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Orthokinetic flocculation in rapid filtration
Wat. Res. Vol. 20, No. 6, pp. 715-724, 1986 Printed in Great Britain. All rights reserved
0043-1354/86 $3.00+0.00 Copyright © 1986 Pergamon Journals Ltd
ORTHOKINETIC FLOCCULATION IN RAPID FILTRATION N. J. D. GRAHAM Public Health and Water Resource Engineering Section, Civil Engineering Department, Imperial College, London SW7, England (Received December 1984)
Abstract---Quantitative measurements have been made of filter pore orthokinetic flocculation using a laboratory-scale model filter and a hydrophobic particle-nonionic polymer system. Interparticle collision efficiency factors, determined by Coulter Counter analysis, have been found to increase with shear rate in contrast with current theoretical interpretations. Comparative collision efficiency factors have been determined in jar test and capillary-tube apparatuses under equivalent conditions to the filter tests. In rapid filtration practice using cationic polymers, and at high shear rates (Gw > 150 s-~) filter pore collision efficiencies are suggested as lying between those determined in tube flow (lower bound) and by jar test (upper bound). Key words--deep bed filters, filtration, flocculation, cationic polyelectrolytes, particle collision efficiency, jar tests, capillary flow
NOMENCLATURE B= ds = dp = G= Gw= = H = K= Ke =
Blake number, B = vadgp/6#(l - e) grain diameter particle diameter localized, uniform velocity gradient flow-weighted velocity gradient root-mean-square velocity gradient Harnaker constant orthokinetic flocculation rate constant experimentally determined flocculation rate constant L = filter bed depth L~p = length of capillary M = molar solution N = total particle concentration Rap = internal radius of capillary Re = Reynolds number Rh = hydraulic radius RSD = relative standard deviation s = internal surface area per unit volume of filter bed T = retention time va = approach velocity of filtration v = superficial velocity of filtra'don (= va/s). Greek letters
%= = ~b = 2o = ;[ =
Particle collision efficiency factor porosity of filter bed solid volume fraction of particles clean bed filter coefficient characteristic wavelength of the van der Waals interaction /~ -- viscosity p = density of water = zeta potential. INTRODUCTION
In filtration practice without coagulant addition to the influent water, particle-grain surface forces, although depressed, are sufficient to substantially moderate particle capture. F o r the same reason Gregory (1964) concluded from filter experiments using Coulter Counter particle analysis that filter
pore particle fiocculation effects are insignificant. However, for particle suspensions that have been chemically destabilized by metal salts or polymer materials (e.g. in direct filtration) the fluid shear within granular media may be sufficient to promote appreciable inter-pore collision and aggregation. The existence of particle fiocculation in filter pores and the influence of this effect on filtration efficiency are currently the subject of some controversy. Some workers have proposed, without clear experimental evidence, that flocculation in the filter bed is an important mechanism (Shea et al., 1971; Cleasby, 1976; Treanor, 1976; Culp, 1977). Other more fundamental filter investigations have suggested the absence of particle flocculation effects under conditions considered favourable to flocculation (Habibian, 1971; Fitzpatrick and Spielman, 1973; Ghosh et al., 1975; Vreeken et al., 1978; Yeh and Ghosh, 1981). Intuitively, it is considered likely that rapid particle flocculation readily observed in jar test experiments would have a parallel in fluid shear flow through filter pores. The only theoretical assessment of this to date by Vreeken et al. (1978) has shown the sensitivity of filter capture efficiency to both submicron and supermicron growth. To date, the only reported work that has considered the direct measurement of filter pore particle flocculation is that of Elson (1979) who employed a fluidized bed with which he was able to show good agreement between experiment and theory. In their studies of the significance of filter pore flocculation in fixed filters, both Ives and AI Dibouni (1979) and Vreeken (1978) abandoned experimental attempts to measure flocculation rates because of excessive particle retention in their model filters. Ives concluded that no techniques could be devised to separate the effects of filtration and flocculation, since attempts to
715
N. J. D. GRAHAM
716
make the filter grain non-retaining (e.g. by increasing electrical double-layer repulsion) also inhibited ftocculation by the same effect. However, the particular characteristic properties of polymer materials as flocculants (e.g. non-ionic polymer bridging), in combination with particle-grain surface forces, was considered in this study to present the possibility of separating substantially, if not totally, the effects of filtration and flocculation. Since the theoretical analysis of fluid flow in filter pores is based on the Kozeny-Carman equation (see section on Theory), in which the filter bed is simplified as a cluster of capillary tubes, comparable flocculation rates in a model cluster of capillary tubes were also to be investigated under conditions identical to the filter experiments. Fluid flow in filter pores is laminar (Cleasby and Baumann, 1962), with fluid viscous forces predominating over fuid inertial forces, and because of flow tortuosity particle interaction is therefore likely to be greater in the filter pores than in an equivalent capillary flow. An assessment of orthokinetic flocculation in capillary flow may therefore provide a "lower bound" on the flocculation behaviour in a comparable filter bed. To make the filter bed and capillary model sufficiently close in their equivalence, the filter grain size and internal capillary diameter were matched to give both geometrical and hydrodynamic similarity. A third, complementary investigation of orthokinetic flocculation rates in a jar-test apparatus was proposed since it was considered that collision efficiency factors, determined from a transitionalturbulent flow regime, would represent "upper bound" values when compared to respective values for flocculation in laminar shear. Evidence to support this assumption has been found by Ives and Bhole (1977) who compared orthokinetic flocculation effects in a paddle-stirred vessel with the quasilaminar flow in a batch Couette apparatus.
Integrating equation (1) gives: K = (Ill)In(No/N).
(3)
First-order rate constants (Re) can therefore be determined directly from the measured decrease in total particle number concentrations and, thus, the interparticle collision efficiency determined as: ap = KE/(4(aG/Tt ) .
(4)
Care is needed, however, since this treatment incorporates the major assumption of particle volume coalescence upon successful collision. Moreover, as the flocculation reaction proceeds the size distribution spectrum of the particle system broadens and thereby weakens the assumption of purely primary particle collision. Ives (1975) derived the following expression for by substituting the Kozeny-Carman equation of pressure gradient for a uniform granular bed into the Camp-Stein function of power dissipation: = 6(x/S)v (1 - e)/edg.
(5)
However, the Kozeny-Carman equation is based upon the idealization of Poiseuille flow through a bundle of identical, cylindrical, non-connected capillaries. Given this assumption, Robinson (1979), has shown that the flow-weighted velocity gradient (Gw) is a more appropriate value to use for Poiseuille flow than the root-mean-square velocity gradient. For Poiseuille flow, Robinson was able to express the flow-weighted velocity gradient in terms of the rootmean-square value: Gw = (8 x/2) ~/15.
(6)
Substituting equation (5) into equation (6) gives: Gw = (16~/10/5)v (1 - e)/dge.
(7)
Using equation (7) and the following transform for the filter bed:
THEORY
The ability to directly measure flocculation rates in the laminar shear flow through filter pores offers the opportunity to evaluate the closeness of the theoretical description of particle collision rates as developed by Ives (1975). For a dilute suspension of completely destabilized monodispersed particles undergoing orthokinetic flocculation the initial rate of change of total particle concentration in a hydrodynamic shear field can be expressed as a pseudo first-order process (Swift and Friedlander, 1964): = KN
(1)
K = 4~p q ~ / g
(2)
-dN/dt
= the root-mean-square velocity gradient prevailing % = the interparticle collision efficiency factor.
and where ~b = t h e solid volume fraction of suspended particles
dN/dL
= (v -~ ) d N / d t
(8)
the flocculation equation becomes: -dU/dL
= ( 6 4 x / l O / 5 n ) % q ~ U ( 1 - g)/dge.
(9)
This equation suggests that, for a given filter where particle capture is negligible, the overall degree of flocculation is independent of flow rate and directly proportional to the internal pore surface per unit pore volume, 6(1 -e)/edg. However, the analysis of Ives (1975) was not able to include the more recently defined appraisal of interparticle hydrodynamic effects. Zeichner and Schowalter (1977) and van de Ven and Mason (1977) have independently considered the effect of hydrodynamic interaction on orthokinetic collision rates and van de Ven gave the following semi-empirical formula for the effective collision efficiency factor of non-Brownian spherical particles
Orthokinetic flocculation in rapid filtration in the absence of double-layer electrical repulsion:
ctp = f (2~/dp)(2H /9~l~Gd~) °18
(10)
where
f ( 2 ~ / d ~ ) = a function for which some numerical values were given by van de Ven = the "characteristic wavelength" of the van der Waals interaction. Equation (10) indicates that as a consequence of hydrodynamic interactions collision efficiencies are inversely dependent on shear rate and particle size. The dependency on shear rate is not large for fullydestabilized suspensions and a 50-fold increase in shear rate would be required to halve the efficiency. Experimental support for this effect has been reported by Curtis and Hocking (1970) and Gregory (1981, 1982). Gregory has applied values appropriate for sheared aqueous suspensions into equation (10) and found ~p values ranging between 10 and 30% of that predicted by Smoluchowski. F o r flow in a capillary tube, Gregory (1981) has shown that the flow weighted average value of GT (velocity gradient x retention time) is given by:
Gw T = 8Leap/3Rcap
(11)
where Leap and Reap are the length and internal radius of the tube. Smoluchowski's integrated pseudo first-order equation can be shown to be [from equations (2) and (3)], in terms of the dimensionless number GT:
N / N o = exp(-4ot~dpGT/rc).
(12)
Thus the extent o f orthokinetic flocculation as a result of laminar tube flow depends primarily on the tube dimensions and, through the collision efficiency factor [equation (10)], inversely on the shear rate. The effect of the distribution of GT values in laminar tube flow is also important and Gregory (1981) has shown that this leads to a degree of flocculation significantly less than expected on the basis of a mean value GwT.
