Heterogeneous condensation of submicron particles in a growth tube

Chemical Engineering Science 74 (2012) 124–134

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Heterogeneous condensation of submicron particles in a growth tube Marco Tammaro a, Francesco Di Natale b,n, Antonio Salluzzo a, Amedeo Lancia b a b

ENEA, Italian National Agency for New Technologies, Energy and the Environment, Research Centre of Portici, Piazzale E. Fermi 1, 80055 Portici, Naples, Italy Department of Chemical Engineering, University of Naples ‘‘Federico II’’, P.le V. Tecchio 80, 80125 Naples, Italy

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 October 2011 Received in revised form 14 January 2012 Accepted 14 February 2012 Available online 28 February 2012

This paper reports a study on the enlargement of particles, produced by a model ethylene/air flame, by heterogeneous condensation of water vapour. This was carried out in an instrumented lab-scale facility based on the use of a growth tube. Tests were performed by varying the temperature of the condensing vapour and the gas residence time in the growth tube. Particle enlargement was favoured by increasing the vapour temperature and the residence time. Experiments can be proficiently described using consolidated models for heterogeneous condensation, provided that the contact angle between the liquid embryo of condensing vapour and the particle surface is considered as an adjustable parameter, variable with temperature. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Heterogeneous condensation Growth tube Submicron particles Ethylene/air flames Effect of temperature Particle abatement

1. Introduction The emission of particulate matter entrained in industrial and vehicles exhaust gases is one of the major health and environmental concerns (e.g. Biswas and Wu, 2005; Menon et al., 2002; Pope et al., 2002). Very fine inhalable particles can remain suspended in the atmosphere for a long time, travel long distances from the emitting sources and, once inhaled, they can reach the deepest regions of the lungs and even entering in the circulatory system. Due to their chemical and physical characteristics, fine particles can produce significant effects on human health: they act both directly, by favoring the accumulation of substances in the respiratory tract, and indirectly, as a carrier of hazardous substances (Pope et al., 2002). Health hazards include heart diseases and altered lung functions, especially in children and older people. Fine particulate matter associated with diesel engines exhaust is also recognised as a carcinogenic substance and is listed as a mobile air toxic source. Adverse effects of particulate matter on the environment are related to reduction of visibility in cities and scenic areas, but, most of all, to the large climate forcing effects of Black Carbon (Menon et al., 2002). The new diagnostic methods for the analysis of particle size and concentration in gas streams have clearly pointed out that the particulate matter emitted by stationary combustion sources (in particular those related to coal or heavy fuel oil combustion)

n

Corresponding author. Tel.: þ39 81 7682246; fax: þ39 81 5936936. E-mail address: [email protected] (F. Di Natale).

0009-2509/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2012.02.023

presents numerical particle size distributions ranging from few nanometres up to several microns, while the one produced by diesel engines is usually smaller than 0.5 mm (Biswas et al., 2009; Maricq, 2006). Social awareness on the effects of particulate pollution in urban area increases sensibly in the last years, moving politics toward the introduction of more restrictive environmental regulations. In particular, these regulations are gradually reducing the minimum, ‘‘cut-off’’, particle size allowed at the emission point of industrial exhaust systems from 10 mm (PM10) to 1 mm (PM1). Similarly, adoption of restrictive regulations is foreseen for diesel engines (e.g. Euro 5 and 6 regulations for cars; USA Tiers 2 and 3 standards for diesel locomotives). In addition, the maritime sector, traditionally refractory to the imposition of environmental regulations, has recently revised its standards (MARPOL Annex VI) to reduce the emissions of coarser particulate matter related to sulphates and nitrates. For these reasons, the effective removal of sub-micrometric particles is receiving a growing attention, pushing forward the development of new processes and technologies. In fact, the traditional particle abatement devices are mainly designed and optimised to treat particles with sizes above 1 mm, and they are far less efficient in collecting sub-micrometric particles, especially those in the range 0.1–2 mm, called Greenfield gap (Seinfeld and Pandis, 1998). Usually, for process industry and combustion units, complex systems including trains of consecutive abatements devices (water scrubber, WS; fabric filters, FF; cyclones, CYC; Venturi scrubbers, VS; electrostatic precipitators, ESP) are adopted (Flagan and Seinfeld, 1988). For diesel engines, the

M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

typical retrofit system is the catalytic DPF (Diesel Particulate Filtration) coupled with EGR (Exhaust Gas Recirculation) unit. This after treatment unit allows high removal efficiency for nanometric particles and they are commonly adopted on cars, but the high pressure drops and the catalyst costs reduce their applicability on heavy-duty diesel engines as those of trucks, trains or ships. A couple of new technologies were proposed in the recent past for the enlargement of submicron particulates: wet electrostatic scrubbing (e.g. Carotenuto et al., 2010; Ha et al., 2010; Jaworek et al., 2006) and heterogeneous condensation (e.g. Fisenko et al., 2007; Heidenreich, 1994; Heidenreich and Ebert, 1995; Jingjing et al., in press; Niklas et al., 2007; Yan et al., 2008). Indeed, heterogeneous condensation is a promising technique to improve the performances of traditional particle collection devices. This technique consists of the condensation of vapour on the ultrafine particles in order to create a coarser liquid–solid aerosol whose size is larger than the upper limit of the Greenfield Gap (about 2 mm). Therefore, the heterogeneous condensation is not a particle collection technique by itself, but a preconditioning technique to be used before other conventional particle collection processes. In the nineteenth century, the enlargement of particles by means of adiabatic expansion of a saturated air sample, was adopted in many particle counter devices (Hering et al., 2005; Hering and Stolzenburg, 2005) and was investigated to measure aerosols particles concentration in atmosphere (Podzimek and Carstens, 1985). The use of heterogeneous condensation as a way to precondition the particles containing gas prior to conventional separators has been also studied (Heidenreich and Ebert, 1995), and it is known that heterogeneous condensation phenomena occurs in water scrubbers (Jingjing et al., in press; Niklas et al., 2007; Yan et al., 2008), even though the relevance of its contribution to the overall particle capture efficiency is not appropriately highlighted. There are two main approaches to trigger heterogeneous condensation phenomenon in a gas stream: (i) the injection of saturated water vapours in cooler particle-laden gases or (ii) the use of an evaporating liquid film that produced a supersaturated environment within which the gas flows. Commonly, in both cases, the device in which the process takes place is called growth tube. The first approach is simpler, but the second may give higher efficiencies and lower liquid consumptions and it is commonly adopted by CPC devices in light of the better performances and of the possible fine-tuning of the process parameters in a wider range of operating conditions. Theoretical calculations showed that the use of a growth tube with evaporating liquid film should assure higher supersaturation values than mixing, when operating between the same temperature extremes (Hering et al., 2005). This is beneficial for the process development, reducing actual plant size and steam cost. At the moment, there is no reliable estimation for steam consumption in growth tubes, but for the case of water steam injection and adiabatic mixing the required steam consumption per unit volume of treated gas is in the range 0.33–0.5 m3 steam/m3 gas (Jingjing et al., in press; Liu et al., 2011). The aim of this work is to investigate the heterogeneous condensation of water vapour on the particles produced by ethylene–air premixed flame in a growth tube. In particular, the experimental work did not aim to prove that heterogeneous condensation is a reliable way to enlarge particle, but was rather focused on establishing how gas–liquid temperature differences and treatment times affect the condensational growth. In fact, these two parameters are expected to be the most relevant ones for the design of a heterogeneous condensation process based on the growth tube concept. To this aim, a dedicated experimental campaign was carried out at low temperature of the evaporating

