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A semiempirical model for particle deposition onto facial skin and eyes. Role of air currents and electric fields
Pergamon
J. Aerosol Sci., Vol. 25, No. 3, pp. 583 593, 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0021-8502/94 $6.00+0.00
0021-8502(94) E0006-J
A S E M I E M P I R I C A L M O D E L FOR PARTICLE D E P O S I T I O N O N T O FACIAL SKIN A N D EYES. ROLE O F AIR CURRENTS AND ELECTRIC FIELDS T. SCHNEIDER,* M. BOHGARDt and A. GUDMUNDSSONt * National Institute of Occupational Health, Lerso Parkalle 105, DK-2100 Copenhagen, Denmark and ) Department of Working Environment, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden (First received 20 August 1993; and in final form 3 January 1994) Ahstract--A semiempirical model has been developed for deposition velocity of particles on the forehead and eyes. It is based on published results of wind tunnel studies of deposition of 2-32/~m airborne particles onto the forehead and realistically-shaped eyes of a manikin. The effects of electric fields and particle charges were included in the model on a purely theoretical basis. The model was used to calculate the combined effects of air currents and electric fields, and it was found that electric fields and particle charges are major determinants for deposition of particles approximately 1/~m in diameter, and air turbulence likely to occur in ventilated rooms is a major determinant for particles larger than 10/~m. The model predicts that deposition of particles from typical indoor environments will be enhanced for persons exposed to electric fields, irrespective of the direction of the field. For a complete characterization, particle concentration, size distribution, mean air velocity, direction and turbulence intensity, electric fields and particle charge distribution should be known. For investigators of exposure to airborne particles and its relation to the office eye syndrome, the model can be used for identifying those parameters which are key for given conditions, thus simplifying the description of exposure. NOMENCLATURE C concentration C~ Cunningham slip correction factor D Brownian diffusion coefficient of particle De, Dep turbulent diffusion coefficient of air and particle, respectively d,, d.= volume equivalent and aerodynamic equivalent diameter, respectively E electric field np number of electron charges 7" turbulence intensity U wind mean velocity U* friction velocity V particle deposition velocity caused by air movements particle deposition velocity caused by electric field riot particle deposition velocity of air movements and electric fields combined VO particle velocity at start of free flight Z distance from surface turbulent boundary layer thickness dynamic shape factor kinematic viscosity of air # dynamic viscosity of air Pp, Po particle unit density O" particle stopping distance particle relaxation time K V
INTRODUCTION T h e facial skin a n d eyes are t a r g e t o r g a n s for p a r t i c u l a t e air c o n t a m i n a n t s . O n c e particles a r e d e p o s i t e d o n the c o r n e a o r the c o n j u n c t i v a , they are r a p i d l y e n c l o s e d in m u c o u s fibrils d u r i n g b l i n k i n g . T h e b l i n k i n g g r a d u a l l y causes these fibrils to a d h e r e to the m u c o u s t h r e a d w h i c h is a l w a y s p r e s e n t i n the l o w e r c o n j u n c t i v a l fornix of n o r m a l eyes. D u r i n g b l i n k i n g , the m u c o u s t h r e a d m o v e s t o w a r d s the i n n e r c o r n e r of the eye a n d f u r t h e r o n to the skin, w h e r e it dries to b e c o m e "sleepy seeds". T h e target o r g a n dose, w h i c h in this case is the a m o u n t of i n s o l u b l e particles p r e s e n t o n the eye surface, is d e t e r m i n e d b y the d e p o s i t i o n a n d c l e a r a n c e rates. 583
584
T. SCHNEIDER et al.
Subjective and objective eye symptoms and effects have been reported in several studies. As an example, handling of man-made mineral fibre ( M M M F ) insulation wool caused accumulation of non-respirable fibres in the eyes, where they could cause microepithelial defects (Stokholm et al., 1982). It has been shown that reduced tear film stability is related to the occurrence of office eye syndrome, and it was hypothesized that tear film stability may be reduced by particles and particle bound surfactants (Franck and Skov, 1989). Vincent and Gibson (1980) defined "fly-dust" as airborne coarse dust which can cause irritation on impact with skin and the eye. Their experiments covered wind speeds ranging between 200 and 700 cm s-1 and median particle diameters ranging between 25 and 175 ktm. They determined subjective response thresholds as a function of Stokes number, but not deposition velocities. Gibson and Vincent (1980) determined the impaction of dust onto eyes of coal mine workers. Dust was sampled from the corner of the eyes by sterile cotton swabs. A dummy head was also exposed. The eyes consisted of realistically-profiled, adhesive-coated, demountable plastic inserts. They found an apparent reduction in particle size in the human eyes compared to what was found in the eyes of the dummy and in the air. The authors showed that the reduction in particle size for the living subject exposed to short "burst releases", as compared to the unblinking dummy, is caused by the blinking response caused by the first sufficiently large particle to hit the eye. From their data, a size-dependent deposition velocity cannot be determined. Schneider and Stokholm (1981) measured the accumulation rate of M M M F in the eyes in relation to the airborne fibre concentration, and found that sampling efficiency of the eyes increased with increasing fibre diameters. These deposition rates will be discussed later. Measurements have shown that particle deposition onto the human head may be increased by electric fields (Wedberg, 1986), but no particle size dependence was given. A model for particle size dependent deposition velocity, including effects of electric fields is thus needed. By analogy to inhalation of particles, this model corresponds to a lung deposition model, which provides the link between airborne particle concentration and the dose delivered to the target organ. E X P E R I M E N T A L DATA Deposition velocities of particles onto the forehead and eyes of a manikin in a wind tunnel have been determined by Gudmundsson et al. (1992, 1993). The test particles were graded aluminum oxide, density 3.84 gem -3 (F500, Washington Mills Electro Minerals Limited, Manchester, U.K.) covering the size range 2-32 #m. Average wind velocity, u, was set at 50 and 100 cm s- ~. The manikin blocked 30% of the 100 x 100 c m 2 tunnel crosssection. The head was upright and was oriented at 0 ° (eyes facing wind), 90 ° and 180 ° relative to the wind direction. Two turbulence intensities were used: 1.3%, obtained by honeycomb flow straighteners followed by a wire mesh, and 19%, generated by a grid, placed 17 cm upstream of the manikin. This free stream turbulence intensity was measured at a distance corresponding to the position of the forehead, and decreased to 10% at a distance corresponding to the back of the head. For comparison, turbulence intensities at 50 cm s- 1 mean air velocity, 110 cm above floor, are of the order of 20% for unventilated and 30% for ventilated spaces (Melikov, 1988). The eye surface was simulated by covering eye prosthesis with gelatine foils (fingerprint lifters). A piece of gelatine foil was also placed on the forehead. The dimensions of the eyes were: diameter of eyeball 24 mm, radius of curvature of cornea 7.8 mm, maximum opening of eyelids about 7 mm. The exposed surface of the eyes was 1.8 c m 2 for the left, and 1.2 c m 2 for the right eye. Eyelashes for cosmetic use were mounted on the upper and lower eyelids. The gelatine foils could be deformed to cover the eye smoothly, and could be mounted flat on the microscope slide after removal. The collected particles were analyzed by optical microscopy with automated image analysis (Gudmundsson et al., 1993). The lower limit of projected area equivalent diameter measurement was 2 ~m. Diameter determination was calibrated against the diameter of aerodynamically-equivalent spheres (Gudmundsson et al., 1991). The airborne particle size specific concentration was sampled through an isokinetic probe and analyzed by an Aerodynamic