Specification of filter bed~capillary dimensions To justify, as closely as possible, comparisons between the measured flocculation rates for the filter bed and the capillary model, hydrodynamic and geometrical equivalence were incorporated into the apparatus specification. Hydrodynamic equivalence was considered by specifying that the flow in the filter pores and through the capillaries would have a similar Reynolds number at a c o m m o n flow weighted mean velocity gradient. Approximate hydrodynamic equivalence was important since the particle collision efficiency factor has already been shown to be affected by hydrodynamic drag and may be influenced by other hydrodynamic effects. By using the Blake number as the Reynolds number for the filter, as outlined by Ives (1970), in which the length term is the mean hydraulic radius of the pores and the velocity term is the mean pore velocity, ensures that the
717
range of local velocity gradients in the pores and the capillary flow, as well as the mean velocity gradient, are similar. Geometric equivalence was considered important in case scale effects were significant. The minimum practical internal diameter of capillary was 0.25 m m and the equivalence calculations were based on this; the calculations are given in the Appendix. A filter grain size (dg) of 1.32 m m was employed in order to approximate to hydrodynamic and geometric similarity with the capillary flow. MATERIALS AND METHODS
The following two particle-polymer systems were employed in the flocculation tests: hydrophilic silica microspheres with cationic polymer and hydrophobic (surface methylated) silica microspheres with polyacrylamide. The hydrophobic silica-polyacrylamide system was developed for the filter tests since the use of a largely nonionic polymer, specifically adsorbed by hydrophobic and hydrogen bonding effects (Rubio and Kitchener, 1976), to destabilize partides carrying a similar charge sign as the filter grains would allow the measurement of inter-pore particle flocculation without influencing particle capture. The hydrophilic silicacationic polymer system was used to compare flocculation rates in the capillary and jar test apparatuses for particles carrying no net overall surface charge.
Suspensions Hydrophobic porous silica microspheres were obtained from Shandon Southern Products Ltd, Runcorn, U.K. The spheres were described by the manufacturer as having a complete monolayer coverage of trimethylsilyl groups, a pore volume of 0.7cm3g -I, a specific surface area of 200 m 2 g-~ (by N 2 adsorption) and a 10 nm mean pore size. A Coulter Counter particle size analysis determined the spheres as being reasonably monosized with a mean dia of 5.4 #m and a RSD of 22.3%. The microspheres were obtained as a dry powder and when wetted with methanol showed good dispersion in distilled water. Electrophoresis measurements (Rank Bros. Particle Electrophoresis Apparatus, Mark II, Cambridge, U.K.) found particle surface potentials of -27.1 mV (RSD= 17%) in deionized water and -21.3 mV (RSD = 13%) in 1 mM NaCI/I mM NaHCO 3 at 25°C. To avoid particle migration to the surface of stirred suspensions because of their strong hydrophobicity, the liquid surface was covered with a thin, wooden float coated with collodion acetone to make its surface hydrophilic. Hydrophilic porous silica microspheres were supplied by AERE Harwell, U.K., having a mean dia of 3.3/~m (RSD = 24.8%) as determined by Coulter Counter and a pore volume of 0.57 cm 3g-~ as quoted by the manufacturer. The microspheres were obtained as a dry powder and showed good dispersion in distilled water. Electrophoresis measurements indicated no significant "ageing" effects in distilled water for 10 < t < 100h, with ( = - 2 6 mV + 8% at 25°C.
Polymers All the polymer materials used in this study were commercial products• Nonionic polyacrylamide was obtained as a commercial synthetic polymer from Cyanamid of Great Britain Ltd, Gosport, U.K. Although no information was available concerning the narrowness of the molecular-weight distribution the average molecular weight of the polymer was stated by the manufacturer to be 10 million. A measure of the purity oftbe polyacrylamide was suggested by there being less than 1% anionic groupings on the polymer chain. The polymer was obtained as a granular solid and continuous gentle
718
N . J . D . GRAHAM
stirring was required to achieve complete solution of the polymer in the preparation of stock solutions. A lower molecular weight polyacrylamide, supplied by Allied Colloids Ltd, Bradford, U.K., was employed as a filter grain precoating material. This straight homopolymer was selected since its approximate molecular weight (inferred from intrinsic viscosity measurements) of 0.3-0.5 × 106 was large enough to offset polymer desorption from the grain, once adsorbed, but not large enough to cause particle flocculation. A tertiary polyamine, supplied in liquid form by Cyanamid of Great Britain Ltd, was used as a floceulant for the hydrophilic silica and had a 100% cationic charge density and an average mol. wt of 100,000. The tertiary polyamine behaves in aqueous solution as a weak base and is only partly charged at neutral pH. The degree of protonation at the test pH was determined by viscosity/pH titration using a Volac U-tube viscometer (Gritfin& George Ltd, U.K.). Since ageing and loss of flocculation activity of aqueous solutions of high-molecular-weight polymers has been reported (Shyluk and Stow, 1969), stock solutions were prepared and used within 24 h.
Filter apparatus The filter column consisted of a 1200 mm length of 65 mm i.d. Pyrex glass tubing. An upflow filter arrangement was chosen to lessen the significance of particle sedimentation effects. The column had seven glass capillary outlet ports fused in a vertical spiral to the column wall. The 7 mm o.d. capillaries were made to extend 5 mm into the column, had their inside end sealed, and a 0.75 mm slit cut into their bottom wall. The ports were connected to right-angle Rotaflo stopcocks which had reduced arms. The stopcocks were aligned vertically with a rising capillary bore side arm connecting to the column and a plain discharge stem pointing vertically downward. The ports were used at different times to measure head loss through the granular bed by connection to a manometer assembly, and for taking flow samples. Influent solutions were drawn from 51 Pyrex beakers and pumped to the filter column via a double head, variable speed, peristaltic pump. Flow control was achieved by a rotameter flow meter and valve on the outlet flow line. The 1 m granular bed was formed using ballotini nonporous glass spheres of 1.32 mm nominal dia. Prior to use in the filter tests, the ballotini was cleaned by immersion in a 10% HCI and 10% HNO 3 solution for a period of 48 h. After rinsing with distilled water the ballotini was dried and stored in dry containers. The filter column was filled with media by first filling with distilled water and then progressively adding given weights of ballotini to fill a predetermined column volume.
Filter tests A residence time evaluation was carried out for the filter bed at the lowest approach velocity by means of a 1% NaCI conductivity tracer. A sharp residence time profile was obtained which gave a value of 1.38 as the numerical ratio of the time-to-peak concentration to the theoretical residence time. For all filter tests a value of 1.50 was adopted for this ratio in the determination of the minimum delay time for filtrate sampling. Prior to each filter test and before the suspension and dilution water flows were initiated, the filter flow conditions were allowed to stabilize using dilution water alone. The Rotaflo valves in the three column sampiing outlets at 2, 52 and 102 cm above the column base were opened and adjusted to discharge freely and isokinetically with the upflow in the column. During filtration samples were taken individually from the discharge of the three column side ports by collecting approx. 1 ml and diluting immediately with 10 ml of clean 1% NaC1 prior to particle analysis. At the completion of each filter test the filter grains were cleaned by allowing the media to stand in 6%
Decon 90 .alkaline detergent solution for a minimum of 2 h and then rinsing with deionized water at a sub-fluidization velocity.
Capillary apparatus A one metre capillary assembly was constructed from 50 individual 0.25 mm bore, 0.5 mm o.d. fused silica capillary columns. The capillary unit was positioned vertically and the suspension and polymer solutions were drawn by a variable speed two-channel peristaltic pump. The flow rate for the influent streams was kept constant throughout the tests to maintain identical mixing conditions. To regulate the flow rate through the column and provide mixed influent samples for particle analysis, a proportion of the influent flow was drawn off by an identical single channel peristaltic pump. At the top end of the column the flow was allowed to discharge freely into a calibrated cylindrical jacket of glass tubing. During the floceulation tests the flow rate through the column was determined by timing flow collection in this calibrated jacket.
Capillary tests Prior to each floceulation test the capillary column was filled with the test solution for 30 rain to allow the internal surface to equilibrate ionically. During each test, inlet and outlet flow samples were taken using a wide bore syringe. Outlet samples were taken after a minimum flow time of three theoretical retention times after the commencement of flow pumping to ensure fully developed flow conditions. The column unit and allied tubing were cleaned after each test by passing 200 ml of 5% Decon 90 alkaline detergent through the column over a period of 15 min, followed by 400 ml of deionized water.
Jar tests Jar tests were carried out as described by Graham (1981).
Particle analysis Orthokinetic flocculation was quantified by measuring changes in the particle size distribution of suspensions using a model TA II Coulter Counter. This has been described in more detail by Graham (1981). RESULTS
Choice o f filter test conditions In order to carry o u t filter experiments t h a t would encourage particle flocculation a n d minimize filter capture a preliminary investigation was carried o u t to consider the effects o f solution p H a n d ionic strength. T h e work o f Ives a n d G r e g o r y (1966) has s h o w n the i m p o r t a n c e o f surface forces in dictating the degree o f particle removal in filter beds; solution ionic s t r e n g t h a n d p H determine in p a r t the m a g n i t u d e o f these surface forces. G r e g o r y (1964) has studied the varia t i o n of electrokinetic potential for ballotini grains with a m o n o v a l e n t a n d di-valent salt c o n c e n t r a t i o n . He concluded t h a t whilst the ballotini potential diminished regularly with increasing salt concent r a t i o n the variation o f potential w i t h p H in solutions o f c o n s t a n t ionic strength a p p e a r e d to be small. T h e v a r i a t i o n in filter efficiency with various solutions o f either low ionic strength or high pH, determined in this study is highlighted in Fig. 1. As expected, a moderately low ionic s t r e n g t h / m o d e r a t e p H solution (1 m M NaCI/1 m M N a H C O 3 ) encouraged sizeable particle capture, whilst high p H solutions a n d de-
Orthokinetic flocculation in rapid filtration
719
100
IO0 9O
~
~ P =8 ~8
80 '° 6O
80
60
5O
®E
4O
~ 30
~
/
2o
o o.
20
"~
10
~
20
g
30
lO
0
0
I
I
50 Filter
bed depth
100 (cm)
Fig. 1. The variation of filter efficiency with nature of solution (100mgl -t silica, Gw= 100s-~). O I mM NaCI/I mM NaHCO3, pH 8.6; • 10.4mM NaOH, pH 11.7; /X 2 mM NaOH, pH 10.6; O deionized water.
