Generalized deposition model of tiny solid particle immersed in turbulent flow

Transcription

1 International Journal o Sustainable and Green Energy 04; 3(6-): 7-4 Published online February, 05 (htt:// doi: 0.648/j.ijrse.s Generalized deosition model o tiny solid article immersed in turbulent low Esam I. Jassim Deartment o Mechanical Engineering, Prince Mohammad Bin Fahd University, Al-Khobar, Saudi Arabia, 395 address: ejassim@mu.edu.sa To cite this article: Esam I. Jassim. Generalized Deosition Model o Tiny Solid Particle Immersed in Turbulent Flow. International Journal o Sustainable and Green Energy. Secial Issue: Renewable Energy and Its Environmental Imaction. Vol. 3, No. 6-, 04, doi: 0.648/j.ijrse.s Abstract: Progress to the correlation o article deosition velocity in turbulent ie low is resented. The develoed model accounts or the Brownian diusivity and inertia eects and is extended to cover the inluence o the low velocity by including Reynolds number in the correlation. The exerimental data and revious roosed models are used in comarison o redicting article deosition rate. It is shown that the new model o deosition velocity is in good agreement with the exerimental data and numerical simulations. Further the aerodynamics has signiicant inluence on the deosition rate and should be concerned when the rocess o article migration and deosition is addressed. The deosition eiciency, the measurement tool o article deosition rate in this work, increases with the increase o diameter or large articles, and with the decrease o diameter or submicron articles. Other actors addressed in this work are eects o article to luid density ratio, ie diameter and the surace roughness. The results showed that increase in density ratio makes the deosition rate o submicron articles to increase too whereas no signiicant eects is noticed or large articles. Carrier ie size is studied and the deosition rate curve shits right with decreasing in ie size. Finally, the deosition rate o articles is ound to increase with increase in surace roughness. Keywords: Particle Deosition, Turbulent Flow, Brownian-Inertia Motion, Surace Roughness. Introduction Particle migration and deosition have taken a considerable attention due to its signiicance in numerous engineering alications ranging rom aerosol air ollution to the microelectronics industry. Other alications including heat exchangers, health eects and chemical industries are o interest in such henomena as well. During ast ew decades, intensive researches have been conducted to describe the deosition henomena o the articles in turbulent low. Schwendiman and Postma (96), Wells and Chamberlain (969), iu and Agarwal (974), Friedlander and Johnston (957), Sehmel (968), and Ilori (97) reorted extensive exerimental data or article deosition rate in turbulent duct lows. Wood (98), and Paavergos and Hedley (984) have rovided a reviews o the exerimental results. In summary, the studied concluded that deosition velocity has a V-shaed variation with a minimum at the article relaxation time o about 0. to 0.5 wall units (Chen et al., 997). The rate o article deosition increases as the relaxation time decreases in the diusion regime whereas it increases when the relaxation time increases in the imaction regime. Theories o article deosition rocess were also addressed by many researchers; Fuchs (964), Wood (98), Hidy (984), Paavergos and Hedley (984), and Hinds (999). Semi-emirical correlations or evaluating article deosition rates in turbulent ducts have been roosed by Friedlander and Johnston (957), Davies (966), and Cleaver and Yates (975); however, the exressions are valid or smooth walls. Further rogress in develoing the deosition model was reorted by Fichman et al. (988), Fan and Ahmadi (993, 994), Chen and Ahmadi (997), Shams et al. (000), and Tian and Ahmadi (007). Numerical studies o transort and deosition o articles in turbulence low ield have been conducted as well in the ast ew decades. Among lot o literatures studied such henomena, i and Ahmadi (99, 993) erormed a series o numerical simulations on deosition o small articles in a turbulent channel low. i et al. (994) resented digital simulation results or article deosition rate in an obstructed turbulent duct low. Finally, Tain and Ahmadi (007)

