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Particle Detachment in Deep Bed Filtration
JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.
186, 307–317 (1997)
CS964663
Particle Detachment in Deep Bed Filtration RENBI BAI
AND
CHI TIEN 1
Department of Chemical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received June 17, 1996; accepted October 28, 1996
The paper examines the behavior of particle detachment in deep bed filtration and the dependence of particle detachment on several filtration operating parameters. Theoretical analysis was carried out by considering the balance of various relevant interaction forces. Based on the results, experiments were conducted to study the effect of particle size, filter grain size, and headloss gradient on particle detachment in deep bed filtration. In one set of experiments, the filter was operated at constant filtration rate in order to build up the headloss across the filter bed continuously. In the other set of experiments, the filter in operation was allowed to experience a short period of flow shock (i.e., to be subject to a higher flow rate during this period). Both sets of experiments confirmed the dependence of particle detachment on particle size, collector gain size, and headloss gradient (degree of filter clogging) of the filter, as predicted by the analysis. q 1997 Academic Press Key Words: particle detachment; particle redeposition; particle size; headloss gradient; flow shear shock; interaction forces; deep bed filtration.
INTRODUCTION
For considerable time, the controversy over whether or not detachment of deposited particles occurs in deep bed filters has occupied the attention of a number of investigators. Most early work did not consider particle detachment in filtration (1, 2). The strongest evidence against the presence of particle detachment was the observations of Stanley (3). Stanley conducted tests using radioactively labeled particles and found that those particles retained at the beginning of a filtration run remained in place during the entire period of experiment. Since then, opinion has moved gradually in favor of the view that particle detachment does occur, at least in later stages of filtration. This change was brought about by increasing experimental evidences, including video and microscopic observations of a model filter by Payatakes et al. (4) and endoscopic observations of the inside of a filter by Ives (5). Based on an analysis of filtration data of changes in particle size distribution of the effluent, Ginn et al. (6) contended that particle detachment was the cause of the shifting of particle size distribution of the effluent toward larger sizes during filtration. Melissa et al. (7) also reported 1
To whom correspondence should be addressed.
experimental results which indicated the occurrence of particle detachment and the dependence of particle detachment on particle size. The reason for particle detachment in filtration was explained either as a result of the flow shear forces overcoming the attachment forces (4) or instabilities caused by arriving particles (5). Even without a consensus on this problem, it was generally believed that increases in interstitial velocity due to the build up of deposit was instrumental in particle detachment. Mints (8) described particle detachment as being directly proportional to the specific deposit. Others (9, 10) assumed that particle detachment was directly proportional to the product of the hydraulic gradient and the specific deposit. As particles retained in a filter are subject to drag forces due to liquid flow, any increase in filtration rate tends to hinder particle deposition or promote the detachment of retained particles as the drag force is directly related to the interstitial fluid velocity. Although attention has been paid to whether or not there is particle detachment during filtration in the past, the effect of flow shear shock in filter operation has so far not been studied. Filters are often operated in groups. When one of the filters in one group is out of work for backwashing, the other filters have to operate at a higher capacity, in other words, to experience a flow shear shock. As a result, particle detachment or inhibition of particle from deposition can be expected. Consequently, a poor filtrate quality may result. The purpose of the present study is to present a simple analysis of the various factors which may affect particle detachment in filtration and to conduct experimental investigations in order to validate the conclusion of the analysis. THEORETICAL CONSIDERATIONS
The retention of particles in a filter bed requires that the adhesion force between a retained particle and a collector (i.e., one of the filter grains) is at least in equilibrium with the hydrodynamic force which tends to detach the particle. Particle detachment in filtration therefore occurs only when the hydrodynamic force overcomes the adhesive force. The mechanisms for particle detachment from filter grains include rolling, sliding, and lifting (11–13). The sliding mechanism implies that a deposited particle may slide be-
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a frictional force Ff arises in the direction opposite to that of FS to prevent the re-entrainment. The basic assumption is that if Ff õ FS , the lifting force Fl would then cause the particle to drift away from the collector and so particle detachment or dislodging in the filter takes place. Adhesion Forces The magnitudes of FL and FD may be given as (14) FL Å
1 Hd 3p 2 12 d ( d / dp ) 2
FD Å
2pee0 ( z 2p / z 2g ) ke 0 kd 1 0 e 02kd
[1]
S
D
2z p zg 0 e 0 kd , [2] z 2p / z 2g
where H is the Hamaker constant, d is the separation distance between the particle and the collector plane, e0 is the dielectric constant (permittivity) in vacuum, e is the relative dielectric constant of fluid, zp and zg are the zeta potentials of the particle and the collector (filter grain), respectively. k is the Debye reciprocal double layer thickness which, in monovalency electrolyte solutions, is given as
r FIG. 1. Schematic diagram of forces acting on a spherical particle attached to a collector plane with a stagnant film of liquid on the surface.
cause of the hydrodynamic tangential drag force acting on it. The rolling mechanism depicts that a deposited particle may roll due to the torque resulting from the asymmetry of the shear force acting on the deposited particle. As particle rolling can occur over a collector surface and does not necessarily lead to particle detachment, the following analysis is therefore based on the sliding and lifting mechanisms. In deep bed filtration, the diameter of filter grains in most cases is two orders larger than those of the particles to be removed. Thus, attachment of particles onto filter grains may therefore be treated as that of a spherical particle onto a collector plane. Figure 1 gives a schematic diagram of this representation. The filter grain has a diameter of dg and the particle diameter is dp . There is a liquid layer of thickness d ( d may be called the equilibrium separation distance) between the filter grain and the attached particle. The main forces acting on the particle include FL , FD , FS , Fl , and Ff , where FL is the London–van der Waals force which acts in the direction normal to the collector plane and is always attractive; FD , the electrical double layer force which also acts in the direction normal to the collector plane and is usually repulsive in water filtration. FL and FD are the adhesion forces responsible for particle attachment. FS is the drag force experienced by the particle due to fluid flow in the tangential direction along the collector plane, and Fl is the lifting force which is in the direction normal to the collector plane. FS and Fl are the two hydrodynamic forces. If the attached particle tends to be re-entrained due to fluid flow,
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kÅ
2e 2NA I , ee0kT
[3]
where e is the elementary charge, NA is the Avogadro’s number, I is the ionic concentration in the fluid, k is Boltzmann’s constant, and T is the absolute temperature. For a particle attached on the collector plane, the equilibrium separation distance d is usually much less than dp , or d / dp É dp , Equation [1] may be reduced to FL Å
Hdp . 12d 2
[4]
The net adhesion force for particle attachment onto the collector’s surface is therefore given by FAdh Å FL 0 FD Å 0
Hdp 12d 2
2pee0 ( z 2p / z 2g ) ke 0 kd 1 0 e 02kd
S
D
2zp zg 0 e 0 kd . z 2p / z 2g
[5]
To study the detachment of deposited particles, the extreme case where the attached particles experience only attractive force is considered. This situation applies to attached particles in close contact with collector surfaces. Hence by neglecting the effect of FD , the maximum adhesion force is (FAdh )Max É FL Å
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Hdp . 12d 2
[6]
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Hydrodynamic Forces
Ff Å kf FL Å kf
According to Saffman (15), the hydrodynamic lifting force for a single sphere in an unbounded linear shear flow may be written as Fl Å kl d 3p ( mn ) 00.5t 1.5 ,
[7]
where kl is the coefficient for lifting force, m is the dynamic viscosity, n is the kinematic viscosity of the fluid, and t is the shear stress acting on the collector plane. The hydrodynamic drag force on a spherical particle of diameter dp in contact with a planar wall in a slow linear shear flow has been calculated by Goldman et al. (16) and O’Neill (17) and can be directly related to the local wall shear stress t as FS Å 2.55lpd 2p t.