I
I
I
I
I
~e
•~ o ~Q. 50
I
I
I
I
I
2
4
6
8
10
Reaction time (mJn)
ionized water seriously limited particle capture. Ideally, deionized water was the most suitable solution for the filter/flocculation tests but complete avoidance of trace ionic contamination was not practically possible. A 10-SM NaC1 solution was considered experimentally to be the most suitable test medium since this was shown to minimize filter capture and provide measureable polymer flocculation rates (see results of jar tests). Jar tests
It was expected that a nonionic polymer such as polyacrylamide would display an optimal concentration in the flocculation of hydrophobic silica, as has been proposed by Michaels (1954). An optimal concentration is consistent with the polymer bridging hypothesis which requires that the particle surfaces should be only partly covered with adsorbed polymer so that attachments with segments from other particles can be formed. Jar test experiments showed that an optimal polymer dose could be defined; this was determined as 5 0 m g g - ' SiO2 in 10-SM NaC1 solution (Graham, 1982). The initial flocculation rate (flocculation period ~< 6 min of jar test) at optimal polymer dosage was found to be 0.211, expressed as a ratio of the Smoluchowski theoretical value (Fig. 2). Graham (1981) has already shown that the optimal dose for the tertiary polyamine, in flocculating hydrophilic silica particles, occurs at the point of zero particle electrophoretic mobility. The initial flocculation rate at optimal polymer dose, in this case, was found to be 0.140, expressed as a ratio of the Smoluchowski theoretical value (Fig. 2). For both particle-polymer systems, comparative measurements were made of flocculation rates at velocity gradients above and below 100 s- ' to confirm that floe disruption was not significant. This is
Fig. 2. Jar test flocculation kinetics at optimum polymer doses for the methylated silica and hydrophilic silica systems (300 mg 1-' silica, G = 100 s-l). O 5.4/t m methylated silica system; • 3.3/~m hydrophilic silica system.
exemplified in Fig. 3 which displays an increasing flocculation rate with velocity gradient in accordance with theoretical predictions when floc disruption is not included. The results shown in Fig. 3 also support the approximation that for jar test conditions the collision efficiency factor is not significantly dependent on mean velocity gradient. Capillary tests
F o r the tests with the methylated silica-polyacrylamide system in 10-SM NaC1, evidence of flocculation in capillary flow was found over a wide
100
8o
u c 60 CoD oc ~ u .Q
~-~ 40
¢).E_. u~ ~ o 20
r! ap~0.1
0
2
I 100 G(s-I) 4
150 I 6
Reoction t i m e
I 8
I 10
(rain)
Fig. 3. The variation in jar test flocculation kinetics with mean velocity gradient (methylated silica system, 100 mg 1-1 silica). © ~ =71 s-I; • ~ = 100 s-I; V G = 125s-L
720
N . J . D . GRAHAM 80-
6O
~ 4o g
2o 0
0
I
I
I
I
o
I •13
.=_
I
I
I
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f o~
"~
'°
N 20
• ,I -m---"-"
,ira-
m--
I
I
I
I
I
I
I
I
I
I
50
100
150
200
250
300
350
400
450
500
Meon
velocity
grodient
Gw(s -1]
Fig. 4. The variation in the degree of flocculation with mean velocity gradient of capillary flow for the methylated silica and hydrophilic silica systems (300 mg 1-~ silica). O 5.4/~m methylated silica system; • 3.3 #m hydrophilic silica system.
range of flow velocities (Gw = 50-450 s - ' ) from both a reduction in particle number concentration and an increase in the particle population mean size (Fig. 4). As suggested by theory [equations (10), (11) and (12)], the extent of particle flocculation was found to decrease with increasing mean velocity gradient. The decrease was significant in the range of G,. of 50-250 s-l, but much less so at higher values up to 450s -l. At 100s - ' , an C~p value of 0.040 was determined which was substantially lower than the corresponding value obtained from the jar test (~p = 0.211). Much greater in effect was the flocculation of the 3.3/~m hydrophilic particles also shown in Fig. 4. The cationic polymer-destabilized particles similarly displayed both a wide flocculation range with mean velocity gradient and a diminishing extent of flocculation with increasing shear rate. In this case, the calculated value of ~p for the capillary flow (0.096 at G,.= 100s -~) although still lower, is in closer agreement with the jar test value (0.140). The flocculation behaviour for the two particle systems in the region 0 < Gw < 50 s -~ could not be measured due to the limitations of the experimental technique. In addition, perikinetic flocculation rates could not be measured experimentally due to particle sedimentation effects, but theory would suggest that for the size of particles used Brownian Diffusion effects are negligible. It is possible to speculate that the flocculation curves would display maxima close to G , = 0 s -j. Filter tests
Initial filter experiments were carried out at 2 mm s -1 (G,. = 50 s -1) with 100 mg 1-' methylated silica and 50 mg g-~ polyacrylamide. These experiments displayed a considerable increase in particle
capture through the addition of polymer and this was assumed to be the result of polymer adsorption on the filter media. To diminish this effect, use was made of a lower-molecular weight polyacrylamide as a precoating polymer for the filter media. Filter precoating was carried out by passing a volume equivalent to approximately three bed volumes of 150mgl -~ (10 times optimal dose for test polymer) polyacrylamide through the filter at 4 mm s-L Unadsorbed polymer was then removed by immediately rinsing the filter with five bed volumes of deionized water at 4 mm s- 1. Filter tests were carried out at four approach velocities corresponding to Gw values of 50, 100, 150 and 200 s -]. At a filter approach velocity equivalent to Gw = 1 0 0 s - 1 some evidence of particle flocculation was found, although of a very minor nature (Table 1). The results shown in Fig. 5 compare the filter outlet and inlet suspension concentrations and size distributions. A consistent trend of increasing extent of flocculation with flow velocity (thus, velocity gradient) was apparent; a four-fold velocity increase gave rise to an overall 8% increase in the particle mean size and a three-fold increase in the total volume of aggregates of approximately twice the initial mean size. DISCUSSION
Implicit in the acceptance of theoretical predictions of the significance of filter pore particle flocculation is the adequacy of the assumption of Smoluchowski kinetics when applied to filter flow. In this there is some doubt since the exact nature and description of the filter pore fluid flow is unknown. Gregory (1981) has clearly demonstrated for the relatively simple case of Poiseuille flow, that the exclusion of a full description of particle residence time distribution can
Orthokinetic flocculation in rapid filtration
721
Table 1. Orthokinetic flocculation rates under optimal conditions Particle type and size
Floccalation system
Destabilization
G,. or (s i)
%,
Hydrophilic silica, 3.3 #m
Tertiary amine polymer in I mM NaCI/I mM NaHCO 3
Jar test
100
0.140
Hydrophilic silica, 3.3/am
Tertiary amine polymer in I mM NaC1/1 mM NaHCO 3
Capillary test
100
0.096
Methylated silica, 5.4#m
Polyacrylamide in 10 SM NaCI
Jar test
100
0.211
Methylated silica, 5.4,um
Polyacrylamide in 10 SM NaCI
Capillary test
100
0.040
Methylated silica, 5.4#m
Polyacrylamide in 10 SM NaCI
Filter bed
100
0.012
*Collision efficiency factor = observed flocculation rate divided by theoretical rate as determined from equation (2). seriously e x a g g e r a t e the overall a m o u n t o f particle collisions. In a d d i t i o n , the a p p r a i s a l b y v a n d e V e n a n d M a s o n (1977) o f t h e influence o f h y d r o d y n a m i c d r a g effects o n particle collision efficiency h a s ex-
p o s e d the p r o b a b i l i t y o f a g r e a t e r d e p e n d e n c y o f filter p o r e f l o c c u l a t i o n rate o n particle size a n d s h e a r rate. T h e clear n e e d to assess q u a n t i t a t i v e l y t h e "in-filter" f l o c c u l a t i o n p r o c e s s has b e e n s h o w n in p r e v i o u s in-
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9~_~
1.o 1.11.2
I
I
I
I
50
100
150
200
250
Meon velocity grodient (s -1)
Fig. 5. Evidence of an increasing degree of filter pore particle flocculation with filter bed mean velocity gradient (comparisons of filter effluent with influent). W R. 20/6--D
722
N . J . D . GRAHAM 0.23 F 0.22 F
...~.11
Jart._.estt . . . .
0,10
0.08
006
Filter /
Operational
_
~oximom ,or %
004 ~"~.
Capillary
o
0.02
0.00
i
100
i 200
300
I 400
• 500
"G, G w (s -~)
Fig. 6. Particle collision efficiency-velocitygradient diagram for the methylated silica system.
vestigations (Ives and AI Dibouni, 1979) to be more than matched by the experimental difficulties in attempting to do so. Since previous destablization methods for particle flocculation have been confined totally to charge neutralization processes [indifferent counter ions (Ives and A1 Dibouni, 1979) or cationic polymer adsorption (Habibian, 1971)], particle capture efficiencies have been similarly magnified as a direct consequence. The adoption of a nonCoulombic, particle-specific destabilization method (in this study) permits the preservation of doublelayer repulsive barriers in order to minimize particle capture. Such a method which features the specific adsorption of high molecular weight polyacrylamide on hydrophobic silica particles has been found in this study to be moderately successful, although special efforts were required to "protect" the filter grains from polymer adsorption (steric stabilization). The general form of the flocculation results from the capillary experiments are entirely consistent with those reported by Gregory (1981, 1982) and Higashitani et al. (1980). The clearly observed behaviour of diminishing ctp values with shear rate for both particle-polymer systems is in complete agreement with the van de Ven theoretical description of orthokinetic collision efficiency in laminar flow (van de Ven and Mason, 1977). Since the capillary model and the filter bed apparatus were designed to be approximately hydrodynamically and geometrically similar, the results of the flocculation experiments using both these apparatuses can be compared by considering the respective ctp values (Fig. 6). It is clear from Fig. 6 that the trend of increasing % values with shear rate for filter pore flocculation conflicts with the experimentally and theoretically established floccula-
tion behaviour in Poiseuille flow (Gregory, 1981). A possible explanation arises from the observed differences in %, for the methylated silica-polyacrylamide system, determined from the jar test and capillary experiments. The substantially greater ~p value determined in the jar test experiment suggests that the very different hydrodynamic regime in the jar test is either giving rise to a substantially greater particle collision rate (not adequately accounted for in the equivalence of ~ for the jar test and G,, for capillary flow) or giving rise to a greater collision efficiency through the overcoming of double-layer potentials by particle inertia effects. In a similar manner, departures in the exact flow regime for filter pore fluid flow compared to Poiseuille flow would be expected to lead to differences in flocculation behaviour. In this case, the effects of particle inertia increasing ~p are considered to be negligible, but significant differences in particle residence time distribution are very likely. It is possible, with the complexities of filter pore fluid flow, that an increasing shear rate might cause increases in the sum of all the individual G T values, giving a greater overall flocculation extent. An additional factor which might be contributory arises from consideration of particle-polymer adsorption kinetics. Gregory (1982) has shown, via a simplistic semi-quantitative discussion that assumes that the adsorption process can be treated as a collision between unequal spheres, that under certain conditions both polymer adsorption and particle collisions can be predominantly orthokinetic in character (diffusion effects are minor) and that the polymer adsorption rate can be significantly slower than the particle collision rate. This effect, with its dependence
0.16
( Jar test
0.14
I I I
0.12
0.10
I I
0.08
t IICoy°r'
0.06 J Operational ,moximum Gw 0.04
0.02
I I 100
I 200
I 300
I 400
I 5o0
G, Gw (s"~ ) Fig. 7. Particle collision efficiency-velocitygradient diagram for the hydrophilic silica system.
