors in the mass loss calculations arise mostly as

result of error in the determination of the mass by the AMS, and the error in the estimation of the

evaporation driving force which arises mostly from the parameterization associated with the vapor

pressure calculation.

A systematic error may arise from the change in the AMS collection efficiency, because it is

calculated for particles with a given coating. This collection efficiency is then applied to particles

partially evaporated. This bias diminishes for large particle number concentration and low coating

thickness.

It is concluded that the AMS-SMPS-TD system is therefore sensitive enough to allow

differentiating between different evaporation processes in the transition regime, and for measuring

the Sherwood number change with particle diameter expected for these pressure and temperature

conditions.

48

4.6 The use of the heat to mass analogy for suspended nano-particles

The heat to mass analogy for evaporation (Eq. (5)) has typically been used for complex

continuum and high Reynolds number situations. In those limits the pure diffusion/conduction

term, such as 2 in Eq. (6) and (7), diminishes in comparison to the Reynolds dependent term. In the

case of nm-sized aerosol suspended in a slow moving flow, the relative velocity is practically zero,

and the Reynolds dependent term is negligible. Therefore the first question that arises is what is the

analogy between heat and mass transfer for the pure conduction/diffusion case?

The constant number in both Eq. (6) and (7) is the same and arises from the same physical

reason – it is a product of the surface to diameter ratio for a sphere. Essentially, the pure

diffusion/conduction mass/heat transfer is dependent on the surface area. The analogy shows that it

depends on the surface area in the same way, and hence the same constant – Sh, Nu = 2.

In light of this, a higher Sherwood number, such as 4.9 which was measured for the 400 nm

PSL presumably coated in a non smooth and rugged manner by BaP (Figure 19 (c)) could be

related to the actual sphere diameter, DSh - the Sherwood diameter, that would give the measured

mass transfer rate:

DSh =1

!ShKn (Dm )"m # m0

I= Dm

ShShKn (Dm )

[nm] (28)

Where ShKn (Dm ) is the theoretical Sherwood number corrected according to the mobility

diameter based Knudsen number (Eq. (12) or similar), and Sh is the measured Sherwood number.

For Sh = 4.72 ± 0.97 (Figure 19 (c)), the resulting Sherwood diameter

isDSh = 1260 ± 260[nm] .

According to the analogy, since no transport properties remain if the Reynolds term is negligible, it

is suggested that DNu = DSh , and consequently the equivalent Nusselt number for a rugged sphere

of Dm mobility diameter, is

NuRe=0 = 2·!(KnDm)·DSh (29)

This analogy allows to use the measured Sherwood diameter to calculate the Nusselt number

for the same particle morphology, and incorporate this into heat transfer calculations between hot

particles and a surrounding cold gas as exist in the seeded solar reactor for instance (Klein et al.

2007).

The second question that arises is the adequacy of this analogy in the transition regime. The

answer according to the transition regime interpolation formulas is yes. Although, Davis (1983)

mentions that for a heavy molecule evaporating through a light gas, as is the case in this research,

the analogy is not exact. So finally, to answer this question a second experiment will have to be

made, with soot particles of the mobility size distribution used in the solar tower experiment (Klein

49

et al. 2007), and this used to calculate the Sherwood diameter and consequently calculate the

Nusselt number for the distribution. Entering these numbers into the CFD - ray tracing coupled

simulation used in (Klein et al. 2007) will reveal the adequacy of this analogy approach.

4.7 Measurement of fractal soot particles

The experimental method developed in this work can be used for measuring highly non-spherical

particles, among them agglomerate soot particles. A few key differences will arise:

1. Since the particles are not spherical, no straightforward mass balance for the calculation of

the coating mass according to SMPS measurement can be performed. Therefore RM will

have to be calculated separately, with a similar coating thickness material on a PSL

spherical particle of an adequate mobility diameter, before and after each experiment.

2. The coating thickness will affect the morphology. Therefore thin coatings are needed. Since

the above coating method cannot be used to obtain thin enough coatings, either larger soot

particles will be used, or an alternative coating system will be used or developed. One can

use the organics adsorbed onto soot, but the monolayer of coated organics exhibit a

diminishing evaporation trend due too diminishing vapor density driving force, as explained

below (Appendix C).

