PII: S0003-4878(99)00016-2
Ann. occup. Hyg., Vol. 43, No. 3, pp. 181±192, 1999
# 1999 British Occupational Hygiene Society
Published by Elsevier Science Ltd. All rights reserved
Printed in Great Britain
0003±4878/99/$20.00 + 0.00
Evaporation of Accumulated Multicomponent Liquids
from Fibrous Filters
PETER C. RAYNOR*$ and DAVID LEITH
University of North Carolina at Chapel Hill, Department of Environmental Sciences and
Engineering, CB# 7400, Rosenau Hall, Chapel Hill, NC 27599, USA
Fibrous ®lters are used for environmental and occupational mist sampling and industrial mist
collection. If compounds in the ®ltered droplets are volatile or semi-volatile, they may evaporate
into the gas passing through the ®lter. In sampling applications, failure to properly account for
evaporation of collected mist will lead to mist concentration estimates that are low. In control
applications, volatilization of ®ltered droplets may release vapors that are harmful to workers
or the public. Also, vapor emitted from mist ®lters may recondense as a hazardous aerosol or
on surfaces to pose a safety or housekeeping problem. Droplets collected by ®brous ®lters
coalesce into larger drops that reside on the ®bers. Results from a numerical model developed
to predict evaporation from these drops agree favorably with experimental data. Measurements
and numerical predictions show that a gas stream leaving a wetted ®brous ®lter can be
saturated with the vapor of semi-volatile compounds retained on the ®lter. In some situations,
the model indicates that the gas stream will be saturated before it passes 0.1 mm into a wetted
®lter. If the liquid retained on a ®lter is a pure compound, the vapor concentration leaving the
®lter is constant when initially clean air passes through. If the liquid is multicomponent, the
downstream vapor concentration in previously uncontaminated air will decrease with time as the
more volatile components evaporate preferentially. Fluctuations in incoming mist and vapor
concentrations can enhance evaporation because more retained liquid will volatilize when
incoming vapor concentrations are low. # 1999 British Occupational Hygiene Society.
Published by Elsevier Science Ltd. All rights reserved.
Keywords: ®ltration; evaporation; oil mist; metalworking ¯uids
p'
NOMENCLATURE
Af
B
c
cf
cs
csat
c0
dd
de
df
DG
h
L
ND
facial area of ®lter
factor representing amount of vapor contributed by
evaporation from ®lter
vapor concentration near drop
vapor concentration in ®lter element
vapor concentration at drop surface
saturated vapor concentration
incoming vapor concentration
drop diameter
diameter of gas volume surrounding drop
®ber diameter
gas phase di€usion coecient
distance between centers of mass of drops along ®bers
®lter thickness
number density of accumulated drops
Received 26 May 1998; in ®nal form 7 December 1998.
*Author to whom correspondence should be addressed.
$Present address: University of Minnesota, Division of
Environmental and Occupational Health, Box 807 Mayo,
420 Delaware St. SE, Minneapolis, MN 55455, USA. Tel.:
+1-612-625-7135; Fax: +1-612-625-0650.
181
P0
Q
Q0
r
Re
S
Sc
Sh
t
t'
u
x
z
z'
a
DP
E
mg
rg
s0
ratio between pressure drop and pressure at upstream
surface
pressure at upstream surface
volumetric ¯ow of gas
volumetric gas ¯ow at front surface of ®lter
radial dimension
Reynolds number
saturation ratio
Schmidt number
Sherwood number
time
non-dimensional time
gas velocity
mole fraction in drop
distance through ®lter depth
fractional distance through ®lter depth
®lter solidity
pressure drop across ®lter
rate of evaporation from drop
gas viscosity
gas density
incoming vapor saturation
Subscript
compound
i
182
P. C. Raynor and D. Leith
INTRODUCTION
In industry, ®brous ®lters are used to collect airborne liquid droplets generated by the application
of metalworking ¯uids during metal machining
(Leith et al., 1996b), the production of chemicals
such as sulfuric acid (Brink et al., 1968), and the
production of compressed gases (Brink et al., 1966).
Workers often wear respirators that contain ®brous
®lters to reduce their exposure to potentially harmful mists. To monitor workers' exposures, industrial
hygienists sample airborne droplets using either
®brous or membrane ®lters.
Mist collection ®lters can be sources of vapor
(Kolganov and Radushkevich, 1967; Olander, 1983).
Cooper et al. (1996) showed that metalworking
¯uids retained on ®brous ®lters evaporated signi®cantly. Gas streams leaving industrial ®lters were
enriched with the more volatile compounds in the
liquids. Cooper and Leith (1998) asserted that air
streams leaving oil-mist-collection ®lters were saturated with the vapor of the oils accumulated on the
®lters. When no mist was present in inlet air, vapor
samples taken upstream and downstream from collection ®lters wetted with oil indicated that substantially more oil vapor was present downstream than
upstream.