2 8 Esam I. Jassim: Generalized Deosition Model o Tiny Solid Particle Immersed in Turbulent Flow comared dierent comutational models or redicting article deosition in the turbulent duct lows. Most earlier and recent works are conirmed that the deosition velocity has a V-shaed variation; however urther studies are still needed to tune the correlation in such a shae that can be more consistence with the available exerimental data. In this work, a ste towards such tuning is resented through erorming modiication to the model o Fan and Ahmadi (993) in order to enhance the rediction o the deosition rate. Comarison with exerimental data and other recent emirical exressions is also reorted. The article diameter ranging rom nm to 00 µm are studied. The eects o article to low density ratio, ie size and roughness are also addressed. The deosition rates o articles o dierent sizes are evaluated and comared with other models. It is shown that the trend o the roosed model is reasonable and in good agreement with the available exerimental data. Further the model imroves the rediction o article deosition rate articularly in the Brownian regime since it considers the article convection diusion rocess instead o diusion alone.. Particle Motion in Turbulent Flow In an accelerating low ield, articles are not able to ollow erectly the direction o luid motion due to their own mass. For instance, in straight-line accelerating (decelerating) motion, articles lag behind (all ahead) the agrangian luid articles. For sub-micron articles, and in the absence o external orce ields, the Brownian or turbulent diusion is the basic mechanisms that drive deosition. For articles larger than about µm, deosition is rimarily due to inertial imaction and gravitational settling. In this section, the mechanism o the motion o articles susended in a moving luid is briely discussed. The eects associated with the articles own inertia becomes maniested articularly in accelerating luid motion. The mechanisms driving article motion are synonymously called deosition mechanisms as the result o such henomena is to make articles migrate to the bounded suraces and deosit there. Since the diameter o the article is much smaller than the carrier ie radius and its density is much greater than that o the gas low, the article equation o motion in the ully turbulent region can be reduced to an equation consisting only o the drag and gravitational orces (Crowe, 006). The general exression or the drag orce F D on a sherical article in a gas o constant velocity can be written as: C F = ρ ) D D π r g u ug ( u ug () Cc Where, C c is the Cunningham non-continuum correction actor, deined as: λ d C c =.34.05ex d λ () The drag coeicient can be estimated rom the ollowing ormulas deending on the article Reynolds number or: CD C D 4 = Re <0. Re 4 3Re 9Re ln Re 6 60 (3a) ( Re ) = [ 0.5 Re ] 4 C D = ( ) Re < Re <500 C D = < Re <.05 0.< Re < (3b) (3c) (3d) The terminal velocity o a sherical article due to gravitational settling can be obtained rom the ollowing exression (Hinds, 999): u ρ d gcc s = (4) 8µ g The above ormula is valid or any article size since the sli correction has been taken into account and can strictly be used or the Stokes low. However, the ormula is quite accurate over the extended range 0. < Re < (Hinds, 999). Note that the buoyancy eects have been neglected in the ormula since the article density is much more than gas density. Methods to calculate u s at higher article Reynolds numbers are given by Hinds (999): 4 ρ u = s dgcc 3C D ρ Where, C D is the drag coeicient estimated rom the iecewise exressions mentioned earlier (Eqs.3a-d). 