Aerosol collection in magnetically stabilized fluidized filters

Papers Aerosol collection inmagnetically stabilized fluidized filters Jesusa Rincon Dpto. de Quimica Analitica e Zngenieria Quimica, Universidad de Alcala de Henares, Alcala de Henares, Madrid, Spain

An experimental study of aerosol filtration in a magnetically stabilized fluidized jilter (MSFF) was conducted in order to compare the performance of MSFFs with fied-bedfilters. The experiments were carried out using polydispersed aerosols from which unit collector efficiencies for aerosols of different sizes (i.e., graded efJiciencies) were determined. The experimentally determined unit collector efficiencies were compared with five empirical correlations of collection ef$ciencies of fixed-bed filters proposed by various investigators during the past decade. The comparisons yielded only order of magnitude agreement, suggesting that the similarity between MSFFs and fixed-bed filters is only approximate.

Keywords: filtration; aerosols; fluidized filters; magnetic stabilization; particles

Introduction A fluidized bed of magnetizable particles can be stabilized by applying an external magnetic field as Rosensweig showed some time ago.‘J Magnetic stabilization suppresses gas bubble formation and retards solids mixing even at high gas flowrates while maintaining low pressure drop across the bed. Earlier work in this area was focused mostly on the transitions between different operating regimes and the effect of the magnetic field on bubbling amplitude and frequency. Subsequently, systematic observations and interpretations of these phenomena have been reported.= Several authors2,7 have mentioned the possible application of this stabilization technique for aerosol filtration because of its potential for continuous particulate removal at high temperatures and pressures. More recently, Tien and coworkers&l0 and Geuzens and Zoenes” have examined the various aspects of aerosol filtration in magnetically stabilized fluidized filters (MSFFs). The work of Warrior and Tien9 and Albert and Tien* was mostly concerned with the dynamic behavior of MSFFs and specifically, the variations of collection efficiency and pressure drop across a filter over relatively long periods of operation. They found that bed bubbling caused by either the small disturbances in filters operated near the zone of marginal stability or Address reprint requests to Dr. Rincon at Dpto. de Quimica Analitica e Ingenieria Quimica, Universidad de Alcala de Henares, Alcala de Henares, Madrid, Spain. Received 15 August 1990; accepted 16 April 1991

0 1991 Buttetworth-Heinemann

the reduction of intergranular magnetic forces in MSFFs due to significant aerosol deposition may decrease both the collection efficiency and pressure drop. They also observed that substantial particle reentrainment occurred in shallow MSFFs while filters of greater depth did not show this feature. In contrast, the experimental work reported in this paper was made in order to examine the behavior of MSFFs during the initial stage of the filtration process. The experiments were conducted under the inertialimpaction-dominated regime. The results were examined and compared with those that would be obtained in an identical filter operating in the fixed-bed mode. Specifically, the aims of the study were first to determine whether, as an approximation, empirical correlations for the initial collection efficiency of granular fixed-bed filters may be used to predict particle collection in MSFFs, and second, based on the data collected, to develop a new correlation for collection efficiency in MSFFs.

Theory In a magnetically stabilized bed, on defluidization, bed height and porosity remain constant with decreasing air velocity. Furthermore, the gas flow rate pressure drop data can be represented by the Carman-Kozeny equation.12 Both observations suggest that fixed beds may be formed at gas velocities above umf with the application of a magnetic field. Therefore, as an approximation, an MSFF may be seen as a fixed-bed filter of uniform voidage. If an MSFF may be considered as a fixed bed, then Separations

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1991, vol. 1

245

Magnetically stabilized fluidized filters: J. Rincon the classical aerosol filtration theory becomes applicable in describing the performance of MSFFs. According to the classical granular filtration theory,13 a fixedbed filter is composed of a number of unit bed elements. A filter’s ability to retain aerosols may be described by the collection efficiency of the unit bed element, E (or the unit collection efficiency). The expression commonly used to relate the total collection efficiency, n with E when the bed is relatively free of deposited particles, ist3 q =

*f = Cinf

1 -

1 -

K,(l

_

E)