Evaporative losses during ®lter sampling of environmental aerosol droplets have been observed for
nitrates (Cheng and Tsai, 1997), sulfates (Eatough et
al., 1995), and organic compounds that include nalkanes and polycyclic aromatic hydrocarbons (Van
Vaeck et al., 1984; Rounds et al., 1993). Tests have
also indicated that evaporation of oil mist sampled
using ®lters can occur in occupational settings
(McAneny et al., 1995; Leith et al., 1996a).
Volatilization of liquid collected on ®brous ®lters
presents several problems. In environmental and occupational sampling, evaporation will lead to negative biases in aerosol concentration measurements.
In industrial mist elimination, evaporation of liquid
retained on collection ®lters may pose a health
hazard if the vapor is a health concern.
Furthermore, in metalworking-¯uid-mist collection,
the air emerging from collectors is often warmer
than the surrounding air due to heat generated
during machining (Cooper and Leith, 1998). When
this warm air cools upon recirculation to the work
environment, vapor may condense to form respirable droplets. Alternatively, the vapor may condense
on cool surfaces to pose a ®re or safety hazard or a
housekeeping problem.
Zhang and McMurry (1987) developed a numerical model based on mass conservation to predict
evaporation of accumulated solid particles or liquid
droplets from a sampling ®lter when a saturated air
stream entered the ®lter. Later, they extended the
model to consider compounds adsorbed to particles
or absorbed into droplets (Zhang and McMurry,
1991). These models assumed that liquid droplets
spread uniformly over ®ber surfaces when they collected beyond a threshold level. However, several
authors have observed that liquid distribution was
non-uniform across the surfaces of thin ®laments or
®lter ®bers (Fairs, 1958; Bondarenko, 1961; Kirsch,
1978; Liew and Conder, 1985). Individual droplets
coalesced to form (i) unduloidal drops (nearly
spherical drops with surfaces that undulate to intersect more smoothly with ®bers) along uninterrupted
lengths of ®bers, (ii) more rounded drops at intersections of ®bers, and (iii) pools spanning many ®bers.
Cheng and Tsai (1997) developed a model to predict
evaporative losses from solid particles collected on
the surface of a ®lter. They solved a convective diffusion equation through a bed of particles. Unlike
Zhang and McMurry (1987), these authors did not
assume that the incoming vapor concentration was
saturated.
No models that re¯ect the observations that ¯uid
resides non-uniformly on ®lter ®bers have been published to predict the evaporation of liquid accumulated within a ®lter. Using an approach similar to
Zhang's and McMurry's (Zhang and McMurry,
1987), we will develop a model that describes evaporation of a multicomponent liquid retained on a ®lter for any incoming vapor composition. In contrast
to Zhang and McMurry, we will assume that collected liquid coalesces as drops within ®lters rather
than spreading over ®ber surfaces. Numerical solution of this model will be compared to experimental results.
THEORY AND MODEL DEVELOPMENT
A ®brous ®lter has a facial area of Af perpendicular to the direction of air¯ow, z. A thin, well-mixed
slice of this ®lter has length dz in the direction of
air¯ow. The ®lter has a solidity, or packing density,
of a. If the vapor-phase concentration of any compound i in the ®lter slice is cf,i, then conservation of
mass for the vapor phase yields
Af …1 ÿ a†
@ cf,i …z,t†
dz
@t
ˆ ND …z†Af Ei …z†dz ÿ
@ ‰cf,i …z,t†Q…z†Š
dz,
@z
…1†
where t represents time, ND is the number density of
accumulated drops present on the ®bers, Ei is the
rate of evaporation of i from a drop residing on a
®ber, and Q is the volumetric ¯ow of the gas. As
shown in Eq. (1), several terms vary with time or
the distance through the ®lter. Flow increases as static pressure decreases through the ®lter. If z is set
equal to zero at the front surface of the ®lter, then
Q can be de®ned by
Evaporation of accumulated multicomponent liquids from ®brous ®lters
ÿ1
DPz
Q…z† ˆ Q0 1 ÿ
,
P0 L
…2†
in which Q0 and P0 are the ¯ow and ambient pressure at the front surface of the ®lter, DP is the pressure drop through the ®lter, and L is the thickness of
the ®lter. Eq. (2) assumes that pressure drop is uniform through the depth of the ®lter. In¯uenced by
both pressure changes and evaporation, the vapor
concentration is de®ned as
DPz
cf,i …z,t† ˆ c0,i …t† 1 ÿ
…3†
‡ Bi …z,t†csat,i ,
P0 L
where c0,i is the incoming vapor concentration, Bi is
a factor tracking the concentration of the vapor
contributed by evaporation from the ®lter (Zhang
and McMurry, 1987), and csat,i is the saturated
vapor concentration. Pressure drop, axial distance,
and time can be non-dimensionalized by
p0 ˆ
DP
,
P0
…4†
z
L
…5†
Q0 t
Af L
…6†
z0 ˆ
and
t0 ˆ
to simplify the equations. The incoming vapor saturation for compound i, s0,i, is de®ned as
c0,i
s0,i ˆ
:
…7†
csat,i
By rearranging Eq. (1) and substituting Eqs (2)±
(7), the expression
ds0,i @ Bi
…1 ÿ a† …1 ÿ p 0 z 0 † 0 ‡ 0
dt
@t
ˆ
1
@ Bi
p0
ND A f L
ÿ
Bi ‡
Ei …8†
0
0
0
…1 ÿ p z † @ z
csat,i Q0
…1 ÿ p 0 z 0 †2
can be developed.