3. The Deosition Velocity Analogous to the settling velocity ro deosition by settling, the deosition velocity is the eective velocity with which articles migrate to a surace. The non-dimensional deosition velocity or articles released with undisturbed concentration is given by: V d = C G av Where, G is the article mass lux to the wall and C av the article average concentration above the surace. The latter is usually taken equal to the average concentration over the cross-section o the conduit (Crowe, 006). Numerous correlations or deosition velocity were resented based on exerimental data. A simle exression or nondimensional deosition velocity roosed by Wells and Chamberlain (967) is given as: u (5) (6) V d / 3 /8 = 0.Sc Re (7) u

3 International Journal o Sustainable and Green Energy 04; 3(6-): However this correlation is valid only within submicron. For other regimes, the correction roosed by Friedlander and Johnstone (957) is requently used. The deosition velocity is calculated as ollows: V d U g / / / ( 55 /( S ) 50.6) / where, is the riction actor; and { 5ln [ 5.04 /( S / ) ] 3.73} S ρ = gdρug 8µ g / S < 5 5 S < S The nondimensional deosition velocity has lotted by combining the above iecewise exressions or dierent riction actor as shown in Fig (). It could be concluded that the deosition velocity increases as the riction actor increases. V d /U g S = 0.06 = 0.04 = 0.0 Fig. (). Deosition velocity vs. sto distance or various riction actors (Eqs.7 & 8) Other emirical models are that suggested by Wood (98) and Fan and Ahmadi (993). The latter is modiied in this study to account or low coniguration. The Wood nondimensional deosition velocity is given by: V d (8) (9) Sc / τ τ (0) = g where Sc is the Schmidt number. The nondimensional article relaxation time and the gravitational sedimentation in horizontal low are resectively given by: τu τ = ν ρd u Cc = 8ρ ν (-a) ν = u g 3 g (-b) The irst term in Eq. (0) is resulted rom the Brownian motion and eddy diusion, and the second term is the consequences o article deosition by the eddy diusionimaction mechanism, while the last term stands or the gravitational sedimentation on the lower wall o horizontal ies (Chen and Ahmadi, 997). Fan and Ahmadi roosed an emirical correlation or deosition o articles including the eects o surace roughness and gravity. For horizontal ducts, the exression takes the orm: V d where 0.084Sc = / 3 ( τ 0) / 3 [ 8e ] 0.4 ( 0.64k 0.5d ) τ = ; 3.08 Sd /( τ ) i V d < 0.4 () ρ S = ; du ρ d = (3) ν and k is the surace roughness ( which is zero or smooth surace) Eq.() consists two terms the irst term reresents the eect o the article diusion and is dominated when the article is in the range o submicron while the second term stands or inertia eect. iteratures have demonstrated that the local article deosition relays both on article size and the actual aerodynamic conditions (Browne, 973; Miguel et al, 004; Sosnowski et al., 007). Exerimental results o Miguel et al (004) showed that deosition eiciency is more sensitive to the Reynolds number. Browne (973) studied analytically the inluence o Reynolds number on the deosition velocity o articles. The results o his analysis showed that signiicant variation occurs to the article deosition rate when the low Reynolds number changes articularly or tiny articles. He also concluded that the variation becomes less as the article size increases. The most recent research accomlished by Sosnowski et al (006) ended u with identical conclusion rom their study on the mechanisms o aerosol article deosition. They concluded that the deosition o submicron articles, caused rimarily by Brownian diusion, is strongly inluenced by local aerodynamic eects. In turn, large articles are less sensitive to such variation due to their high inertia. Consequently, it is essential to investigate the signiicance o low Reynolds number that was droed rom the Fan and Ahmadi emirical exression o article deosition. A modiication has alied to the irst term o Eq. () by involving the eect o low coniguration. Wells and Chamberlain correlation, Eq. (7), is a roer ormula that can describe the behaviour o article deosition in the Brownian