125

liquid and small treatment times, when heterogeneous condensation is not completed for all the particle sizes, and the effect of process parameters can be better revealed.

2. Theoretical framework The generation of a liquid–solid aerosol by heterogeneous condensation of a vapour on a particle can be divided into two stages that can be assumed as consecutives (e.g. Fletcher, 1958; Smorodin and Hopke, 2006). The first step involves the Nucleation, i.e., the formation of a liquid embryo on the particle surface; the second step is the Growth, i.e. condensation of the vapour around the embryo and the consequent enlargement of the liquid–solid aerosol. Studies on these topics started in the end of XIX century and a detailed analysis of the historical background and the Stateof-Art on both the nucleation and the growth phenomena were reported in several papers dating back to the last 10–20 years (e.g. Heidenreich, 1994; Heidenreich and Ebert, 1995). A brief summary of the fundamental theories for the nucleation of water droplets on particles and for the growing of the liquid–solid aerosol is reported here. In the following, the classical assumptions of smooth, spherical and homogeneous particles are considered. Moreover, equations for insoluble solids are reported only. Heterogeneous condensation is an energetically unfavourable process, since the creation of a liquid droplet requires an increase of the free energy of the water molecules (Fisenko et al., 2007; Hering et al., 2005; Hering and Stolzenburg, 2005; Brin et al., 2009; Fisenko and Brin, 2006). In order to overcome the energetic barrier and activate the condensation, the vapour must be oversaturated. This condition is commonly represented by a parameter called supersaturation, S, defined as the ratio between partial vapour pressure Pv and the vapour pressure at the gas temperature T, Pv,N1(T) S¼

Pv P v,1 1ðTÞ

ð1Þ

Both the theory and the experiments demonstrated that the smaller the particle the higher the supersaturation required to activate condensational growth. This effect is described by the Kelvin relation (e.g. McDonald, 1962), which define the smallest diameter of a thermodynamically stable droplet in an environment at given supersaturation, dK dK ¼

4sM W rl Rv TlnS

ð2Þ

In this equation, Mw, rl, and s are, respectively, the molecular weight, the liquid density, and the surface tension of the condensing species while Rv is the universal gas constant. It is worth noticing that, although this equation was developed to describe homogeneous droplets, the same relations hold to describe the liquid embryo formed on a surface, as proven by Fletcher (Fletcher, 1958) and Smorodin (Smorodin and Hopke, 2004). Each step of the heterogeneous condensation, namely the nucleation and the growth, is characterised by a specific rate. The nucleation rate represents the number of embryo, of a given size de, formed per second and per particle and is generally defined as (e.g. Fletcher, 1958)   DGn 2 J ¼ pKdp exp  kB T

ð3Þ

where K is a kinetic constant, kB the Boltzmann constant, dp the particle diameter and DGn is the free energy of formation of a liquid embryo (in equilibrium with its vapour phase) on the particle. Several models were presented in the literature to

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calculate DGn following either the assumptions that an uniform liquid shell immediately surrounds each particle (e.g. Krastanov, 1957) or that initially, the liquid forms one or more embryos on given points of the particle (Fletcher, 1958; Smorodin and Hopke, 2006; Meszaros, 1969; Fan et al., 2009; Lee et al., 2003). This second approach is usually preferred and gives rise to the following expression for DGn given by Fletcher (Fletcher, 1958)

DG ¼

3ðRv T rl lnSÞ2

 f ðm,xÞ

f ðm,xÞ ¼

   xm xm3  xm  1mx 3 1þ þ x3 23 þ 3mx2 þ 1 h h h h

Heterogeoneous condensation only 2.0 Scr

)

Very slow heterogeoneous condensation J < 1/s 1.0

cos y ¼ m ¼

0.5 50

ð8Þ

where svs is the surface tension between vapour and solid; sls is the surface tension between liquid and solid; svl is the surface tension between vapour and liquid. Commonly, a critical supersaturation Shet is conventionally cr defined in the pertinent literature as the level of S required to allow formation of one liquid embryo per second. Application of the Fletcher model for an insoluble and spherical particle for J¼1(1/s) gives vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 2 u u 8pM 2W s3 1 t 4 ð9Þ Shet f ðm,xÞ 5 cr ¼ exp Rv T rl 3kB TlnðpKd2 Þ p