Orthokinetic flocculation in rapid filtration
723
Table 2. Initialorthokineticflocculationrates under optimum conditionsas indicated by others Birkner and Morgan (1968) Graham (1981) Particle type and s i z e Polystyrene latex, Porous silicamicrosphere, 1.3/~m 7.6/~m Destabilizingpolymer Polyethylenimine Various cationic (approx. mol. wt) (3.5 x 104) (105-7 × 10 6) Flocculations y s t e m Paddle-stirred vessel, Paddle-stirredvessel, 1.2mM NaHCO3 ImM NaCI/ImMNaHCO3 (s t) 93 100 %* 0.029 0.112-0.543 *Collision efficiencyfactor= observed flocculationrate divided by theoretical rate determined from equation(2).
on the nature of the polymer-particle mixing arrangements and flocculation shear rate, taken with a changing residence time distribution with filter flow velocity, may contribute to the observed improvement in ~p and flocculation extent with shear rate. Figures 6 and 7 show the demarcated region for filter pore flocculation hypothesized in this study. The relative insensitivity of ~ to shear rate in the jar test represents the upper bound for ~p and a G~ value of 300 s ~represents the operational limit in practice for the filter pore shear rate. Further study is required to consider whether variations in the geometry and the hydrodynamics of the jar test appreciably affect the magnitude of ~p, and thus whether the applicability of the jar test determination as an upper bound is valid. The assertion that flocculation in an equivalent capillary flow represents a lower bound for ~p in filter pores is not conclusive (Fig. 6). The apparent opposite trend in ~p variation with shear rate for filter pore flocculation invalidates the direct use of capillary models as a simple rigorous method of assessing minimum ~p values for filter beds. However, peak ~p values for filter pore flocculation, associated with high shear rates, were found to lie within the region bounded by the jar test and capillary results. The range of ~p values associated with this region was wide for the methylated silica-polyacrylamide system, but very much narrower for the cationic polymer system (Fig. 7). It is possible to speculate that for cationic polymer-particle systems the jar test value for ~p represents a close upper bound on the value in filter pore flow at maximum shear rates. For particle destabilization by cationic polymers a range of reported values for ~p in jar test experiments is shown in Table 2. Graham (1981) found that the largest ~p value (0.543) was associated with the highest molecular weight cationic polymer typically used in water treatment practice (mol. wt ~ - 107). This value may therefore be taken as an indication of the greatest degree of flocculation likely in the pore openings of a filter under certain specific conditions. From this, the consequent contribution of filter pore particle flocculation to overall filter performance in direct filtration can be assessed theoretically and this will be described subsequently.
CONCLUSIONS (I) Filter pore particle flocculation can be quantified to a modest degree of accuracy by the use of a specific, nonionic polymer-particle system. (2) Collision efficiency factors determined in equivalent tube flow conditions do not necessarily represent lower bound values for filter pore flocculation. (3) Filter experiments displayed a trend of increasing collision efficiency factor and overall extent of flocculation with shear rate, in marked contrast to existing theoretical interpretations. An explanation based on the complex hydrodynamic flow pattern in a granular filter is proposed. (4) Filter pore collision efficiency factors at high shear rates may lie between those determined for equivalent tube flow and by jar test; the jar test values may represent an upper bound for the filter conditions. (5) Filter pore collision efficiency factors may be as high as 0.5 for suspensions destabilized by high molecular weight cationic polymers. Acknowledgements--The financial support of the University
of London Central Research Fund and the Public Works and Municipal Services Congress and Exhibition Council are gratefully acknowledged. The author is indebted to the Engineering Geology Unit of the Institute of Geological Sciences for technical cooperation.
REFERENCES
Birkner F. B. and Morgan J. J. (1968) Polymer flocculation kinetics of dilute colloidal suspensions. J. Am. Wat. Wks Ass. 60, 175-191. Cleasby J. L. (1976) Research achievements---existingand expected. J. Am. Wat. Wks Ass. 68, 272-274. Cleasby J. L. and Baumann E. R. (1962) Selection of sand filtration rates. J. Am. Wat. Wks Ass. 54, 579-602. Culp R. L. (1977) Direct filtration. J. Am. Wat. Wks Ass. 69, 375-378. Curtis A. S. G. and Hocking L. M. (1970) Collision efficiency of equal spherical particles in a shear flow. Trans. Faraday Soc. 66, 1381-1390. Elson T. P. (1979) Flocculation in fluidized beds. Symposium Particle Growth Processes, 6th Annual Research Meeting, University College, London. Institution of Chemical Engineers. Fitzpatrick J. A. and Spielman L. A. (1973) Filtration of
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N . J . D . GRAHAM
aqueous latex suspensions through beds of glass spheres. J. Colloid Interface Sci. 43, 350-369. Ghosh M. M., Jordan T. A. and Porter R. L. (1975) Physicochemical approach to water and wastewater filtration. J. envir. Engng Div. Am. Soc. cir. Engrs 101, EEl, 71-86. Graham N. J. D. (1981) Orthokinetic flocculation rates for amorphous silica microspheres with cationic polyelectrolytes. Colloid S u r f 3, 61-77. Graham N. J. D. (1982) Significance of filter pore particle flocculation in direct filtration. Ph.D. thesis, University of London. Gregory J. (1964) Molecular forces and electrokinetic effects in filtration. Ph.D. thesis, University of London. Gregory J. (1981) Flocculation in laminar tube flow. Chem. Engng Sci, 36, 1789-1794. Gregory J. (1982) In The Effect o f Polymers on Dispersion Properties (Edited by Tadros T. F.). Academic Press, London. Habibian M. T. (1971) The role of polyelectrolytes in water filtration. Ph.D. thesis, University of North Carolina. Higashitani K., Miyafusa S., Matsuda T. and Matsuno Y. (1980) Axial change of total particle concentration in poiseuille flow. Y. Colloid Interface Sci. 77, 21-28. Ives K. J. (1970) Rapid filtration. Wat. Res. 4, 201-223. Ives K. J. (1975) In The Scientific Basis o f Filtration (Edited by Ives K. J.). NATO ASI Series. Noordhoff, Leyden. Ives K. J. and AI Dibouni M. (1979) Orthokinetic flocculation of latex microspheres. Chem. Engng Sci. 34, 983-991. Ives K. J. and Bhole A. G. (1977) Study of flowthrough couette flocculators--II. Laboratory studies of flocculation kinetics. Wat. Res. 11, 209-215. Ives K. J. and Gregory J. (1966) Surface forces in filtration. Proc. Soc. Wat. Treat. Exam. 15, 93-116. Michaels A. S. (1954) Aggregation of suspensions by polyelectrolytes. Ind. Engng Chem. 46, 1485-1490. Robinson B. (1979) Personal communication, Iowa State University, Rubio J. and Kitchener J. A. (1976) The mechanism of adsorption of poly(ethylene oxide) flocculant on silica. J. Colloid Interface Sci. 57, 132-142. Shea T. G., Gates W. E. and Argaman Y. A. (1971) Experimental evaluation of operating variables in contact flocculation. J. Am. Wat. Wks Ass. 63, 41~,8. Shyluk W. P. and Stow F. S. (1969) Aging and loss of flocculation activity of aqueous polyacrylamide solutions. J. appl. Polym. Sci. 13, 1023-1036. Spielman L. A. (1975) In The Scientific Basis o f Filtration (Edited by Ives K. J.). NATO ASI Series, Noordhoff, Leyden. Swift D. L. and Friedlander S. K. (1964) The coagulation of hydrosols by brownian motion and laminar shear flows. J. Colloid Sci. 19, 621~:~47. Treanor A. I. J. (1976) Recent developments in depth filtration. Process Biochem. 11, 34-37. Ven T. G. van de and Mason S. G. (1977) The microrheology of colloidal dispersions--VII. Orthokinetic doublet formation of spheres. Colloid Polym. Sci. 255, 468°479. Vreeken C. (1978) Personal communication, University of Technology, Delft. Vreeken C., Heertjes P. M. and Wesselingh J. A. (1978) The effect of particle coagulation on the performance of filter beds. Symposium Deposition and Filtration o f Particles from Gases and Liquids, Loughborough University, 1978, pp. 21-29. Society of Chemical Industry, London.
Yeh H-H. and Ghosh M. M. (1981) Selecting polymers for direct filtration. J. Am. Wat. Wks Ass. 73, 211 218. Zeichner G. R. and Schowalter W. R. (1977) Use of trajectory analysis to study stability of colloidal dispersions in flow fields. A I C h E J. 23, 243-254.
APPENDIX Specification o f Filter Bed~Capillary Equivalence Velocity gradient From Robinson (1979), the flow weighted velocity gradient for a smooth capillary is given by the expression: Gw_c~p = 64v J15dca p
(1)
where dcap = the internal diameter of the capillary va = the mean tube velocity. The flow weighted velocity gradient for a granular filter bed has already been shown to be [equation (7), where v = v,/e]: Gw_filt = (16x/10/5)va(1 - e)/dxe 2.
(2)
Reynolds number For flow in a smooth capillary, the Reynolds number expressed in terms of the hydraulic radius is as follows: Recap = pv~dcap/4#.
(3)
For flow in the filter pores, Ives (1970) has shown that the flow regime can be characterized by a modified Reynolds number in which the length term is the mean hydraulic radius of the pores, and velocity term is the mean pore velocity (approach velocity). The modified Reynolds number is called the Blake number (B), so that: Re~jt = B = v od~p /61t( l - ~).
(4)
Reynolds number--velocity gradient equivalence The Reynolds number equations (3) and (4) can be expressed in terms of the flow weighted velocity gradients by the substitution of equations (1) and (2), as follows: Recap = 15pd~p G . . . . p/256/1
(5)
Rena = 5pd~e 2Gw_ ~lt/96# x/10(1 - ~)2.
(6)
For equivalence, (Recap/Gw-c~p) = (Re~lt/Gw ~,t) so that: dg = 3dcap(l - ~)(lO)°'zs/~x/2.
(7)
Geometrical similarity The simplest two-dimensional filter grain arrangement is one where three ~rains are in contact with each other. If the grains are assumed to be circular and equal in diameter, then the diameter of a circular cpaillary that will fit in the void space and touching the three grains is: d~ = dg(Z/x/3 - 1).
(8)
Thus, for geometrical similarity: dg ~ dcap43/(2 - x/3).
(9)
Experimental values The smallest practical value for d~p was 0.25 mm and the bed porosity was assumed to be 0.41. The following values were determined from equations (7) and (9): For geometric similarity For hydrodynamic similarity
de = 1.62 mm dg = 0.68 mm.