4 0 Esam I. Jassim: Generalized Deosition Model o Tiny Solid Particle Immersed in Turbulent Flow region because it takes into account the convective term o diusion which emerges in the Reynolds number. Hence, a new exression combining Fan and Ahmadi and Wells and Chamberlain correlations is ormed and to be studied in this work. The new correlation takes the orm: V d 0.Sc = / 3 / 8 ( τ 0) / 3 [ 8e ] 0.4 Re ( 0.64k 0.5d ) τ /( τ ) i V d < 0.4 (4) Eq.(4) is the exression adoted in this work and will be studied to assess its validity in redicting the rate o article deosition. 4. The Deosition Rate A basic quantity characterizing convective transort o a article is the enetration ratio, or enetration raction, deined as the raction o the inlowing articles that exit the low system. It can be written as: C = (5) out C 0 Where, C out and C 0 are the article concentrations (either mass or number) at the outlet and inlet, resectively. For ully develoed turbulent low in a circular ie o length, the deosition velocity V d may be considered as constant along the tube, and the enetration raction can be exress as (Crowe, 006): 4V = d UgD ex (6) Where, U g is the carrier gas velocity; D is the ie diameter. Alternatively, Collection eiciency can be deined as the raction o the inlowing articles that is lost by deosition: there is however more data or deosition rom aerosols alications. Hence, we do comarison here or article deosition rom turbulent gas streams. The simulation results or articles deosition or turbulent air low in a 40 mm diameter ie with m length and Reynolds number o 5000 based on the ie diameter are resented in this section. Air at 70 K with µ =.0 x 0-5 kg m s -, and ρ =.3 kg m -3 is used in the analysis with the article to air density ratio about 750. The mean ree ath (λ) aeared in Eq. () is 6 nm as was calculated by Maxwell (868). Figure () comares the suggested model with those o earlier studies or horizontal ie. The exerimental data o Kavasnak et al. (993), the numerical simulation results o Tian et al. (007) and Shams et al. (000), and the emirical equations o Friedlander et al. (957), Wood (98) and Fan and Ahmadi (993) are lotted in this igure. The exerimental data and the simulation results show that the deosition velocities have a V-shaed variation. The emirical equation o Friedlander redicts similar trend however the discreancy with the exerimental and numerical results is signiicant. As well, the models o Wood (98) and Fan and Ahmadi (993) are almost constant or tiny articles. In turn, the suggested model gives better trend than Fan and Ahmadi curve and agrees well with the exerimental and numerical results. The modiied model divides the rocess o deosition into three regions, the Brownian dominated region, the inertia dominated region, and the interace region. In the Brownian region, the deosition rate increases with decrease in article size as illustrated in Fig. (3). For large articles, turbulence eddy imaction becomes signiicant and dominates the deosition rocess (Chen and Ahmadi, 997). Hence, the deosition eiciency increases with article size. Both motions are signiicant in the transition regions. For very large articles, the article inertia becomes very large and essentially not inluenced by other orces since the article deosition rate aroaches constant. The tendency o such articles occurs at relaxation time τ >0 as shown in Fig. (3). 4V = = d ex UgD η g (7) The above exression enables the calculation o enetration through knowledge o the deosition velocity. 5. Comarison o the Proosed Model with Exerimental Data and Other Models To areciate the rocess o article deosition redicted by current model, we comared the theoretical redictions o the model against some exerimental data and semiemirical correlations. Although exerimental data or article deosition rom turbulent lows is relatively scarce, Fig. (). Comarison o non-dimensional deosition velocity as redicted by current model and earlier results in horizontal ie.