Shet cr

100

150

ð7Þ

svs sls svl

decreases by increasing particle size and gas temperature. Although in line of principle higher values of supersaturation are desired to activate the smaller particles, there is a practical limit for an effective heterogeneous condensation. This is represented by the occurrence of homogeneous nucleation that takes place when nuclei of molecules of condensable components form spontaneously, without the support of any solid surface. This is an undesired phenomenon that causes a depletion of vapour and, thus, an undesired reduction of actual supersaturation level of the gas phase. Homogeneous nucleation rate can be calculated with the Kashchiev (Kashchiev, 2006) model. By analogy with the heterogeneous condensation, a critical value of supersaturation level for homogeneous condensation, Shom cr , can be considered. Typical values of Shom are 2–5 (Heidenreich, 1994; Heidenreich cr and Ebert, 1995; Fan et al., 2009). Fig. 1 reports a comparison of K Shom and Shet cr cr , together with the value of Scr, that is the supersaturation level required to allow stable formation of a water nucleus of diameter dK (Eq. (2)) on a particle with diameter dp (Eq. (7)). Fig. 1 shows the existence of a region of supersaturation levels where heterogeneous condensation can be achieved

ScrK

No condensation

and

It is worth noticing that the possible values of de are determined by the Kelvin relation according to Eq. (2), and are functions of T and S. Theoretically, the value of y depends on the wetting degree of the particle surface and on the liquid and the vapour tension, according to the Young’s equation (Fletcher, 1958; Smorodin and Hopke, 2006; Meszaros, 1969; Fan et al., 2009; Lee et al., 2003)

het

1.5

In this formula, m ¼cos y, y being the contact angle between the particle surface and liquid, h is a geometric factor pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð6Þ h ¼ 1þ x2 2mx

dp de

hom

2.5

ð5Þ

x¼

Scr

3.0

ð4Þ

where f(m, x) is the Fletcher geometrical factor (

Heterogeoenous and Homogenous condensation

S, -

8pMw 2 s3

n

3.5

200

250 300 dp, nm

350

400

450

500

Fig. 1. Critical supersaturation levels for homogeneous (Shom cr ) and heterogeneous (Shet cr ) condensation, and of the equilibrium supersaturation level given by Kelvin’s K equation (Scr ) as a function of particle diameter. P¼ 1 atm, T¼300 K; liquid:water; gas:air; spherical particles with m ¼0.95.

without undesired vapour depletions caused by homogenous condensation. Once the liquid embryo becomes stable on the particle surface, a liquid–solid aerosol is formed and the liquid embryo can enlarge thanks to condensation of vapour that is regulated by the classical laws of heat and mass transfer around a single droplet. Heidenreich (Heidenreich, 1994), in a review on the condensational droplet growth in the air–water system, demonstrated that heat flux between droplets and vapour can be related only to heat conduction and by diffusing molecules, neglecting the Dufour effect. The same author showed that the mass balance on a droplet in a binary air–water gas mixture can take in account only for the mass flux due to diffusion: the Stefan-flow and the Soret effect contributions can be neglected since they account for less than 1.5% of the overall mass transfer rate. It was also found that heat and mass balances can be simplified by the assumptions that: (i) temperature inside the droplet is uniform; (ii) the gas is a continuous phase (i.e. droplet Knudsen number, Kn, is far less than 1); (iii) the droplets, if smaller than 5 mm, are rigid non-deformable spheres (Clift et al., 1978); (iv) no-slip velocity condition for the gas flows at the droplet surface; (v) the binary air–water mixture has physical properties constant with temperature. Under these assumptions the heat and mass balance become (Heidenreich, 1994; Heidenreich and Ebert, 1995; Clift et al., 1978; Miller et al., 1998) cmd

dT d þ hl I ¼ Q dt

dmd 1 2 dd ¼ I ¼ prl d 2 dt dt

ð10Þ

ð11Þ

where Q is the total heat flux and I is the total mass flux to the droplet; Td is the temperature of the droplet and hl, c, md, d are the specific enthalpy of the liquid, the specific heat capacity, the mass and the diameter of the droplet respectively.

M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

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It was found that for S r2, the condensational growth of a droplet can be well described by the analytical solution provided by Fuchs (Fuchs, 1959) under the assumption of a pseudo-steady state droplet temperature. The expression of I was given first by Maxwell (see Fuchs (Fuchs, 1959)) I¼

2pd  M w D ðP v,a Pv,1 Þ Rv T

ð12Þ

where D is the diffusivity of water, T is assumed as the film temperature at the droplet surface estimated as (TN þTd)/2, and Pv,a, is the vapor pressure at the droplet surface, that can be related to the saturation vapor pressure over a flat liquid surface at temperature Td and radius according to the equation (Heidenreich and Ebert, 1995)   4sM w ð13Þ P v,a ¼ P1ðT d Þexp Rv T d rl d The expression for the time course of droplet temperature Td is T d ðtÞ ¼ T 1 

Il 2pdK w

Fig. 2. Experimental apparatus.

ð14Þ

where l is the specific heat of vaporisation of water and Kw is the thermal conductivity. Eq. (14) is non-linear due to the dependence of I upon Td, but is independent from d. Once Td is calculated, Eq. (11) can be integrated over time considering the initial condition: t ¼0, d ¼d0 and Td ¼Td,0. Solution of Eq. (11) is not straightforward since both I and Td are functions of time and numerical solutions are usually preferred. Although the growth model is rigorously valid to describe the droplet growth in a continuous flow, this can be used also for heterogeneous condensation, assuming that the liquid–solid aerosol behaves as a homogeneous, isolated droplet with initial diameter d0 and temperature equal to that of the gas. Indeed, this approximation becomes reasonable only when the embryos enlarge enough to surround the particle, so that the model fails to describe the first instants of embryos growth. However, in practice, this time-lapse is very small and the model can be reasonably used to describe heterogeneous condensation (Heidenreich and Ebert, 1995). It is worth noticing that the models for nucleation and growth rates are strongly dependent on the assumptions that particles are spherical and that the gas is a continuous medium (Kn51). These two assumptions allow a ‘‘geometric’’ view of the particle– embryo system (Fletcher, 1958; Smorodin and Hopke, 2004) that may fail to describe the actual physics of a nanometric, nonspherical soot particle produced by a flame. Furthermore, the nucleation model and the same thermodynamics model of the heterogeneous condensations require the knowledge of surface tensions of the embryo–particle systems (Eqs. (2), (4) and (8)). These parameters affect the value of the contact angle, y, which is expected to be a complex function of the actual shape of the particle, its chemical structure and surface homogeneity, the presence of impurities in the condensing gas and of the temperature. Therefore, it should be noticed that the proposed equations for heterogeneous condensation can be safely used only if y is known a priori, from specific experiments, or if it is used as a parameter for numerical fitting of experiment.