kf Å k *f 1 S,
6(1 0 e0 ) . dg
As 2 d p U. dg
[10]
V V Å , e e0 0 s
[11]
where V is the filtration rate and s is the bulk specific deposit in the filter bed (namely volume of deposit per unit filter volume). e is the filter bed porosity, and e0 is the clean filter bed porosity. Introducing Eq. [11] into Eq. [10] gives As 2 V dp . dg e0 0 s
[12]
F *f Å k *f
6(1 0 e0 ) Hdp . dg 12d 2
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[17]
Using Eqs. [17] and [12], the net force F, acting on an attached particle in a deep bed filter along the tangential direction is given as F Å F *f 0 FS Å k *f 1 3pm
6(1 0 e0 ) Hdp 0 2.551 dg 12d 2
As 2 V dp . dg e0 0 s
[18]
Accordingly, one may conclude that in deep bed filtration (1) there is no particle detachment if F § 0, and (2) there is a sliding of the deposited particle and subsequently its detachment if F õ 0. Further, it is desirable to replace s in Equation [18] with a more measurable quantity. When s ! e0 , the bulk specific deposit s may be related to the headloss gradient, i Å DH/ DL, approximately to be (19) i Å i 0 / khs,
The friction force Ff against particle sliding may be assumed to be proportional to the adhesive force, i.e.,
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[16]
Substituting Eq. [16] into Eq. [13], one has
In a bed packed with filter grains, the approach velocity U may be approximated to be the average pore velocity of the bed, or
FS Å 2.55l 1 3pm
6(1 0 e0 ) . dg
[9]
where AS is defined as 2(1 0 p 5 )/w [w Å 2 0 3p / 3p 5 0 2p 6 , p Å (1 0 e ) 1 / 3 and e is the porosity of a filter bed] and U is the approach fluid velocity. Introducing Eq. [9] into Eq. [8], one has
UÅ
[15]
Therefore Eq. [14] becomes kf Å k *f
FS Å 2.55l 1 3pm
[14]
where k *f is a proportionality constant and S is the specific surface area of a deep bed filter, defined as the surface area per unit filter bed volume. For a filter bed packed with uniform grains of size dg , S is given as SÅ
As t Å 3m U, dg
[13]
where kf is the coefficient of sliding friction. A similar treatment as Eq. [13] was also used by Visser (18). Equation [13] is based on a particle attached to a single collector. In a deep bed filter randomly packed with uniform filter grains, one must, however, consider the effect of neighboring filter grains. This may be achieved by assuming
[8]
Equations [7] and [8] are valid with linear velocity gradient near the surface. Using Happel’s model, the shear stress acting on the collector may be estimated as (14)
Hdp , 12d 2
[19]
where i 0 is the clean bed headloss gradient and kh is the
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coefficient for headloss increase due to particle retention. From Eq. [19], one may express s as sÅ
1 (i 0 i 0 ). kh
[20]
For a packed bed with spherical grains and under laminar flow, the Kozeny-Carman equation may be used to estimate i 0 as i 0 Å 180
mV (1 0 e0 ) 2 mV Å kh 0 2 , g rd 2g e 30 dg
[21]
where kh 0 Å 180 1 (1 0 e0 ) 2 /(g re 30 ) is the headloss coefficient for clean filter bed. Substituting Equations [20] and [21] into [18], one has F Å k *f
6(1 0 e0 ) Hdp 0 2.551 dg 12d 2 As 2 khV dp dg e0kh 0 (i 0 i 0 )
1 3pm
[22]
or F Å k *f
6(1 0 e0 ) Hdp dg 12d 2
0 ksmAs dg d 2p
V , e0kh d 0 (d 2g i 0 kh 0mV ) 2 g
[23]
where ks Å kh 1 2.551 1 3p with kh and kh 0 defined as before. Equation [ 22 ] or [ 23 ] indicates that the magnitude of F is dependent upon dp , dg , V, i , and d. Figure 2 illustrates the effect of dp , dg , V, and i on F . The values of the variables used in the calculation of the results shown in Figs. 2 ( a ) – 2 ( c ) are given in Table 1. The reason for selecting these values will be given later. It can be seen from these figures that F may change from positive to negative values; the latter indicating the possibility for particle detachment. From Fig. 2 ( a ) , one may conclude that larger particles under higher hydraulic gradients are more likely to be detached in filtration than smaller particles under lower hydraulic gradients. For a hydraulic gradient up to i Å 25, particles smaller than 4 mm will probably not be detached at all. In Fig. 2 ( b ) , it is observed that the small particles ( dp Å 2 mm) do not shown the possibility of detachment for filtration rate up to 20 m/ h, but for the large particle ( dp Å 14 mm) , on the other hand, detachment may occur at a filtration rate as low as 4 m/ h. Compared with the results in Fig. 2 ( a ) , Fig. 2 ( c ) indicates that particle detachment may be greatly reduced in a bed of smaller grain size ( dg Å 0.45 mm) , where it is shown that particles
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FIG. 2. Illustration of the variables affecting the magnitude of the net tangential force F for particle detachment in deep bed filtration. (a) dg Å 0.65 mm, V Å 4.8 m/h. (b) dg Å 0.65 mm, i Å i0 . (c) dg Å 0.45 mm, V Å 4.8 m/h.
up to about 6 mm may not be detached even though the hydraulic gradient arises to as high as i Å 25. EXPERIMENTAL WORK
Based on the results given before, experiments were conducted to investigate the effects of particle size, grain size,
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TABLE 1 Parameter Values Used in the Calculation of Fig. 2 kf* Å 3.79 1 1006 m
H Å 1.4 1 10020 kg m2/s2
m Å 0.001 kg /mrs
e0 Å 0.4
kh Å 110
d Å 3 1 10010 m
i0 Å 0.5 dg Å 0.00065 m kf Å 0.0035 dg Å 0.00045 m kf Å 0.0051
flow rate, and headloss (hydraulic) gradient on particle detachment in deep bed filtration. Details of the experiments are described in the following section. FIG. 4. Particle size distribution of the influent suspensions.
Material and Methods The experimental apparatus and the process flow scheme used in the experiment is shown schematically in Fig. 3. Test suspensions and clean water were held respectively in two storage tanks (2). A pump (1) was used to lift the fluid (suspension or clean water) from the respective storage tanks to an elevated constant-head tank (5). The fluid was then fed from this tank to the filter (7) at its top (i.e., the flow was downward). The filtrate from the filter then passed through the flow controllers (9) and flowmeters (10), and was discharged into the drain through the effluent constanthead tank (11). The test filter was made of a 138 mm diame-
FIG. 3. Schematic diagram of the experimental setup and the process flow scheme.
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ter plexiglass tube. Manometer and sampling points (8) with an internal diameter of 3 mm were placed in pairs into the bed at depths (from the inlet): 0, 25, 75, 125, 175, 225, 275, and 375 mm. These points were used for sampling and measuring the headloss. Ballotini glass beads of two different sizes (i.e., dg Å 0.6 Ç 0.71 mm and dg Å 0.42 Ç 0.5 mm) were used as the filter media. The porosity of the bed for the two media sizes was maintained at 0.402 and 0.396, respectively. Polydispersed suspensions were used in this study and a PVC powder (Corvic P72/757) was used for preparing the suspensions. The particles were spherical and their size ranged from less than 0.5 to about 14 mm. Test suspensions were prepared by first mixing the particles in a heavy duty emulsifier and then diluting the mixture with tap water to desired concentrations. Figure 4 gives the size distribution of the influent suspension. Samples were taken continuously through a peristaltic pump during the operation at a rate capable withstanding the effect of sedimentation (100 ml/ h) (20). Suspension samples were analyzed using a Coulter Counter, Model IIe (Coulter Electronics, Inc.). After each run, the filter media were taken out and manually cleaned using tap water, and then the bed was repacked to the original bed porosity for next operation. The primary objective of the experiments was to collect data which may reveal the presence of particle detachment and/or redeposition in filtration. Two sets of experiments were conducted. The first set was conducted at a rate of V Å 4.8 m/h until the total headloss across the filter bed (L Å 375 mm) HT reached a value of 1.2 m for the bed of dg Å 0.6 Ç 0.71 mm or 1.6 m for the bed of dg Å 0.42–0.5 mm. Samples and headloss measurements were carried out at the time corresponding to HT Å 0.4, 0.8, 1.2, and 1.6 m (for the finer media filtration), respectively. These experiments were made in order to observe particle detachment and/or redeposition in a normal filtration operation. For the second set of experiments, the filter in operation was made to experience a short period of flow shear shock (i.e., a sudden increase in flow rate). The procedure used
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TABLE 2 Experimental Program and Conditions Median size (mm)
Porosity
Temperature (7C)
Filtration rate (m/h)
First shock flow rate (m/h)
Second shock flow rate (m/h)
Total headloss before flow shock, HT (m)
A B
0.6–0.71 0.42–0.5
0.402 0.396
15.6–16.3 15.3–16.2
4.8 4.8
— —
— —
1.2 1.6
A B C D E F G
0.6–0.71 0.6–0.71 0.6–0.71 0.42–0.5 0.42–0.5 0.42–0.5 0.42–0.5
0.402 0.402 0.402 0.396 0.396 0.396 0.396
Ç Ç Ç Ç Ç Ç Ç
4.8 4.8 4.8 4.8 4.8 4.8 4.8
9.6 9.6 9.6 9.6 9.6 9.6 9.6
12 12 — 12 12 — —
0.4 0.8 1.2 0.4 0.8 1.2 1.6
Experiment I
II
17.4 17.9 18 15.7 16.6 15.3 16.2
18.6 18.6 18.7 16.3 17.2 16.2 16.6
Note. Influent concentration was about 110–120 mg/L.
was as follows. The filter was operated at a flow rate of 4.8 m/h until one of the pre-set headlosses (i.e., 0.4, 0.8, 1.2, or 1.6 m) was reached. The suspension flow was then replaced by clean water at the same flow rate. Once the clean water had displaced the suspension, the flow rate was increased to 9.6 m/h, and this was allowed to continue for 10 minutes. In some cases the flow rate of clean water was further increased to 12 m/h. This higher flow rate was only applied to those runs with preset headloss not greater than 0.8 m. Afterwards the flow of suspension at 4.8 m/h was resumed. Sampling and measurements were made before, during, and after the flow shear shock. These experiments yielded information on particle detachment and/or redeposition in filtration when a filter experienced a sudden increase in the flow rate and therefore the headloss gradients. A summary of all the experiments is given in Table 2.