The analysis of evaporation rates of drops that
have coalesced on ®bers is similar to Maxwell's derivation of evaporation of an isolated spherical drop
into an in®nite medium (Maxwell, 1878). Fick's ®rst
and second laws of di€usion (Crank, 1975) can be
combined to give the equation
@ ci …r†
Ei
ˆÿ
r2 ,
@r
4pDG,i
…9†
in which ci is the concentration of vapor in the
region surrounding the drop, r is the radial dimension originating at the center of the drop, and DG,i
is the di€usion coecient of compound i through
the surrounding gas (Davies, 1978). Eq. (9) can be
integrated from ci=cs,i, the concentration of i at the
drop surface, at r=dd/2 to ci=cf,i at r=de/2. The
183
term dd refers to the diameter of the accumulated
drop, which is assumed to be spherical, and de is the
diameter of a spherical region of gas surrounding
the drop. Performing the integration and rearranging terms yields
Ei ˆ
2pDG,i dd de
…cs,i ÿ cf,i †
de ÿ dd
…10†
as the rate of evaporation from the coalesced drop.
For ideal mixtures, Raoult's Law,
cs,i ˆ x i csat,i ,
…11†
in which xi is the mole fraction of i in the drop, can
be used to estimate the vapor concentration at the
drop surface. Eq. (11) assumes that vapor concentrations for mixtures are proportional to their mole
fractions. Although this assumption is appropriate
for mixtures of similar compounds, activity coecients should be considered for dissimilar compounds (Smith and Van Ness, 1975).
The number density of accumulated drops, ND,
can be calculated from h, the average distance
between centers of mass of drops accumulated along
®bers. From observations of the spontaneous break
up of liquid layers on thin ®laments into unduloids,
Bondarenko (1961) measured h to be about ®ve
times the diameter of the liquid cylinder if the accumulated liquid were spread evenly over the surface
of the ®bers. The saturation ratio, S, of the ¯uid in
the ®lter slice is the fraction of the void volume that
is occupied by liquid. Since the diameter of the imaginary liquid cylinder will depend on S, h can be
de®ned as
1
2
S…1 ÿ a†
hˆ5
‡ 1 df ,
a
…12†
in which df is the diameter of the ®lter ®bers. In
turn, ND can be calculated as
ND ˆ
4a
:
pd 2f h
…13†
If the volume of the spherical region surrounding
each drop is de®ned as the inverse of ND, then
de ˆ
6
pND
1
3
:
…14†
This de®nition of de was chosen to restrain evaporation in the model as much as possible. Assuming
that all drops within the ®lter slice are the same size,
dd can be calculated by
dd ˆ
6S…1 ÿ a†
pND
1
3
:
…15†
When a retained drop is held motionless by ®lter
®bers, the passing air may enhance evaporation by
disturbing the di€usion ®eld around the drop.
Davies (1978) accounts for the e€ect of gas velocity
184
P. C. Raynor and D. Leith
by using the non-dimensional Sherwood number,
Shi, which is de®ned as the actual evaporation rate
of compound i divided by the vaporization rate if
the gas velocity did not enhance evaporation. The
Sherwood number is expressed as
1
1
Shi ˆ 1 ‡ 0:276 Re 2 Sci3 ,
…16†
where Re is the Reynolds number,
Re ˆ
rg udd
,
mg
…17†
in which rg and mg are the gas density and viscosity,
and u is the gas velocity. The quantity Sci is the
Schmidt number
mg
Sci ˆ
…18†
rg DG,i
for compound i.