Particle deposition onto facial skin and eyes
585
Table 1. Experimental deposition velocities (averages over several runs) taken from Gudmundsson et al. (1993)(cm s-1). T= turbulence intensity Orientation Turbulence intensity
0° 1.3%
0° 19%
90° 1.3%
180° 1.3%
da,(#m)
Forehead
2.7 4.7 7.9 12.9 20.5 28.7
0.074 0.12 0.11 0.15 0.21 0.24
o. 14 0.21 0.21 0.41 0.87 0.98
0.05 0.08 0.08 0.17 0.28 0.47
0.06 0.09 0.12 0.22 0.48 0.85
Eyes
2.7 4.7 7.9 12.9 20.5 28.7
0.017 0.024 0.029 0.040 0.050 0.050
0.033 0.043 0.034 0.10 0.22 0.27
-------
0.006 0,009 0.009 0.004 0.006 0.010
Particle Sizer (TSI). The results were corrected for internal wall losses. F o r the present work, the data which were averaged over several runs, shown in Table 1, were used. The data for a wind velocity of 50 cm s-1 were considered less reliable and were not used. F o r a discussion of the experimental uncertainties, see G u d m u n d s s o n et al. (1993). MODEL The particle transport from the turbulent free stream to the forehead and eye will be described as a two step process. (1) At distances greater than the thickness, 6, of the turbulent b o u n d a r y layer, the transport process is approximated by the model of impaction onto a sphere of diameter 20 cm. Since wind velocity u < 100 cm s - 1, and dae < 30/~m, the Stokes n u m b e r is less than 0.03. I m p a c t i o n thus will be neglected. Particle drift velocity, vc, caused by electrostatic forces is neglected. Concentrations and air flow fields outside the b o u n d a r y layer thus are approximated by the free stream conditions. Only stationary conditions are considered. (2) The particle transport across the turbulent b o u n d a r y layer is described by the combined effect of electric drift velocity and Brownian and turbulent diffusion. The electric field is assumed to be uniform across the local area represented by the exposed area of the eye and the sampling foil on the forehead. The surface is assumed to be smooth, and to be a perfect sink. Gravity is not considered separately for the following reasons. First, the model is intended to cover deposition o n t o vertical surfaces, the curvature of the forehead and eye being neglected. Second, gravity can in principle be included in the model to be described, by vector addition of electric and gravitational forces acting on the particle. Given these assumptions, the flux, J, of particles to the surface is then described by the steady state diffusion equation dC+
J=-(D+Dep)~-~z
ilvelC,
(1)
where C is the particle concentration, D, Dep are the Brownian and turbulent diffusivity of particle, respectively, z is the positive distance from surface and i is + 1 if repulsion, - 1 if attraction. N o assumptions have yet been made regarding the relation between D~v and air turbulent diffusivity D,. Equation (1) does not include image forces. The particle relaxation time r is
pvd2~C~(d,) z-
18/~x
pod~,C~(da,) -
18~u
'
(2)
T. SCHNEIDER et
586
al.
where dr, dac are the volume equivalent and aerodynamic equivalent diameter, respectively, Pp, P0 are the particle density and unit density, respectively, C~ is the Cunningham slip correction factor, p is the dynamic viscosity of air and x is the dynamic shape factor. Mark et al. (1985) determined x for the same type of aluminum oxide test dust, and found on average r = 1.24 for various sized powders. With a density of 3.84 g c m - 3, one then gets the relation d~,= 1.8dv, where dv is the volume equivalent diameter of the (compact) particles. The turbulent transport process can be formulated in dimensionless terms by introducing the friction velocity, which is u*
= Xf~a'
(3)
where fo is the wall shear stress and p. is the density of air. The dimensionless parameters are then deposition velocity
V + =- U / U *
relaxation time
"C+ = "~(U* ) 2 / V
distance from surface
Z + : ZU*/V
stopping distance
(7 + = (7It*/~
Brownian diffusion particle turbulent diffusion
D + =O/v + D~p = D~p/v
concentration
C + = C/C~.
boundary layer thickness
6 + = 6u*/v.
The dimensionless version of equation (1) then becomes v + = - ( D + +D~p) dC+ dz + +iv + C +,
(4)
which can be solved by separation of variables: fc
dC+
+~,+)v+ + i v + C +
- ~ '
dz+
. D+ +D~p
.
(5)
The sign convention for v + has been changed to make v + positive for flux towards the surface. According to these assumptions, the concentration outside the turbulent boundary layer 3 + is equal to the free stream concentration Coo(C~ = 1). In the following it will be assumed that particle and air turbulent diffusion are equal (D~v=D~). This assumption will be discussed later. Several models for D~ have been proposed in the literature. A simple relation is based on Prandtl's mixing length expression near a surface (Corner and Pendlebury, 1951) D~(z) = k~z"
(6)
for z < 3, and with n = 2. k, is a constant depending on the flow field. Since then, several authors have used this expression to model homogeneous turbulent flow in an enclosure. Crump and Seinfeld (1981) extended the model to include n =m, and Shimada et al. (1987) included surface roughness, while using n = 2.7. In the present model, n = 2 is chosen, and this choice is to be discussed later. This implies that the constant ks has the dimension [s- 1], and k+ = k,v/(u*) 2. A crucial step in the model is to give a physical interpretation of the lower limit of integration, a +. At distances z + > a +, there will be both in- and outgoing flux caused by the turbulent motion of the air. At z + =(7+, the outgoing component of the particle flux has approached zero. For inertialess particles (7+= 0 (Crump and Seinfeld, 1981). Friedlander and Johnstone (1957) proposed the free flight model to include particle inertia. In this
Particle deposition onto facialskin and eyes
587
model, there is a remaining ingoing flux at distance a +, caused by particles which detach from the turbulent eddies and continue by free flight to the surface. Then the free flight distance is equal to the stopping distance a + and given by a + = v~"T+,
(7)
where v~" is the inward velocity of the particle imparted by the turbulent motion close to the surface (in the absence of electric or other fields). Particles only have to reach within one particle radius, d+/2 of the surface, and this distance must be added to the stopping distance. This was done in the numerical calculations, but since the results showed that d+/2 ~ a + for the present conditions, this has been omitted in the equations for simplicity. In the stationary case, the particle flux J is independent of z, thus
J = vC~ = VoC(a)
(8)
v + =v~C+(a+).
(9)
from which The solution of equation (5) is, for v+ = 0 /)+ =
1-C+(a
+)
(10)
l+(a +, 3 +)
Elimination of C+(a +) by use of equation (9), leads to the final result v+ -
1
(11)
T+
tr+ ~-l+(a+, 6+) where the integral I + is given by l+(a+,6+) =
+ dz + _ 1 - t a n - 1+ + D+ +k+(z+) 2 -x/k+D
f[
~
1
( x / +~]/ D~-~-~+(6 + )2 ) k+
tan-X (ff~-~-(a+) z )
_~ ~ - tan -
(12) x/~+D +
The approximation in equation (12) is valid for k+ (6 + )2/D + ~ 1, or D+ (6 +) >>D +, i.e. at the outer part of the boundary layer turbulent diffusion dominates over Brownian diffusion (see also Crump and Seinfeld, 1981). For a non-vanishing electric drift velocity, vc, normal to the surface, the resulting total + deposition velocity Vtot is
+
iv[
Vtot= exp (iv+ I +(a +, 6 + ) ) - 1
(1 -C+(tr+)exp(iv+I+(a+, 6+)))
(13)
and by again eliminating C + (a +) the final result is obtained +
/)tot =
iv +
,
(14)
( l +r~---4iv+ ) exp(iv+ l+ (a +,6+))-- I where i = + 1 for repulsion and i = - 1 for attraction. Equation (14) can be extended to cover force fields which are not normal to the surface, e.g. inclusion of gravity, by substituting i = cos (®), where (9 = n if the deposition velocity vector is towards and normal to the surface (see e.g. Shimada et al. (1989)). Some approximations will now be made to simplify equations (11), (12) and (14). The integral, equation (12), can be simplified by series expansion of tan- x (x) = n / 2 - l / x - . . . ,
588
T. SCHNEIDERet al.
giving
I +(~+,`5+)~_k+ ~
to+) 2,> 1 •.