particle detachment in smaller size media occurred to a lesser degree and took place at higher headloss gradients than those in a larger media. It is also interesting to note that particles smaller than 4 mm did not show any detachment in this study. Moreover, removal of particles less than 2 mm was actually improved (lower concentration ratio) at higher
RESULTS
Particle Detachment During Normal Operation Set I experiments were conducted at constant flow rate without any interruption during operation. To show the dynamics of particle removal and detachment during filtration, Figure 5 presents suspension particle concentrations at L Å 25 mm at times when the hydraulic gradient reached specified values. The results shown are concentration ratio (relative to the influent values) versus particle diameter. A concentration ratio of unity indicates that the particle concentration (volume) remains the same as that of the influent. Therefore particle detachment is shown if the concentration ratios exceed unity. Thus there is incontrovertible evidence (as shown in Fig. 5) that detachment of particles does occur in filtration. As predicted by the analysis, particle detachment was found to depend largely upon the particle size, grain size, and headloss gradient. Larger particles were shown to be more likely to detach and detachment became more significant at higher headloss gradient i. By comparing results of Fig. 5(a) with that of Fig. 5(b), it is clear that
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FIG. 5. Dynamics of particle removal and detachment in a filter bed with different grain sizes and under different headloss gradients, i (V Å 4.8 m/h, L Å 25 mm). (a) dg Å 0.60–0.71 mm. (b) dg Å 0.42–0.5 mm.
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(higher headloss gradient i), there is no evidence of particle detachment (i.e., concentration exceeds the influent values). Particle Detachment with a Flow Shear Shock In set II experiments, the flow rate and therefore the headloss gradient through the filter bed was suddenly increased for a while during filtration operation. The purpose was the observation of particle detachment under a flow shear shock. This condition happens in practice in water treatment plants when some filters are taken out of operation and the remaining ones have to receive additional flow. Samples were collected for analysis within the first 5 minutes during the flow shear shock. Figure 8 shows some typical results from a coarse media filter. The results here are examined in four particle size groups instead of in individual particle size for easy of presentation. The four groups of particles are defined as: Group 1, dp Å 0.63 Ç 1.26 mm; Group 2, dp Å 1.26 Ç 2.52 mm; Group 3, dp Å 2.52 Ç 5.04 mm; and Group 4, dp Å 5.04 Ç 12.7 mm, respectively. Particle detachment can be determined by whether or not particle concentrations taken at different bed depth were higher than those of the influent ( at L Å
FIG. 6. Dynamics of particle removal and detachment with different grain sizes and under different headloss gradients, i (V Å 4.8 m/h, L Å 75 mm). (a) dg Å 0.60–0.71 mm. (b) dg Å 0.42–0.5 mm.
headloss gradient i. This may be attributed to the fact that hydraulic gradient has little effect on the removal of small particles. Rather, filter ripening played a role in the enhancement of their removal. In Fig. 6, suspension concentration results taken at L Å 75 mm from the same experiments are shown. Generally speaking, all the trends observed in this figure are similar to those shown in Fig. 5. The improvement of removal for small particles at higher headloss gradient can be seen more clearly here. For the filter packed with larger grains [ dg Å 0.6 Ç 0.71 mm in Fig. 6(a)], only detachment for particles larger than 10 mm at high headloss gradient was observed at this bed depth (L Å 75 mm). For the smaller grain filter [dg Å 0.42 Ç 0.5 mm in Fig. 6(b)]; however, no particle detachment was observed at all at this bed depth. Comparing the results of Fig. 6 with those of Fig. 5, one is readily coming to the conclusion that the detached particles in the upper bed layers have been re-collected or redeposited at the immediate lower bed layers. In Fig. 7, total suspension particle concentration (on volume basis) profiles are presented. The results suggest that particle removal took place mainly in the first 100 mm of the filter media. Although the total concentration of the effluent was found to increase with the clogging of the filter
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FIG. 7. Change of total particle concentration profiles during filtration (V Å 4.8 m/h). [Note: the value of HT indicates the total headloss across the entire filter bed when the samples were taken]. (a) dg Å 0.6–0.72 mm. (b) dg Å 0.42–0.5 mm.
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mm, and particle redeposition was accomplished at about 175 mm bed depth. For the more clogged bed [ Fig. 8 ( b ) ] , particle detachment occurred over a much greater depth. The highest detachment of particles was at L Å 125 mm and redeposition of the detached particles took place within a depth of 275 mm. In Fig. 9, the results for the finer media filter are presented. The general tendency is similar to that of the coarser media filter. The main difference is that both particle detachment and redeposition occurred in smaller depth and the extent of particle detachment was less significant than those observed in the coarser media filter. As the pore sizes of the finer media filter were smaller, particle detachment was less likely to occur and recapture of detached particle was, however, more favored in the bed. It is interesting to note that particle concentrations in Groups 1 and 2 were not returned to their original levels of the influent at all bed depths (Figs. 8 and 9). In many cases, concentrations of Groups 1 and 2 particles increased with the increase in bed depth while the recapturing for larger particles (i.e., group 4 particles) was dramatic. It may be possible that some of the detached large particles were actually clusters composed of both larger and smaller particles.
FIG. 8. Particle concentration profiles of the coarser media filter during the first 5 min’ flow shear shock (dg Å 0.6 Ç 0.71 mm, shear flow rate Vs Å 9.6 m/h). (a) HT Å 0.4 m H2O before flow shock. (b) HT Å 1.2 m H2O before flow shock.
0 ) . The results clearly indicated the occurrence of particle detachment and redeposition within the filter bed. As can be seen from the figure, particles in all four size groups were detached during the flow shear shock, shown by the higher concentrations of the effluent in the top bed layers than that in the influent. The redeposition of detached particles were also suggested in the figure by the decrease of the concentration remaining with the bed depth in the bottom bed layers. Both particle detachment and redeposition were found to be strongly dependent upon the particle sizes. The detachment was observed to be much more profound for larger particles than for smaller ones. For example, group 4 particles showed the highest amount of detachment in the top bed layers ( about four times ) and group 1 particles the lowest. Contrary to particle detachment, however, the detached group 4 particles were most ready to be recaptured in the following bed layers followed by those of group 3. It appeared that the most difficult one to be recaptured was group 2 particles rather than the smallest ones in group 1. Particle detachment and redeposition were also influenced by the state of filter clogging ( i.e., the headloss gradient i ) . For the less clogged bed [ Fig. 8 ( a ) ] , the highest particle detachment occurred at a depths of L Å 25 and 75
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FIG. 9. Particle concentration profiles of the finer media filter during the first 5 min’ flow shear shock (dg Å 0.42 Ç 0.5 mm, shear flow rate Vs Å 9.6 m/h). (a) HT Å 0.4 m H2O before flow shock. (b) HT Å 1.6 m H2O before flow shock.
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to be dominant during the initial stages of polydisperse suspension filtration. After a flow shock, flow of the test suspension was resumed at the initial flow rate. The headloss gradient across the filter bed was reduced significantly ( up to 35% Ç 45%, results not shown ) . A comparison of the extent of particle removal before and after the flow shear shock is shown in Figs. 11 and 12. Figure 11 gives the removal of the smallest particles in the suspension ( i.e., Group 1 ) . Although the headloss gradient was reduced, the removal of Group 1 particles after the flow shear shock was less than before. For the more clogged filter bed [ Fig. 11 ( b ) ] , the decrease in removal after the flow shock was even more pronounced than that in a less clogged filter bed [ Fig. 11 ( a ) ] . It is clear that the headloss gradient plays no significant role in the filtration of these small particles. In Fig. 12, the removal behavior of the particles in Group 4 shows some differences from that of Group 1 particles in Fig. 11. Here it is observed that the removal of Group 4 particles increased in the upper layers, as a consequence of the decrease of the headloss gradient in these bed layers after the flow shear shock. Particularly in Fig. 12 ( b ) , detachment of Group 4 particles before
FIG. 10. Particle concentration profiles of the coarser media filter during the second time flow shear shock (dg Å 0.6 Ç 0.71 mm, shear shock flow rate Vs Å 12 m/h). (a) HT Å 0.4 m H2O before flow shock. (b) HT Å 0.8 m H2O before flow shock.