Substituting Eqs (3), (11) and (16) into Eq. (10)
gives
2pDG,i Shi csat,i dd de Ei ˆ
x i ÿ s0,i …1 ÿ p 0 z 0 †
de ÿ dd
ÿ Bi
…19†
for the evaporation rate of a single drop into the
surrounding ¯ow. Eq. (19) can be substituted into
Eq. (8) to yield
@ Bi
1
@ Bi
ˆÿ
…1 ÿ p 0 z 0 †…1 ÿ a† @ z 0
@t0
ÿ
p0
ds0,i
Bi ÿ …1 ÿ p 0 z 0 † 0
dt
…1 ÿ p 0 z 0 †2 …1 ÿ a†
…20†
2pND Af LDG,i Shi dd de
Q0 …de ÿ dd †…1 ÿ a†
x i ÿ s0,i …1 ÿ p 0 z 0 † ÿ Bi :
‡
Eq. (20) can be discretized in the z-dimension
using backward-di€erence ®nite di€erence formulas.
The equation can also be discretized temporally.
The resulting system of equations is solved iteratively over small time increments at a series of nodes
through the depth of the ®lter. Each node represents
a section of the ®lter depth. Terms containing Bi
that do not vary with time are weighted with a
Crank±Nicolson approximation so that information
from both the beginning and the end of a time increment is used during the solution of the equations.
During each time increment, mass is added to the
®lter numerically if mist is present in the incoming
air stream. This ®ltration is modeled according to
standard single-®ber eciency theory (Hinds, 1982).
The single-®ber eciency model, though not
described here, uses a ¯ow ®eld developed by
Kuwabara (1959) and mechanisms for droplet col-
lection by di€usion, interception, and impaction
(Lee and Liu, 1982; Stechkina et al., 1969).
The numerical model is solved iteratively using a
FORTRAN program. Quantities calculated during
each time step are used as initial conditions for the
next. As input, the program requires the incoming
droplet size distribution, the liquid-phase composition by droplet size, and the vapor composition.
The droplet size distribution of an evaporating mist
can be calculated using a model developed previously (Raynor et al., 1996). Data on compound
properties, ®lter characteristics, and ambient conditions are also required. The program reports contributions to the outlet vapor composition by liquid
evaporating from the ®lter, the saturation ratio and
composition of the retained liquid at each node, and
the total mass of liquid accumulated on the ®lter.
EXPERIMENTS
To evaluate the ®lter evaporation model and numerical solution technique, experiments were conducted to measure evaporation from test ®lters
using di€erent ¯uids and test conditions. The following sections describe the experiments and the
measurements and data required as input to the
FORTRAN program.
Filter evaporation tests
The bench-scale test apparatus illustrated in Fig.
1 was constructed to pass mist to small ®lters that
were custom-made from glass ®bers. Room air was
drawn under vacuum through a ®lter into PVC tubing with an inner diameter of 1.27 cm. The air
passed through a calibrated ¯ow obstruction across
which pressure drop was monitored to maintain air¯ow. Mist from a single-jet Collision nebulizer
(BGI, Inc., Waltham, MA) was introduced into the
¯ow before the air entered a 7.6 cm diameter, 1808
elbow. After returning to tubing, the ¯ow entered a
stainless steel expansion that ended in the 5.08 cm
10.16 cm test ®lter that was 0.88 cm thick. Upon
leaving the ®lter, the ¯ow entered a 10.2 cm wide
15.2 cm high 7.6 cm deep stainless steel chamber
and passed through a contraction into 3.6 cm diameter pipe that led to a vacuum pump.
The test ®lters were made from two di€erent
classi®cations of glass ®bers (Evanite Fiber
Corporation, Corvalis, OR). The ®ber diameters
were measured by optical microscopy as 2.9 and
8.5 mm on average. The geometric means of the ®ber
diameters were 2.6 and 8.0 mm, respectively, and
both classi®cations had a geometric standard deviation of 1.5. The ®bers were suspended in an aqueous solution and drawn through a mesh to produce
®lters that ranged in solidity from 0.0181 to 0.0364.
Filters were rinsed with methanol to desorb any organic compounds that may have contaminated the
Evaporation of accumulated multicomponent liquids from ®brous ®lters
185
Fig. 1. Test apparatus.
®ber surfaces. The initial mass of a test ®lter was
recorded before the ®lter was placed into the test apparatus.
Nine experiments were conducted for comparison
to the numerical model. Mist was loaded onto the
test ®lter for 15 to 30 minutes. The total aerosol
mass collected on a ®lter during an experiment ranged between 193.2 and 224.6 mg, or between 3.74
and 4.35 mg/cm2. Afterward, clean air was passed
through the ®lter. During this clean air period, a
tubing bypass was used so that any liquid accumulated in the original tubing and elbow would be
unable to evaporate into the air entering the test ®lter. Periodically, the clean air¯ow was stopped so
that the ®lter could be weighed. The experiment
continued until the mass of the ®lter equalled the initial ®lter mass or until a suitable time, such as 24 or
36 hours, had passed without the ®lter reaching its
initial mass.