(15)
The following approximation will hold if either r+/o + 4~1+(a +, ,5+), or the approximation, equation (15) holds, in conjunction with r + ,~ l/k~" 1 v + -
-
-
(16)
I+(a+,`5+)"
If furthermore the relation v+ < v + holds, equation (14) reduces to
• +
+
lUe
[ i~,; )
Utot --
exp \ v ~
117) - 1
Until now, no assumptions have been made regarding the dependence of o + on particle relaxation time and air turbulent diffusivity. We will use the empirical relation o + = 1.49(r +) °'51
(18)
determined by Sehmel (1970) for particles ranging 0 . t < r + < 1000 for turbulent flow in vertical tubes. This relation was determined by fitting a deposition model to experimental data, and that turbulent diffusivity for turbulent tube flow was given by (Lin et al., 1953) D ~+= f "+
z + ~<5
13
(a) (19)
D+ = 5 - 0 . 9 5 9
5
(b).
Equation (18) was obtained assuming D~p = D~. According to Sehmel (1970), equation 18 thus should be used to predict the free flight velocity, when assuming D~p=D~. In the present model the additional assumption is made that equation (18) also holds when D, is given by equation (6), and not by equation (19). In order to complete the model, the parameters k + and u* must be determined. Fluid mechanical computation of u* was not attempted. Instead, the parameters were found by a fitting procedure. First, equations (2), (15), (16) and (18) were combined to give
c=a.k2.d~;°2.(u*t 2°2
a = 1.49 l-~m' )
'
(20)
neglecting Cunningham's correction, since for all experimental data, d,e > 2 #m. It is seen that the unknown parameters k+ and u* in this equation are coupled via the product k[ (u*) TM. Thus, their absolute values cannot be determined solely from the experimental data. This problem was overcome by calculating u* for one set of experimental conditions by using the following approach. For homogeneous turbulent flow in an enclosed vessel, Shimada et al. (1989) found that the following relation was a good approximation: u* = ~
1
URMS,
121 )
where uRm is the root mean square value of air velocity fluctuations. Thus, 1
u*=~-~ T.u, where T is the turbulence intensity.
where
T=URMSu100%,
(22)
Particle deposition onto facial skin and eyes
589
This equation was used to calculate u* for the experimental condition high turbulence (19%) and orientation 0 °. For these conditions, u* = 30 (cm s - 1), and this value was used in the remaining calculations. All in all, there were seven sets of external conditions (u*, j = 1. . . . . 7), and six different diameters (dae p, p = 1. . . . . 6), Table 1. The fitting was then done by minimizing 6
7
SSE = E
Z Lvpj-" . + . 1aae . o 2p , [Uj,, ) .o212 age ..I
(23)
p = l j = l
in a two-step procedure, using the M I N E R R routine of M A T H C A D (1991). vpi are the experimental data given in Table 1. First, an initial value of k~+ was chosen, then the u* determined by minimization. With these values of u*, a new value of k~+ was found by minimization, etc. This procedure gave k + = = 0.0059 and the values for u* in Table 2. The experimental data, non-dimensionalized by the corresponding values of k~+ and u*, are shown in Fig. 1. The model prediction, using equation (11) is also shown. Having determined all parameters in the model it is now possible to explore the range of particle diameters, within which the approximations (15) and (16) are valid for the range of experimental conditions. With these values, approximation (15) holds for D --,~0.013(u*) 2 z
(24)
and thus for d,e > 2 #m for u* = 3.2 cm s - 1, and for d~ > 0.5/tin for u* = 30 cm s - 1. Equation (16) approximates equation (11) to within ___5% for 2.5 #m < d~ < 30/~m. Figure 2 shows the model fits to the experimental data from Table 1. Finally, the model will be used to predict the effect of a homogeneous electric field. The migration velocity v, in a homogeneous electric field is given by v~(dr,,) = n p e E C c ( d m ) 3rr~xdm '
(25)
where np is the number of electron charges, e is the electron charge and E is the electric field.
Table 2. Fitted values of friction velocity u* (cm s-1) Orientation turbulence intensity
0° 1.3%
0° 19%
90° 1.3%
180° 1.3%
Forehead Eye
16 7.5
30 15
19 --
26 3.2
0.1
0.01 o
-Io
o
o
o o o
o o
0.001 ~Ii*-3.2
1 E-4 0.001
0.01
0.1
1
10
100
Fig. 1. Non-dimensionalized deposition velocitydata with model (solid line).
590
T. SCHNEIDER et al.
(a)
1 I
- ~
i'~ ~7~-I~ '
o.1
O.Ol I
~\,A
*
1~.3%
~\+ 'D
1.3% 0 ° 1.3%
90 °
0.001
10 Dae, pm
100
(b) X
MMMF
0.1 ~E
.--~x x ~
i oo 1 9 ~o " / []
O
>0.01
o t.3~ ±
0.001
lSO o 1.3~ 1
~
~-.
~
~
[]
• ~
~-~ 10
100
Dae, pm Fig. 2. Experimental deposition velocities and model predictions. (a) Forehead; (b) eyes. M M M F : measurements at work place during handling of man-made mineral fibre products calculated from data given by Schneider and Stokholm (1981)
In order to explore the relative contribution of electric fields to the overall deposition velocity in absence of the experimental data, the range of particle charges and electric fields encountered in industrial and indoor environment settings must be estimated from other data. Most industrial aerosols will carry both negative and positive charges. The degree of charging can be expressed in terms of the median of the number of charges, irrespective of sign, carried by particles of given aerodynamic diameter dae (Vincent, 1986):
Inplm= ad,~,
(26)
where da= is in #m and A and N are constants. For workplaces, A ranges from 2 to 50, and N ranges from 0.7 to 1.9. The magnitude and sign of the electric fields at the forehead can be estimated from the following. Measurements on a manikin head, placed in front of a 21 x 28 cmz metal screen gave the expressions in Table 3 for the electric field E as a function of distance between head and screen, screen surface potential Us and manikin potential Uh (Norberg, 1986). Us may reach + 20,000, V (Skotte, 1988). G6the et al. (1989) found that Uh ranged between - 3 8 0 0 and + 1800 V. Emax corresponding to these values is also shown in Table 3. There are as yet
Table 3. Electric fields at forehead of manikin head placed in front of a screen (Norberg, 1986). Positive E: attraction, negative E: repulsion of positive particles to forehead Distance
Electric field (Vcm -1)
Em,,(V cm -1)
Emin(V c m - 1 ) (U~=0)
30 cm 40 cm 50 cm
E=0.033 U s - 0 . 1 0 4 Uh E = 0.024 Us -- 0.098 Uh E=0.018 U~-0.095 Uh
1060 850 720
-- 190 -- 175 -- 170
Particle deposition onto facial skin and eyes
591
1
oE 0.1
0.01
. . . . . . i
~ 10 Dae, IJm i
i
..... i
i
100
Fig. 3. Modelpredictionof deposition velocityon forehead,turbulenceintensity1.3% and orientation 0°. Effectof electric fieldsfor deposition of unit density,spherical particleswith median charge given by equation (26),and with half of the particlescarryingpositive,half carryingnegativecharge (net charge-neutral).