After being detached, these particles were further scattered by flow shear or collision with filter grains. As a result, the concentrations of smaller particles were increased along the bed depth as their removal was difficult. On the other hand, the concentrations of the large particles detached declined along the bed layers as these particle clusters were either scattered or redeposited. Under a fixed higher flow rate, particle detachment was found not to continue throughout the entire flow shear shock period, but only within a short period initially, say about 5 minutes. With a further increase in flow rate, particle detachment was once again observed. Figure 10 shows the results of particle detachment due to the second flow shock in a coarse media filter bed. The presence of particle detachment and redeposition was obvious, but the extent was not as significant as those observed during the first flow shock (Fig. 8). Furthermore, detachment and redeposition of particles were limited mainly to larger particles (i.e., Group 4 particles). It was possible that the detached particles in the second flow shock were mainly from those which were deposited during the beginning of the filtration operation. As pointed out by Bai (20), deposition of large particles tended
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FIG. 11. Comparisons of concentration profiles of particles of dp Å 0.63 Ç 1.26 mm before and after the flow shear shock ( dg Å 0.6 Ç 0.71 mm, V Å 4.8 m/h). (a) HT Å 0.8 m H2O before flow shock. (b) HT Å 1.2 m H2O before flow shock.
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FIG. 12. Comparisons of concentration profiles of particles of dp Å 5.04 Ç 10.08 mm before and after the flow shear shock ( dg Å 0.6 Ç 0.71 mm, V Å 4.8 m/h). (a) HT Å 0.8 m H2O before flow shock. (b) HT Å 1.2 m H2O before flow shock.
the flow shock was clearly indicated ( the higher effluent concentration at L Å 25 mm than that in the influent at L Å 0 ) . Removal of these particles was largely improved and no particle detachment was observed after the flow shock. The results in Figs. 11 and 12 suggest that the headloss gradient plays some role in the detachment and deposition of larger particles. We now attempt to relate the experimental observation with the results of our analysis. The analysis relates particle detachment with particle size, filter grain size, filtration rate, and the local headloss gradient in the filter bed. Good agreement was found between the predicted results of Fig. 2 and the experimental results shown in Fig. 5. For example, both sets of results indicate that particle detachment occurs when a high headloss gradient is present in a filter bed; larger deposited particles are more likely to be detached by flow shear force while smaller particles are not affected to any significant extent; and particle detachment is more likely in a coarse media filter than in a fine media one. However, application of Eqs. [ 22 ] or [ 23 ] to predict particle detachment is dependent upon the values of a number of parameters and variables used ( see Table 1 ) . Among these variables, the values of
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m, e0 , dg , and kh 0 are readily available. The Hamaker constant between colloidal particles separated by a water layer has been estimated to be H Å 1.4 1 10 020 kgrm2 / s 2 ( 13, 21 ) . The equilibrium separation distance between the filter grains and the attached particles is generally very small. Both Tabor ( 22 ) and Raveendran and Amirtharajah ( 13 ) have chosen d to be 3 1 10 010 m. The headloss increase parameter kh may be expected to change with many operating variables, but a value of kh Å 110 was used in constructing Fig. 2 according to the suggestion of Ives ( 19 ) . There is some uncertainty about the value of the sliding friction coefficient kf . No such values for kf have been reported for water filtration. In air filtration, for particle detachment from rough surface, the sliding friction coefficient may range from 0.1 to 1.9 ( 23 ) . In this study, with kf Å 0.0035 ( for dg Å 0.00065 m) and kf Å 0.0051 ( for dg Å 0.00045 m) , the calculated results agree reasonably well with experiments. For example, in the bed layer of L Å 25 mm of a filter with dg Å 0.6 – 0.71 mm at headloss gradients of i Å 7.88, 14.52 and 20.20, respectively, calculations predicted that detachment may occur for deposited particles larger than 5.2, 6.5, and 8.5 mm, respectively, which agreed well with experimental values of 4.5, 6.4, and 10.5 mm [ Fig. 5 ( a ) ] . Although the assigned values of kf are considerably lower than those used by Soltani et al. ( 23 ) , for water filtration with relatively smooth filter grains, k f may in fact have a much lower value. If a higher value of kf ( say 0.1 ) was used, for example, one would predict no particle detachment, which is contrary to the experimental observation. It should be noted, however, that the present study was not designed for an evaluation of kf . Generally speaking, the present work has yielded some important results. On the theoretical side, the simple relationship between the occurrence of particle detachment with particle size, filter grain size, flow rate, and headloss gradient is useful for subsequent development of models for filtration operation. On the practical side, the study showed that flow shock may cause significant particle detachment and the penetration of small particles into the filter. It is normal in practice that filters in operation often receive a sudden flow rate increase, i.e., a flow shock when some filters are taken out of work or for backwashing. As bacteria or pathogens may be regarded as small size particles, their penetration into filter and their poor retention require further attention for future investigations. APPENDIX: NOMENCLATURE
As C0 CL dp d *g
A function defined as 2(1 0 p 5 )/w Total volume concentration of particles in influent Total volume concentration of particles in the sample taken at L Diameter of suspended particle Diameter of a reference filter grain
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dg e F FAdh FD Ff FL Fl FS g H HT
zp zg k m
Diameter of filter grain The elementary charge Net tangential force Adhesion force for particle attachment Double layer force Frictional force against sliding London-van der Waals force Hydrodynamic lifting force Hydrodynamic shear force Gravitational acceleration Hamaker constant Total headloss across the entire filter bed (L Å 375 mm) Ionic concentration Hydraulic gradient (headloss gradient) in a filter bed layer Initial hydraulic gradient (headloss gradient) in a filter bed layer Boltzmann’s constant Coefficient of sliding friction Proportionality constant of Eq. [14] Coefficient of headloss increase with the amount of particle retention Coefficient defined as 180 1 (1 0 e ) 2 /(g re 3 ) for clean filter bed Coefficient of lifting force Coefficient defined as kh 1 2.551 1 3p Filter bed depth Avogadro’s number Defined as (1 0 e ) 1 / 3 Absolute temperature Approach velocity of fluid toward a model collector grain Filtration rate Flow rate in flow shear shock Defined as 2 0 3p / 3p 5 0 2p 6 Surface-to-surface separation between a particle and a collector grain Permittivity in vacuum; porosity of the clean filter bed Relative permittivity of fluid media; porosity of the filter bed Zeta potential of the suspended particle Zeta potential of the collector grain Reciprocal of double layer thickness Dynamic viscosity of the fluid
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Kinetic viscosity of the fluid Shear stress Specific deposit in the filter bed Density of the fluid ACKNOWLEDGMENT
The financial support received from the National Science and Technology Board as a seed grant awarded to the Environmental Technology Enterprise, National University of Singapore is acknowledged.
REFERENCES 1. Mohanka, S. S., J. San. Eng. Div., ASCE 95, 1079–1095 (1969). 2. Ives, K. J., ‘‘Theory of Filtration,’’ Special Subject No. 7, Int. Wat. Supply Assoc. Congress (Vienna), 1969. 3. Stanley, D. R., Proc. ASCE 81, 1–23 (1955). 4. Payatakes, A. C., Parks, H. Y., and Petrie, J., Chem. Eng. Sci. 36, 1319– 1335 (1981). 5. Ives, K. J., Wat. Res. 23, 861–866 (1989). 6. Ginn, T., Amirtharajah, A., and Karr, P. R., J. AWWA 84, 66–76 (1992). 7. Melissa, C. M., Daniel, C. M., Robert, S. C., and Lawler, D., J. AWWA 85, 82–93 (1993). 8. Mints, D. M., ‘‘Modern Theory of Filtration,’’ Special Subject No. 10, Int. Wat. Supply Assoc. Congress (Barcelona), 1966. 9. Adin, A., and Rebhun, M., J. AWWA 69, 444–453 (1977). 10. Vigneswaran, S., and Chang, J. S., Water Air Soil Pollut. 29, 155–164 (1986). 11. Vaidyanathan, R., and Tien, C., Chem. Eng. Sci. 43, 289–302 (1988). 12. Sharma, M. M., J. Colloid Interface Sci. 149, 121–134 (1992). 13. Raveendran, P., and Amirtharajah, A., J. Envir. Eng. 121, 860–868 (1995). 14. Tien, C., ‘‘Granular Filtration of Aerosols and Hydrosols.’’ Butterworths Publisher, Boston, 1989. 15. Saffman, P. G., J. Fluid Mech. 22, 385–400 (1965). 16. Goldman, A. J., Cox, R. G., and Brenner, H., Chem. Eng. Sci. 22, 653– 660 (1967). 17. O’Neill, M. E., Chem. Eng. Sci. 23, 1293–1298 (1968). 18. Visser, J., in ‘‘Surface and Colloid Science’’ (E. Matijevic, Ed.). Wiley, New York, 1976. 19. Ives, K. J., in ‘‘Mathematical Models and Design Methods in SolidLiquid Separation’’ (A. Rushton, Ed.), pp. 91–149. Martinus Nijhoff Publishers, 1985. 20. Bai, R., The effect of particle size distribution and flow shear force on the performance of deep bed filtration, Ph.D. Thesis, The University of Dundee, U.K., 1994. 21. Israelachvili, N. J., Surface Sci. Rep., Amsterdam 14, 109–159 (1992). 22. Tabor, D., J. Colloid Interface Sci. 58, 2–13 (1977). 23. Soltani, M., Ahmadi, G., Bayer, R. G., and Gaynes, M. A., J. Adhesion Sci. Technol. 9, 453–473 (1995).