$E ‘

where ceff and ci,f denote, respectively, the effluent and influent particle concentrations, H, the bed height, E, its porosity, and d,, the collector diameter. Kr is a constant, and the following values have been used for Kr : 1.5 by D’Ottavio and Goren,14 1S/(1 - a)213by Tardos et al., I5 [6/(1 - E)~~T]“~by Pendse and Tien,16 Yoshida and Tien,r7 and Jung et a1.r8 It is obvious that depending on the value of Kr used, different values of E are found from the same experimental data. This, however, does not present any difficulty since the E obtained by using a particular value of K1 can be readily converted to those based on the other values of K,. Equation 1 may be used to determine E from experimental results of influent and effluent concentrations during the initial period of filtration. The unit collector efficiency is usually assumed to be the sum of the collection efficiencies due to the various operative mechanisms of particle collection:

diffusion, inertial impaction, gravity, and interception. Therefore, one may write Z% = (E~)D + (ZL)i +

6%)~

+ (G)z

where the subscripts D, i, G, and Z refer to the four different collection mechanisms: Brownian diffusion, inertial impaction, gravity, and interception. The subscript o denotes the initial state. Over the years, a large number of investigators14,17-22have proposed correlations (theoretical, empirical, or semiempirical) for predicting the single (or unit) collector efficiencies due to these mechanisms. These correlations, together with Equation 2, can be used for estimating E,.

Experiment Apparatus The apparatus used in this work is shown in Figure I and was similar to the one used earlier by Warrior and Tien9 with some minor modifications. It can be briefly described as follows. Air supplied from the compressor was passed through a series of prefilters, dryers, and filters to remove impurities and moisture, then split into two parts, one of which was used to operate the aerosol generator. The exit air stream from the generator was combined with the other part at the mixing chamber and entered into the experimental filter. The experimental filter itself consisted of magnetite grains supported by a 70 Tyler mesh screen with open-

Notation AT

B c ceff Cinf

D ds

H Hmf KI NC

246

Happel’s hydrodynamic factor, 1 - 1.%X’ + 1.5Q? - (Y’6 dimensionless number defined as 2(1 - (Y’S)I(Y” magnetic field Cunningham’s correction factor effluent particle concentration influent particle concentration diffusion coefficient aerosol diameter collector diameter dimensionless pore constriction diameter single collection efficiency dimensionless parameter, 1 + 1.75NR,/[150(1 - a)] bed height minimum fluidization bed height dimensionless constant dimensionless number for sedimentation, 2&(p,p)gC/9u~ Peclet number, ud,lD Stokes number, udzp,CIp modified Stokes number, NslF effective Stokes number, f(Ns,, NR~, E)

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1991, vol. 1

(2)

NR NR~ U Umf

relative size parameter, da/d, Reynolds number, ud,plp superficial gas velocity minimum fluidization velocity

Greek letters ff ffl (Y” & El. r) P PU (+

solids fraction dimensionless constant (1 - &)I/3 dimensionless constant, 2 - 3a’ + 5a!‘5 - 20!‘6 bed porosity gas viscosity total collection efficiency gas density aerosol density specific deposit

Subscripts D fr G 0

diffusion inertia interception gravity initial

Magnetically stabilized fluidized filters: J. Rincon Table 1

-J-d?

Characteristics

of the collector particles

-ter

fi

absohte filter

silica gel

mr

3

Tyler mesh

Average size (pm)

Density

24-32 32-46 48-70

595 385 250

4.16 4.16 4.16

(g/cm3) 0.420 0.240 0.102

was used to prepare the test aerosols. The particle diameter ranged from 0.5-2.0 pm. The collector particles (i.e., filter grains) were magnetite grains of three different size fractions supplied by N/L Chemical MacIntyre Division (Tahawus, NY, USA). Table 1 lists their relevant properties. The experimental variables considered in this work included gas velocity, magnetic field intensity, and collector and aerosol diameters. Table 2 gives the ranges of the variables covered in the experiments.