no data for the reduction of the electric field on the surface of the eye, as compared with the forehead, but theoretical work is in progress. The effect of electric fields and particle charging is illustrated by calculating the total deposition velocity onto the forehead for a net charge neutral aerosol. The particles are assumed to be spherical and having density 1 g cm-3. The net charge neutral aerosol is simulated by the simple case, where 50% of particles of each diameter carry a positive and 50% a negative charge, and with Inp]= 10d ~. The result is shown in Fig. 3. DISCUSSION The model predicts the diameter dependence of the experimental data well, Figs 1 and 2. Use of n=2.7 (a value used by Shimada et al. (1987) for a stirred tank) gave a steeper, and equation (19) a still steeper, diameter dependence. One of the key elements in the model is the friction velocity (Table 2). It is physically plausible that a reduction in turbulence intensity from 19% to 1.3% reduces u*. However, the observed factor of 2 for both forehead and eyes is much less than the factor 15 predicted by equation (22). It is not easily understood that the deposition velocity increases from orientation 0 ° to 90 °. For very small particles at least, where the mass transfer can be described by Brownian diffusion, the analogy between mass and heat transfer can be used (Liu and Ahn, 1987). Heat transfer of cylinders in cross flow has been studied extensively (Zukauskas and Ziugzda, 1975). The results show a decrease in local heat transfer when going from the front stagnation point to 700-90 °, followed by an increase. Deposition velocities measured for orientation 180 ° were larger than for orientation 90 ° as expected from the analogy to heat transfer, but exceeded the deposition velocity for 0 °. Kim and Flynn (1991) have shown that a zone of backstreaming air extends to 15 cm from the nose as measured at 7% turbulence, and very little dependent on mean air velocity. Vincent and Humphries (1978) have argued that the concentration Cw inside such a wake is less than the free stream concentration C~ and that Cw/C~ decreases with increasing particle Stokes number. Since Coo was measured outside the wake, this could explain the reduced diameter dependence of the deposition velocity, but would also predict a reduced deposition velocity at 180° compared with 0 °. Deposition on the eye was not uniform, and was highest on the cornea. It is physically plausible that a protrusion (cornea) in the centre of a retraction (eye surface, relative to face) produces this effect. In the model, deposition velocity is calculated as an average over the exposed surface. In this way, deposition velocities were normalized to the same area. A statistical test showed that there was no difference for deposition velocity to left and right eye for 0 ° orientation. This means that within the range of exposed area (1.2-1.8 cm2), deposition is proportional to the exposed area. AS 25:3-K
592
T. SCHNEIDERet al.
The model structure and parameter values are only preliminary and need to be confirmed by more extensive experiments, including a range of air velocities. Figure 3 shows that for net charge-neutral aerosols, the effect of an electric field will always be to increase deposition. A person working in a high field, e.g. as generated from a poorly-shielded CRT-screen, will always experience an increased particle deposition onto facial skin and eyes. At the same time, deposition will also be increased on the VDU screen. It can be concluded that electric fields dominate deposition for diameters around 1 #m, that the exact shape of the charge distribution affects deposition for larger particles, and that turbulence (Fig. 2) will be dominating, except for extreme fields and charges, for d > 10 #m. However, experiments should be carried out to confirm these predictions. Charging of aerosol and manikin had not been completely eliminated, and the effect was measured for eye deposition at 0 °, turbulence intensity 1.3% (Gudmundsson et al., 1993). Calculations with the above model indicate that charging would not have affected the values of u* >30 cm s-1, have some effect for u*~ 15 cm s-1, and be considerable for u*< 7 cm s-1. Even weak electric fields (1 V cm-1) swamp deposition due to image forces for stagnation flow onto a horizontal plate, and in the absence of electric fields image forces would be most important for particles in the range 0.1-1 #m (Turner et al., 1989). In the derivation of equation (14) it was assumed that the free flight distance was not changed when an electric field is present• It is to be expected that if ve ~ v0, this change will be negligible. For the values of u* given in Table 2, and for the aerosol charge distributions given in Fig. 3, it is found that the condition ve <0.1 Vo is fulfilled for 0.1
(27)
N/Po
where d I is the fibre diameter, l is the fibre length and Pl is the fibre density. Figure 2b shows that the order of magnitude and the slope agrees well with the wind tunnel data. In summary, the model shows that variations in particle charge, electric fields and turbulence could have a larger effect on the particle accumulation rate in the eyes and on the skin than have typical variations in indoor aerosol concentrations. For investigations of exposure to airborne particles and its relation to the office eye syndrome, the model can be used for identifying those parameters which are key for given conditions, thus simplifying the description of exposure. Acknowledgement--This work has been supported by the Danish Work EnvironmentFoundation,grant 1990-03.
Particle deposition onto facial skin and eyes
593
REFERENCES Corner, J. and Pendlebury, E. D. (1951) The coagulation and deposition of a stirred aerosol. Proc. Phys. Soc. London B64, 645. Crump, J. G. and Seinfeld, J. H. (1981) Turbulent deposition and gravitational sedimentation of an aerosol in a vessel of arbitrary shape. J. Aerosol Sci. 12, 405. Dunnett, S. J. and Ingham, D. B. (1988) An empirical model for the aspiration efficiencies of blunt aerosol samplers orientated at an angle to the oncoming flow. Aerosol Sci. Technol. 8, 245. Francl/, C. and Skov, P, (1989) Foam and inner eye canthus in office workers, compared with an average Danish population as control group. Acta Ophthalmol. 67, 61. Friedlander, S. K. and Johnstone, H. F. (1957) Deposition of suspended particles from turbulent gas streams. Ind. Eng. Chem. 49, 1151. Gibson, H. and Vincent, J. H. (1980) On the impaction of airborne coarse dust into the eyes of human subjects. Ann. Occup. Hyg. 23, 35. Gordon, G. (1951) Observations upon the movement of the eyelids. Brit. J. Ophthalmol. 35, 339. G6tbe, C.