5 International Journal o Sustainable and Green Energy 04; 3(6-): E-005 E-006 Kvasnak et al. (993) Tian et al. (007) Shams et al. (000) Friedlander et al. (957) Fan & Ahmadi.(993) Wood (98) Present Model E-007 E-006 E τ Fig. (3). Comarison o deosition eiciency evaluated rom current model with the earlier results in horizontal ie. 6. Results and Discussion In this section, inluences o article density, ie size, and ie roughness using the modiied model are discussed. Comarison with revious literatures to assess the rediction o article deosition in a turbulent ie low is rovided as well. 6.. Particle Density relaxation time or two density ratios. The deosition rate shits slightly to let with the decrease o density ratio. This trend is in agreement with that redicted by Chen and Ahmadi (997) and Fan and Ahmadi (993). 6.. Pie Size As stated earlier, ie with 40 mm diameter has been used as the base case in the study. To demonstrate the inluence o the ie size on the rate o article deosition, another ie with diameter o 0 mm is selected. The low Reynolds number is ket constant in this articular analysis while the air velocity is varied. Figure (5) shows the deosition eiciency as a unction o the nondimensional relaxation time or the two ies. The deosition curve shits to the right when the ie size decreases. It imlies that by reducing the size o the carrier ie, the article deosition rate increases in the diusion region as a result o Brownian motion exerienced by the articles. In contrast, the article deosition rocess becomes less eicient or large articles due to high drag orce; however, the drag orce no longer aects the very large articles since the high inertia o such articles dominates the rocess o deosition The eect o article to luid density ratio is resented here. Density ratios o 000 and 000 are comared to igure out the behaviour o deosition rate resonding to article density D ie 0 mm 40 mm E-007E-006E τ Fig. (5). Inluence o ie diameter on the article deosition eiciency Fig. (4). Particle deosition eiciency versus nondimensional article relaxation time or dierent density ratio Figure 4 shows the deosition eiciency as a unction o Due to scarce in literatures concern with the eect o ie size, we comared the results o the model with that redicted by Fan and Ahmadi s correlation. Both results are lotted in Figure (6) so one can easily sight the behaviour o each model. The only discreancy between the models is that lie in the imaction region. The conclusion obtained rom the correlation o Fan and Ahmadi reads that the deosition rate becomes larger or smaller ie size or all regions. This could be returned to the act that articles have tendency to reaches the wall o small ies aster than that o large ies. The conclusion is acceted only i the carrier velocity or both ies is same; however in such case Reynolds number will be dierent and that violates the assumtion mentioned

6 Esam I. Jassim: Generalized Deosition Model o Tiny Solid Particle Immersed in Turbulent Flow earlier which assumed no change in Reynolds number has occurred mm (Fan&Ahmadi) 0mm (Present) 40mm (Fan&Ahmadi) 40mm (Present) E-007E-006E τ Fig. (6). Comarison o deosition eiciency redicted by current model and Fan and Ahmadi model or dierent ie diameters Consequently, the inluence o the carrier gas velocity should be taken into account i we want to describe the rocess o deosition recisely. The modiied model considered such eect by involving the velocity o the carrier luid in the ormula as listed in Eq. (4). The inluence o the air velocity aears in the continuum region through the variation occurs in the drag orce while its eectiveness descends in the diusion region since in this region articles migration is controlled by diusion Surace Roughness V d E-005 k/d=0 k/d=0.00 k/d=0.0 E-007 E-006 E τ Fig. (7). Deosition velocity as a unction o relaxation time at various surace roughnesses Dierent average surace roughness heights are studied ranging rom smooth surace (k=0) to relatively coarse surace (k~% o ie diameter). It is noticed that surace roughness signiicantly alters the deosition velocity curve articularly in the range o interace region. However, the range becomes vast or coarse roughness, as shown in Fig. (7). Browne (973) came u with almost congruent conclusion. He studied the deosition velocity or articles ranging rom 0.0 to 0 µm lows in a.5 cm diameter ie having relative surace roughness (k/d) o 0.00 and the carrier luid was air. His conclusion on the eect o surace roughness showed that very large eect occurred as a result o roughness excet on articles o size larger than ~ 0 microns. Identical conditions were alied to our model to comare the rediction o the velocity deosition using the resent exression. Figure (8) illustrates the inluence o surace roughness when the modiied model is used and one can conclude that the eect o surace roughness ades ater ~ 0 µm which is in very good agreement with the Browne s conclusion. V d E-005 Smooth (k=0) Rough (k=0.00) d (µm) Fig. (8). Deosition velocity redicted by current model as a unction o article size The article deosition rate is remarkably varied with surace roughness. Figure (9) resents the variation o deosition eiciency as a unction o relaxation time or dierent relative roughness. It is clearly shown that the more the coarse ie wall, the higher the deosition rate. In return, the an and Ahmadi model is less sensitive to the roughness, as illustrated in Fig. (0). Although the dierence between the current model, Eq.4, and Fan and Ahmadi model, Eq., did not involve the roughness terms, the article deosition rate redicted by the new model is more reliable as it describes the eect o the wall roughness better than Fan and Ahmadi s model. The urose o this section is to resent the inluence o the surace roughness on article deosition rocess.