Other than that the experiment will be similar. Since the number concentration of soot particles can

be much higher then used in this experiment (200-1600 #/cc) the coating thickness can be much

thinner (Figure 7), which coincides with the criterion of 2. Also, the thin coating will eliminate the

problem that arises when thick coating is evaporated, namely differences in RM between the bypass

and through TD parts.

Additionally, in this experiment, soot particles and PSL particles of the same mobility

diameter will be measured alternatively for each evaporation driving force, to eliminate any bias as

seen in some of the results above.

4.8 Correlation of heat and mass transfer vs. particle size and shape

The ultimate purpose of our measurement system developed in this research is to enable

measurement of the Sherwood number for non-spherical particles. As shown in Figure 20, The

results obtained here, for spherical particles, reasonably fit the known correlations for spherical

particles, such as Davies (1978) (Eq. 12) that correlate between the Knudsen number and the

Sherwood number.

50

The next step will be measurements of non-spherical particles, characterized by their

mobility and vacuum-aerodynamic diameters, and using these measurements, obtain a correlation

of the Sherwood number vs. these parameters.

For soot particles, a description similar to that given by DeCarlo et al. (2004) of fractal

aggregates could be used, with the end result being a correlation Sh = Sh(Dm ,Dva ,Dpp ) , where

Dpp is the primary particle diameter (the particle aggregated to form the soot aggregate), estimated

from electron microscopy. The correlation should be similar to Eq. 12 (or another spherical particle

correlation, for instance Seinfeld and Pandis (2006) p. 545) for Dm = Dva

!p

= Dpp , and give higher

Sherwood numbers for the same Knudsen number (where Kn = Kn(Dm ,Dva ) ) and non spherical

particles Dm ! Dva

"p

> Dpp .

Additionally, a correlation based on the actual distributions of mobility and vacuum-

aerodynamic diameters will be useful, and measurements of real soot batch particles will be

conducted for the purpose of developing such a correlation.

5 Conclusion A heat-mass analogy approach was taken in order to measure the Nusselt number of heat

transfer between nano-sized aerosols and the bath gas. The approach is an extrapolation of the

continuum analogy between the heat and mass transfer.

The SMPS-AMS-TD system has shown the ability to repetitively measure changes in

Sherwood number of different size spherical aerosols coated by BaP, as affected by the Knudsen

number in the transition regime, but requires further research to understand the discrepancy

between the temperature sweep and flow sweep measurements, and other artifacts arising from bias

in the measurement.

The measurements agree with theory within measurement error indicating that the process is

purely diffusional and the zero relative velocity assumption, between the particle and the gas, is

correct. This further indicates that the analogy applied here is for pure diffusion vs. pure

conduction, and since these are both surface area dependent quantities a simple approach for use of

the analogy has been suggested in the form of the Sherwood diameter – defined as the diameter of a

sphere that would give the measured Sherwood number according to mass transfer theory.

The coating thickness should be minimal for the purpose of measuring the real Sherwood

number for non-spherical particles, which is the aim of this research. Moreover, it was found that

thick coating affects the bouncing efficiency of particles in the AMS detector. Therefore, a thin

coating needs to be applied, and this research shows that our coating system is not adequate.

51

Katrib et al. (2004) shows a method of coating spherical PSL particles with 2-30 nm layer

oleic acid, in a completely spherical manner – which means the coating is complete, with no

uncoated areas. This method could be used for our purpose, with oleic acid or any other suitable

material, since the material coating the particle is of no relevance to the Sherwood number

measured.

Finally, this measurement technique will be further used to obtain a correlation between the

Sherwood number and particle morphology, as defined by its mobility diameter, vacuum-

aerodynamic diameter, and other relevant parameters.

Appendix A Calculating the Sherwood number from a non isothermal aerosol mass transfer experiment

For an isothermal mass transfer process, the mass transfer coefficient is defined as the linear

relationship between the mass transfer rate and the concentration gradient across the

evaporating/condensing surface (equation (4)).

Integrating over the entire surface, for a spherical like aerosol, and integrating over the time of

flight of the aerosol in the specified conditions, gives the mass transfer coefficient as

hm =!mS

1"sat!t

, whereS is the surface of the aerosol, and !" was taken as zero. In the same

manner the Sherwood number can be estimated as Sh = !mS

D"sat!t·Df

.

For non isothermal conditions, where !sat = !sat (T ),Df = Df (T ) , the mass transfer coefficient can

be calculated by the following approach:

1. Sh = dmdt

D!satS·Df

! dm = Sh SD!satDf dt! dm! = Sh S

D"satDf dt!