-J., Ancker, K., Bjurstr6m, R., Holm, S. and Langworth, S. (1989) Electric potential difference against the surroundings and discomfort in indoor environment. Ann. Occup. Hyg. 33, 263. Gudmundsson, A., Petersen, O. H., Schneider, T. and Bohgard, M. (1991) Particle size calibration between the aerodynamic particle sizer and optical microscope for wind tunnel studies with particles of fused alumina. J. Aerosol Sci. 22 suppl. I, $347. Gudmundsson, A., Schneider, T., Petersen, O. H., Vinzents, P. S., Bohgard, M. and Akseisson, K. R. (1992) Determination of particle deposition velocity onto the human eye. J. Aerosol Sci. 23 Suppl. 1, $563. Gudmundsson, A., Schneider, T., Petersen, O. H., Vinzents, P. S., Bohgard, M. and Akselsson, K. R. (1993) Experimentell best~imning av luftburna partiklars deposition p~ ytan av 6gon (in Swedish). Lund University report, LUNDD/TMAT-93/3005 + 76. Kim, T. and Flynn, M. R. (1991) Airflow pattern around a worker in a uniform freestream. Am. Ind. Hyg. Assoc. J. 52, 287. Lin, C. S,, Moulton, R. W. and Pytnam, G. L. (1953) Mass transfer between solid walls and fluid streams. Ind. Eng. Chem. 645, 636. Liu, B. Y. H. and Ahn, K. (1987) Particle deposition on semiconductor wafers. Aerosol Sci. Technol. 6, 215. Mark, D., Vincent, J. H., Gibson, H. and Wiberspoon, W. A, (1985) Application of closely graded powders of fused almunia as test dusts for aerosol studies. J. Aerosol Sci. 16, 125. MATHCAD (1991) MathSoft Inc., Cambridge, Massachusetts, U.S.A. Melikov, A. K. (1988) Quantifying draft risks. Technical Review No. 2. Brfiel & Kjaer, N~erum, Denmark. Norberg, A. (1986) Electrostatic environment around VDU's (Elektrostatisk milj6 vid bildsk~irmar). Uppsala University, Uppsala. Schneider, T. (1987) Mass concentration of airborne man-made mineral fibres. Ann. Occup. HyO. 31, 211. Schneider, T. and Stokholm, J. (1981) Accumulation of fibres in the eyes of workers handling man-made mineral fibres. Scand. J. Work Envir. HIth 7, 271. Sehmel, G. A. (1970) Particle deposition from turbulent air flow. J. geophys. Res. 75, 1766. Shimada, M., Okuyama, K. and Kousaka, Y. (1989) Influence of particle inertia on aerosol deposition in a stirred turbulent flow field. J. Aerosol Sci. 20, 419. Shimada, M., Okuyama, K., Kousaka, Y. and Ohshima, K. (1987) Turbulent and Brownian diffusive deposition of aerosol particles onto a rough wall. J. Chem. Eng. Jpn 20, 57. Skotte, J. (1988) Low-frequency Fields from VDU Screens (Lavfrekvente felter red dataskcerme) (in Danish with English summary). Arbejdsmiljofondet, Copenhagen. Stokhoim, J., Norn, M. and Schneider, T. (1982) Ophthalmologic effects of man-made mineral fibers. Scand. J. Work Envir. Hlth 8, 185. Turner, J. R., Liguras, D. K. and Fissan, H. J. (1989) Clean room application of particle deposition from stagnation flow: electrostatic effects. J. Aerosol Sci. 20, 403. Vincent, J. H. (1986) Industrial hygiene implications of the static electrification of workplace aerosols. J. Electrostat. 18, 113. Vincent, J. H. and Gibson, H. (1980) The responses of human subjects to the facial impaction of airborne coarse dust. Atmos. Envir. 14, 473. Vincent, J. H. and Humphries, W. (1978) The collection of airborne dusts by bluff bodies. Chem. Eng. Sci. 33, 1147. Wedberg, W. C. (1986) The influence of static electricity on aerosol deposition in indoor environments. In Aerosols: Formation and Reactivity 2nd Int. Aerosol Conf. Berlin, pp. 793-795. Pergamon Press, Oxford. Zukauskas, A. and Ziugzda, J. (1975) Heart Transfer of a Cylinder in Crossflow. Hemisphere, New York.
J. Aerosol Sci., Vol. 25, No. 3, pp. 583 593, 1994 Copyright © 1994 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0021-8502/94 $6.00+0.00
0021-8502(94) E0006-J
A S E M I E M P I R I C A L M O D E L FOR PARTICLE D E P O S I T I O N O N T O FACIAL SKIN A N D EYES. ROLE O F AIR CURRENTS AND ELECTRIC FIELDS T. SCHNEIDER,* M. BOHGARDt and A. GUDMUNDSSONt * National Institute of Occupational Health, Lerso Parkalle 105, DK-2100 Copenhagen, Denmark and ) Department of Working Environment, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden (First received 20 August 1993; and in final form 3 January 1994) Ahstract--A semiempirical model has been developed for deposition velocity of particles on the forehead and eyes. It is based on published results of wind tunnel studies of deposition of 2-32/~m airborne particles onto the forehead and realistically-shaped eyes of a manikin. The effects of electric fields and particle charges were included in the model on a purely theoretical basis. The model was used to calculate the combined effects of air currents and electric fields, and it was found that electric fields and particle charges are major determinants for deposition of particles approximately 1/~m in diameter, and air turbulence likely to occur in ventilated rooms is a major determinant for particles larger than 10/~m. The model predicts that deposition of particles from typical indoor environments will be enhanced for persons exposed to electric fields, irrespective of the direction of the field. For a complete characterization, particle concentration, size distribution, mean air velocity, direction and turbulence intensity, electric fields and particle charge distribution should be known. For investigators of exposure to airborne particles and its relation to the office eye syndrome, the model can be used for identifying those parameters which are key for given conditions, thus simplifying the description of exposure. NOMENCLATURE C concentration C~ Cunningham slip correction factor D Brownian diffusion coefficient of particle De, Dep turbulent diffusion coefficient of air and particle, respectively d,, d.= volume equivalent and aerodynamic equivalent diameter, respectively E electric field np number of electron charges 7" turbulence intensity U wind mean velocity U* friction velocity V particle deposition velocity caused by air movements particle deposition velocity caused by electric field riot particle deposition velocity of air movements and electric fields combined VO particle velocity at start of free flight Z distance from surface turbulent boundary layer thickness dynamic shape factor kinematic viscosity of air # dynamic viscosity of air Pp, Po particle unit density O" particle stopping distance particle relaxation time K V
INTRODUCTION T h e facial skin a n d eyes are t a r g e t o r g a n s for p a r t i c u l a t e air c o n t a m i n a n t s . O n c e particles a r e d e p o s i t e d o n the c o r n e a o r the c o n j u n c t i v a , they are r a p i d l y e n c l o s e d in m u c o u s fibrils d u r i n g b l i n k i n g . T h e b l i n k i n g g r a d u a l l y causes these fibrils to a d h e r e to the m u c o u s t h r e a d w h i c h is a l w a y s p r e s e n t i n the l o w e r c o n j u n c t i v a l fornix of n o r m a l eyes. D u r i n g b l i n k i n g , the m u c o u s t h r e a d m o v e s t o w a r d s the i n n e r c o r n e r of the eye a n d f u r t h e r o n to the skin, w h e r e it dries to b e c o m e "sleepy seeds". T h e target o r g a n dose, w h i c h in this case is the a m o u n t of i n s o l u b l e particles p r e s e n t o n the eye surface, is d e t e r m i n e d b y the d e p o s i t i o n a n d c l e a r a n c e rates. 583