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CS964663
Particle Detachment in Deep Bed Filtration RENBI BAI
AND
CHI TIEN 1
Department of Chemical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 Received June 17, 1996; accepted October 28, 1996
The paper examines the behavior of particle detachment in deep bed filtration and the dependence of particle detachment on several filtration operating parameters. Theoretical analysis was carried out by considering the balance of various relevant interaction forces. Based on the results, experiments were conducted to study the effect of particle size, filter grain size, and headloss gradient on particle detachment in deep bed filtration. In one set of experiments, the filter was operated at constant filtration rate in order to build up the headloss across the filter bed continuously. In the other set of experiments, the filter in operation was allowed to experience a short period of flow shock (i.e., to be subject to a higher flow rate during this period). Both sets of experiments confirmed the dependence of particle detachment on particle size, collector gain size, and headloss gradient (degree of filter clogging) of the filter, as predicted by the analysis. q 1997 Academic Press Key Words: particle detachment; particle redeposition; particle size; headloss gradient; flow shear shock; interaction forces; deep bed filtration.
INTRODUCTION
For considerable time, the controversy over whether or not detachment of deposited particles occurs in deep bed filters has occupied the attention of a number of investigators. Most early work did not consider particle detachment in filtration (1, 2). The strongest evidence against the presence of particle detachment was the observations of Stanley (3). Stanley conducted tests using radioactively labeled particles and found that those particles retained at the beginning of a filtration run remained in place during the entire period of experiment. Since then, opinion has moved gradually in favor of the view that particle detachment does occur, at least in later stages of filtration. This change was brought about by increasing experimental evidences, including video and microscopic observations of a model filter by Payatakes et al. (4) and endoscopic observations of the inside of a filter by Ives (5). Based on an analysis of filtration data of changes in particle size distribution of the effluent, Ginn et al. (6) contended that particle detachment was the cause of the shifting of particle size distribution of the effluent toward larger sizes during filtration. Melissa et al. (7) also reported 1
To whom correspondence should be addressed.
experimental results which indicated the occurrence of particle detachment and the dependence of particle detachment on particle size. The reason for particle detachment in filtration was explained either as a result of the flow shear forces overcoming the attachment forces (4) or instabilities caused by arriving particles (5). Even without a consensus on this problem, it was generally believed that increases in interstitial velocity due to the build up of deposit was instrumental in particle detachment. Mints (8) described particle detachment as being directly proportional to the specific deposit. Others (9, 10) assumed that particle detachment was directly proportional to the product of the hydraulic gradient and the specific deposit. As particles retained in a filter are subject to drag forces due to liquid flow, any increase in filtration rate tends to hinder particle deposition or promote the detachment of retained particles as the drag force is directly related to the interstitial fluid velocity. Although attention has been paid to whether or not there is particle detachment during filtration in the past, the effect of flow shear shock in filter operation has so far not been studied. Filters are often operated in groups. When one of the filters in one group is out of work for backwashing, the other filters have to operate at a higher capacity, in other words, to experience a flow shear shock. As a result, particle detachment or inhibition of particle from deposition can be expected. Consequently, a poor filtrate quality may result. The purpose of the present study is to present a simple analysis of the various factors which may affect particle detachment in filtration and to conduct experimental investigations in order to validate the conclusion of the analysis. THEORETICAL CONSIDERATIONS
The retention of particles in a filter bed requires that the adhesion force between a retained particle and a collector (i.e., one of the filter grains) is at least in equilibrium with the hydrodynamic force which tends to detach the particle. Particle detachment in filtration therefore occurs only when the hydrodynamic force overcomes the adhesive force. The mechanisms for particle detachment from filter grains include rolling, sliding, and lifting (11–13). The sliding mechanism implies that a deposited particle may slide be-
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a frictional force Ff arises in the direction opposite to that of FS to prevent the re-entrainment. The basic assumption is that if Ff õ FS , the lifting force Fl would then cause the particle to drift away from the collector and so particle detachment or dislodging in the filter takes place. Adhesion Forces The magnitudes of FL and FD may be given as (14) FL Å
1 Hd 3p 2 12 d ( d / dp ) 2
FD Å
2pee0 ( z 2p / z 2g ) ke 0 kd 1 0 e 02kd
[1]
S
D
2z p zg 0 e 0 kd , [2] z 2p / z 2g
where H is the Hamaker constant, d is the separation distance between the particle and the collector plane, e0 is the dielectric constant (permittivity) in vacuum, e is the relative dielectric constant of fluid, zp and zg are the zeta potentials of the particle and the collector (filter grain), respectively. k is the Debye reciprocal double layer thickness which, in monovalency electrolyte solutions, is given as
r FIG. 1. Schematic diagram of forces acting on a spherical particle attached to a collector plane with a stagnant film of liquid on the surface.
cause of the hydrodynamic tangential drag force acting on it. The rolling mechanism depicts that a deposited particle may roll due to the torque resulting from the asymmetry of the shear force acting on the deposited particle. As particle rolling can occur over a collector surface and does not necessarily lead to particle detachment, the following analysis is therefore based on the sliding and lifting mechanisms. In deep bed filtration, the diameter of filter grains in most cases is two orders larger than those of the particles to be removed. Thus, attachment of particles onto filter grains may therefore be treated as that of a spherical particle onto a collector plane. Figure 1 gives a schematic diagram of this representation. The filter grain has a diameter of dg and the particle diameter is dp . There is a liquid layer of thickness d ( d may be called the equilibrium separation distance) between the filter grain and the attached particle. The main forces acting on the particle include FL , FD , FS , Fl , and Ff , where FL is the London–van der Waals force which acts in the direction normal to the collector plane and is always attractive; FD , the electrical double layer force which also acts in the direction normal to the collector plane and is usually repulsive in water filtration. FL and FD are the adhesion forces responsible for particle attachment. FS is the drag force experienced by the particle due to fluid flow in the tangential direction along the collector plane, and Fl is the lifting force which is in the direction normal to the collector plane. FS and Fl are the two hydrodynamic forces. If the attached particle tends to be re-entrained due to fluid flow,
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kÅ
2e 2NA I , ee0kT
[3]
where e is the elementary charge, NA is the Avogadro’s number, I is the ionic concentration in the fluid, k is Boltzmann’s constant, and T is the absolute temperature. For a particle attached on the collector plane, the equilibrium separation distance d is usually much less than dp , or d / dp É dp , Equation [1] may be reduced to FL Å
Hdp . 12d 2
[4]
The net adhesion force for particle attachment onto the collector’s surface is therefore given by FAdh Å FL 0 FD Å 0
Hdp 12d 2
2pee0 ( z 2p / z 2g ) ke 0 kd 1 0 e 02kd
S
D
2zp zg 0 e 0 kd . z 2p / z 2g
[5]
To study the detachment of deposited particles, the extreme case where the attached particles experience only attractive force is considered. This situation applies to attached particles in close contact with collector surfaces. Hence by neglecting the effect of FD , the maximum adhesion force is (FAdh )Max É FL Å
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Hdp . 12d 2
[6]
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Hydrodynamic Forces
Ff Å kf FL Å kf
According to Saffman (15), the hydrodynamic lifting force for a single sphere in an unbounded linear shear flow may be written as Fl Å kl d 3p ( mn ) 00.5t 1.5 ,
[7]
where kl is the coefficient for lifting force, m is the dynamic viscosity, n is the kinematic viscosity of the fluid, and t is the shear stress acting on the collector plane. The hydrodynamic drag force on a spherical particle of diameter dp in contact with a planar wall in a slow linear shear flow has been calculated by Goldman et al. (16) and O’Neill (17) and can be directly related to the local wall shear stress t as FS Å 2.55lpd 2p t.