3. Experimental apparatus In Fig. 2 the experimental system adopted for the heterogeneous condensation tests is described. The particles were produced by premixed ethylene–air flame whose equivalence ratio is F. The equivalence ratio of a system is the ratio between the actual and the stoichiometric values of the ethylene-to-air ratio: a value of F greater than 1 represents rich combustion conditions while a value

lower than 1 indicates oxidising, or lean, conditions. During experiments the equivalence ratio is adjusted with the two flowmeters (FC1) that controlled the ethylene and air flows to the burner. The flue gases emitted by the flame are diluted with indoor air and sampled by means of a hood connected to an extractor fan. The gas flow rate was controlled by the flowmeter FC2. The gas was then cooled to approach its dew point temperature (Ti), and actual value of the gas temperature, T0, and relative humidity, RH, are measured at the exit of the cooling unit. This unit was a typical glass condenser with cold water coils inside. Water temperature was controlled by a thermostatic bath. To prevent the presence of accidental droplets in the gas, two Drechsel (d1 and d2) were placed along the gas line before the growth tube. The saturated gas was then sent to the growth tube. The growth tube consisted in a 40 cm long and 1.5 cm internal diameter glass cylinder. The tube diameter was determined taking in account the diffusion rate of vapour from the walls to the centreline and the need of minimising the interferences between the gas and the liquid flows. The tube length was chosen to allow a gas residence time of 0.5–2.5 s. The water inlet to the growth tube was designed as tangential so to assure a perfect adhesion of water with the tube walls. Of course vapour condensation occurred until the temperature of the gas was lower than that of the liquid film. To this aim, the liquid film temperature was kept at the desired value, Tw, by means of a thermostatic bath, and liquid temperatures at the entrance and the exit of the growth tube were both measured. The aerosol size distribution (ASD) and concentration in gas streams were measured using a Laser Aerosol Spectrometer (TSI Model 3340) that allows measuring particle size in the range 90–7500 nm. Sampling points were available close to the growth tube inlet and outlet sections. The experimental campaign was composed of thirty-six tests, organised in two main groups, corresponding to two equivalence ratios F, of 2.38 and 3.30. Each group was composed of six subgroups, each of which made by three tests with constant residence time (tres), dilution ratio (Dr, equal to the ratio between dilution air and combustion smokes) and total flow (Qg). Each tern of tests in a group consisted in one ‘‘blank test’’ (without any water in the growth tube) and 2 tests with different water temperatures, respectively, of 309 and 317 K. Details of the experimental conditions are reported in Table 1. During a test, the burner was turned on at given ethylene and air flow rates, and the dilution air flow rate, the water flow at the growth tube and the exchanger were fixed at the desired levels. The laser aerosol spectrometer was connected to the growth tube

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M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

Table 1 Experimental plan. Group 1: QC2H4 ¼ 59 ml/min, Qair ¼355 ml/min, F ¼ 2.38; Group 2: QC2H4 ¼ 82 ml/min, Qair ¼ 355 ml/min, F ¼ 3.30. Operating conditions U, (m/s)

T0, (K)

RH, (%)

tres, (s)

Dr

Qg, (l/min)

0.42

291

0.90

0.94

9.86

4.5

0.38

292

0.92

1.06

8.65

4.00

0.33

293

0.97

1.20

7.45

3.50

0.28

293

0.99

1.40

6.24

3.00

0.24

293

1.00

1.70

5.03

2.50

0.19

294

1.00

2.12

3.83

2.00

Group 2

Test

Tw, (K)

Test

Tw, (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Blank 309 317 Blank 309 317 Blank 309 317 Blank 309 317 Blank 309 317 Blank 309 317

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Blank 309 317 Blank 309 317 Blank 309 317 Blank 309 317 Blank 309 317 Blank 309 317

test

test

test

test

test

test

test

test

test

test

test

test

1000

Φ = 2.38; T = 309K, tres = 0.94 s

100

dN/dlogdp, 1/cm3

inlet until the particle size distribution became stationary, and the inlet ASD was recorded. Then the spectrometer was connected to the growth tube outlet and the ASD was measured over time. Each ASD reported in the following was the mean of more than 20 samples measured during an experimental run. Tests were all repeated in triplicate and the standard deviation is lower than 12%. The blank tests were performed in order to take into account for all the scavenging phenomena occurring in the entire equipment when heterogeneous condensation is absent. The two tests at the different temperature provide information on the actual particle size distribution at the exit of the growth tube in two different operating conditions. Of course, these are the results of both the heterogeneous condensation and equipment scavenging phenomena.