7 International Journal o Sustainable and Green Energy 04; 3(6-): k/d E-007 E-006 E τ Fig. (9). Deosition eiciency as a unction o relaxation time redicted by current model at dierent ie roughness 00 0 k/d E-007 E-006 E τ Fig. (0). Deosition eiciency as a unction o relaxation time redicted by Fan and Ahmadi model at dierent ie roughness 7. Conclusion In this work, deosition o articles in a turbulent ie low is studied using modiied correlation o article deosition velocity. The inluence o the gas carrier velocity has been taken into account in the new model and the analysis showed that it is in good agreement with the exerimental data and numerical results. The deosition eiciency o articles o dierent sizes, which may be inerred as a measurement o deosition rate, are evaluated rom the roosed model and comared with other models available in literatures. The eect o density ratio, carrier size and surace roughness are also studied. Based on the resented results, the ollowing conclusions may be derived: Deosition o articles is strongly inluenced by local aerodynamics eects. The deosition velocity and deosition eiciency in turbulent ie low ollows a V-shaed curve. The deosition eiciency increases both with the increase o diameter or large articles, and with the decrease o diameter or submicron articles. Increase in density ratio results in increase in the deosition rate or submicron sizes. Reducing the size o the carrier ie shits the article deosition rate curve to the right. This imlies that or articles controlled by diusion motion, the rate o articles deosit on the ie wall increases as ie size decreases. In turn, the deosition rate decreases when the size o ie decreases. Unlike other semi-emirical models, the current correlation redicts the inluence o surace roughness in excellent agreement with the revious studies. The deosition rate o articles increases in remarkable manner as a results o roughness. Nomenclature C 0 Initial Particle Concentration C de Number o Deosited Particle C c Cunningham correction actor C D Drag Coeicient d Particle diameter (m) D Pie diameter (m) Friction Coeicient Penetration Coeicient g Gravity (m/s ) J lux vector (articles/m /sec) k B Boltizmann Constant Pie length (m) m Mass (kg) n article concentration r Radius o Particle (m) Re Reynolds Number S Sto Distance (m) St Stoke Number Sc Schmidt Number t time (s) T Temerature (K) u Velocity in the (x) direction (m/s) u Friction Velocity (m/s) u s Settling Velocity (m/s) U g Mean gas velocity (m/s) V d Deosition Velocity (m/s) V 0 Initial Velocity (m/s) Greek Symbols ρ Density (kg/m 3 ) µ g Gas dynamic viscosity (N.s/m ) λ g Mean Free Path (m) ν g Gas Kinematics Viscosity (m /s) τ V Relaxation time (s) η g Collection eiciency Г Diusivity (m /s) Subscrits g Gas Particle

8 4 Esam I. Jassim: Generalized Deosition Model o Tiny Solid Particle Immersed in Turbulent Flow Reerences [] Browne,. W. B. (973). Deosition o articles on rough suraces during turbulent gas-low in a ie. Atmosheric Environment, 8, [] Chen, Q. and Ahmadi, G. (997). Deosition o articles in a turbulent ie low. Journal o Aerosol Science, 8, [3] Cleaver, J. W. and Yates, B. (975). A sublayer model or the deosition o articles rom a turbulent low. Chem.Engng Sci. 30, [4] Crowe, C.T. (006). Multihase Flow Handbook. Taylor & Francis Grou, F. [5] Davies, C. N. (966). Aerosol Science. Academic Press, ondon. [6] Fan, F-G. and Ahmadi, G. (993). A sublayer model or turbulent deosition o articles in vertical ducts with smooth and rough suraces. Journal o Aerosol Science, 4, [7] Fan, F.