0043-1354/86 $3.00+0.00 Copyright © 1986 Pergamon Journals Ltd
ORTHOKINETIC FLOCCULATION IN RAPID FILTRATION N. J. D. GRAHAM Public Health and Water Resource Engineering Section, Civil Engineering Department, Imperial College, London SW7, England (Received December 1984)
Abstract---Quantitative measurements have been made of filter pore orthokinetic flocculation using a laboratory-scale model filter and a hydrophobic particle-nonionic polymer system. Interparticle collision efficiency factors, determined by Coulter Counter analysis, have been found to increase with shear rate in contrast with current theoretical interpretations. Comparative collision efficiency factors have been determined in jar test and capillary-tube apparatuses under equivalent conditions to the filter tests. In rapid filtration practice using cationic polymers, and at high shear rates (Gw > 150 s-~) filter pore collision efficiencies are suggested as lying between those determined in tube flow (lower bound) and by jar test (upper bound). Key words--deep bed filters, filtration, flocculation, cationic polyelectrolytes, particle collision efficiency, jar tests, capillary flow
NOMENCLATURE B= ds = dp = G= Gw= = H = K= Ke =
Blake number, B = vadgp/6#(l - e) grain diameter particle diameter localized, uniform velocity gradient flow-weighted velocity gradient root-mean-square velocity gradient Harnaker constant orthokinetic flocculation rate constant experimentally determined flocculation rate constant L = filter bed depth L~p = length of capillary M = molar solution N = total particle concentration Rap = internal radius of capillary Re = Reynolds number Rh = hydraulic radius RSD = relative standard deviation s = internal surface area per unit volume of filter bed T = retention time va = approach velocity of filtration v = superficial velocity of filtra'don (= va/s). Greek letters
%= = ~b = 2o = ;[ =
Particle collision efficiency factor porosity of filter bed solid volume fraction of particles clean bed filter coefficient characteristic wavelength of the van der Waals interaction /~ -- viscosity p = density of water = zeta potential. INTRODUCTION
In filtration practice without coagulant addition to the influent water, particle-grain surface forces, although depressed, are sufficient to substantially moderate particle capture. F o r the same reason Gregory (1964) concluded from filter experiments using Coulter Counter particle analysis that filter
pore particle fiocculation effects are insignificant. However, for particle suspensions that have been chemically destabilized by metal salts or polymer materials (e.g. in direct filtration) the fluid shear within granular media may be sufficient to promote appreciable inter-pore collision and aggregation. The existence of particle fiocculation in filter pores and the influence of this effect on filtration efficiency are currently the subject of some controversy. Some workers have proposed, without clear experimental evidence, that flocculation in the filter bed is an important mechanism (Shea et al., 1971; Cleasby, 1976; Treanor, 1976; Culp, 1977). Other more fundamental filter investigations have suggested the absence of particle flocculation effects under conditions considered favourable to flocculation (Habibian, 1971; Fitzpatrick and Spielman, 1973; Ghosh et al., 1975; Vreeken et al., 1978; Yeh and Ghosh, 1981). Intuitively, it is considered likely that rapid particle flocculation readily observed in jar test experiments would have a parallel in fluid shear flow through filter pores. The only theoretical assessment of this to date by Vreeken et al. (1978) has shown the sensitivity of filter capture efficiency to both submicron and supermicron growth. To date, the only reported work that has considered the direct measurement of filter pore particle flocculation is that of Elson (1979) who employed a fluidized bed with which he was able to show good agreement between experiment and theory. In their studies of the significance of filter pore flocculation in fixed filters, both Ives and AI Dibouni (1979) and Vreeken (1978) abandoned experimental attempts to measure flocculation rates because of excessive particle retention in their model filters. Ives concluded that no techniques could be devised to separate the effects of filtration and flocculation, since attempts to
715
N. J. D. GRAHAM
716
make the filter grain non-retaining (e.g. by increasing electrical double-layer repulsion) also inhibited ftocculation by the same effect. However, the particular characteristic properties of polymer materials as flocculants (e.g. non-ionic polymer bridging), in combination with particle-grain surface forces, was considered in this study to present the possibility of separating substantially, if not totally, the effects of filtration and flocculation. Since the theoretical analysis of fluid flow in filter pores is based on the Kozeny-Carman equation (see section on Theory), in which the filter bed is simplified as a cluster of capillary tubes, comparable flocculation rates in a model cluster of capillary tubes were also to be investigated under conditions identical to the filter experiments. Fluid flow in filter pores is laminar (Cleasby and Baumann, 1962), with fluid viscous forces predominating over fuid inertial forces, and because of flow tortuosity particle interaction is therefore likely to be greater in the filter pores than in an equivalent capillary flow. An assessment of orthokinetic flocculation in capillary flow may therefore provide a "lower bound" on the flocculation behaviour in a comparable filter bed. To make the filter bed and capillary model sufficiently close in their equivalence, the filter grain size and internal capillary diameter were matched to give both geometrical and hydrodynamic similarity. A third, complementary investigation of orthokinetic flocculation rates in a jar-test apparatus was proposed since it was considered that collision efficiency factors, determined from a transitionalturbulent flow regime, would represent "upper bound" values when compared to respective values for flocculation in laminar shear. Evidence to support this assumption has been found by Ives and Bhole (1977) who compared orthokinetic flocculation effects in a paddle-stirred vessel with the quasilaminar flow in a batch Couette apparatus.
Integrating equation (1) gives: K = (Ill)In(No/N).
(3)
First-order rate constants (Re) can therefore be determined directly from the measured decrease in total particle number concentrations and, thus, the interparticle collision efficiency determined as: ap = KE/(4(aG/Tt ) .
(4)
Care is needed, however, since this treatment incorporates the major assumption of particle volume coalescence upon successful collision. Moreover, as the flocculation reaction proceeds the size distribution spectrum of the particle system broadens and thereby weakens the assumption of purely primary particle collision. Ives (1975) derived the following expression for by substituting the Kozeny-Carman equation of pressure gradient for a uniform granular bed into the Camp-Stein function of power dissipation: = 6(x/S)v (1 - e)/edg.
(5)
However, the Kozeny-Carman equation is based upon the idealization of Poiseuille flow through a bundle of identical, cylindrical, non-connected capillaries. Given this assumption, Robinson (1979), has shown that the flow-weighted velocity gradient (Gw) is a more appropriate value to use for Poiseuille flow than the root-mean-square velocity gradient. For Poiseuille flow, Robinson was able to express the flow-weighted velocity gradient in terms of the rootmean-square value: Gw = (8 x/2) ~/15.
(6)
Substituting equation (5) into equation (6) gives: Gw = (16~/10/5)v (1 - e)/dge.
(7)
Using equation (7) and the following transform for the filter bed:
THEORY
The ability to directly measure flocculation rates in the laminar shear flow through filter pores offers the opportunity to evaluate the closeness of the theoretical description of particle collision rates as developed by Ives (1975). For a dilute suspension of completely destabilized monodispersed particles undergoing orthokinetic flocculation the initial rate of change of total particle concentration in a hydrodynamic shear field can be expressed as a pseudo first-order process (Swift and Friedlander, 1964): = KN
(1)
K = 4~p q ~ / g
(2)
-dN/dt
= the root-mean-square velocity gradient prevailing % = the interparticle collision efficiency factor.
and where ~b = t h e solid volume fraction of suspended particles
dN/dL
= (v -~ ) d N / d t
(8)
the flocculation equation becomes: -dU/dL
= ( 6 4 x / l O / 5 n ) % q ~ U ( 1 - g)/dge.
(9)
This equation suggests that, for a given filter where particle capture is negligible, the overall degree of flocculation is independent of flow rate and directly proportional to the internal pore surface per unit pore volume, 6(1 -e)/edg. However, the analysis of Ives (1975) was not able to include the more recently defined appraisal of interparticle hydrodynamic effects. Zeichner and Schowalter (1977) and van de Ven and Mason (1977) have independently considered the effect of hydrodynamic interaction on orthokinetic collision rates and van de Ven gave the following semi-empirical formula for the effective collision efficiency factor of non-Brownian spherical particles
Orthokinetic flocculation in rapid filtration in the absence of double-layer electrical repulsion:
ctp = f (2~/dp)(2H /9~l~Gd~) °18
(10)
where
f ( 2 ~ / d ~ ) = a function for which some numerical values were given by van de Ven = the "characteristic wavelength" of the van der Waals interaction. Equation (10) indicates that as a consequence of hydrodynamic interactions collision efficiencies are inversely dependent on shear rate and particle size. The dependency on shear rate is not large for fullydestabilized suspensions and a 50-fold increase in shear rate would be required to halve the efficiency. Experimental support for this effect has been reported by Curtis and Hocking (1970) and Gregory (1981, 1982). Gregory has applied values appropriate for sheared aqueous suspensions into equation (10) and found ~p values ranging between 10 and 30% of that predicted by Smoluchowski. F o r flow in a capillary tube, Gregory (1981) has shown that the flow weighted average value of GT (velocity gradient x retention time) is given by:
Gw T = 8Leap/3Rcap
(11)
where Leap and Reap are the length and internal radius of the tube. Smoluchowski's integrated pseudo first-order equation can be shown to be [from equations (2) and (3)], in terms of the dimensionless number GT:
N / N o = exp(-4ot~dpGT/rc).
(12)
Thus the extent o f orthokinetic flocculation as a result of laminar tube flow depends primarily on the tube dimensions and, through the collision efficiency factor [equation (10)], inversely on the shear rate. The effect of the distribution of GT values in laminar tube flow is also important and Gregory (1981) has shown that this leads to a degree of flocculation significantly less than expected on the basis of a mean value GwT.
Specification of filter bed~capillary dimensions To justify, as closely as possible, comparisons between the measured flocculation rates for the filter bed and the capillary model, hydrodynamic and geometrical equivalence were incorporated into the apparatus specification. Hydrodynamic equivalence was considered by specifying that the flow in the filter pores and through the capillaries would have a similar Reynolds number at a c o m m o n flow weighted mean velocity gradient. Approximate hydrodynamic equivalence was important since the particle collision efficiency factor has already been shown to be affected by hydrodynamic drag and may be influenced by other hydrodynamic effects. By using the Blake number as the Reynolds number for the filter, as outlined by Ives (1970), in which the length term is the mean hydraulic radius of the pores and the velocity term is the mean pore velocity, ensures that the
717
range of local velocity gradients in the pores and the capillary flow, as well as the mean velocity gradient, are similar. Geometric equivalence was considered important in case scale effects were significant. The minimum practical internal diameter of capillary was 0.25 m m and the equivalence calculations were based on this; the calculations are given in the Appendix. A filter grain size (dg) of 1.32 m m was employed in order to approximate to hydrodynamic and geometric similarity with the capillary flow. MATERIALS AND METHODS
The following two particle-polymer systems were employed in the flocculation tests: hydrophilic silica microspheres with cationic polymer and hydrophobic (surface methylated) silica microspheres with polyacrylamide. The hydrophobic silica-polyacrylamide system was developed for the filter tests since the use of a largely nonionic polymer, specifically adsorbed by hydrophobic and hydrogen bonding effects (Rubio and Kitchener, 1976), to destabilize partides carrying a similar charge sign as the filter grains would allow the measurement of inter-pore particle flocculation without influencing particle capture. The hydrophilic silicacationic polymer system was used to compare flocculation rates in the capillary and jar test apparatuses for particles carrying no net overall surface charge.