silica gel

dryer

Procedure

Figure 1

Schematic

diagram

of the experimental

apparatus

ings of 210 pm inside a plexiglass column, 5.08 cm internal diameter, and 77 cm high. This column widened into a disengagement chamber for removing elutriated fluidized particles. Sampling probes and pressure taps were placed at both the top and bottom of the filter bed. To stabilize the fluidized filter, a magnetic field was provided by two magnetic coils surrounding the filter. The magnetic field was created by winding 560 m of 18 AWG magnet wire around two plexiglass columns, 15.2 cm internal diameter and 8 cm high. Each coil had a resistance of 11.84 ohm and, when connected in series, could produce a magnetic field intensity up to 200 oersted. A homemade DC power source supplied a maximum of 5 amp of current to the coils. Two fans were placed next to the coils to cool and reduce the heating effect if necessary. The performance of the MSFF was determined by sampling the influent and effluent streams. Aerosol concentrations of gas samples were determined by connecting the proper probe to a TSI Aerodynamic Particle Analyzer interfaced with an Apple IIc Microcomputer. Systems and variables Talc powder with density of 2.14 g/cm3 and approximately represented by the formula Mg6(Si02)4(0H)4

Before each experiment, dry silica gel was placed into the dryer and the desired amount of magnetite particles, previously screened and washed, was charged into the column. After these preliminary steps, the compressor was switched on, the aerosol generator started, and the purge line opened. Once the operation of the aerosol generator reached the steady state, the purge line was closed and the aerosols were allowed to pass through the filter bed with the magnetic field turned on. The measurements lasted approximately 40 minutes. During this period, aerosol samples were taken successively at both the inlet and outlet of the filter and analyzed by the Aerodynamic Particle Sizer.

Table 2

Experimental

Experiment

variables

d, (pm)

UIKnf

H,f

(ml

B

(oersteds)

E-l * E-2

250 250

1.50 1.50

1.8 1O-2 1.8 1O-2

100 150

;:; E-5 E-6 E-7’ E-8 E-9 E-10 E-l 1 E-12 E-13 E-14 E-15 E-16 E-17 E-18

250 250 250 250 250 385 385 385 385 385 595 595 595 595 595

2.00 1.50 2.00 2.00 2.50 2.50 1.50 1.50 1.50 2.00 2.50 1.25 1.25 1.25 1.50 1.75

1.8 1.8 1.8 1.8 1.8 1.7 1.7 1.7 1.7 1.7 1.6 1.6 1.6 1.6 1.6

200 150 150 200 150 200 100 150 200 150 150 100 150 200 150 150

* Experiments

conducted

Separations

under marginal

Technology,

1O-2 lo-* 1O-2 IO-* lo-* lo-* 10-2 10-2 10-2 10-2 IO-2 lo-* lo-? lo-* lo-* lo-*

state of stability.

1991, vol. 1

247

Magnetically stabilized fluidized filters: J. Rincon Data treatment The measurements made in the filtration experiments were the influent and effluent aerosol concentrations, cinf and ten, at various times. The total collection efficiency, obtained according to its definition, is r)=

Cinf -

Cefj

Gnf

Equation

1 may be rewritten as

4

E”=z [ K,(l

1 - E)

1Ml- %I

I

Figure 2

In applying Equation 4 for determining E, from experimental data, H is taken to be the bed height at the incipience of fluidization, H,,,f, instead of the actual bed height, H. The difference between H and H,,,f, however, was rather small and insignificant under the conditions used in the experimental work. As pointed out earlier, as an approximation, E, may be expressed as 6%)~

+

(&)I

(2)

where (E,)o, (Eo)i, (Eo)c and (E,)I are, respectively, the initial collection efficiencies due to diffusion, inertia, sedimentation, and interception. Among several investigators, Rajagopalan and Tien19 gave expressions for (EJD and (E,)G and Lee*’ for (E,), . They are (EJD = 4Af’3N;:‘3

(6)

(Eo)c = (1 - E)‘~NG

(7)

(&Jr =

lS(1 - &)5’3

(8)

A&

where A,, NJ+, NG, Np,, and AT are dimensionless numbers whose definitions are given in the notations. One can therefore apply Equations 2, 6, 7, and 8 to determine (Eo)i by first estimating (E,)o, (Eo)c, and (Eo)I from Equations 6-8 and then subtracting them from the experimentally determined E, . Similarly, one can also obtain (Eo)l,i defined as E, - (E,)D - (E,)G.