-G. and Ahmadi, G. (994). On the sublayer model or turbulent deosition o aerosol articles in the resence o gravity and electric ields. Aerosol Science Technology,, [8] Fichman, M., Gutinger, C. and Pnueli, D. (988). A model or turbulent deosition o aerosols. Journal o Aerosol Science, 9, [9] Friedlander, S. K. and Johnstone, H. H. (957). Deosition o susended articles rom turbulent gas stream. Industrial and Engineering Chemistry, 49, [0] Fuchs, N. A. (964). The Mechanics o Aerosol. Pergamon, Oxord. [] Hidy, G. M. (984). Aerosols, an Industrial and Environmental Science. Academic Press, New York. [] Hinds, W.C., (999). Aerosol Technology: Proerties, Behaviour, and Measurement o Airborne Particles. nd Edition, Wiley, New York. [3] Ilori, T. A. (97). Turbulent deosition o aerosol articles inside ies. PhD. thesis, University o Minnesota. [4] Kvasnak, W., Ahmadi, G., Bayer, R., & Gaynes, M. (993). Exerimental investigation o dust article deosition in a turbulent channel low. Journal o Aerosol Science, 5, [5] i, A. and Ahmadi, G. (99). Disersion and deosition o sherical articles rom oint sources in a turbulent channel low. Journal o Aerosol Science Technology, 6, [6] i, A. and Ahmadi, G. (993). Deosition o aerosols on suraces in a turbulent channel low. International Journal o Engineering Science, 3, [7] i, A., Ahmadi, G., Bayer, R. G. and Gaynes, M. A. (994). Aerosol article deosition in an obstructed turbulent duct low. Journal o Aerosol Science, 5, 9-. [8] iu, B. Y. H. and Agarwal, J. K. (974). Exerimental observation o aerosol deosition in turbulent lows. Journal o Aerosol Science, 5, [9] Maxwell J. C., (868). On the dynamical theory o gases. Philos. Mag., vol. II, [0] Miguel, A. F., A. F., Reis, A., & Aydin, M. (004). Aerosol article deosition and distribution in biurcating ventilation ducts. Journal o Hazardous Materials, B6, [] Paavergos, P. G. and Hedley, A. B. (984). Particle deosition behavior rom turbulent low. Cheical Engineering Research and Design, 6, [] Schwendiman,. C. and Postma, A. K. (96). Hanord aboratory Reort HW-SA-36, Richland, Washington, U.S.A., also (96) Tech. In. Div. Reort TID-768, Book (USAEC). [3] Sehmel, G. A. (968). Aerosol deosition rom turbulent airstreams in vertical conduits, Batelle Northwest aboratory Reort BNW-578, Richland, Washington, U.S.A. [4] Shams, M., Ahmadi, G., & Rahimzadah, H. (000). A sublayer model or deosition o nano- and micro-articles in turbulent lows. Chemical Engineering Science, 55, [5] Sosnowski, T. R., Moskal, A., & Gradon,. (007). Mechanism o aerosol article deosition in the Oro-Pharynx under non-steady airlow. Annals o Occuational Hygiene, 5, 9-5. [6] Tian,. and Ahmadi, G. (007). Particle deosition in turbulent duct low-comarisons o dierent model redictions. Journal o Aerosol Science, 38, [7] Wells, A.C. and Chamberlain, A.C. (967). Transort o Small Particles to Vertical Suraces. British Journal o Alied Physics, 8, 793. [8] Wells, A. C. and Chamberlain, A. C. (969). Deosition o dust rom turbulent gas streams. Atmosheric Environment, 3, [9] Wood, N. B. (98). A simle method or the calculation o turbulent deosition to smooth and rough suraces. Journal o Aerosol Science,,