Group 1

10 N (dp,max) 1

0.1

4. Experimental results Fig. 3 reports the typical experimental result of heterogeneous condensation tests. In particular, these were obtained for the experiments with F ¼2.38, water temperature of 309 K and residence time of 0.94 s (Test no. 1 and 2 in Table 1). In Fig. 3, the full symbols represent the blank tests, i.e. the particle size distribution generated by the flame and measured at the end of the growth tube. The empty symbols represent the particle size distribution at the exit of the growth tube when heterogeneous condensation occurs. It is worth noticing that the ASD at the inlet of the growth tube almost coincided with that and at the outlet of the growth tube without any water inside, i.e. during blank tests. For the sake of clarity, the inlet ASD is not reported in Fig. 3. The comparison of the two distributions clearly point out that below a critical particle diameter, dcr, no condensation occurred. The coarser particles, instead, were enlarged due to the heterogeneous condensation growth and a liquid–solid aerosol with size up to 2.5 mm was formed. In particular, for the sake of simplicity, we can define a reference maximum particle size, dmax, as the larger aerosol size with a given concentration N(dmax). This concentration is arbitrarily set to 1 particle per cm3 as reported in Fig. 3 so that dmax represents the 99.9th percentile of the aerosol size distribution.

dcr

dp,max

0.01 0

500

1000

1500 dp, nm

2000

2500

3000

Fig. 3. Typical particle size distribution obtained during heterogeneous condensation tests. Full symbols: Blank test no.1; Empty symbols: Test no. 2.

All the experimental tests gave qualitative results similar to those reported in Fig. 3, and the following Table 2 reports the values of dcr and dmax measured for all the investigated conditions. For the sake of completeness, Table 2 also reports the value of the 90th and the 95th percentile of the aerosol size distribution (named d90 and d95 in the following), that must be compared with their corresponding values of the inlet particle size distribution respectively equal to 180 nm and 220 nm circa for all tests. Although experiments were planned for two different values of F, equal to 2.38 and 3.30, no apparent differences were observed from the two cases. Indeed, the only visible effect was a slightly higher particle concentration, around 10–15%, obtained for the tests at higher F. Therefore, in the following, results are reported regardless of the equivalence ratio.

M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

Table 2 Critical, 90th percentile, 95th percentile and maximum (99.9th percentile) aerosol diameters as a function of the operating conditions (^ ¼ 2.38). Tw, (K) tres, (s) 0.94

1.06

1.20

1.40

1.70

2.12

309 dcr, (nm) d90, (nm) d95, (nm) dmax, (nm)

350 336 484 1000

160 350 465 1800

160 370 490 1800

125 410 618 1750

190 412 547 2200

120 420 650 2000

317 dcr, (nm) d90, (nm) d95, (nm) dmax, (nm)

350 257 195 1000

100 315 243 1000

o90 336 253 1100

o 90 410 336 2000

130 447 364 2360

112 500 340 2500

Data in Table 2 shows that the value of the critical diameter gradually moved towards finer particles for longer residence times, even though this trend is a little bit scattered at Tw ¼317 K. Similarly, the values of dmax, d90 and d95 present a generally increasing trend by increasing the residence time. These results are quite easy to understand since higher particle residence times mean that the particles persist in a supersaturated environment for longer times, allowing the condensation of more vapor and the formation of larger liquid–solid aerosols. Furthermore, experimental results show that particle enlargement is favored by higher temperatures and, if enlargement of 90 nm particles are desired under the examined conditions, a residence time close to 2 s should be adopted at Tw ¼309 K, but this time is almost halved at 317 K. However, the degree of particle enlargement, as resumed by the value of dmax, appears to be quite less influenced by Tw. Nevertheless, to enlarge all particles above 1 mm and allow their removal by conventional particle collection technologies (either VS, FF, ESP), higher residence times and higher water temperatures are necessary.

5. Model results The analysis of the experimental data requires the modelling of the dynamics of embryo nucleation and aerosol growth in the supersaturated environment of the growth tube. The objective of the model is to obtain the size distribution of the liquid–solid aerosol at the exit of the growth tube at different investigated conditions, once the inlet particle size distribution is known. To this aim, the heterogeneous condensation process was modelled considering the fate of each particle flowing in the growth tube under the assumptions that 1. The gravity forces, and then the slip velocity, is negligible. 2. The particles were homogenously distributed in the gas stream. 3. The gas flow in the growth tube was laminar and in steady state, so that axial symmetric Poiseuille-like velocity profile was established. 4. The particles follow the gas streamlines like they were free of inertia, so that they moved longitudinally along the growth tube without changing their radial position. 5. The particle concentration was sufficiently low to assure that heterogeneous condensation negligibly influences the water vapour concentration profile generated by the liquid film in the growth tube. The first four assumptions are easy to accept once the gas properties and the geometry of the growth tube are known.

129

The last one, instead, requires some comments. Indeed, Heidenreich (Heidenreich, 1994; Heidenreich and Ebert, 1995) demonstrated that when heterogeneous condensation is achieved by steam injection, the concentration of particles plays a relevant role in determining the actual condensation level: when the vapour condenses on the particle, in absence of any continuous external source, the supersaturation level decreases until the condensation becomes impossible. The highest the particle concentration is, the faster the vapour depletion and the reduction of supersaturation. In the growth tube, instead, there is a continuous supply of vapour from the evaporating liquid until equilibrium conditions establish in the gas phase. If vapour condenses on the particles, additional liquid evaporates from the film to approach equilibrium. In the investigated conditions, particle concentration is of the order of 104 particles per cm3. Preliminary calculations showed that in our tests, condensing vapour flow was below 1% of that generated by the evaporating liquid. In these conditions, the hypothesis no. 4 is considered valid. Experiments gave a further confirmation of this assumption since the tests with different C2H4/air volume produced very similar particle distribution and no apparent effect on particle enlargement was observed. The main consequence of the hypothesis no. 5 is that the temperature and vapour concentration profiles of the gas stream flowing within the growth tube, could be calculated by solving the mass and energy balance in laminar flow, i.e. the classical Graetz problem, for which an analytical solution exists (e.g. Bird et al., 2007; Weigand, 1996) if the physical properties are assumed to be constant with temperature, which is a realistic approximation in the investigated conditions. The Graetz problem was solved assuming that the liquid film temperature, and, therefore, the vapour concentration at the film–gas interface, was constant along the growth tube length (Dirichlet boundary conditions). This condition was experimentally verified by measuring inflow and outflow water temperature, which resulted different for about 0.1–0.2 1C. A schematic representation of the model used to describe heterogeneous condensation in the growth tube is reported in Fig. 4. The solutions of the Graetz problem gave the values of gas temperature, T(r, z), and of water partial pressure, Pv,N(r, z), in all points of the growth tube. From these values, the local supersaturation level, S(r, z), were calculated according to Eq. (1). Each liquid–solid aerosol of initial size dn, flowed along the longitudinal coordinate of the growth tube at radial position r, and was characterised by a diameter d(r, z, dn) that, in absence of condensation phenomena remained equal to the particle one, dn, and that became higher than dn if condensation occurs. To calculate the ASD at the exit of the growth tube the following algorithm was developed for each particle size value, dn, of the inlet size distribution: indeed only some values of dn were selected dividing the ASD in intervals of fixed size Ddn. The concentration of particles in this size interval was cn. A finite volume method was adopted for calculation. By invoking the axial symmetry properties of the velocity, temperature and water partial pressure profiles in the growth tube, this was reduced to a two-dimensional domain that corresponded to a growth tube half-plane. Such domain was then divided in X  Y cells defined by X radial and Y longitudinal space intervals of size Dr and Dz (the mesh depicted in Fig. 4). In each cell, the values of gas temperature, water partial pressure and supersaturation were assumed to coincide with their values calculated from the aforementioned analytical solution of the Graetz problem at the central point of the cell. Rotation of the half plane by 3601 reproduced the actual growth tube geometry. Each two-dimensional cell obviously becomes a three-dimensional ring that we conventionally call again ‘‘cell’’ in the following.