The test conditions, shown in Table 1, permitted
examination of changes in ¯uid type, temperature,
air¯ow, ®ber diameter, and solidity. The compounds
hexadecane, tetradecane, and bis(2-ethylhexyl) sebacate (BEHS) (Aldrich Chemical Co., Milwaukee,
WI) were used individually and in a mixture that
was 42.7% tetradecane/20.4% hexadecane/36.9%
BEHS by mass. The mineral seal oil (Polar, Inc.,
Dayton, OH) was a brand used in metalworking.
Reported temperatures are averages and standard
deviations weighted over the duration of a test by
times between temperature measurements.
Data required for modeling
The FORTRAN program required a variety of
data as input. To determine the initial composition
of the mineral seal oil, 1 mL of oil diluted by carbon
disul®de was injected into a Hewlett±Packard 5890
Series II gas chromatograph (GC) using helium as
the carrier gas. The GC was equipped with a DB-5
60 m, 0.25 mm i.d. column (J&W Scienti®c, Folsom,
CA) and a Hewlett±Packard 5972 Mass Selective
Detector. The injector temperature was 2808C. The
oven temperature was initially 608C. After a hold
time of 0.2 min, the oven temperature was raised
158C/min until it reached 2508C and then 128C/min
until it reached 3008C, where it was held for 5 minutes.
Since prior analyses indicated that the oil was
composed primarily of n-alkanes ranging from dodecane (C12H26) to tricosane (C23H48), the ion at m/
z 57 in the mass spectra, representing a common
alkane fragment, C4 H ‡
9 , was used to quantify these
compounds by single-ion monitoring. For compounds present in smaller amounts, peaks that did
not represent one of the twelve identi®ed alkanes
were assigned to one of these alkanes by GC reten-
Table 1. Test conditions.
Test
Fluid
1
2
3
4
5
6
7
8
9
Hexadecane
Hexadecane
Hexadecane
Hexadecane
Hexadecane
BEHS
Tetradecane
Mixturea
Mineral Seal Oil
a
Velocity
(cm/s)
Solidity
Fiber
diameter
(mm)
25
25
25
25
5
25
25
25
25
0.0187
0.0182
0.0364
0.0276
0.0185
0.0183
0.0181
0.0181
0.0192
2.9
2.9
2.9
8.5
2.9
2.9
2.9
2.9
2.9
Temperature
21 standard
deviation (8C)
Droplet mass
median
diameter (mm)
Droplet
geometric
standard
deviation
E€ective ®ber
diameter (mm)
22.420.20
26.820.16
22.120.15
22.320.17
22.420.11
21.720.20
23.020.33
21.820.11
21.920.19
1.73
1.73
1.73
1.49
2.71
1.40
1.91
1.38
1.75
1.56
1.56
1.56
1.68
1.88
1.68
1.38
1.75
1.47
3.8
4.1
3.7
12.7
3.9
4.2
4.0
4.2
3.9
42.7% Tetradecane/20.4% Hexadecane/36.9% BEHS by mass
186
P. C. Raynor and D. Leith
Table 2. Assumed composition of mineral seal oil, see
text.
Compound
Chemical formula
Mole fraction
Dodecane
Tridecane
Tetradecane
Pentadecane
Hexadecane
Heptadecane
Octadecane
Nonadecane
Eicosane
Uneicosane
Docosane
Tricosane
C12H26
C13H28
C14H30
C15H32
C16H34
C17H36
C18H38
C19H40
C20H42
C21H44
C22H46
C23H48
0.008
0.022
0.052
0.082
0.159
0.229
0.229
0.108
0.056
0.031
0.017
0.007
tion time. That is, the integrated area for each unidenti®ed peak was added to the area of the identi®ed alkane with the closest retention time. The
composition of the mineral seal oil determined this
way is presented in Table 2.
The size distributions of the droplets that reached
the ®lter were measured by introducing mist into the
test apparatus when no ®lter was present and
sampling from the chamber using a Sierra Cascade
Impactor (Andersen Samplers, Inc., Atlanta, GA).
Mass median diameters and geometric standard deviations are reported in Table 1. A model for droplet evaporation (Raynor et al., 1996) was used to
estimate the initial size distribution produced by a
nebulizer that would yield the measured size distribution after traveling through the apparatus. This
model determined droplet compositions and vapor
concentrations for input to the ®lter evaporation
model.