Where the integral is taken over the entire time of flight through the non-isothermal

conditions, and under the assumption of small evaporation extent, so the characteristic

diameter, and the surface area of the aerosol remains approximately the same. Since the

integral over the mass flux is the total evaporated mass, the result becomes, assuming

negligible change in diameter:

2. Sh = !m DS· 1"satDf dt#

, Which for spherical aerosols reduces to

Shsphere = !m 1"D

· 1#satDf dt$

52

Appendix B Theoretical estimation of the diffusion coefficient of nitrogen-PAH mixture

In order to calculate the Sherwood number Shsphere = !m 1"D

· 1#satDAB dt$

, the diffusion

coefficient needs first be estimated. Since no experimental values where found for Coronene or

BaP, a theoretical solution is used as follows:

1. The Lennard-Jones potential parameters - !(r) = 4" #r

$%&

'()1

2 * #r

$%&

'()6+

,--

.

/00

- ! , the maximum

depth of the potential well, and ! , the characteristic molecule diameter, are

! = 8.16 !A, "

#= 980.9K for Coronene. For BaP no experimental numbers where found, so

he general fit for PAHs was used - ! = 1.234·Mw0.33 and

!

kb= 37.15·Mw0.58 (Wang and

Frenklach 1994).

2. The diffusion coefficient is given by the Chapman Enskog theory (Bird, Warren, and

LightFoot 2002)

DAB = 0.0018583 T 3 1MA

+1MB

!"#

$%&

1p' AB

2 (D,AB

where M is the molecular mass, T is the temperature in kelvin, p is the pressure in

atmospheres, ! AB = 0.5(! A +! B ) , and !D,AB is the binary diffusion collision integral

which is a function of the reduced temperature T * = T !"AB

where !AB = !A!B and given

by !D,AB =1.06036T *0.1561 +

0.193exp(0.47635T *)

+1.03587

exp(1.52996T *)+

1.76474exp(3.89411T *)

where for nitrogen gas ! = 3.667 !A, "

#= 99.8K

53

Appendix C

Measuring the desorption energy of PAHs from suspended aerosols

Attempts have been made to measure the evaporation energy of PAHs from soot particles.

The predominant method so far (Guilloteau et al. 2008), used flame produced soot, and evaporating

the adsorbed PAHs evaporate under set conditions. This was done at low pressures (~13 Pascal)

and not far from ambient temperatures (260-320 K).

The result is a decrease of mass, to a residual amount of PAHs coating left on the soot

particles. This residue decreases as the cylinder temperature increases.

In our experiment, where a particle was coated with a PAH multilayer, the evaporation rate

was constant. The difference arises from the vapor pressure behavior. In our experiments, the vapor

density around a fully coated particle is solely a function of temperature. For the same temperature

- the same vapor density is attained. In Guilloteau et al. (2008), the vapor density driving force

continuously diminishes, down to zero, as can be indicated by the decaying mass loss curve with

driving force (residence time, for the same temperature), [PAH] = [PAH]0 ! exp("kdes (T )) . This

can be explained by the same partial coating method as before (Figure 22). The soot particles are

initially coated by a monolayer of PAH material. Since the apparent vapor density is related to the

areas of zero coating, and the monolayer evaporates leaving behind an increasingly growing area of

non coated particle, this results in a continuously diminishing vapor density driving force, until the

desorption energy is equal to the PAH-soot bond energy and no more PAH evaporates.

Our technique measures the direct evaporation from suspended particles, as occurs

naturally. This makes measuring the desorption energy a very interesting endeavor. In order for this

to be achieved, the residence time will need to be longer, as indicated by the evaporation times in

(Guilloteau et al. 2008), which were up to 17 hours.

Keeping particles suspended for an hour while flowing through a loop of coil suspended in

a temperature-controlled bath could achieve this goal. For a 5 hour experiment, in 50 cc/min flow

rate, a 7.5 meter 2 inch diameter coil could be used. The penetration rate for 200 nm PSL spheres

would be 87% (Hinds 1999), and higher flow rates will allow for shorter resident times, 1000

cc/min will give 15 minutes resident time, and a higher penetration of 98%.

A question of resolution arises - is the AMS sensitive enough to measure this monolayer

evaporation? Only by using a high particle number concentration and extremely long measurements

to allow for extensive averaging, as indicated in Figure 7.

54

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