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M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

Fig. 4. Scheme of the descriptive model for heterogeneous condensation.

The aerosol passed through each of the cells, at position z from the tube inlet, after a residence time equal to z/Uz(r, z), Uz(r, z) being the gas (and the particle) velocity along the z direction in the radial position r. Of course, particle remained in the cell for a time interval Dt ¼ Dz/Uz(r, z). One of the main point of the studies on heterogeneous condensation is the need to find out if and where, in the growth tube, the nucleation of water embryos takes place on a particle of given size dn. Indeed, it is worth noticing that the theory on the stability and the rate of formation of embryos resumed by Eqs. (2)–(8) provide information on (i) the smallest size of embryo, dK, that is stable under specific environmental conditions (Eq. (2)) and (ii) the rate of formation, Jde(r,z,dn), of an embryo of generic size de under the same conditions (Eqs. (3)–(8)). The value of Jde(r,z,dn) decreases with the embryo size, and, therefore, the rate of formation of an embryo of size dk is the highest possible. According to Eq. (2), the value of dK is a function of T(r,z), S(r,z) and of the physical properties of the system. Therefore, the value of dK changes in each cell of the domain, that is dK ¼ dK(r,z). The model proposed here considers that nucleation was studied by considering all the value of embryo size, de, represented by each value of dK(r,z) that are possible in the calculation domain. For each cell of an r line, from z ¼0 to z ¼L, and for each dp, the algorithm calculates the nucleation rate for each value of de. The nucleation starts in the cell z ¼z0 where the number of nucleated embryo of size de, nde(r,z,dn), exceeds unit nde ðr,z,dn Þ ¼

Z 0

z

 Y  X Jðr,z,dn Þ Ji ðr,z,dn Þ dz ¼ Dz Z 1 U z ðr,zÞ U zi ðr,zÞ i¼1

ð15Þ

This summation is, however, set back to zero if the value of de is lower than dK in each cell zrz0. In fact, if this happens, the embryo of size de is unstable and is assumed to disappear. In the specific conditions investigated in this work, the summation usually reduces to one (at Tw ¼ 309 K), sometimes two (at Tw ¼317 K), terms which refer to the value in z0 and in z0  Dz. If this condition was verified for a given z0 position, nucleation and embryo growth take place in the subsequent cells according to the supersaturation levels and to the mass and heat transfer conditions. The nucleation phase theoretically ended once the particle surface was completely surrounded by a water shell, i.e. when the embryos on the particle surface melted together to create a shell. Preliminary calculations on Fletcher (Fletcher, 1958) model, coupled with the estimation of dK(r,z) coming from Kelvin equation, and on the rate of condensations of water droplet of the same size of the embryos (Heidenreich, 1994; Heidenreich and Ebert, 1995), showed that in our conditions each embryo grew fast enough to cover the entire particle surface after few

tens of milliseconds. Therefore, it was assumed that once an embryo formed in a cell, in the subsequent cell the liquid–solid aerosol already became a particle surrounded by a shell of water whose size increased according to the Heidenreich (Heidenreich, 1994; Heidenreich and Ebert, 1995) models for vapour condensation on a homogenous liquid droplet. To apply this model, the values of liquid water temperature and of condensing droplet size must be calculated with the non-linear systems of equations reported in paragraph 2. To this aim, a simple trial and error algorithm was used: droplet temperature was calculated by coupling Eq. (14) with the expression of I(r,z,dn) and Pv,a(r,z,dn) given by Eqs. (12) and (13) assuming a tentative droplet diameter equal the aerosol diameter at the previous cell, dn ¼ d(r, z  Dz, dn). Once the value of Td(r,z,dn) is known, Eq. (2) can be solved to determine the value of d(r,z,dn). With this value of the aerosol size, the new values of I(r,z,dn) and Pv,a(r,z,dn) were calculated and if they differed from the previous ones for more than 1%, the procedure was repeated with a new value of dn until convergence. Of course the accuracy of this procedure depends on the cell size, but it was found that the use of X ¼10 radial cell and Y¼100 longitudinal cell gave satisfactory results. The values of the ASD at the exit of the growth tube was calculated starting from the values of d(r,L,dn) and of the corresponding values of the initial concentration of particle of size dn: all the particles in the outflow sections are classified in linear intervals of 100 nm from 0 to 7500 nm centred around reference diameters, indicated as dj. The overall concentration of a particle in the size interval centred on dj is the summation of the corresponding values of cn(r) of the selected particles, that is cðdj Þ ¼