kf Å k *f 1 S,
6(1 0 e0 ) . dg
As 2 d p U. dg
[10]
V V Å , e e0 0 s
[11]
where V is the filtration rate and s is the bulk specific deposit in the filter bed (namely volume of deposit per unit filter volume). e is the filter bed porosity, and e0 is the clean filter bed porosity. Introducing Eq. [11] into Eq. [10] gives As 2 V dp . dg e0 0 s
[12]
F *f Å k *f
6(1 0 e0 ) Hdp . dg 12d 2
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[17]
Using Eqs. [17] and [12], the net force F, acting on an attached particle in a deep bed filter along the tangential direction is given as F Å F *f 0 FS Å k *f 1 3pm
6(1 0 e0 ) Hdp 0 2.551 dg 12d 2
As 2 V dp . dg e0 0 s
[18]
Accordingly, one may conclude that in deep bed filtration (1) there is no particle detachment if F § 0, and (2) there is a sliding of the deposited particle and subsequently its detachment if F õ 0. Further, it is desirable to replace s in Equation [18] with a more measurable quantity. When s ! e0 , the bulk specific deposit s may be related to the headloss gradient, i Å DH/ DL, approximately to be (19) i Å i 0 / khs,
The friction force Ff against particle sliding may be assumed to be proportional to the adhesive force, i.e.,
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[16]
Substituting Eq. [16] into Eq. [13], one has
In a bed packed with filter grains, the approach velocity U may be approximated to be the average pore velocity of the bed, or
FS Å 2.55l 1 3pm
6(1 0 e0 ) . dg
[9]
where AS is defined as 2(1 0 p 5 )/w [w Å 2 0 3p / 3p 5 0 2p 6 , p Å (1 0 e ) 1 / 3 and e is the porosity of a filter bed] and U is the approach fluid velocity. Introducing Eq. [9] into Eq. [8], one has
UÅ
[15]
Therefore Eq. [14] becomes kf Å k *f
FS Å 2.55l 1 3pm
[14]
where k *f is a proportionality constant and S is the specific surface area of a deep bed filter, defined as the surface area per unit filter bed volume. For a filter bed packed with uniform grains of size dg , S is given as SÅ
As t Å 3m U, dg
[13]
where kf is the coefficient of sliding friction. A similar treatment as Eq. [13] was also used by Visser (18). Equation [13] is based on a particle attached to a single collector. In a deep bed filter randomly packed with uniform filter grains, one must, however, consider the effect of neighboring filter grains. This may be achieved by assuming
[8]
Equations [7] and [8] are valid with linear velocity gradient near the surface. Using Happel’s model, the shear stress acting on the collector may be estimated as (14)
Hdp , 12d 2
[19]
where i 0 is the clean bed headloss gradient and kh is the
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coefficient for headloss increase due to particle retention. From Eq. [19], one may express s as sÅ
1 (i 0 i 0 ). kh
[20]
For a packed bed with spherical grains and under laminar flow, the Kozeny-Carman equation may be used to estimate i 0 as i 0 Å 180
mV (1 0 e0 ) 2 mV Å kh 0 2 , g rd 2g e 30 dg
[21]
where kh 0 Å 180 1 (1 0 e0 ) 2 /(g re 30 ) is the headloss coefficient for clean filter bed. Substituting Equations [20] and [21] into [18], one has F Å k *f
6(1 0 e0 ) Hdp 0 2.551 dg 12d 2 As 2 khV dp dg e0kh 0 (i 0 i 0 )
1 3pm
[22]
or F Å k *f
6(1 0 e0 ) Hdp dg 12d 2
0 ksmAs dg d 2p
V , e0kh d 0 (d 2g i 0 kh 0mV ) 2 g
[23]
where ks Å kh 1 2.551 1 3p with kh and kh 0 defined as before. Equation [ 22 ] or [ 23 ] indicates that the magnitude of F is dependent upon dp , dg , V, i , and d. Figure 2 illustrates the effect of dp , dg , V, and i on F . The values of the variables used in the calculation of the results shown in Figs. 2 ( a ) – 2 ( c ) are given in Table 1. The reason for selecting these values will be given later. It can be seen from these figures that F may change from positive to negative values; the latter indicating the possibility for particle detachment. From Fig. 2 ( a ) , one may conclude that larger particles under higher hydraulic gradients are more likely to be detached in filtration than smaller particles under lower hydraulic gradients. For a hydraulic gradient up to i Å 25, particles smaller than 4 mm will probably not be detached at all. In Fig. 2 ( b ) , it is observed that the small particles ( dp Å 2 mm) do not shown the possibility of detachment for filtration rate up to 20 m/ h, but for the large particle ( dp Å 14 mm) , on the other hand, detachment may occur at a filtration rate as low as 4 m/ h. Compared with the results in Fig. 2 ( a ) , Fig. 2 ( c ) indicates that particle detachment may be greatly reduced in a bed of smaller grain size ( dg Å 0.45 mm) , where it is shown that particles
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FIG. 2. Illustration of the variables affecting the magnitude of the net tangential force F for particle detachment in deep bed filtration. (a) dg Å 0.65 mm, V Å 4.8 m/h. (b) dg Å 0.65 mm, i Å i0 . (c) dg Å 0.45 mm, V Å 4.8 m/h.
up to about 6 mm may not be detached even though the hydraulic gradient arises to as high as i Å 25. EXPERIMENTAL WORK
Based on the results given before, experiments were conducted to investigate the effects of particle size, grain size,
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TABLE 1 Parameter Values Used in the Calculation of Fig. 2 kf* Å 3.79 1 1006 m
H Å 1.4 1 10020 kg m2/s2
m Å 0.001 kg /mrs
e0 Å 0.4
kh Å 110
d Å 3 1 10010 m
i0 Å 0.5 dg Å 0.00065 m kf Å 0.0035 dg Å 0.00045 m kf Å 0.0051
flow rate, and headloss (hydraulic) gradient on particle detachment in deep bed filtration. Details of the experiments are described in the following section. FIG. 4. Particle size distribution of the influent suspensions.
Material and Methods The experimental apparatus and the process flow scheme used in the experiment is shown schematically in Fig. 3. Test suspensions and clean water were held respectively in two storage tanks (2). A pump (1) was used to lift the fluid (suspension or clean water) from the respective storage tanks to an elevated constant-head tank (5). The fluid was then fed from this tank to the filter (7) at its top (i.e., the flow was downward). The filtrate from the filter then passed through the flow controllers (9) and flowmeters (10), and was discharged into the drain through the effluent constanthead tank (11). The test filter was made of a 138 mm diame-
FIG. 3. Schematic diagram of the experimental setup and the process flow scheme.
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ter plexiglass tube. Manometer and sampling points (8) with an internal diameter of 3 mm were placed in pairs into the bed at depths (from the inlet): 0, 25, 75, 125, 175, 225, 275, and 375 mm. These points were used for sampling and measuring the headloss. Ballotini glass beads of two different sizes (i.e., dg Å 0.6 Ç 0.71 mm and dg Å 0.42 Ç 0.5 mm) were used as the filter media. The porosity of the bed for the two media sizes was maintained at 0.402 and 0.396, respectively. Polydispersed suspensions were used in this study and a PVC powder (Corvic P72/757) was used for preparing the suspensions. The particles were spherical and their size ranged from less than 0.5 to about 14 mm. Test suspensions were prepared by first mixing the particles in a heavy duty emulsifier and then diluting the mixture with tap water to desired concentrations. Figure 4 gives the size distribution of the influent suspension. Samples were taken continuously through a peristaltic pump during the operation at a rate capable withstanding the effect of sedimentation (100 ml/ h) (20). Suspension samples were analyzed using a Coulter Counter, Model IIe (Coulter Electronics, Inc.). After each run, the filter media were taken out and manually cleaned using tap water, and then the bed was repacked to the original bed porosity for next operation. The primary objective of the experiments was to collect data which may reveal the presence of particle detachment and/or redeposition in filtration. Two sets of experiments were conducted. The first set was conducted at a rate of V Å 4.8 m/h until the total headloss across the filter bed (L Å 375 mm) HT reached a value of 1.2 m for the bed of dg Å 0.6 Ç 0.71 mm or 1.6 m for the bed of dg Å 0.42–0.5 mm. Samples and headloss measurements were carried out at the time corresponding to HT Å 0.4, 0.8, 1.2, and 1.6 m (for the finer media filtration), respectively. These experiments were made in order to observe particle detachment and/or redeposition in a normal filtration operation. For the second set of experiments, the filter in operation was made to experience a short period of flow shear shock (i.e., a sudden increase in flow rate). The procedure used
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TABLE 2 Experimental Program and Conditions Median size (mm)
Porosity
Temperature (7C)
Filtration rate (m/h)
First shock flow rate (m/h)
Second shock flow rate (m/h)
Total headloss before flow shock, HT (m)
A B
0.6–0.71 0.42–0.5
0.402 0.396
15.6–16.3 15.3–16.2
4.8 4.8
— —
— —
1.2 1.6
A B C D E F G
0.6–0.71 0.6–0.71 0.6–0.71 0.42–0.5 0.42–0.5 0.42–0.5 0.42–0.5
0.402 0.402 0.402 0.396 0.396 0.396 0.396
Ç Ç Ç Ç Ç Ç Ç
4.8 4.8 4.8 4.8 4.8 4.8 4.8
9.6 9.6 9.6 9.6 9.6 9.6 9.6
12 12 — 12 12 — —
0.4 0.8 1.2 0.4 0.8 1.2 1.6
Experiment I
II
17.4 17.9 18 15.7 16.6 15.3 16.2
18.6 18.6 18.7 16.3 17.2 16.2 16.6
Note. Influent concentration was about 110–120 mg/L.
was as follows. The filter was operated at a flow rate of 4.8 m/h until one of the pre-set headlosses (i.e., 0.4, 0.8, 1.2, or 1.6 m) was reached. The suspension flow was then replaced by clean water at the same flow rate. Once the clean water had displaced the suspension, the flow rate was increased to 9.6 m/h, and this was allowed to continue for 10 minutes. In some cases the flow rate of clean water was further increased to 12 m/h. This higher flow rate was only applied to those runs with preset headloss not greater than 0.8 m. Afterwards the flow of suspension at 4.8 m/h was resumed. Sampling and measurements were made before, during, and after the flow shear shock. These experiments yielded information on particle detachment and/or redeposition in filtration when a filter experienced a sudden increase in the flow rate and therefore the headloss gradients. A summary of all the experiments is given in Table 2.