Results and discussion Previous experiments Preliminary tests were conducted to determine the optimal bed height to be used experimentally. Results of these tests showed that with a bed height of 1.8 cm or greater, the total collection efficiency was close to 100% (Figure 2). It is well known that the total collection efficiency should be significantly less than 100% for an accurate estimation of theunit collector efficiency from experimental measurements. One possible way of doing this is to reduce the bed height to its smallest value possi248

Separations

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1991, vol. 1

0

I

I

I

I

I

1

0.7

a9

1.1

1.3

1.5

1.7

1.9

4 (4

where K, is given as

& = (E~)D + (&)i +

1

0.5

Total collection efficiency in MSFFs

ble. However, it was also found that, for the experimental conditions used in this work, a minimum bed height of 1.5 cm was required in order to prevent bed bubbling and/or spouting. This condition was therefore used in subsequent experiments. However, even with this low bed height, spouting was nevertheless observed in two runs (see later sections for more details). Accuracy

of the experimental

data

The accuracy of the experimentally determined initial collection efficiencies can be assessed by examining the internal consistency of the E,, data and the data reproducibility; namely, by comparing the results obtained from different runs under identical conditions. The internal consistency of the data can be seen by examining the time dependence of E, obtained in an experimental run. It is worth noting that since the experiments were conducted using dilute aerosols over relatively short periods of time (<9 mg/m3 in influent concentration and approximately 40 minutes in duration), the amount of particles collected was slight and the specific deposit value was always ~10~~. The effect of particle deposition was therefore negligible. Accordingly, the values of E, obtained at different time should be roughly the same. This self-consistency is shown in Figure 3. The reproducibility of the results can be seen by comparing the measurements obtained from two independent runs (E-4 and E-5) carried out under identical conditions (except the influent concentration) shown in Figures 4A and 4B, where the values of cid, ceff, and cefflcinf vs. time are presented. It was found that, for a given run, the influent concentration fluctuated (Figure 4A), indicating either the limitations of the aerosol generator in producing aerosol suspensions at constant concentrations or the inaccuracy of the particle counter. The first. reason seems more likely since the effluent concentrations oscilated as well (although the amplitude of the fluctuations was much less). Figure 4B shows that the concentration ratio, c& cinf, obtained from these two runs remained essentially constant and independent of the influent concentration

Magnetically I

I

I

I

1

I

stabilized fluidized filters: J. Rincon

I,

I

I

’

I

I

: E-4 : 20.4 Clnn 250 lrm :

EXP

30-

U 20 -

‘c

B :

150

OWStEdS

:

7.0.4crms

dc:

25OJUII

8 :

150 oerstads

”

key

Exp. No.

I

I

I

12

21

30

.

Time (min) Figure 4B

I

I

I

I

I

I

I

06

08

10

1.2

1*

lb

1 1s 2.0

I

NQx lo2 Figure 3 Variation with time of the individual ciency in stabilized filters

collection

effi-

(6920 part./cm3 for run E-4, and 6440 part./cm3 for run E-5). These findings suggest that both the internal consistency and the reproducibility of the data are good. The particle size distributions at both the influent and effluent streams of run E-4 are presented in Figure 5. The influent stream had a higher proportion of small particles (less than 0.66 pm) than the effluent stream. Although the size distribution of the influent streams were slightly different for runs E-4 and E-5; similar results were seen in both cases, attesting to the reliability of the particle counter.

Evolution with time of the concentration

ratio, c&c~,~

Two experimental runs (runs E-l and E-7) were made under marginally stable conditions. The value of E, vs. Ns, of run E-7 at different times are shown in Figure 6 and the pressure drop history in Figure 7. Unlike Figure 3, the total collection efficiency de-

sag1

oa!

95

80

50

20

5

Figure 4A Evolution with time of influent and effluent particle concentrations

Particle size distributions

Separations

EXP

: E-4

u:

2OACWs

B

: 150 08.

of the influent and effluent

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1991, vol. 1

249

Magnetically stabilized fluidized filters: J. Rincon

EXP :. E-7

: 2!js cm/s

u

dc : 250 )Im

B : 150 oenteds

n sampling

at 3 min.;

0 : 8.4-tOe6

12

(1

0 : 3.4.10-5

11

21

11

u:s.a.lo~;

1’

30

”