1 X

cn ðrÞ

8n : dðr,L,dn Þ A ½dj 50 nm; dj þ50 nm

ð16Þ

n¼1

This modelled particle size distribution was compared with the corresponding experimental one and the value of the contact angle, y, was then determined by best fitting of experimental result. Indeed, it was found that y can be considered as a function of temperature only, so that a value of y equal to 0.318 rad was adopted to describe all the data at Tw ¼309 K while a value of 0.478 rad provided the best description of data at Tw ¼317 K. These correspond to values of m equal to 0.95 for 309 K and 0.888 for 317 K. It is worth noticing that a value of m close to 1 is typically assumed to describe insoluble hydrophobic particles (Fletcher, 1958). Finally, with reference to the physical meaning of the regression parameter y, it is interesting to note that the best fitting of experiments is obtained by considering a value of the contact angle that increases with temperature. Indeed, former evidences (e.g. Karmouch and Ross, 2010; Park and Aluru, 2009)

M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

pointed out that the contact angle for water condensation on several kinds of homogeneous solid surfaces reduces by a few degrees by increasing temperature, even though Yecta-Fard and Pontec (Yekta-Fard and Ponter, 1988) showed an opposite trend. However, it is worth remembering that the parameter y adopted here resumes all the assumptions that are at the very bases of the nucleation rate and of the growth rate models. Among them it is worth to consider the particle sphericity, the homogeneity of the particle surface and, above all, the assumption that an embryo formed on a 100 nm particle, which may be as small as 10–50 nm, behaves as a continuous liquid and follows the same geometric laws proposed by Fletcher and Kelvin models, disrespectfully of its nanometric size. All these considerations led to the conclusion that y can be actually considered as a reliable adjustable parameter and that its real nature and its dependence on the process parameters and on the physical and chemical properties of the particulate phase need further investigations. Two sample results are reported in Fig. 5, which describes the comparison between modelled and experimental values of the particle size distribution at the exit of the growth tube for two different operating conditions (corresponding, respectively, to the tests nos. 11 and 3 of Table 1). Experimental values of the corresponding inlet particle size distributions are also reported. It clearly appears that at both temperatures, modelled aerosol size distribution gives a very good representation of experiments.

1000

131

This good matching between model and experiments is observed for all the performed tests, and may be well summarised by comparing the values of the mean size of the liquid–solid aerosol size distribution davg and of values of dmax. This comparison is reported in Fig. 6 that shows a very good matching between experiments and models, with differences always lower than 15%. The heterogeneous condensation model used therein provided a simple explanation for the experimental results concerning the existence of dcr and the actual value of dmax. Fig. 7 reports the contour plots for supersaturation and for the condensational growth driving force (Pv,a  Pv,N) in the half-plane of the growth tube for a given condition (Tw ¼309 K, tres ¼2.10 s, dn ¼500 nm). The supersaturation plot shows that, due to the peculiar temperature and vapour pressure profiles in the growth tube, there is a region, within 1–2 mm from the growth tube wall, where supersaturation level is very close to 1. In this area only the coarser particles may enlarge, while the smaller particles can undergo heterogeneous condensation only far from the walls. The value of dcr is related to the largest value of supersaturation achieved in the growth tube; to allow nucleation, the supersaturation level must higher than Shet cr , which is a function of particle diameter as reported in Eq. (9).

104

Tw = 309K

Φ = 2.38; T = 309K, tres = 1.40 s, θ=0.318

103 dN/dLogdp, 1/cm

3

d, nm

100

10

102

1

101 0.1 0

500

1000

1500

2000

2500

104

3000

dp or d, nm

Tw= 317K

1000

Φ = 2.38; T = 317K, tres= 0.94 s, θ = 0.478

103 d, nm

dN/dLogdp, 1/cm

3

100

10

102 davg, nm (Exp.) dmax, nm (Exp.)

1 Modelled Initial Exit 0.1 0

500

1000

1500

2000

2500

3000

dp or d, nm Fig. 5. Comparison between experimental and modelled particle size distributions at the exit of the growth tube for two different operating conditions. Particles size distributions at the growth tube inlet are also reported.

101 0.8

davg, nm (Mod.) dmax, nm (Mod.)

1.0

1.2

1.4 1.6 t res, s

1.8

2.0

2.2

Fig. 6. Comparison between values of davg and dmax obtained from experiments and from model calculations at different residence times and for the two water file temperature.

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M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

is a function of supersaturation; moving toward the growth tube exit, the supersaturation profile gradually flattens to the value of 1, showing a reduction of the driving force for the mass flux and a slower droplet growth, according to Eqs. (2) and (12). This phenomenon can be also considered as the origin of the dependence of dmax on the gas residence time observed in the experiments.

1.0

0

0.8

0.6

5

6. Conclusion

z/L

1 .0 1

0.2

1.015

0.0 0.0

0.2

0

20

5 30

0

30

1.01.09 17.05600 1.045 1.030

0.4

0

1 .0 1 5

1 .0 6 0 75 1 .0 90

03

0

1 .0

04

0

1.

1.

10

0.4

0.6

0

20 0

0

0.8

1.0 0.0

0.2

r/R

0.4

100

0.6

0.8

1.0

r/R

Fig. 7. Modelling of heterogeneous condensation of 500 nm particle in the halfplane of the growth tube (F ¼2.38, Tw ¼ 309 K, tres ¼ 2.12 s). A. Supersaturation level; B. Pv,a  Pv,N, Pa.

Dimensionless aerosol size, d/d 0

6

r/R = 0.20 r/R = 0.40

r/R = 0

5

r/R = 0.30 r/R = 0.60

4 3

r/R = 0.80

2 r/R = 0.90

1 0 0.2

0.4

0.6

0.8

1.0

z/L Fig. 8. Evolution of the dimensionless liquid–solid aerosol diameter, d/dn, for 500 nm particle in the half-plane of the growth tube (F ¼2.38, Tw ¼309 K, tres ¼ 2.1 s).