584
T. SCHNEIDER et al.
Subjective and objective eye symptoms and effects have been reported in several studies. As an example, handling of man-made mineral fibre ( M M M F ) insulation wool caused accumulation of non-respirable fibres in the eyes, where they could cause microepithelial defects (Stokholm et al., 1982). It has been shown that reduced tear film stability is related to the occurrence of office eye syndrome, and it was hypothesized that tear film stability may be reduced by particles and particle bound surfactants (Franck and Skov, 1989). Vincent and Gibson (1980) defined "fly-dust" as airborne coarse dust which can cause irritation on impact with skin and the eye. Their experiments covered wind speeds ranging between 200 and 700 cm s-1 and median particle diameters ranging between 25 and 175 ktm. They determined subjective response thresholds as a function of Stokes number, but not deposition velocities. Gibson and Vincent (1980) determined the impaction of dust onto eyes of coal mine workers. Dust was sampled from the corner of the eyes by sterile cotton swabs. A dummy head was also exposed. The eyes consisted of realistically-profiled, adhesive-coated, demountable plastic inserts. They found an apparent reduction in particle size in the human eyes compared to what was found in the eyes of the dummy and in the air. The authors showed that the reduction in particle size for the living subject exposed to short "burst releases", as compared to the unblinking dummy, is caused by the blinking response caused by the first sufficiently large particle to hit the eye. From their data, a size-dependent deposition velocity cannot be determined. Schneider and Stokholm (1981) measured the accumulation rate of M M M F in the eyes in relation to the airborne fibre concentration, and found that sampling efficiency of the eyes increased with increasing fibre diameters. These deposition rates will be discussed later. Measurements have shown that particle deposition onto the human head may be increased by electric fields (Wedberg, 1986), but no particle size dependence was given. A model for particle size dependent deposition velocity, including effects of electric fields is thus needed. By analogy to inhalation of particles, this model corresponds to a lung deposition model, which provides the link between airborne particle concentration and the dose delivered to the target organ. E X P E R I M E N T A L DATA Deposition velocities of particles onto the forehead and eyes of a manikin in a wind tunnel have been determined by Gudmundsson et al. (1992, 1993). The test particles were graded aluminum oxide, density 3.84 gem -3 (F500, Washington Mills Electro Minerals Limited, Manchester, U.K.) covering the size range 2-32 #m. Average wind velocity, u, was set at 50 and 100 cm s- ~. The manikin blocked 30% of the 100 x 100 c m 2 tunnel crosssection. The head was upright and was oriented at 0 ° (eyes facing wind), 90 ° and 180 ° relative to the wind direction. Two turbulence intensities were used: 1.3%, obtained by honeycomb flow straighteners followed by a wire mesh, and 19%, generated by a grid, placed 17 cm upstream of the manikin. This free stream turbulence intensity was measured at a distance corresponding to the position of the forehead, and decreased to 10% at a distance corresponding to the back of the head. For comparison, turbulence intensities at 50 cm s- 1 mean air velocity, 110 cm above floor, are of the order of 20% for unventilated and 30% for ventilated spaces (Melikov, 1988). The eye surface was simulated by covering eye prosthesis with gelatine foils (fingerprint lifters). A piece of gelatine foil was also placed on the forehead. The dimensions of the eyes were: diameter of eyeball 24 mm, radius of curvature of cornea 7.8 mm, maximum opening of eyelids about 7 mm. The exposed surface of the eyes was 1.8 c m 2 for the left, and 1.2 c m 2 for the right eye. Eyelashes for cosmetic use were mounted on the upper and lower eyelids. The gelatine foils could be deformed to cover the eye smoothly, and could be mounted flat on the microscope slide after removal. The collected particles were analyzed by optical microscopy with automated image analysis (Gudmundsson et al., 1993). The lower limit of projected area equivalent diameter measurement was 2 ~m. Diameter determination was calibrated against the diameter of aerodynamically-equivalent spheres (Gudmundsson et al., 1991). The airborne particle size specific concentration was sampled through an isokinetic probe and analyzed by an Aerodynamic
Particle deposition onto facial skin and eyes
585
Table 1. Experimental deposition velocities (averages over several runs) taken from Gudmundsson et al. (1993)(cm s-1). T= turbulence intensity Orientation Turbulence intensity
0° 1.3%
0° 19%
90° 1.3%
180° 1.3%
da,(#m)
Forehead
2.7 4.7 7.9 12.9 20.5 28.7
0.074 0.12 0.11 0.15 0.21 0.24
o. 14 0.21 0.21 0.41 0.87 0.98
0.05 0.08 0.08 0.17 0.28 0.47
0.06 0.09 0.12 0.22 0.48 0.85
Eyes
2.7 4.7 7.9 12.9 20.5 28.7
0.017 0.024 0.029 0.040 0.050 0.050
0.033 0.043 0.034 0.10 0.22 0.27
-------
0.006 0,009 0.009 0.004 0.006 0.010
Particle Sizer (TSI). The results were corrected for internal wall losses. F o r the present work, the data which were averaged over several runs, shown in Table 1, were used. The data for a wind velocity of 50 cm s-1 were considered less reliable and were not used. F o r a discussion of the experimental uncertainties, see G u d m u n d s s o n et al. (1993). MODEL The particle transport from the turbulent free stream to the forehead and eye will be described as a two step process. (1) At distances greater than the thickness, 6, of the turbulent b o u n d a r y layer, the transport process is approximated by the model of impaction onto a sphere of diameter 20 cm. Since wind velocity u < 100 cm s - 1, and dae < 30/~m, the Stokes n u m b e r is less than 0.03. I m p a c t i o n thus will be neglected. Particle drift velocity, vc, caused by electrostatic forces is neglected. Concentrations and air flow fields outside the b o u n d a r y layer thus are approximated by the free stream conditions. Only stationary conditions are considered. (2) The particle transport across the turbulent b o u n d a r y layer is described by the combined effect of electric drift velocity and Brownian and turbulent diffusion. The electric field is assumed to be uniform across the local area represented by the exposed area of the eye and the sampling foil on the forehead. The surface is assumed to be smooth, and to be a perfect sink. Gravity is not considered separately for the following reasons. First, the model is intended to cover deposition o n t o vertical surfaces, the curvature of the forehead and eye being neglected. Second, gravity can in principle be included in the model to be described, by vector addition of electric and gravitational forces acting on the particle. Given these assumptions, the flux, J, of particles to the surface is then described by the steady state diffusion equation dC+
J=-(D+Dep)~-~z
ilvelC,
(1)
where C is the particle concentration, D, Dep are the Brownian and turbulent diffusivity of particle, respectively, z is the positive distance from surface and i is + 1 if repulsion, - 1 if attraction. N o assumptions have yet been made regarding the relation between D~v and air turbulent diffusivity D,. Equation (1) does not include image forces. The particle relaxation time r is
pvd2~C~(d,) z-
18/~x
pod~,C~(da,) -
18~u
'
(2)
T. SCHNEIDER et
586
al.
where dr, dac are the volume equivalent and aerodynamic equivalent diameter, respectively, Pp, P0 are the particle density and unit density, respectively, C~ is the Cunningham slip correction factor, p is the dynamic viscosity of air and x is the dynamic shape factor. Mark et al. (1985) determined x for the same type of aluminum oxide test dust, and found on average r = 1.24 for various sized powders. With a density of 3.84 g c m - 3, one then gets the relation d~,= 1.8dv, where dv is the volume equivalent diameter of the (compact) particles. The turbulent transport process can be formulated in dimensionless terms by introducing the friction velocity, which is u*
= Xf~a'
(3)
where fo is the wall shear stress and p. is the density of air. The dimensionless parameters are then deposition velocity
V + =- U / U *
relaxation time
"C+ = "~(U* ) 2 / V
distance from surface
Z + : ZU*/V
stopping distance
(7 + = (7It*/~
Brownian diffusion particle turbulent diffusion
D + =O/v + D~p = D~p/v
concentration
C + = C/C~.
boundary layer thickness
6 + = 6u*/v.
The dimensionless version of equation (1) then becomes v + = - ( D + +D~p) dC+ dz + +iv + C +,
(4)
which can be solved by separation of variables: fc
dC+
+~,+)v+ + i v + C +
- ~ '
dz+
. D+ +D~p
.