Many properties of the compounds are available
in the literature (Lide, 1992; Yaws, 1994). Gasphase di€usion coecients were calculated using an
empirical relationship (Fuller et al., 1966). The density of tetradecane, hexadecane, and BEHS were
measured by determining the mass of known
volumes of ¯uid. Surface tensions for the same compounds and the mineral seal oil, required for the
droplet evaporation model, were measured with a
Model 21 Surface Tensiomat (Fisher Scienti®c,
Pittsburgh, PA). The vapor pressure for heptadecane was estimated as the geometric average of the
vapor pressures of hexadecane and octadecane
obtained from the literature (Yaws, 1994). Vapor
pressures for uneicosane, docosane, and tricosane
were estimated by extrapolating from literature
values for the other n-alkanes assuming a linear relationship between the logarithm of vapor pressure
and carbon number. No data were available for the
vapor pressure of BEHS so that evaporation of pure
BEHS and the tetradecane/hexadecane/BEHS mixture could not be modeled independently.
The pressure drops measured during the experiments were lower than calculated from standard
pressure-drop equations. The variability of the ®ber
diameters or a lack of homogeneity of the ®lter may
have caused this di€erence. Following a recommendation from Davies (1952), e€ective ®ber diameters
were calculated from the measured pressure drops
and solidities. The e€ective ®ber diameters, listed in
Table 1, were then used in the model for ®ber diameter. All of the e€ective diameters were within the
95% con®dence intervals for the optically-measured
mean ®ber diameters.
With these input data, the program was run and
the output was compared to results of the measurements discussed earlier. Convergence for the program was tested by using di€erent time intervals for
iteration. For typical input, a time step of 0.01 s
produced values of Bi that were within about 0.1%
of the values calculated with a time step of 0.001 s.
Filter depth intervals as small as 10 mm were
required in the model for ecient ®lters in which
collection rates decreased rapidly with depth.
RESULTS AND DISCUSSION
Figure 2 shows the mass of ¯uid retained on the
test ®lter versus time after clean air began to pass
through the ®lter for tests 1 (hexadecane) and 7 (tetradecane) and for the model runs that simulated
those experiments. In both cases, the models
matched the experimental data well. Both the experimental and model results show that the ®lters lost
mass linearly with time. Similar linear changes in ®lter mass with time were exhibited by tests 2 through
5. With knowledge of the ¯ow rate, the concentration of vapor leaving the ®lter was calculated
from the mass change rate. Results from these computations for tests 1 through 5 and 7 are presented
in Table 3 for both the experiments and model runs.
In addition, saturated vapor concentrations calculated for the test conditions are included.
Table 3 shows that the calculations of vapor concentration from the model were slightly lower than
those observed experimentally. Several reasons for
this di€erence exist. First, literature data for vapor
pressure may have been slightly inaccurate. The
published equations for calculating vapor pressure
for tetradecane and hexadecane were valid over
broad temperature ranges of 6 to 4198C for tetradecane and 18 to 4488C for hexadecane (Yaws, 1994).
Since the temperatures in the experiments were near
the low ends of these ranges, small errors may have
entered the calculations. Second, measurements of
temperature or ¯ow may have been inaccurate.
Although the temperature variability presented in
Table 1 cannot explain the di€erences between the
model and experimental results, biases in temperature measurement might have a€ected vapor pressure calculations substantially. Also, some ¯ow error
could be expected for test 5 since the pressure drop
associated with the ¯ow ori®ce at a ®ltration velocity of 5 cm/s was small and dicult to maintain.
Evaporation of accumulated multicomponent liquids from ®brous ®lters
187
Fig. 2. Experimental results and model predictions for ®lter mass versus time for test 1 (hexadecane) and test 7 (tetradecane).
Finally, the di€erences between the experimental
data and model results may have been due to inaccuracies in the model.
If we assume that the model predicted ®lter evaporation accurately, Table 3 shows that the model
indicated that the air leaving the test ®lters was saturated with the vapor of the accumulated ¯uid in all
cases. The Peclet number,
Pe ˆ
ude
,
DG,i
…21†
compares the importance of the convective ¯ow
through the ®lter to the di€usion of vapor away
from accumulated drops. For the front surface of
the ®lter in test 1, Pe was 2.2, which means that diffusion was of the same magnitude as convection
within the microstructure of the ®lter. This analysis
suggests that saturation of the passing gas with the
vapor of the accumulated liquid occurred rapidly
inside the ®lter.
Figure 3 shows the local ®lter saturation ratio
predicted by the evaporation model for the test 1 ®lter versus depth through the ®lter for several times
through the model run. This ®gure suggests that the
saturation ratio increased sharply along a front that
moved deeper into the ®lter with time. The saturation ratio at a given depth through the ®lter
decreased little until the passing air had removed the
accumulated liquid from the leading portions of the
®lter. These computations provide further evidence
that the liquid retained on the ®lters saturated the
passing air readily.