This is confirmed by Fig. 8, which describes the evolution of liquid–solid aerosol over the growth tube length. Heterogeneous condensation seems to take place mainly on the particles close to the centreline of the growth tube and in the first 20% of the tube length (around 8 cm from the growth tube inlet section). In this area the particles promptly reach diameters around 2.7–2.9 mm. Afterward, they do have significant enlargement. Furthermore, the aerosol size increases non-monotonically moving from the tube wall r/R ¼0.99 and the centreline r/R ¼0. This result can be related to the reduction of the driving force for heterogeneous condensation, which is expressed in Fig. 7B as the difference among the water partial pressure close to the droplet surface and in the bulk of the gas phase (Pv,a  Pv,N). Of course, such difference

This work reported the study of the heterogeneous condensation as a technique of pre-conditioning the sub-micrometric particles contained in a gas with the aim of increasing their dimensions enough to allow the use of consolidate gas cleaning techniques. This problem is particularly relevant for particles in the Greenfield gap, for which the conventional depuration techniques are quite ineffective. For this purpose instrumented lab scale equipment was designed, constructed and tested. The core of the equipment was the growth tube, which consisted in a glass tube where the particle laden gas flow came into contact with a supersaturated water vapour environment, generated by a liquid film flowing on the tube internal wall. Experiments showed that by increasing the treatment time, the value of the critical diameter, i.e. the minimum particle size that is subjected to heterogeneous condensation, gradually moves towards finer particles, even though this trend was a little bit scattered for Tw ¼317 K. Similarly, the maximum size of the liquid–solid aerosol, dmax, presented an increasing trend by increasing the residence time. Furthermore, experimental results showed that particle condensation was strongly favored by higher difference of temperatures between liquid and gas, so that the time required to enlarge a particle as fine as 90 nm is halved by increasing the temperature from 309 to 317 K. The main results of the study provide deeper insights both on the physical description of the heterogeneous condensation process and on the possible application at industrial scale of growth tube devices. A descriptive model based on the theories of heterogeneous nucleation, condensational growth and on the analytical solution of the Graetz problem in laminar flow, was used to estimate the final particle size distribution at the exit of the growth tube. The results of this model were successfully compared with experimental results, using a value of the contact angle of 0.318 rad for Tw ¼309 K and 0.478 rad for Tw ¼317 K. The variation of y with temperature is expected to be related to the alteration of temperature on microscopic particle–water interactions. On the one hand, it was shown that the contact angle can be reliably used as an adjustable parameter to describe experimental results in a new system (soot/water/flue-gas and air in the investigated conditions) for which detailed description of the physics of embryo nucleation is not available. In this sense, the parameter y is used here to take into account for the discrepancies between the actual experimental conditions and the assumptions at the very basis of the models used to describe the physics of nucleation phenomena, above all the hypothesis of homogeneous spherical particles and of a liquid embryo modelled as a continuous fluid disrespectfully of the nanometric size of the investigated aerosol. Although we strongly envisage that detailed studies are required to address the value of y for particles of different size and different origin, the design of industrial devices to treat a specific, complex, gas stream, can be safely based on the conduction of specific experiments and the use of the proposed model to

M. Tammaro et al. / Chemical Engineering Science 74 (2012) 124–134

estimate an averaged value of the contact angle for the desired system. With reference to the industrial application of growth tube devices, the experimental results showed that the heterogeneous condensation can be easily carried out. Nevertheless, the proposed model showed that the most active region of the growth tube was concentrated in the first 6–10 cm of the growth tube and 2–3 mm far from the tube wall, while the remaining volume was quite ineffective. In this sense, this experimental configuration was not optimising the heterogeneous condensation and different solutions should be investigated, but for its simple design, this system should be worth of consideration for large scale industrial applications.

x (–)

133

Ratio between particle diameter and critical embryo diameter

Greek symbols

F (–) Equivalence ratio y (rad) Contact angle between the particle surface and liquid l (J/kg) Latent heat of condensation

n (m/s) Mean velocity of vapour molecules r (kg/m3) Gas density rl (kg/m3) Water density s, svl (N/m) Surface tension between vapour and liquid svs (N/m) Surface tension between vapour and solid sls (N/m) Surface tension between liquid and solid

Nomenclature D (m2/s) Dr (–) D (m) d (m) dn (m) d90 (m) d95 (m) de (m) dk (m) dp (m) dcr (m) davg (m) dmax (m)

Diffusion coefficient Dilution ratio Diameter Aerosol or droplet diameter Tentative aerosol diameter 90th percentile of the aerosol size distribution 95th percentile of the aerosol size distribution Embryo diameter Kelvin embryo/drop diamter Particle diameter Critical particle diameter Mean diameter of the aerosol size distribution Maximum diameter—99.9th percentile of the aerosol size distribution f(m,x) (–) Geometric factor G (kJ/mol) Free energy H (J) Enthalpy of vapour h (–) Geometric factor I (Kg/s) Mass flux J (1/s) Nucleation rate K (1/(m2 s2)) Kinetic constant in Fletcher model (Fletcher, 1958) kB (J/K) Boltzmann constant Kn (–) Knudsen number Kw (W/mK) Water thermal conductivity Mw (g/mol) Water molecular weight md (kg) Droplet mass m cos y P1 (kPa) Saturation vapour pressure Pv (kPa) Vapour partial pressure Pv,a (kPa)Vapor partial pressure on particle surface Pv,N(kPa) Vapor partial pressure in the bulk of gas phase Q (J/s) Total heat flux Qg (l/min) Total gas flow RH (%) Relative humidity Rv (kg m2/kmol) Ideal gas constant Rc (m) Critical radius r (m) Radius S (–) Supersaturation Shet Heterogeneous critical supersaturation cr (–) Shom (–) Homogeneous critical supersaturation cr SKcr (–) Critical supersaturation by Kelvin’s equation T (K) Gas temperature Td (K) Droplet temperature Tw (K) Liquid film temperature TN (K) Gas temperature in the bulk of gas phase T0 (K) Gas temperature at the growth tube inlet t (s) Time tres (s) Residence time Uz (m/s) Gas velocity

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