(5)
The sign convention for v + has been changed to make v + positive for flux towards the surface. According to these assumptions, the concentration outside the turbulent boundary layer 3 + is equal to the free stream concentration Coo(C~ = 1). In the following it will be assumed that particle and air turbulent diffusion are equal (D~v=D~). This assumption will be discussed later. Several models for D~ have been proposed in the literature. A simple relation is based on Prandtl's mixing length expression near a surface (Corner and Pendlebury, 1951) D~(z) = k~z"
(6)
for z < 3, and with n = 2. k, is a constant depending on the flow field. Since then, several authors have used this expression to model homogeneous turbulent flow in an enclosure. Crump and Seinfeld (1981) extended the model to include n =m, and Shimada et al. (1987) included surface roughness, while using n = 2.7. In the present model, n = 2 is chosen, and this choice is to be discussed later. This implies that the constant ks has the dimension [s- 1], and k+ = k,v/(u*) 2. A crucial step in the model is to give a physical interpretation of the lower limit of integration, a +. At distances z + > a +, there will be both in- and outgoing flux caused by the turbulent motion of the air. At z + =(7+, the outgoing component of the particle flux has approached zero. For inertialess particles (7+= 0 (Crump and Seinfeld, 1981). Friedlander and Johnstone (1957) proposed the free flight model to include particle inertia. In this
Particle deposition onto facialskin and eyes
587
model, there is a remaining ingoing flux at distance a +, caused by particles which detach from the turbulent eddies and continue by free flight to the surface. Then the free flight distance is equal to the stopping distance a + and given by a + = v~"T+,
(7)
where v~" is the inward velocity of the particle imparted by the turbulent motion close to the surface (in the absence of electric or other fields). Particles only have to reach within one particle radius, d+/2 of the surface, and this distance must be added to the stopping distance. This was done in the numerical calculations, but since the results showed that d+/2 ~ a + for the present conditions, this has been omitted in the equations for simplicity. In the stationary case, the particle flux J is independent of z, thus
J = vC~ = VoC(a)
(8)
v + =v~C+(a+).
(9)
from which The solution of equation (5) is, for v+ = 0 /)+ =
1-C+(a
+)
(10)
l+(a +, 3 +)
Elimination of C+(a +) by use of equation (9), leads to the final result v+ -
1
(11)
T+
tr+ ~-l+(a+, 6+) where the integral I + is given by l+(a+,6+) =
+ dz + _ 1 - t a n - 1+ + D+ +k+(z+) 2 -x/k+D
f[
~
1
( x / +~]/ D~-~-~+(6 + )2 ) k+
tan-X (ff~-~-(a+) z )
_~ ~ - tan -
(12) x/~+D +
The approximation in equation (12) is valid for k+ (6 + )2/D + ~ 1, or D+ (6 +) >>D +, i.e. at the outer part of the boundary layer turbulent diffusion dominates over Brownian diffusion (see also Crump and Seinfeld, 1981). For a non-vanishing electric drift velocity, vc, normal to the surface, the resulting total + deposition velocity Vtot is
+
iv[
Vtot= exp (iv+ I +(a +, 6 + ) ) - 1
(1 -C+(tr+)exp(iv+I+(a+, 6+)))
(13)
and by again eliminating C + (a +) the final result is obtained +
/)tot =
iv +
,
(14)
( l +r~---4iv+ ) exp(iv+ l+ (a +,6+))-- I where i = + 1 for repulsion and i = - 1 for attraction. Equation (14) can be extended to cover force fields which are not normal to the surface, e.g. inclusion of gravity, by substituting i = cos (®), where (9 = n if the deposition velocity vector is towards and normal to the surface (see e.g. Shimada et al. (1989)). Some approximations will now be made to simplify equations (11), (12) and (14). The integral, equation (12), can be simplified by series expansion of tan- x (x) = n / 2 - l / x - . . . ,
588
T. SCHNEIDERet al.
giving
I +(~+,`5+)~_k+ ~
to+) 2,> 1 •.
(15)
The following approximation will hold if either r+/o + 4~1+(a +, ,5+), or the approximation, equation (15) holds, in conjunction with r + ,~ l/k~" 1 v + -
-
-
(16)
I+(a+,`5+)"
If furthermore the relation v+ < v + holds, equation (14) reduces to
• +
+
lUe
[ i~,; )
Utot --
exp \ v ~
117) - 1
Until now, no assumptions have been made regarding the dependence of o + on particle relaxation time and air turbulent diffusivity. We will use the empirical relation o + = 1.49(r +) °'51
(18)
determined by Sehmel (1970) for particles ranging 0 . t < r + < 1000 for turbulent flow in vertical tubes. This relation was determined by fitting a deposition model to experimental data, and that turbulent diffusivity for turbulent tube flow was given by (Lin et al., 1953) D ~+= f "+
z + ~<5
13
(a) (19)
D+ = 5 - 0 . 9 5 9
5
(b).
Equation (18) was obtained assuming D~p = D~. According to Sehmel (1970), equation 18 thus should be used to predict the free flight velocity, when assuming D~p=D~. In the present model the additional assumption is made that equation (18) also holds when D, is given by equation (6), and not by equation (19). In order to complete the model, the parameters k + and u* must be determined. Fluid mechanical computation of u* was not attempted. Instead, the parameters were found by a fitting procedure. First, equations (2), (15), (16) and (18) were combined to give
c=a.k2.d~;°2.(u*t 2°2
a = 1.49 l-~m' )
'
(20)
neglecting Cunningham's correction, since for all experimental data, d,e > 2 #m. It is seen that the unknown parameters k+ and u* in this equation are coupled via the product k[ (u*) TM. Thus, their absolute values cannot be determined solely from the experimental data. This problem was overcome by calculating u* for one set of experimental conditions by using the following approach. For homogeneous turbulent flow in an enclosed vessel, Shimada et al. (1989) found that the following relation was a good approximation: u* = ~
1
URMS,
121 )
where uRm is the root mean square value of air velocity fluctuations. Thus, 1
u*=~-~ T.u, where T is the turbulence intensity.
where
T=URMSu100%,
(22)
Particle deposition onto facial skin and eyes
589
This equation was used to calculate u* for the experimental condition high turbulence (19%) and orientation 0 °. For these conditions, u* = 30 (cm s - 1), and this value was used in the remaining calculations. All in all, there were seven sets of external conditions (u*, j = 1. . . . . 7), and six different diameters (dae p, p = 1. . . . . 6), Table 1. The fitting was then done by minimizing 6
7
SSE = E
Z Lvpj-" . + . 1aae . o 2p , [Uj,, ) .o212 age ..I
(23)
p = l j = l
in a two-step procedure, using the M I N E R R routine of M A T H C A D (1991). vpi are the experimental data given in Table 1. First, an initial value of k~+ was chosen, then the u* determined by minimization. With these values of u*, a new value of k~+ was found by minimization, etc. This procedure gave k + = = 0.0059 and the values for u* in Table 2. The experimental data, non-dimensionalized by the corresponding values of k~+ and u*, are shown in Fig. 1. The model prediction, using equation (11) is also shown. Having determined all parameters in the model it is now possible to explore the range of particle diameters, within which the approximations (15) and (16) are valid for the range of experimental conditions. With these values, approximation (15) holds for D --,~0.013(u*) 2 z
(24)
and thus for d,e > 2 #m for u* = 3.2 cm s - 1, and for d~ > 0.5/tin for u* = 30 cm s - 1. Equation (16) approximates equation (11) to within ___5% for 2.5 #m < d~ < 30/~m. Figure 2 shows the model fits to the experimental data from Table 1. Finally, the model will be used to predict the effect of a homogeneous electric field. The migration velocity v, in a homogeneous electric field is given by v~(dr,,) = n p e E C c ( d m ) 3rr~xdm '
(25)
where np is the number of electron charges, e is the electron charge and E is the electric field.
Table 2. Fitted values of friction velocity u* (cm s-1) Orientation turbulence intensity
0° 1.3%
0° 19%
90° 1.3%
180° 1.3%
Forehead Eye
16 7.5
30 15
19 --
26 3.2
0.1
0.01 o
-Io
o
o
o o o
o o
0.001 ~Ii*-3.2
1 E-4 0.001
0.01
0.1
1
10
100
Fig. 1. Non-dimensionalized deposition velocitydata with model (solid line).