The results in Table 3 demonstrate that the evaporation rate was not a€ected by changes in ®ber diameter or ®lter solidity within the ranges considered
here. Temperature increases caused increases in
evaporation due to associated increases in vapor
pressures. Lowering the ®ltration velocity slowed
evaporation because less air passed through the ®lter.
Since the model indicated that the air leaving the
®lters was saturated with vapor, the test 6 results for
BEHS were used to estimate the vapor pressure of
BEHS. The loss of mass from the BEHS ®lter
occurred at a rate of 0.296 mg/hr, which corresponds to a vapor pressure of 2.7510ÿ6 mm Hg for
BEHS at the test temperature of 21.78C.
Experimental data and model results using this predicted vapor pressure are shown in Fig. 4.
Experimental results and model predictions for
test 8, in which the test ¯uid was a mixture of tetradecane, hexadecane, and BEHS, are also presented
in Fig. 4. Within the ®rst four hours, the curve
shows three distinct slopes where evaporation of
each of the three constituents predominated.
Tetradecane evaporated rapidly at ®rst. Once tetra-
Table 3. Experimental, modeled, and saturated vapor concentrations.
Test
1
2
3
4
5
7
Test concentration295%
con®dence interval (mg/m3)
Model concentration
(mg/m3)
Saturated concentration
(mg/m3)
14.020.25
23.420.19
13.820.89
13.020.36
14.720.44
113.225.8
13.1
21.2
13.1
12.9
13.0
102.5
13.1
21.0
12.8
12.9
13.1
101.8
188
P. C. Raynor and D. Leith
Fig. 3. Model predictions for saturation ratio versus ®lter depth for several times during test 1 (hexadecane).
decane evaporated, the evaporation of hexadecane
was most evident. Eventually, the ®lter mass
decreased at the same rate as in test 6 since BEHS
was the only compound remaining.
Fig. 5 shows the ®lter mass versus time for mineral seal oil in test 9. The modeling results matched
the experimental data well. This agreement indicates
that simulating the mineral seal oil as a mixture of
n-alkanes was reasonable. The di€erences between
the experimental and modeled results may have
been due to inaccuracies in estimates of ¯uid composition, temperature, or vapor pressure. As with
test 8, the rate of evaporation slowed with time
because the more volatile compounds evaporated
quickly from the ®lter, leaving the less volatile compounds to evaporate at a progressively slower rate.
In Fig. 6, model predictions are presented for
post-®lter, vapor-phase mole fractions versus time
for alkanes tetradecane through uneicosane in test 9.
As evaporation progressed, the model suggested
that each compound dominated the overall rate of
evaporation incrementally as composition changed
from more to less volatile compounds. As would be
expected, model composition changed more quickly
early in the test as the most volatile compounds left
the ®lter rapidly. With time, the most abundant
compound remained prevalent for longer periods.
In all the tests and model runs, the results demonstrate that evaporation of liquid accumulated on ®lters occurred readily. This ®nding can be important
in several circumstances. In mist collection equipment, clean air may pass through ®lters during
breaks, shift changes, or o€-shift hours. If this situation occurs, the air will emerge from the collector
saturated with vapor. If a mist collector is supposed
to be 100% ecient for removal of droplets, this
Fig. 4. Experimental results and model predictions for ®lter mass versus time for test 6 (BEHS) and test 8 (mixture). The
portion of the ®gure shaded gray has an expanded time scale relative to the portion shaded white.
Evaporation of accumulated multicomponent liquids from ®brous ®lters
189
Fig. 5. Experimental results and model predictions for ®lter mass versus time for test 9 (mineral seal oil).
loss of collected material will lower the e€ective collection eciency. For situations where the `cleaned'
air is recirculated, the vapor in the saturated air
may have the opportunity to recondense as mist
droplets or on surfaces, thereby causing a health or
safety hazard. Regarding assessment of personal exposures, evaporation from sampling ®lters will lead
to underestimates of mist concentrations.
The model can be used to estimate how evaporation in¯uences ®lter collection in practical situations. For instance, in a machining operation,
generation of metalworking ¯uid mists may occur
cyclically as parts are machined and then passed
along to the next operation, or as individual oper-
ations are performed successively on a single work
piece. The model was run six times with mineral seal
oil according to the conditions shown in Table 4.
Mineral seal oil, though used sparingly as a metalworking ¯uid itself, has properties that are similar
to other straight oils and the oil portion of a soluble
oil emulsion. The runs were selected to show the importance of evaporation plus the e€ects of changing
the length of time that no mist is being loaded onto
the ®lter during a one-minute cycle. The incoming
vapor concentrations in the model were set to zero
when the incoming mist concentration was zero
even though some background vapor may be present in real situations. When mist was present in the
Fig. 6. Model predictions for vapor-phase mole fractions leaving ®lter versus time for the most prevalent compounds in
the mineral seal oil used in test 9.