Suspensions Hydrophobic porous silica microspheres were obtained from Shandon Southern Products Ltd, Runcorn, U.K. The spheres were described by the manufacturer as having a complete monolayer coverage of trimethylsilyl groups, a pore volume of 0.7cm3g -I, a specific surface area of 200 m 2 g-~ (by N 2 adsorption) and a 10 nm mean pore size. A Coulter Counter particle size analysis determined the spheres as being reasonably monosized with a mean dia of 5.4 #m and a RSD of 22.3%. The microspheres were obtained as a dry powder and when wetted with methanol showed good dispersion in distilled water. Electrophoresis measurements (Rank Bros. Particle Electrophoresis Apparatus, Mark II, Cambridge, U.K.) found particle surface potentials of -27.1 mV (RSD= 17%) in deionized water and -21.3 mV (RSD = 13%) in 1 mM NaCI/I mM NaHCO 3 at 25°C. To avoid particle migration to the surface of stirred suspensions because of their strong hydrophobicity, the liquid surface was covered with a thin, wooden float coated with collodion acetone to make its surface hydrophilic. Hydrophilic porous silica microspheres were supplied by AERE Harwell, U.K., having a mean dia of 3.3/~m (RSD = 24.8%) as determined by Coulter Counter and a pore volume of 0.57 cm 3g-~ as quoted by the manufacturer. The microspheres were obtained as a dry powder and showed good dispersion in distilled water. Electrophoresis measurements indicated no significant "ageing" effects in distilled water for 10 < t < 100h, with ( = - 2 6 mV + 8% at 25°C.
Polymers All the polymer materials used in this study were commercial products• Nonionic polyacrylamide was obtained as a commercial synthetic polymer from Cyanamid of Great Britain Ltd, Gosport, U.K. Although no information was available concerning the narrowness of the molecular-weight distribution the average molecular weight of the polymer was stated by the manufacturer to be 10 million. A measure of the purity oftbe polyacrylamide was suggested by there being less than 1% anionic groupings on the polymer chain. The polymer was obtained as a granular solid and continuous gentle
718
N . J . D . GRAHAM
stirring was required to achieve complete solution of the polymer in the preparation of stock solutions. A lower molecular weight polyacrylamide, supplied by Allied Colloids Ltd, Bradford, U.K., was employed as a filter grain precoating material. This straight homopolymer was selected since its approximate molecular weight (inferred from intrinsic viscosity measurements) of 0.3-0.5 × 106 was large enough to offset polymer desorption from the grain, once adsorbed, but not large enough to cause particle flocculation. A tertiary polyamine, supplied in liquid form by Cyanamid of Great Britain Ltd, was used as a floceulant for the hydrophilic silica and had a 100% cationic charge density and an average mol. wt of 100,000. The tertiary polyamine behaves in aqueous solution as a weak base and is only partly charged at neutral pH. The degree of protonation at the test pH was determined by viscosity/pH titration using a Volac U-tube viscometer (Gritfin& George Ltd, U.K.). Since ageing and loss of flocculation activity of aqueous solutions of high-molecular-weight polymers has been reported (Shyluk and Stow, 1969), stock solutions were prepared and used within 24 h.
Filter apparatus The filter column consisted of a 1200 mm length of 65 mm i.d. Pyrex glass tubing. An upflow filter arrangement was chosen to lessen the significance of particle sedimentation effects. The column had seven glass capillary outlet ports fused in a vertical spiral to the column wall. The 7 mm o.d. capillaries were made to extend 5 mm into the column, had their inside end sealed, and a 0.75 mm slit cut into their bottom wall. The ports were connected to right-angle Rotaflo stopcocks which had reduced arms. The stopcocks were aligned vertically with a rising capillary bore side arm connecting to the column and a plain discharge stem pointing vertically downward. The ports were used at different times to measure head loss through the granular bed by connection to a manometer assembly, and for taking flow samples. Influent solutions were drawn from 51 Pyrex beakers and pumped to the filter column via a double head, variable speed, peristaltic pump. Flow control was achieved by a rotameter flow meter and valve on the outlet flow line. The 1 m granular bed was formed using ballotini nonporous glass spheres of 1.32 mm nominal dia. Prior to use in the filter tests, the ballotini was cleaned by immersion in a 10% HCI and 10% HNO 3 solution for a period of 48 h. After rinsing with distilled water the ballotini was dried and stored in dry containers. The filter column was filled with media by first filling with distilled water and then progressively adding given weights of ballotini to fill a predetermined column volume.
Filter tests A residence time evaluation was carried out for the filter bed at the lowest approach velocity by means of a 1% NaCI conductivity tracer. A sharp residence time profile was obtained which gave a value of 1.38 as the numerical ratio of the time-to-peak concentration to the theoretical residence time. For all filter tests a value of 1.50 was adopted for this ratio in the determination of the minimum delay time for filtrate sampling. Prior to each filter test and before the suspension and dilution water flows were initiated, the filter flow conditions were allowed to stabilize using dilution water alone. The Rotaflo valves in the three column sampiing outlets at 2, 52 and 102 cm above the column base were opened and adjusted to discharge freely and isokinetically with the upflow in the column. During filtration samples were taken individually from the discharge of the three column side ports by collecting approx. 1 ml and diluting immediately with 10 ml of clean 1% NaC1 prior to particle analysis. At the completion of each filter test the filter grains were cleaned by allowing the media to stand in 6%
Decon 90 .alkaline detergent solution for a minimum of 2 h and then rinsing with deionized water at a sub-fluidization velocity.
Capillary apparatus A one metre capillary assembly was constructed from 50 individual 0.25 mm bore, 0.5 mm o.d. fused silica capillary columns. The capillary unit was positioned vertically and the suspension and polymer solutions were drawn by a variable speed two-channel peristaltic pump. The flow rate for the influent streams was kept constant throughout the tests to maintain identical mixing conditions. To regulate the flow rate through the column and provide mixed influent samples for particle analysis, a proportion of the influent flow was drawn off by an identical single channel peristaltic pump. At the top end of the column the flow was allowed to discharge freely into a calibrated cylindrical jacket of glass tubing. During the floceulation tests the flow rate through the column was determined by timing flow collection in this calibrated jacket.
Capillary tests Prior to each floceulation test the capillary column was filled with the test solution for 30 rain to allow the internal surface to equilibrate ionically. During each test, inlet and outlet flow samples were taken using a wide bore syringe. Outlet samples were taken after a minimum flow time of three theoretical retention times after the commencement of flow pumping to ensure fully developed flow conditions. The column unit and allied tubing were cleaned after each test by passing 200 ml of 5% Decon 90 alkaline detergent through the column over a period of 15 min, followed by 400 ml of deionized water.
Jar tests Jar tests were carried out as described by Graham (1981).
Particle analysis Orthokinetic flocculation was quantified by measuring changes in the particle size distribution of suspensions using a model TA II Coulter Counter. This has been described in more detail by Graham (1981). RESULTS
Choice o f filter test conditions In order to carry o u t filter experiments t h a t would encourage particle flocculation a n d minimize filter capture a preliminary investigation was carried o u t to consider the effects o f solution p H a n d ionic strength. T h e work o f Ives a n d G r e g o r y (1966) has s h o w n the i m p o r t a n c e o f surface forces in dictating the degree o f particle removal in filter beds; solution ionic s t r e n g t h a n d p H determine in p a r t the m a g n i t u d e o f these surface forces. G r e g o r y (1964) has studied the varia t i o n of electrokinetic potential for ballotini grains with a m o n o v a l e n t a n d di-valent salt c o n c e n t r a t i o n . He concluded t h a t whilst the ballotini potential diminished regularly with increasing salt concent r a t i o n the variation o f potential w i t h p H in solutions o f c o n s t a n t ionic strength a p p e a r e d to be small. T h e v a r i a t i o n in filter efficiency with various solutions o f either low ionic strength or high pH, determined in this study is highlighted in Fig. 1. As expected, a moderately low ionic s t r e n g t h / m o d e r a t e p H solution (1 m M NaCI/1 m M N a H C O 3 ) encouraged sizeable particle capture, whilst high p H solutions a n d de-
Orthokinetic flocculation in rapid filtration
719
100
IO0 9O
~
~ P =8 ~8
80 '° 6O
80
60
5O
®E
4O
~ 30
~
/
2o
o o.
20
"~
10
~
20
g
30
lO
0
0
I
I
50 Filter
bed depth
100 (cm)
Fig. 1. The variation of filter efficiency with nature of solution (100mgl -t silica, Gw= 100s-~). O I mM NaCI/I mM NaHCO3, pH 8.6; • 10.4mM NaOH, pH 11.7; /X 2 mM NaOH, pH 10.6; O deionized water.