particle detachment in smaller size media occurred to a lesser degree and took place at higher headloss gradients than those in a larger media. It is also interesting to note that particles smaller than 4 mm did not show any detachment in this study. Moreover, removal of particles less than 2 mm was actually improved (lower concentration ratio) at higher
RESULTS
Particle Detachment During Normal Operation Set I experiments were conducted at constant flow rate without any interruption during operation. To show the dynamics of particle removal and detachment during filtration, Figure 5 presents suspension particle concentrations at L Å 25 mm at times when the hydraulic gradient reached specified values. The results shown are concentration ratio (relative to the influent values) versus particle diameter. A concentration ratio of unity indicates that the particle concentration (volume) remains the same as that of the influent. Therefore particle detachment is shown if the concentration ratios exceed unity. Thus there is incontrovertible evidence (as shown in Fig. 5) that detachment of particles does occur in filtration. As predicted by the analysis, particle detachment was found to depend largely upon the particle size, grain size, and headloss gradient. Larger particles were shown to be more likely to detach and detachment became more significant at higher headloss gradient i. By comparing results of Fig. 5(a) with that of Fig. 5(b), it is clear that
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FIG. 5. Dynamics of particle removal and detachment in a filter bed with different grain sizes and under different headloss gradients, i (V Å 4.8 m/h, L Å 25 mm). (a) dg Å 0.60–0.71 mm. (b) dg Å 0.42–0.5 mm.
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(higher headloss gradient i), there is no evidence of particle detachment (i.e., concentration exceeds the influent values). Particle Detachment with a Flow Shear Shock In set II experiments, the flow rate and therefore the headloss gradient through the filter bed was suddenly increased for a while during filtration operation. The purpose was the observation of particle detachment under a flow shear shock. This condition happens in practice in water treatment plants when some filters are taken out of operation and the remaining ones have to receive additional flow. Samples were collected for analysis within the first 5 minutes during the flow shear shock. Figure 8 shows some typical results from a coarse media filter. The results here are examined in four particle size groups instead of in individual particle size for easy of presentation. The four groups of particles are defined as: Group 1, dp Å 0.63 Ç 1.26 mm; Group 2, dp Å 1.26 Ç 2.52 mm; Group 3, dp Å 2.52 Ç 5.04 mm; and Group 4, dp Å 5.04 Ç 12.7 mm, respectively. Particle detachment can be determined by whether or not particle concentrations taken at different bed depth were higher than those of the influent ( at L Å
FIG. 6. Dynamics of particle removal and detachment with different grain sizes and under different headloss gradients, i (V Å 4.8 m/h, L Å 75 mm). (a) dg Å 0.60–0.71 mm. (b) dg Å 0.42–0.5 mm.
headloss gradient i. This may be attributed to the fact that hydraulic gradient has little effect on the removal of small particles. Rather, filter ripening played a role in the enhancement of their removal. In Fig. 6, suspension concentration results taken at L Å 75 mm from the same experiments are shown. Generally speaking, all the trends observed in this figure are similar to those shown in Fig. 5. The improvement of removal for small particles at higher headloss gradient can be seen more clearly here. For the filter packed with larger grains [ dg Å 0.6 Ç 0.71 mm in Fig. 6(a)], only detachment for particles larger than 10 mm at high headloss gradient was observed at this bed depth (L Å 75 mm). For the smaller grain filter [dg Å 0.42 Ç 0.5 mm in Fig. 6(b)]; however, no particle detachment was observed at all at this bed depth. Comparing the results of Fig. 6 with those of Fig. 5, one is readily coming to the conclusion that the detached particles in the upper bed layers have been re-collected or redeposited at the immediate lower bed layers. In Fig. 7, total suspension particle concentration (on volume basis) profiles are presented. The results suggest that particle removal took place mainly in the first 100 mm of the filter media. Although the total concentration of the effluent was found to increase with the clogging of the filter
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FIG. 7. Change of total particle concentration profiles during filtration (V Å 4.8 m/h). [Note: the value of HT indicates the total headloss across the entire filter bed when the samples were taken]. (a) dg Å 0.6–0.72 mm. (b) dg Å 0.42–0.5 mm.
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mm, and particle redeposition was accomplished at about 175 mm bed depth. For the more clogged bed [ Fig. 8 ( b ) ] , particle detachment occurred over a much greater depth. The highest detachment of particles was at L Å 125 mm and redeposition of the detached particles took place within a depth of 275 mm. In Fig. 9, the results for the finer media filter are presented. The general tendency is similar to that of the coarser media filter. The main difference is that both particle detachment and redeposition occurred in smaller depth and the extent of particle detachment was less significant than those observed in the coarser media filter. As the pore sizes of the finer media filter were smaller, particle detachment was less likely to occur and recapture of detached particle was, however, more favored in the bed. It is interesting to note that particle concentrations in Groups 1 and 2 were not returned to their original levels of the influent at all bed depths (Figs. 8 and 9). In many cases, concentrations of Groups 1 and 2 particles increased with the increase in bed depth while the recapturing for larger particles (i.e., group 4 particles) was dramatic. It may be possible that some of the detached large particles were actually clusters composed of both larger and smaller particles.
FIG. 8. Particle concentration profiles of the coarser media filter during the first 5 min’ flow shear shock (dg Å 0.6 Ç 0.71 mm, shear flow rate Vs Å 9.6 m/h). (a) HT Å 0.4 m H2O before flow shock. (b) HT Å 1.2 m H2O before flow shock.
0 ) . The results clearly indicated the occurrence of particle detachment and redeposition within the filter bed. As can be seen from the figure, particles in all four size groups were detached during the flow shear shock, shown by the higher concentrations of the effluent in the top bed layers than that in the influent. The redeposition of detached particles were also suggested in the figure by the decrease of the concentration remaining with the bed depth in the bottom bed layers. Both particle detachment and redeposition were found to be strongly dependent upon the particle sizes. The detachment was observed to be much more profound for larger particles than for smaller ones. For example, group 4 particles showed the highest amount of detachment in the top bed layers ( about four times ) and group 1 particles the lowest. Contrary to particle detachment, however, the detached group 4 particles were most ready to be recaptured in the following bed layers followed by those of group 3. It appeared that the most difficult one to be recaptured was group 2 particles rather than the smallest ones in group 1. Particle detachment and redeposition were also influenced by the state of filter clogging ( i.e., the headloss gradient i ) . For the less clogged bed [ Fig. 8 ( a ) ] , the highest particle detachment occurred at a depths of L Å 25 and 75
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FIG. 9. Particle concentration profiles of the finer media filter during the first 5 min’ flow shear shock (dg Å 0.42 Ç 0.5 mm, shear flow rate Vs Å 9.6 m/h). (a) HT Å 0.4 m H2O before flow shock. (b) HT Å 1.6 m H2O before flow shock.
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to be dominant during the initial stages of polydisperse suspension filtration. After a flow shock, flow of the test suspension was resumed at the initial flow rate. The headloss gradient across the filter bed was reduced significantly ( up to 35% Ç 45%, results not shown ) . A comparison of the extent of particle removal before and after the flow shear shock is shown in Figs. 11 and 12. Figure 11 gives the removal of the smallest particles in the suspension ( i.e., Group 1 ) . Although the headloss gradient was reduced, the removal of Group 1 particles after the flow shear shock was less than before. For the more clogged filter bed [ Fig. 11 ( b ) ] , the decrease in removal after the flow shock was even more pronounced than that in a less clogged filter bed [ Fig. 11 ( a ) ] . It is clear that the headloss gradient plays no significant role in the filtration of these small particles. In Fig. 12, the removal behavior of the particles in Group 4 shows some differences from that of Group 1 particles in Fig. 11. Here it is observed that the removal of Group 4 particles increased in the upper layers, as a consequence of the decrease of the headloss gradient in these bed layers after the flow shear shock. Particularly in Fig. 12 ( b ) , detachment of Group 4 particles before
FIG. 10. Particle concentration profiles of the coarser media filter during the second time flow shear shock (dg Å 0.6 Ç 0.71 mm, shear shock flow rate Vs Å 12 m/h). (a) HT Å 0.4 m H2O before flow shock. (b) HT Å 0.8 m H2O before flow shock.