190
P. C. Raynor and D. Leith
Table 4. Model conditions to demonstrate e€ects of ¯uctuations in incoming mist and vapor concentrations on ®lter
evaporation.
Model Run
Evaporation
Time on during 60 s cycle (s)
Time o€ during 60 s cycle (s)
A
B
C
D
E
F
Not included
Included
Not included
Included
Not included
Included
60
60
30
30
12
12
0
0
30
30
48
48
model, it was distributed lognormally with a mass
median diameter of 1.5 mm and a geometric standard deviation of 2.5 initially. After aging for a droplet evaporation model time of 5 s (Raynor et al.,
1996), the mist entered the ®lter at a concentration
of 19.5 mg/m3 with an accompanying total vapor
concentration of 5.5 mg/m3. The simulations were
conducted for a model time of 4 hours.
Fig. 7 presents the results from these runs. The
masses predicted to reside on ®lters after 4 hours for
runs B, D, and F were divided by the mass predictions for runs A, C, and E respectively to show the
e€ect of the cycle time on ®lter collection. The eciency of the ®lters in these model runs was the
same throughout. The results indicate that the quantity of mist retained by the ®lters decreased with the
fraction of time the mist was present. When mist
was present all of the time, nearly 100% of collected
mist remained on the ®lter after 4 hours. When mist
was present only 12 s of every minute, about half of
the collected ¯uid evaporated into the air stream. If
background vapor were included in the model when
no mist was present, the retention of liquid shown
in Fig. 7 would be higher. Fluid retention would be
expected to decrease for a lower incoming mist concentration or a more volatile ¯uid.
The ®ndings in Fig. 7 have implications for the
design of mist collectors. They suggest that it is important to maintain a steady concentration of mist
entering a collection ®lter to minimize evaporation.
Having large mist collectors servicing many metalworking machines, for instance, might lead to less
evaporation than having small collectors connected
to individual machines. Because many machines are
not likely to cycle together, the load to a large mist
collector will be more constant. For exposure assessment, these ®ndings suggest that variations in mist
concentrations during sampling can have signi®cant
e€ects upon the quantities measured.
The mass loadings in this study were smaller than
quantities of liquid accumulated typically on industrial ®lters. Nonetheless, ¯ows passing through
industrial ®lters wetted by semi-volatile compounds
are likely to be saturated with vapor because air is
saturated more easily as the amount of liquid present increases.
CONCLUSIONS
Using di€usion theory and conservation of mass,
a model has been developed to predict evaporation
Fig. 7. Model predictions for the percentage of collected mineral seal oil mist that remains on a ®lter after four hours
when mist and vapor input are cycled on and o€ for the times indicated.
Evaporation of accumulated multicomponent liquids from ®brous ®lters
of semi-volatile liquids collected on ®brous air ®lters. This model improves upon existing models by
assuming that liquid accumulates as drops on ®bers
rather than spreading evenly over ®ber surfaces.
Model predictions and experimental measurements
of evaporation from ®lters suggest that the air passing through a wetted ®lter can be saturated easily
with vapor. If the retained liquid is pure when clean
air passes through the ®lter, the evaporation rate
will be constant until all of the ¯uid has evaporated.
However, if the liquid is a mixture, results indicate
that the more volatile compounds will evaporate
®rst. Fluctuations in the concentration of mist being
®ltered may lead to additional volatilization of collected ¯uid.
The ®ndings suggest that failing to account for ®lter evaporation can cause signi®cant underestimation of exposures to semi-volatile mists. In mist
control applications, oily liquids can evaporate and
then, upon recirculation to the workplace, recondense in either the air, to form potentially hazardous
mists, or on cool surfaces, to present safety or
housekeeping problems. Excess air¯ow to mist collectors should, therefore, be minimized in such situations. For example, turning o€ air¯ow to mist
collectors when metalworking machines are idle can
potentially reduce workplace vapor concentrations
considerably. Also, using large, centralized mist collectors to provide control for many machines will
lead to less evaporation than using small collectors
dedicated to individual machines since ¯uctuations
in incoming concentrations will be smaller for the
centralized collector.
AcknowledgementsÐThe work presented in this paper was
made possible by a gift from the Ford Motor Company
and the United Auto Workers to support research in air
engineering at the University of North Carolina, and by
EPA STAR Fellowship #U-914812. The authors also
thank the Hewlett±Packard Company for donating the gas
chromatograph/mass spectrometer used in this study and
Evanite Fiber Corporation for supplying the ®bers.
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