I
I
I
I
I
~e
•~ o ~Q. 50
I
I
I
I
I
2
4
6
8
10
Reaction time (mJn)
ionized water seriously limited particle capture. Ideally, deionized water was the most suitable solution for the filter/flocculation tests but complete avoidance of trace ionic contamination was not practically possible. A 10-SM NaC1 solution was considered experimentally to be the most suitable test medium since this was shown to minimize filter capture and provide measureable polymer flocculation rates (see results of jar tests). Jar tests
It was expected that a nonionic polymer such as polyacrylamide would display an optimal concentration in the flocculation of hydrophobic silica, as has been proposed by Michaels (1954). An optimal concentration is consistent with the polymer bridging hypothesis which requires that the particle surfaces should be only partly covered with adsorbed polymer so that attachments with segments from other particles can be formed. Jar test experiments showed that an optimal polymer dose could be defined; this was determined as 5 0 m g g - ' SiO2 in 10-SM NaC1 solution (Graham, 1982). The initial flocculation rate (flocculation period ~< 6 min of jar test) at optimal polymer dosage was found to be 0.211, expressed as a ratio of the Smoluchowski theoretical value (Fig. 2). Graham (1981) has already shown that the optimal dose for the tertiary polyamine, in flocculating hydrophilic silica particles, occurs at the point of zero particle electrophoretic mobility. The initial flocculation rate at optimal polymer dose, in this case, was found to be 0.140, expressed as a ratio of the Smoluchowski theoretical value (Fig. 2). For both particle-polymer systems, comparative measurements were made of flocculation rates at velocity gradients above and below 100 s- ' to confirm that floe disruption was not significant. This is
Fig. 2. Jar test flocculation kinetics at optimum polymer doses for the methylated silica and hydrophilic silica systems (300 mg 1-' silica, G = 100 s-l). O 5.4/t m methylated silica system; • 3.3/~m hydrophilic silica system.
exemplified in Fig. 3 which displays an increasing flocculation rate with velocity gradient in accordance with theoretical predictions when floc disruption is not included. The results shown in Fig. 3 also support the approximation that for jar test conditions the collision efficiency factor is not significantly dependent on mean velocity gradient. Capillary tests
F o r the tests with the methylated silica-polyacrylamide system in 10-SM NaC1, evidence of flocculation in capillary flow was found over a wide
100
8o
u c 60 CoD oc ~ u .Q
~-~ 40
¢).E_. u~ ~ o 20
r! ap~0.1
0
2
I 100 G(s-I) 4
150 I 6
Reoction t i m e
I 8
I 10
(rain)
Fig. 3. The variation in jar test flocculation kinetics with mean velocity gradient (methylated silica system, 100 mg 1-1 silica). © ~ =71 s-I; • ~ = 100 s-I; V G = 125s-L
720
N . J . D . GRAHAM 80-
6O
~ 4o g
2o 0
0
I
I
I
I
o
I •13
.=_
I
I
I
I o
f o~
"~
'°
N 20
• ,I -m---"-"
,ira-
m--
I
I
I
I
I
I
I
I
I
I
50
100
150
200
250
300
350
400
450
500
Meon
velocity
grodient
Gw(s -1]
Fig. 4. The variation in the degree of flocculation with mean velocity gradient of capillary flow for the methylated silica and hydrophilic silica systems (300 mg 1-~ silica). O 5.4/~m methylated silica system; • 3.3 #m hydrophilic silica system.
range of flow velocities (Gw = 50-450 s - ' ) from both a reduction in particle number concentration and an increase in the particle population mean size (Fig. 4). As suggested by theory [equations (10), (11) and (12)], the extent of particle flocculation was found to decrease with increasing mean velocity gradient. The decrease was significant in the range of G,. of 50-250 s-l, but much less so at higher values up to 450s -l. At 100s - ' , an C~p value of 0.040 was determined which was substantially lower than the corresponding value obtained from the jar test (~p = 0.211). Much greater in effect was the flocculation of the 3.3/~m hydrophilic particles also shown in Fig. 4. The cationic polymer-destabilized particles similarly displayed both a wide flocculation range with mean velocity gradient and a diminishing extent of flocculation with increasing shear rate. In this case, the calculated value of ~p for the capillary flow (0.096 at G,.= 100s -~) although still lower, is in closer agreement with the jar test value (0.140). The flocculation behaviour for the two particle systems in the region 0 < Gw < 50 s -~ could not be measured due to the limitations of the experimental technique. In addition, perikinetic flocculation rates could not be measured experimentally due to particle sedimentation effects, but theory would suggest that for the size of particles used Brownian Diffusion effects are negligible. It is possible to speculate that the flocculation curves would display maxima close to G , = 0 s -j. Filter tests
Initial filter experiments were carried out at 2 mm s -1 (G,. = 50 s -1) with 100 mg 1-' methylated silica and 50 mg g-~ polyacrylamide. These experiments displayed a considerable increase in particle
capture through the addition of polymer and this was assumed to be the result of polymer adsorption on the filter media. To diminish this effect, use was made of a lower-molecular weight polyacrylamide as a precoating polymer for the filter media. Filter precoating was carried out by passing a volume equivalent to approximately three bed volumes of 150mgl -~ (10 times optimal dose for test polymer) polyacrylamide through the filter at 4 mm s-L Unadsorbed polymer was then removed by immediately rinsing the filter with five bed volumes of deionized water at 4 mm s- 1. Filter tests were carried out at four approach velocities corresponding to Gw values of 50, 100, 150 and 200 s -]. At a filter approach velocity equivalent to Gw = 1 0 0 s - 1 some evidence of particle flocculation was found, although of a very minor nature (Table 1). The results shown in Fig. 5 compare the filter outlet and inlet suspension concentrations and size distributions. A consistent trend of increasing extent of flocculation with flow velocity (thus, velocity gradient) was apparent; a four-fold velocity increase gave rise to an overall 8% increase in the particle mean size and a three-fold increase in the total volume of aggregates of approximately twice the initial mean size. DISCUSSION
Implicit in the acceptance of theoretical predictions of the significance of filter pore particle flocculation is the adequacy of the assumption of Smoluchowski kinetics when applied to filter flow. In this there is some doubt since the exact nature and description of the filter pore fluid flow is unknown. Gregory (1981) has clearly demonstrated for the relatively simple case of Poiseuille flow, that the exclusion of a full description of particle residence time distribution can
Orthokinetic flocculation in rapid filtration
721
Table 1. Orthokinetic flocculation rates under optimal conditions Particle type and size
Floccalation system
Destabilization
G,. or (s i)
%,
Hydrophilic silica, 3.3 #m
Tertiary amine polymer in I mM NaCI/I mM NaHCO 3
Jar test
100
0.140
Hydrophilic silica, 3.3/am
Tertiary amine polymer in I mM NaC1/1 mM NaHCO 3
Capillary test
100
0.096
Methylated silica, 5.4#m
Polyacrylamide in 10 SM NaCI
Jar test
100
0.211
Methylated silica, 5.4,um
Polyacrylamide in 10 SM NaCI
Capillary test
100
0.040
Methylated silica, 5.4#m
Polyacrylamide in 10 SM NaCI
Filter bed
100
0.012
*Collision efficiency factor = observed flocculation rate divided by theoretical rate as determined from equation (2). seriously e x a g g e r a t e the overall a m o u n t o f particle collisions. In a d d i t i o n , the a p p r a i s a l b y v a n d e V e n a n d M a s o n (1977) o f t h e influence o f h y d r o d y n a m i c d r a g effects o n particle collision efficiency h a s ex-
p o s e d the p r o b a b i l i t y o f a g r e a t e r d e p e n d e n c y o f filter p o r e f l o c c u l a t i o n rate o n particle size a n d s h e a r rate. T h e clear n e e d to assess q u a n t i t a t i v e l y t h e "in-filter" f l o c c u l a t i o n p r o c e s s has b e e n s h o w n in p r e v i o u s in-
10-B--
SE
~g
4
Q_
o
_=3 : L ~ _
o
-
I
0.7
--
®'s® 80-8~ o 0.9°~g o_='6 ~,'~E= o
9~_~
1.o 1.11.2
I
I
I
I
50
100
150
200
250
Meon velocity grodient (s -1)
Fig. 5. Evidence of an increasing degree of filter pore particle flocculation with filter bed mean velocity gradient (comparisons of filter effluent with influent). W R. 20/6--D
722
N . J . D . GRAHAM 0.23 F 0.22 F
...~.11
Jart._.estt . . . .
0,10
0.08
006
Filter /
Operational
_
~oximom ,or %
004 ~"~.
Capillary
o
0.02
0.00
i
100
i 200
300
I 400
• 500
"G, G w (s -~)
Fig. 6. Particle collision efficiency-velocitygradient diagram for the methylated silica system.
vestigations (Ives and AI Dibouni, 1979) to be more than matched by the experimental difficulties in attempting to do so. Since previous destablization methods for particle flocculation have been confined totally to charge neutralization processes [indifferent counter ions (Ives and A1 Dibouni, 1979) or cationic polymer adsorption (Habibian, 1971)], particle capture efficiencies have been similarly magnified as a direct consequence. The adoption of a nonCoulombic, particle-specific destabilization method (in this study) permits the preservation of doublelayer repulsive barriers in order to minimize particle capture. Such a method which features the specific adsorption of high molecular weight polyacrylamide on hydrophobic silica particles has been found in this study to be moderately successful, although special efforts were required to "protect" the filter grains from polymer adsorption (steric stabilization). The general form of the flocculation results from the capillary experiments are entirely consistent with those reported by Gregory (1981, 1982) and Higashitani et al. (1980). The clearly observed behaviour of diminishing ctp values with shear rate for both particle-polymer systems is in complete agreement with the van de Ven theoretical description of orthokinetic collision efficiency in laminar flow (van de Ven and Mason, 1977). Since the capillary model and the filter bed apparatus were designed to be approximately hydrodynamically and geometrically similar, the results of the flocculation experiments using both these apparatuses can be compared by considering the respective ctp values (Fig. 6). It is clear from Fig. 6 that the trend of increasing % values with shear rate for filter pore flocculation conflicts with the experimentally and theoretically established floccula-
tion behaviour in Poiseuille flow (Gregory, 1981). A possible explanation arises from the observed differences in %, for the methylated silica-polyacrylamide system, determined from the jar test and capillary experiments. The substantially greater ~p value determined in the jar test experiment suggests that the very different hydrodynamic regime in the jar test is either giving rise to a substantially greater particle collision rate (not adequately accounted for in the equivalence of ~ for the jar test and G,, for capillary flow) or giving rise to a greater collision efficiency through the overcoming of double-layer potentials by particle inertia effects. In a similar manner, departures in the exact flow regime for filter pore fluid flow compared to Poiseuille flow would be expected to lead to differences in flocculation behaviour. In this case, the effects of particle inertia increasing ~p are considered to be negligible, but significant differences in particle residence time distribution are very likely. It is possible, with the complexities of filter pore fluid flow, that an increasing shear rate might cause increases in the sum of all the individual G T values, giving a greater overall flocculation extent. An additional factor which might be contributory arises from consideration of particle-polymer adsorption kinetics. Gregory (1982) has shown, via a simplistic semi-quantitative discussion that assumes that the adsorption process can be treated as a collision between unequal spheres, that under certain conditions both polymer adsorption and particle collisions can be predominantly orthokinetic in character (diffusion effects are minor) and that the polymer adsorption rate can be significantly slower than the particle collision rate. This effect, with its dependence
0.16
( Jar test
0.14
I I I
0.12
0.10
I I
0.08
t IICoy°r'
0.06 J Operational ,moximum Gw 0.04
0.02
I I 100
I 200
I 300
I 400
I 5o0
G, Gw (s"~ ) Fig. 7. Particle collision efficiency-velocitygradient diagram for the hydrophilic silica system.