After being detached, these particles were further scattered by flow shear or collision with filter grains. As a result, the concentrations of smaller particles were increased along the bed depth as their removal was difficult. On the other hand, the concentrations of the large particles detached declined along the bed layers as these particle clusters were either scattered or redeposited. Under a fixed higher flow rate, particle detachment was found not to continue throughout the entire flow shear shock period, but only within a short period initially, say about 5 minutes. With a further increase in flow rate, particle detachment was once again observed. Figure 10 shows the results of particle detachment due to the second flow shock in a coarse media filter bed. The presence of particle detachment and redeposition was obvious, but the extent was not as significant as those observed during the first flow shock (Fig. 8). Furthermore, detachment and redeposition of particles were limited mainly to larger particles (i.e., Group 4 particles). It was possible that the detached particles in the second flow shock were mainly from those which were deposited during the beginning of the filtration operation. As pointed out by Bai (20), deposition of large particles tended
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FIG. 11. Comparisons of concentration profiles of particles of dp Å 0.63 Ç 1.26 mm before and after the flow shear shock ( dg Å 0.6 Ç 0.71 mm, V Å 4.8 m/h). (a) HT Å 0.8 m H2O before flow shock. (b) HT Å 1.2 m H2O before flow shock.
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FIG. 12. Comparisons of concentration profiles of particles of dp Å 5.04 Ç 10.08 mm before and after the flow shear shock ( dg Å 0.6 Ç 0.71 mm, V Å 4.8 m/h). (a) HT Å 0.8 m H2O before flow shock. (b) HT Å 1.2 m H2O before flow shock.
the flow shock was clearly indicated ( the higher effluent concentration at L Å 25 mm than that in the influent at L Å 0 ) . Removal of these particles was largely improved and no particle detachment was observed after the flow shock. The results in Figs. 11 and 12 suggest that the headloss gradient plays some role in the detachment and deposition of larger particles. We now attempt to relate the experimental observation with the results of our analysis. The analysis relates particle detachment with particle size, filter grain size, filtration rate, and the local headloss gradient in the filter bed. Good agreement was found between the predicted results of Fig. 2 and the experimental results shown in Fig. 5. For example, both sets of results indicate that particle detachment occurs when a high headloss gradient is present in a filter bed; larger deposited particles are more likely to be detached by flow shear force while smaller particles are not affected to any significant extent; and particle detachment is more likely in a coarse media filter than in a fine media one. However, application of Eqs. [ 22 ] or [ 23 ] to predict particle detachment is dependent upon the values of a number of parameters and variables used ( see Table 1 ) . Among these variables, the values of
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m, e0 , dg , and kh 0 are readily available. The Hamaker constant between colloidal particles separated by a water layer has been estimated to be H Å 1.4 1 10 020 kgrm2 / s 2 ( 13, 21 ) . The equilibrium separation distance between the filter grains and the attached particles is generally very small. Both Tabor ( 22 ) and Raveendran and Amirtharajah ( 13 ) have chosen d to be 3 1 10 010 m. The headloss increase parameter kh may be expected to change with many operating variables, but a value of kh Å 110 was used in constructing Fig. 2 according to the suggestion of Ives ( 19 ) . There is some uncertainty about the value of the sliding friction coefficient kf . No such values for kf have been reported for water filtration. In air filtration, for particle detachment from rough surface, the sliding friction coefficient may range from 0.1 to 1.9 ( 23 ) . In this study, with kf Å 0.0035 ( for dg Å 0.00065 m) and kf Å 0.0051 ( for dg Å 0.00045 m) , the calculated results agree reasonably well with experiments. For example, in the bed layer of L Å 25 mm of a filter with dg Å 0.6 – 0.71 mm at headloss gradients of i Å 7.88, 14.52 and 20.20, respectively, calculations predicted that detachment may occur for deposited particles larger than 5.2, 6.5, and 8.5 mm, respectively, which agreed well with experimental values of 4.5, 6.4, and 10.5 mm [ Fig. 5 ( a ) ] . Although the assigned values of kf are considerably lower than those used by Soltani et al. ( 23 ) , for water filtration with relatively smooth filter grains, k f may in fact have a much lower value. If a higher value of kf ( say 0.1 ) was used, for example, one would predict no particle detachment, which is contrary to the experimental observation. It should be noted, however, that the present study was not designed for an evaluation of kf . Generally speaking, the present work has yielded some important results. On the theoretical side, the simple relationship between the occurrence of particle detachment with particle size, filter grain size, flow rate, and headloss gradient is useful for subsequent development of models for filtration operation. On the practical side, the study showed that flow shock may cause significant particle detachment and the penetration of small particles into the filter. It is normal in practice that filters in operation often receive a sudden flow rate increase, i.e., a flow shock when some filters are taken out of work or for backwashing. As bacteria or pathogens may be regarded as small size particles, their penetration into filter and their poor retention require further attention for future investigations. APPENDIX: NOMENCLATURE
As C0 CL dp d *g
A function defined as 2(1 0 p 5 )/w Total volume concentration of particles in influent Total volume concentration of particles in the sample taken at L Diameter of suspended particle Diameter of a reference filter grain
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dg e F FAdh FD Ff FL Fl FS g H HT
zp zg k m
Diameter of filter grain The elementary charge Net tangential force Adhesion force for particle attachment Double layer force Frictional force against sliding London-van der Waals force Hydrodynamic lifting force Hydrodynamic shear force Gravitational acceleration Hamaker constant Total headloss across the entire filter bed (L Å 375 mm) Ionic concentration Hydraulic gradient (headloss gradient) in a filter bed layer Initial hydraulic gradient (headloss gradient) in a filter bed layer Boltzmann’s constant Coefficient of sliding friction Proportionality constant of Eq. [14] Coefficient of headloss increase with the amount of particle retention Coefficient defined as 180 1 (1 0 e ) 2 /(g re 3 ) for clean filter bed Coefficient of lifting force Coefficient defined as kh 1 2.551 1 3p Filter bed depth Avogadro’s number Defined as (1 0 e ) 1 / 3 Absolute temperature Approach velocity of fluid toward a model collector grain Filtration rate Flow rate in flow shear shock Defined as 2 0 3p / 3p 5 0 2p 6 Surface-to-surface separation between a particle and a collector grain Permittivity in vacuum; porosity of the clean filter bed Relative permittivity of fluid media; porosity of the filter bed Zeta potential of the suspended particle Zeta potential of the collector grain Reciprocal of double layer thickness Dynamic viscosity of the fluid
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Kinetic viscosity of the fluid Shear stress Specific deposit in the filter bed Density of the fluid ACKNOWLEDGMENT
The financial support received from the National Science and Technology Board as a seed grant awarded to the Environmental Technology Enterprise, National University of Singapore is acknowledged.
REFERENCES 1. Mohanka, S. S., J. San. Eng. Div., ASCE 95, 1079–1095 (1969). 2. Ives, K. J., ‘‘Theory of Filtration,’’ Special Subject No. 7, Int. Wat. Supply Assoc. Congress (Vienna), 1969. 3. Stanley, D. R., Proc. ASCE 81, 1–23 (1955). 4. Payatakes, A. C., Parks, H. Y., and Petrie, J., Chem. Eng. Sci. 36, 1319– 1335 (1981). 5. Ives, K. J., Wat. Res. 23, 861–866 (1989). 6. Ginn, T., Amirtharajah, A., and Karr, P. R., J. AWWA 84, 66–76 (1992). 7. Melissa, C. M., Daniel, C. M., Robert, S. C., and Lawler, D., J. AWWA 85, 82–93 (1993). 8. Mints, D. M., ‘‘Modern Theory of Filtration,’’ Special Subject No. 10, Int. Wat. Supply Assoc. Congress (Barcelona), 1966. 9. Adin, A., and Rebhun, M., J. AWWA 69, 444–453 (1977). 10. Vigneswaran, S., and Chang, J. S., Water Air Soil Pollut. 29, 155–164 (1986). 11. Vaidyanathan, R., and Tien, C., Chem. Eng. Sci. 43, 289–302 (1988). 12. Sharma, M. M., J. Colloid Interface Sci. 149, 121–134 (1992). 13. Raveendran, P., and Amirtharajah, A., J. Envir. Eng. 121, 860–868 (1995). 14. Tien, C., ‘‘Granular Filtration of Aerosols and Hydrosols.’’ Butterworths Publisher, Boston, 1989. 15. Saffman, P. G., J. Fluid Mech. 22, 385–400 (1965). 16. Goldman, A. J., Cox, R. G., and Brenner, H., Chem. Eng. Sci. 22, 653– 660 (1967). 17. O’Neill, M. E., Chem. Eng. Sci. 23, 1293–1298 (1968). 18. Visser, J., in ‘‘Surface and Colloid Science’’ (E. Matijevic, Ed.). Wiley, New York, 1976. 19. Ives, K. J., in ‘‘Mathematical Models and Design Methods in SolidLiquid Separation’’ (A. Rushton, Ed.), pp. 91–149. Martinus Nijhoff Publishers, 1985. 20. Bai, R., The effect of particle size distribution and flow shear force on the performance of deep bed filtration, Ph.D. Thesis, The University of Dundee, U.K., 1994. 21. Israelachvili, N. J., Surface Sci. Rep., Amsterdam 14, 109–159 (1992). 22. Tabor, D., J. Colloid Interface Sci. 58, 2–13 (1977). 23. Soltani, M., Ahmadi, G., Bayer, R. G., and Gaynes, M. A., J. Adhesion Sci. Technol. 9, 453–473 (1995).
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