0 : 5.4.10

A

11

0 A

I

0.6

I

I

I

I

I

I

oa

1.0

l.2

1.4

1.6

18

2.0

Ns,x lo2 Figure 6 Variation with time of the individual ciency in marginally stabilized filters

collection

effi-

creased and fluctuated significantly with time. In contrast to the results obtained in other runs, the pressure drop across the bed of run E-7 did not remain constant with time. In fact, the pressure drop decreased at a time (see Figure 7), coinciding with the observed decrease in E, (see Figure 6). Visual observation of the bed structure during runs E-l and E-7 indicated bed spouting at the time pressure drop decrease took place. Bed spouting, however, did not persist in either run. Instead there was a rearrangement of the magnetite particles, leading to the presence of a metastable bed structure. Therefore, one may hypothesize the following sequence of events taking place in these two runs. Bed spouting led to channel formation and, 1

I

consequently, to a decline in both pressure drop and collection efficiency. Then, the magnetite granules rearranged themselves due to intergranular magnetic forces, and the channels were partially destroyed. Consequently, both the efficiency and pressure drop increased as shown in Figures 6 and 7. This hypothesis is consistent with the fact that these two runs were conducted under conditions of marginal stability. The MSFF operated near its marginal state is believed to possess a metastable structure. The decline in collection efficiency and pressure drop may be attributed to the growth of instabilities due to small disturbances in a metastable state.‘* The experimental runs E-9, E-10, and E-11 were made under identical conditions except for the magnetic field intensity. The results are shown in Figure 8 in which the total collection efficiency is given as a function of the Stokes number. It can be seen that increasing magnetization beyond that necessary for stabilization has no further effect. Similar results were obtained with other collector sizes at various gas velocities. Finally, it is worth noting that, in determining E, from experimental results obtained under stable conditions, the average values of E, over the entire time period were used. For experiments performed under conditions of marginal stability, E, was taken as the average value before the onset of the significant decline of E,. Comparison of magnetically jilters with fixed-bed jilters

stabilized jluidized

Several investigators 8,9~11 have attempted comparisons of the performance of MSFFs with fixed-bed filters. These comparisons, however, were based on overall collection efficiency and do not offer any conclusions as to the degree of agreement between experimentally determined unit collector efficiencies and predicted values for fixed-bed filters. In contrast to the earlier

I

3-

2-

” 0

c $

A 0

A %

EXP: E-7

l-

: 36 Cllv~ 01 lOOoers1eds B= 150 “ B= 200

”

I : 255 GUI lc: 250 flu 5: 150 Dml* I

I

I

10

20

30

NSI Time (min) Figure 7

250

Pressure drop vs. time in marginally

Separations

stabilized beds

Technology, 1991,vol. 1

Figure 8 ters

Effect of the magnetic

field strength in stabilized fil-

Magnetically Table 3

Correlations

stabilized fluidized filters: J. Rincon

for the initial collection efficiency Remarks

Expressions

Authors Paretsky (1972)

(E,)j = 2/v&:3

For Nst < 0.01

Meisen and Mathur (1974)

(E& = 7.5 10-4

For Nsr < 0.01

Schmidt et al. (1978)

(,Qj = 3.75Ns,

For Nst < 0.05

Thambimuthu

Eo)i

(1980)

For 2 1O-3 < Ns, < 2 lo-* 0.33 < E < 0.40

3

NSC =

Nst + 0.062~

1

N3.55

D’Ottavio and Goren (1983)

(.&Ii =

Nste,, = [A(a) + l.l4N~:(l

Ste/f 1.67 + N3.== SCerf

A(a) =

- (r)-“*INS,

6-6a” (6 - 9a”3 + 9aY3 - 6a2)

a=l-E N& = FNsr

2(N;r)3.g Gall et al. (1985)

(.&Ii =

4.3 1O-6 + (N;f)3.g

F = 1 + 1.75NR,l[150(1

- E)]

B = 7 - 6 exp(-O.O065N& Yoshida and Tien (1985)

(E,),, = B [Nsl + 0.48 (4 - 9

- s)“*F] For NR 2 0.002 Nst < 0.01

(E&,

= 19 [lOON&

+ 0.19 (4 - F c

Jung et al. (1989)