590
T. SCHNEIDER et al.
(a)
1 I
- ~
i'~ ~7~-I~ '
o.1
O.Ol I
~\,A
*
1~.3%
~\+ 'D
1.3% 0 ° 1.3%
90 °
0.001
10 Dae, pm
100
(b) X
MMMF
0.1 ~E
.--~x x ~
i oo 1 9 ~o " / []
O
>0.01
o t.3~ ±
0.001
lSO o 1.3~ 1
~
~-.
~
~
[]
• ~
~-~ 10
100
Dae, pm Fig. 2. Experimental deposition velocities and model predictions. (a) Forehead; (b) eyes. M M M F : measurements at work place during handling of man-made mineral fibre products calculated from data given by Schneider and Stokholm (1981)
In order to explore the relative contribution of electric fields to the overall deposition velocity in absence of the experimental data, the range of particle charges and electric fields encountered in industrial and indoor environment settings must be estimated from other data. Most industrial aerosols will carry both negative and positive charges. The degree of charging can be expressed in terms of the median of the number of charges, irrespective of sign, carried by particles of given aerodynamic diameter dae (Vincent, 1986):
Inplm= ad,~,
(26)
where da= is in #m and A and N are constants. For workplaces, A ranges from 2 to 50, and N ranges from 0.7 to 1.9. The magnitude and sign of the electric fields at the forehead can be estimated from the following. Measurements on a manikin head, placed in front of a 21 x 28 cmz metal screen gave the expressions in Table 3 for the electric field E as a function of distance between head and screen, screen surface potential Us and manikin potential Uh (Norberg, 1986). Us may reach + 20,000, V (Skotte, 1988). G6the et al. (1989) found that Uh ranged between - 3 8 0 0 and + 1800 V. Emax corresponding to these values is also shown in Table 3. There are as yet
Table 3. Electric fields at forehead of manikin head placed in front of a screen (Norberg, 1986). Positive E: attraction, negative E: repulsion of positive particles to forehead Distance
Electric field (Vcm -1)
Em,,(V cm -1)
Emin(V c m - 1 ) (U~=0)
30 cm 40 cm 50 cm
E=0.033 U s - 0 . 1 0 4 Uh E = 0.024 Us -- 0.098 Uh E=0.018 U~-0.095 Uh
1060 850 720
-- 190 -- 175 -- 170
Particle deposition onto facial skin and eyes
591
1
oE 0.1
0.01
. . . . . . i
~ 10 Dae, IJm i
i
..... i
i
100
Fig. 3. Modelpredictionof deposition velocityon forehead,turbulenceintensity1.3% and orientation 0°. Effectof electric fieldsfor deposition of unit density,spherical particleswith median charge given by equation (26),and with half of the particlescarryingpositive,half carryingnegativecharge (net charge-neutral).
no data for the reduction of the electric field on the surface of the eye, as compared with the forehead, but theoretical work is in progress. The effect of electric fields and particle charging is illustrated by calculating the total deposition velocity onto the forehead for a net charge neutral aerosol. The particles are assumed to be spherical and having density 1 g cm-3. The net charge neutral aerosol is simulated by the simple case, where 50% of particles of each diameter carry a positive and 50% a negative charge, and with Inp]= 10d ~. The result is shown in Fig. 3. DISCUSSION The model predicts the diameter dependence of the experimental data well, Figs 1 and 2. Use of n=2.7 (a value used by Shimada et al. (1987) for a stirred tank) gave a steeper, and equation (19) a still steeper, diameter dependence. One of the key elements in the model is the friction velocity (Table 2). It is physically plausible that a reduction in turbulence intensity from 19% to 1.3% reduces u*. However, the observed factor of 2 for both forehead and eyes is much less than the factor 15 predicted by equation (22). It is not easily understood that the deposition velocity increases from orientation 0 ° to 90 °. For very small particles at least, where the mass transfer can be described by Brownian diffusion, the analogy between mass and heat transfer can be used (Liu and Ahn, 1987). Heat transfer of cylinders in cross flow has been studied extensively (Zukauskas and Ziugzda, 1975). The results show a decrease in local heat transfer when going from the front stagnation point to 700-90 °, followed by an increase. Deposition velocities measured for orientation 180 ° were larger than for orientation 90 ° as expected from the analogy to heat transfer, but exceeded the deposition velocity for 0 °. Kim and Flynn (1991) have shown that a zone of backstreaming air extends to 15 cm from the nose as measured at 7% turbulence, and very little dependent on mean air velocity. Vincent and Humphries (1978) have argued that the concentration Cw inside such a wake is less than the free stream concentration C~ and that Cw/C~ decreases with increasing particle Stokes number. Since Coo was measured outside the wake, this could explain the reduced diameter dependence of the deposition velocity, but would also predict a reduced deposition velocity at 180° compared with 0 °. Deposition on the eye was not uniform, and was highest on the cornea. It is physically plausible that a protrusion (cornea) in the centre of a retraction (eye surface, relative to face) produces this effect. In the model, deposition velocity is calculated as an average over the exposed surface. In this way, deposition velocities were normalized to the same area. A statistical test showed that there was no difference for deposition velocity to left and right eye for 0 ° orientation. This means that within the range of exposed area (1.2-1.8 cm2), deposition is proportional to the exposed area. AS 25:3-K
592
T. SCHNEIDERet al.
The model structure and parameter values are only preliminary and need to be confirmed by more extensive experiments, including a range of air velocities. Figure 3 shows that for net charge-neutral aerosols, the effect of an electric field will always be to increase deposition. A person working in a high field, e.g. as generated from a poorly-shielded CRT-screen, will always experience an increased particle deposition onto facial skin and eyes. At the same time, deposition will also be increased on the VDU screen. It can be concluded that electric fields dominate deposition for diameters around 1 #m, that the exact shape of the charge distribution affects deposition for larger particles, and that turbulence (Fig. 2) will be dominating, except for extreme fields and charges, for d > 10 #m. However, experiments should be carried out to confirm these predictions. Charging of aerosol and manikin had not been completely eliminated, and the effect was measured for eye deposition at 0 °, turbulence intensity 1.3% (Gudmundsson et al., 1993). Calculations with the above model indicate that charging would not have affected the values of u* >30 cm s-1, have some effect for u*~ 15 cm s-1, and be considerable for u*< 7 cm s-1. Even weak electric fields (1 V cm-1) swamp deposition due to image forces for stagnation flow onto a horizontal plate, and in the absence of electric fields image forces would be most important for particles in the range 0.1-1 #m (Turner et al., 1989). In the derivation of equation (14) it was assumed that the free flight distance was not changed when an electric field is present• It is to be expected that if ve ~ v0, this change will be negligible. For the values of u* given in Table 2, and for the aerosol charge distributions given in Fig. 3, it is found that the condition ve <0.1 Vo is fulfilled for 0.1
(27)
N/Po
where d I is the fibre diameter, l is the fibre length and Pl is the fibre density. Figure 2b shows that the order of magnitude and the slope agrees well with the wind tunnel data. In summary, the model shows that variations in particle charge, electric fields and turbulence could have a larger effect on the particle accumulation rate in the eyes and on the skin than have typical variations in indoor aerosol concentrations. For investigations of exposure to airborne particles and its relation to the office eye syndrome, the model can be used for identifying those parameters which are key for given conditions, thus simplifying the description of exposure. Acknowledgement--This work has been supported by the Danish Work EnvironmentFoundation,grant 1990-03.
Particle deposition onto facial skin and eyes
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