Orthokinetic flocculation in rapid filtration
723
Table 2. Initialorthokineticflocculationrates under optimum conditionsas indicated by others Birkner and Morgan (1968) Graham (1981) Particle type and s i z e Polystyrene latex, Porous silicamicrosphere, 1.3/~m 7.6/~m Destabilizingpolymer Polyethylenimine Various cationic (approx. mol. wt) (3.5 x 104) (105-7 × 10 6) Flocculations y s t e m Paddle-stirred vessel, Paddle-stirredvessel, 1.2mM NaHCO3 ImM NaCI/ImMNaHCO3 (s t) 93 100 %* 0.029 0.112-0.543 *Collision efficiencyfactor= observed flocculationrate divided by theoretical rate determined from equation(2).
on the nature of the polymer-particle mixing arrangements and flocculation shear rate, taken with a changing residence time distribution with filter flow velocity, may contribute to the observed improvement in ~p and flocculation extent with shear rate. Figures 6 and 7 show the demarcated region for filter pore flocculation hypothesized in this study. The relative insensitivity of ~ to shear rate in the jar test represents the upper bound for ~p and a G~ value of 300 s ~represents the operational limit in practice for the filter pore shear rate. Further study is required to consider whether variations in the geometry and the hydrodynamics of the jar test appreciably affect the magnitude of ~p, and thus whether the applicability of the jar test determination as an upper bound is valid. The assertion that flocculation in an equivalent capillary flow represents a lower bound for ~p in filter pores is not conclusive (Fig. 6). The apparent opposite trend in ~p variation with shear rate for filter pore flocculation invalidates the direct use of capillary models as a simple rigorous method of assessing minimum ~p values for filter beds. However, peak ~p values for filter pore flocculation, associated with high shear rates, were found to lie within the region bounded by the jar test and capillary results. The range of ~p values associated with this region was wide for the methylated silica-polyacrylamide system, but very much narrower for the cationic polymer system (Fig. 7). It is possible to speculate that for cationic polymer-particle systems the jar test value for ~p represents a close upper bound on the value in filter pore flow at maximum shear rates. For particle destabilization by cationic polymers a range of reported values for ~p in jar test experiments is shown in Table 2. Graham (1981) found that the largest ~p value (0.543) was associated with the highest molecular weight cationic polymer typically used in water treatment practice (mol. wt ~ - 107). This value may therefore be taken as an indication of the greatest degree of flocculation likely in the pore openings of a filter under certain specific conditions. From this, the consequent contribution of filter pore particle flocculation to overall filter performance in direct filtration can be assessed theoretically and this will be described subsequently.
CONCLUSIONS (I) Filter pore particle flocculation can be quantified to a modest degree of accuracy by the use of a specific, nonionic polymer-particle system. (2) Collision efficiency factors determined in equivalent tube flow conditions do not necessarily represent lower bound values for filter pore flocculation. (3) Filter experiments displayed a trend of increasing collision efficiency factor and overall extent of flocculation with shear rate, in marked contrast to existing theoretical interpretations. An explanation based on the complex hydrodynamic flow pattern in a granular filter is proposed. (4) Filter pore collision efficiency factors at high shear rates may lie between those determined for equivalent tube flow and by jar test; the jar test values may represent an upper bound for the filter conditions. (5) Filter pore collision efficiency factors may be as high as 0.5 for suspensions destabilized by high molecular weight cationic polymers. Acknowledgements--The financial support of the University
of London Central Research Fund and the Public Works and Municipal Services Congress and Exhibition Council are gratefully acknowledged. The author is indebted to the Engineering Geology Unit of the Institute of Geological Sciences for technical cooperation.
REFERENCES
Birkner F. B. and Morgan J. J. (1968) Polymer flocculation kinetics of dilute colloidal suspensions. J. Am. Wat. Wks Ass. 60, 175-191. Cleasby J. L. (1976) Research achievements---existingand expected. J. Am. Wat. Wks Ass. 68, 272-274. Cleasby J. L. and Baumann E. R. (1962) Selection of sand filtration rates. J. Am. Wat. Wks Ass. 54, 579-602. Culp R. L. (1977) Direct filtration. J. Am. Wat. Wks Ass. 69, 375-378. Curtis A. S. G. and Hocking L. M. (1970) Collision efficiency of equal spherical particles in a shear flow. Trans. Faraday Soc. 66, 1381-1390. Elson T. P. (1979) Flocculation in fluidized beds. Symposium Particle Growth Processes, 6th Annual Research Meeting, University College, London. Institution of Chemical Engineers. Fitzpatrick J. A. and Spielman L. A. (1973) Filtration of
724
N . J . D . GRAHAM
aqueous latex suspensions through beds of glass spheres. J. Colloid Interface Sci. 43, 350-369. Ghosh M. M., Jordan T. A. and Porter R. L. (1975) Physicochemical approach to water and wastewater filtration. J. envir. Engng Div. Am. Soc. cir. Engrs 101, EEl, 71-86. Graham N. J. D. (1981) Orthokinetic flocculation rates for amorphous silica microspheres with cationic polyelectrolytes. Colloid S u r f 3, 61-77. Graham N. J. D. (1982) Significance of filter pore particle flocculation in direct filtration. Ph.D. thesis, University of London. Gregory J. (1964) Molecular forces and electrokinetic effects in filtration. Ph.D. thesis, University of London. Gregory J. (1981) Flocculation in laminar tube flow. Chem. Engng Sci, 36, 1789-1794. Gregory J. (1982) In The Effect o f Polymers on Dispersion Properties (Edited by Tadros T. F.). Academic Press, London. Habibian M. T. (1971) The role of polyelectrolytes in water filtration. Ph.D. thesis, University of North Carolina. Higashitani K., Miyafusa S., Matsuda T. and Matsuno Y. (1980) Axial change of total particle concentration in poiseuille flow. Y. Colloid Interface Sci. 77, 21-28. Ives K. J. (1970) Rapid filtration. Wat. Res. 4, 201-223. Ives K. J. (1975) In The Scientific Basis o f Filtration (Edited by Ives K. J.). NATO ASI Series. Noordhoff, Leyden. Ives K. J. and AI Dibouni M. (1979) Orthokinetic flocculation of latex microspheres. Chem. Engng Sci. 34, 983-991. Ives K. J. and Bhole A. G. (1977) Study of flowthrough couette flocculators--II. Laboratory studies of flocculation kinetics. Wat. Res. 11, 209-215. Ives K. J. and Gregory J. (1966) Surface forces in filtration. Proc. Soc. Wat. Treat. Exam. 15, 93-116. Michaels A. S. (1954) Aggregation of suspensions by polyelectrolytes. Ind. Engng Chem. 46, 1485-1490. Robinson B. (1979) Personal communication, Iowa State University, Rubio J. and Kitchener J. A. (1976) The mechanism of adsorption of poly(ethylene oxide) flocculant on silica. J. Colloid Interface Sci. 57, 132-142. Shea T. G., Gates W. E. and Argaman Y. A. (1971) Experimental evaluation of operating variables in contact flocculation. J. Am. Wat. Wks Ass. 63, 41~,8. Shyluk W. P. and Stow F. S. (1969) Aging and loss of flocculation activity of aqueous polyacrylamide solutions. J. appl. Polym. Sci. 13, 1023-1036. Spielman L. A. (1975) In The Scientific Basis o f Filtration (Edited by Ives K. J.). NATO ASI Series, Noordhoff, Leyden. Swift D. L. and Friedlander S. K. (1964) The coagulation of hydrosols by brownian motion and laminar shear flows. J. Colloid Sci. 19, 621~:~47. Treanor A. I. J. (1976) Recent developments in depth filtration. Process Biochem. 11, 34-37. Ven T. G. van de and Mason S. G. (1977) The microrheology of colloidal dispersions--VII. Orthokinetic doublet formation of spheres. Colloid Polym. Sci. 255, 468°479. Vreeken C. (1978) Personal communication, University of Technology, Delft. Vreeken C., Heertjes P. M. and Wesselingh J. A. (1978) The effect of particle coagulation on the performance of filter beds. Symposium Deposition and Filtration o f Particles from Gases and Liquids, Loughborough University, 1978, pp. 21-29. Society of Chemical Industry, London.
Yeh H-H. and Ghosh M. M. (1981) Selecting polymers for direct filtration. J. Am. Wat. Wks Ass. 73, 211 218. Zeichner G. R. and Schowalter W. R. (1977) Use of trajectory analysis to study stability of colloidal dispersions in flow fields. A I C h E J. 23, 243-254.
APPENDIX Specification o f Filter Bed~Capillary Equivalence Velocity gradient From Robinson (1979), the flow weighted velocity gradient for a smooth capillary is given by the expression: Gw_c~p = 64v J15dca p
(1)
where dcap = the internal diameter of the capillary va = the mean tube velocity. The flow weighted velocity gradient for a granular filter bed has already been shown to be [equation (7), where v = v,/e]: Gw_filt = (16x/10/5)va(1 - e)/dxe 2.
(2)
Reynolds number For flow in a smooth capillary, the Reynolds number expressed in terms of the hydraulic radius is as follows: Recap = pv~dcap/4#.
(3)
For flow in the filter pores, Ives (1970) has shown that the flow regime can be characterized by a modified Reynolds number in which the length term is the mean hydraulic radius of the pores, and velocity term is the mean pore velocity (approach velocity). The modified Reynolds number is called the Blake number (B), so that: Re~jt = B = v od~p /61t( l - ~).
(4)
Reynolds number--velocity gradient equivalence The Reynolds number equations (3) and (4) can be expressed in terms of the flow weighted velocity gradients by the substitution of equations (1) and (2), as follows: Recap = 15pd~p G . . . . p/256/1
(5)
Rena = 5pd~e 2Gw_ ~lt/96# x/10(1 - ~)2.
(6)
For equivalence, (Recap/Gw-c~p) = (Re~lt/Gw ~,t) so that: dg = 3dcap(l - ~)(lO)°'zs/~x/2.
(7)
Geometrical similarity The simplest two-dimensional filter grain arrangement is one where three ~rains are in contact with each other. If the grains are assumed to be circular and equal in diameter, then the diameter of a circular cpaillary that will fit in the void space and touching the three grains is: d~ = dg(Z/x/3 - 1).
(8)
Thus, for geometrical similarity: dg ~ dcap43/(2 - x/3).
(9)
Experimental values The smallest practical value for d~p was 0.25 mm and the bed porosity was assumed to be 0.41. The following values were determined from equations (7) and (9): For geometric similarity For hydrodynamic similarity
de = 1.62 mm dg = 0.68 mm.