- $$)“* c

F] c

For Nsr < 1.2

(E,),, = 0.2589N;f:;’

studies, the present work gives unit collector efficiencies of aerosol particles of specified sizes. This body of data can be used to give a more exact comparison with fixed-bed filters than what was attempted before. A number of authors have developed correlations for unit collector efficiencies due to inertial impaction or the combination of inertial impaction and interception. A partial listing of these correlations is given in Table 3. Jung et a1.t8 showed that significant differences exist even among the more recent correlations. For example, D’Ottavio and Gorent established their correlations using a combination of the Stokes number, Reynolds number, and bed porosity (i.e., through a modified Stokes number, Nsr,e,r) as the independent variable. Thambimuthu,20 on the other hand, ignored the possible effect of the Reynolds number. The more recent work of Gal et a1.22 showed that omitting the Reynolds number may be incorrect. Among the various available correlations,’ although their accuracy and reliability are not known exactly, it is likely that the more recent correlations should provide better predictions because of the advances in particle-counting instrumentations made in recent years. The five correlations used in the comparison were all developed during the past decade. They are the correlations proposed by Thambimuthu,20 D’Ottavio and Gorent Gal et a1.,22 Yoshida and Tien,” and Jung et a1.18The first three correlations are based on the respective investigators’ own data, while the other two were developed using data obtained by several investigators . To compare the collector efficiency of MSFFs ob-

For NR 5 0.002 Ns, < 0.01

tained in this study with predictions from correlations of fixed-bed filters, the ratio of the predicted (&)i to experimental (Eo)i at various Nsr was first calculated and the results are shown in Figures 9-11. Figures 9A-C give the data obtained using magnetite particles of diameter of 250 pm. The correlations that best fit the experimental data are those of Yoshida and Tien and Thambimuthu. The comparisons with the correlation of Gal et al. show that, at both large and small Stokes numbers, experimental and predicted values of (Eo)i differ by more than one order of magnitude. Correlations by D’Ottavio and Goren and Jung et al. underestimate the collection efficiency over the entire range of the Stokes number used in this experimental study. For experiments using magnetite particles 385 pm in diameter, the quality of the comparison varied with the gas velocity (Figures IOA-C). Thus, for ulu,f = 1.5, the best agreement was found with correlations by Thambimuthu and Yoshida and Tien, followed by Gal’s. The correlations of D’Ottavio and Goren and Jung et al. underpredict (Eo)i. For larger velocity ratios, namely, ulu,,f = 2.0 and ulu,f = 2.5, the correlation by Jung et al. gave the best agreement, followed by the correlation of D’Ottavio and Goren. The other three correlations all overestimate (Eo)i . For magnetite particles 595 wrn in diameter, the correlations of Yoshida and Tien and Thambimuthu gave the best agreement with data for u/u,,,~ = 1.25 and 1.50 (Figures IZA and ZZB). For ulu,,,f = 1.75 these correlations together with those of Jung et al. gave a more accurate prediction than the other two (Figure IIC). Separations

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1991, vol. 1

251

I---0 0 0 A A

D’Ottavio and Goren, 1983 Yoshida and Tien, 1985 Thambiiuthu, 1980 Gal et al., 1985 Jung et al., 1989

I I II I I I If 0 DQttavio and Goren, 1983 0 Yoshida and Tien, 1985 0 Thambimuthu, 1980 A Gal et al., 1985 A Jung et al., 1989 A

I

I

III

I

0 D’Ottavio and Goren, 1983 l Yoshida and Tien, 1985 0 Thamhimuthu, 1980 A A Gal et al., 1985 A Jung et al., 1989 A

A

u/u, = 1.5

10' -

A

u/u_ = 2.0

A A

0 8i

8

A

An

a

A

100

0 B

0

A

o

t0

A

ii

A

.=

0

A A

0

A 0

0 A

0

A

b IIll

I

I J-d_Lz 0

A

A

0

9

0

A

0

A

A A

A

A

A

I

II

10-2

10-2

Nst Figure 9

Comparison

of experimental I

-

0 0 0 A A

10' -

data with results from correlations

I I’ I I I II DWttavio and Goren, 198? Yoshida and Tien, 1985 Thambiiuthu, 1980 Gal et al., 1985 Jung et al., 1989 A

I 0

I

(d, = 250 pm) I11

I

III

D’Ottavio and Goren, 1983 l Yoshida and Tien, 1985 0 Thambimuthu, 1980 A A Gal et al., 1985 4 Jung et al., 1989 A A u/uml =

u/u, = 1.5

2.0

0

A

A

08

A A

cp

0

@‘O

A

8.

A@

Am

0

B

loo AD

OA A

0 0

.8

.

A

A

10-l

A :

0

0

A

li-_dLl 1o-2

b I

llldl

I

I

II

10-2 %t

Figure 10

252

Comparison

Separations

of experimental

Technology,

data with results from correlations

1991, vol. 1

(d, = 385 wm)

Or

1

Magnetically stabilized fluidized filters: J. Rincon Table 4

Summary

of correlations

that best fit the experimental

Run

d, pm

E

E-l E-4 E-8 E-9 E-12 E-13 E-14 E-17 E-18

250 250 250 385 385 385 595 595 595

0.523 0.523 0.523 0.495 0.495 0.495 0.464 0.464 0.464

*J, Jung et al.; T, Thambimuthu;

data

NU 2.0 2.0 2.0 1.3 1.3 1.3 8.4 8.4 8.4

NR*

10-3-8.0 10-3-8.0 10-3-8.0 10-3-5.2 10-3-5.2 10-3-5.2 lo-“-3.3 1O-4-3.3 10-4-3.3

1O-3 1O-3 1O-3 1O-3 1O-3 1O-3 1O-3 1O-3 10-3

-

10’ -

I I III I I lr o D’Ottavio and Goren, 1983 0 Yoshida and Tien, 1985 0 Thambimutbu, 1980

* Gal et al., 1985 A ‘Jung et al., 1989 u/a,

2.7 3.6 4.5 9.8 13.1 16.3 22.1 26.5 30.7

4.8 6.5 8.1 7.4 9.9 1.2 7.0 6.5 9.7

10-3-3.1 10-3-4.2 10-3-5.2 10-3-4.8 10-3-6.4 10-3-8.0 10-3-4.5 10-3-4.2 10-3-6.3

1O-2 IO-* lo-* 1O-2 1O-2 lo-* 10-Z 1O-2 lo-*

T, T, T, T,

Y-T Y-T Y-T Y-T J J T, Y-T T, Y-T, J T, Y-T, J

Y-T, Yoshida and Tien.

While Thambimuthu’s and Yoshida and Tien’s correlations tend to overestimate the efficiency at high Stokes numbers, the correlation of Yoshida and Tien underestimates (Ei)o at low Stokes numbers. A summary of the comparisons is given in Table 4. In the last three figures (Figures 9-lZ), it can be seen that the five correlations, on the average, tend to underestimate (Ei)o at low Ns, and overestimate at high Nst. Although the overestimation may be attributed to

1

Correlation*

Nst

A

I

0

0 0 A A

the bouncing off effect of impacting aerosols, which becomes significant at high particle inertia, there is no ready explanation for the underestimation except that correlations of (Ei)o based on fixed-bed filter data are not sufficiently accurate for predicting aerosol collection on MSFFs. It follows that there is a need to develop a correlation of (Ei)o for MSFFs. Such a correlation was attempted, and the result is given in Figure I2 in which log (Ei)o is plotted against

I

I II

u/u,,,= A

I

II

1 0

0 Yoshida and Tien, 1985 0 Thambimuthu, 1980

a Gal et al., 1985 A Jung et al., 1989

A

A

= US

I

D’Ottavio and Goren, 1983 Yoshida and Tien, 1985 Thambimuthu, 1980 Gel et al., 1985 AA Jung et al., 1989 *

1.50 A

8

A

0

00

A

0

0.

00 A 0 -0

l

8

.

O AA i AA

0

A

A

0

A

Ir

0

9

A

I

A

0 A

_$

0

0

d

qo ql?l

q :*

A 0

E?: l

b

C I

I

III

I

I

II

1

lo-*

Nst Figure 11

Comparison

of experimental

data with results from correlations

(d, = 595 pm)

Separations

Technology,

1991, vol. 1

253

Magnetically

stabilized fluidized filters: J. Rincon

for his encouragement course of this work.

O.,O”-’

and suggestions

during the

References 1.

Rosensweig, R.E. Magnetic stabilization of the state of uniform fluidization. Ing. Eng. Chem. Fundam. 1979, 18, 260269

2. 3.

4. 5.

6. Figure 12 number

Inertial

collection

efficiency

vs. effective

Stokes 7. 8.

log N;, e where Nst,en is the effective Stokes number. The resu t may be expressed according to

9

9.

(9)

10.

As seen from Figure 12, there exists considerable scattering among the data points, and this correlation is capable of predicting (Ei)o within the same order of magnitude. In contrast to the five correlations that, on the average, predict (Et)0 for fixed-bed filters within a factor of two or three, Equation 9 is a less accurate correlation. That Equation 9 has less accuracy can be at least partially attributed to the fact that polydispersed aerosols of irregular shapes were used in the present work, while the five correlations of fixed-bed filters were based on experiments conducted with monodispersed spherical particles. Future studies using better defined test aerosols may therefore be desirable.

11.

1988, 67, 229-242

12.

13. 14. 15.

16.

This study was conducted at the Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY, USA, during the author’s visit there (1989-1990). The author would like to thank the Ministry of Science and Education of the Spanish Government for providing the financial support for the visit and to Professor Chi Tien of Syracuse University

677-686

17.

Yoshida, H. and Tien, C. A new correlation of the initial collection efficiency of granular aerosol filtration. AIChE J.

18.

Jung, Y.; Walata, S.A. and Tien, C. Experimental determination of the initial collection efficiency of granular beds in the inertial-impaction-dominated region. Aerosol Sci. Technol. 1989, 11, 168-182 Rajagopalan, R. and Tien, C. Trajectory analysis of deep bed filtration with sphere-in-cell porous media model. AIChE J.

19.

1976, 22, 523-533

20. 21. 22.

* The definition of Nsr.eAis shown in Table 3.

Separations

Cohen, A.H. Aerosol filtration in magnetically stabilized fluidized beds. Masters Thesis, 1986. Syracuse University, Syracuse, NY, USA Tien, C. Granular Filtration of Aerosols and Hydrosols. BOSton: Butterworths, 1989 D’Ottavio, T. and Goren, S.L. Aerosol capture in granular beds in the impaction dominated regime. Aerosol Sci. Technol. 1983, 6,91-108 Tardos, G.I., Gutfinger, G. and Abuaf, N. Deposition of dust oarticles in a fluidized bed filter. Israel J. Technol. 1974, 12, i84-190 Pendse, H. and Tien, C. General correlation of the initial collection efficiency of granular filter beds. AZChE J. 1982,28,

1985. 31, 1752-1754

Acknowledgments

254

Rosensweig, R.E. Fluidization: Hydrodynamic stabilization with a magnetic field. Science 1979, 204, 57-60 Sieguell, J.H. Radial dispersion and flow distribution of gas in magnetically stabilized beds. Ind. Eng. Process Des. Dev. 1982, 21, 135-141 Lee. W-K. The reoloav of maaneticallv stabilized fluidized solids. AlChE Symp. Skr. 1983,222(79); 87-96 Stevens, J.G., Sieguell, J.H., Rosensweigh, R.F., Mikus, T. and Lee, W.K. Magnetically stabilized fluidized beds with time-varying magnetic fields. Powder Tech&. 1988,56, 119128 Geuzens, P. and Zoenes, D. Magnetically stabilized fluidization. I: Gas and solids flow. Chem. Eng. Commun. 1988, 67, 217-228 Katz, H. and Sears, J.T. Electric field phenomena in fluidized and fixed beds. Can. J. Chem. Eng. 1969, 47,50-53 Albert, R.V. and Tien, C. Particle collection in magnetically stabilized fluidized filters. AIChE J. 1985, 31, 288-295 Warrior, M. and Tien, C. Experimental investigation of aerosol filtration in magnetically stabilized fluidized bed filters. Chem. Eng. Sci. 1986, 41, 1711-1721 Cohen, A.H. and Tien, C. Aerosol filtration in a magnetically stabilized fluidized bed. Powder Tech., 1991, in press Geuzens, P. and Zoenes, D. Magnetically stabilized fluidization. II: Continuous gas filtration. Chem. Eng. Commun.

Technology,

1991, vol. 1

Thambimuthu, K.V. Gas filtration in fixed and fluidized beds. Ph.D. diss., 1980. University of Cambridge Lee, K.W. Maximum penetration of aerosol particles in granular bed filters. J. Aerosol Sci. 1981, 12, 79-87 Gal, E., Tardos, G. and Pfeffer, R. A study of inertial effects in granular bed filtration. AZChE J. 1985, 31, 1093-l 104