COLLISION EFFICIENCIES OF ALGAE AND KAOLIN IN
DEPTH FILTER: THE EFFECT OF SURFACE PROPERTIES
OF PARTICLES
CHIHPIN HUANG**M, JILL RUHSING PAN and SHUHUI HUANG
Institute of Environmental Engineering, National Chiao Tung University, Hsinchu 30039, Taiwan, R.O.C.
(First received October 1997; accepted in revised form July 1998)
AbstractÐColumn ®ltration experiments with 2 mm-F glass beads were conducted to investigate the behavior of colloids during ®ltration. Algae and kaolin were used as model particles, while the chemical system was altered by changing the electrolyte concentration and pH. The collision eciencies from the interaction between colloids and the ®lter medium were calculated with a semi-empirical approach of the single sphere model and clean-bed ®ltration theory. The experimental results indicate that ionic strength enhance the removal eciencies for both algae and kaolin particles signi®cantly. The removal eciency of the ®lter for algae decreased with the increase in pH for up to pH 6. No signi®cant change was observed beyond pH 6. Removal eciencies for kaolin decreased with an increase in pH. It is con-cluded that collision eciencies are sensitive to ion strength and pH. # 1999 Elsevier Science Ltd. All rights reserved
Key wordsЮltration, algae, kaolin, collision eciency, zeta potential
SYMBOLS
Z single-collector eciency
Pe Peclet number, de®ned as Pe=2acU/DBM
NLO London force parameter, de®ned as
H/9pmap2U
NR interception parameter, de®ned as ap/ac
NG gravitational parameter, de®ned as
2ap2(rpÿr)g/9mU
As Happel's parameter, de®ned as
2(1 ÿ p5)/w, p = (1 ÿ e)1/3, w = 2 ÿ 3p +
3p5ÿ2p6
DBM Brownian diusivity, de®ned as kT/(6pmap)
ap radii of suspended particles (m)
ac radii of the collectors (m)
U approach velocity to a collector (m/s) H Hamaker constant (J)
(C/C0)0 clean bed removal eciency
e porosity of the ®lter bed
L column depth (m)
INTRODUCTION
The ®ltration process is divided into two sequential steps involving transportation and attachment (O'Melia, 1985). Macroscopically, the colloidal
par-ticles are ®rst transported from the bulk of the ¯uid to the vicinity of the stationary surface by physical forces, followed by attachment to the collectors through various chemical interaction at short distance (Amirtharajah and Wetstein, 1980). The theory of depth ®ltration has been studied in two directions (Mau, 1992): (1) a macroscopic approach called phenomenological theory, which applies mass balance to describe the ®ltration condition and (2) a microscopic approach, known as trajectory theory, which focuses on the properties of particle motion near a collector. The phenomenological theory of ®ltration has two shortcomings: the lack of gen-erality and the failure to provide a fundamental understanding of the mechanism of deposition. Conversely, the trajectory theory examines the deposition of each particle on the collector as sus-pension ¯ows through the collector. The trajectory models may be divided into two categories: one is an external ¯ow model and the other one is an in-ternal ¯ow model. Both models assume particle paths far from grains following ¯uid streamlines. As a particle approaches a collector, the motion de-viates from the streamline because of various forces acting on the particle. These forces are represented by the transportation and attachment mechanism. Our goal, through the investigation of the particle ®ltration in a packed column, is to calculate single-collector eciency (Z) and to determine the collision (or attachment) eciency (a) with the observed removal eciency and the calculated value of Z.
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The rationale of Z involves the physical aspect of a better understood ®ltration model, while a accounts for the less important factors in the chemical aspect (Elimelech, 1992). Litton and Olson (1993) have successfully adopted this concept in evaluating the importance of porous medium selection and preparation method in determining attachment eciency. In this study, the method developed by Rajagopalan and Tien (1976) was applied to obtain the single-collector collision eciency. Green algae and kaolin were the model colloidal particles in our column ®ltration experiments. Our approaches ®rst involved presenting the ®ltration eciencies of particles with adjusting the pH and ionic strength of suspension and then we applied the semi-empirical model and ®ltration theory to esti-mate their collision eciencies in the ®lter.
THEORETICAL APPROACH
With the combination of trajectory and dimen-sional analysis, the process of ®ltration can be formulated. The calculation of the single-collector eciency has been derived by Rajagopalan and Tien (1976) as follows:
Z 4A1=3
s Pÿ2=3e 0:72AsN1:8LON15=8R
0:0024AsN1:2GNÿ0:4R 1 where Pe represents the role of diusion and NL0
re¯ects van der Waals interaction. NR, indicating
the importance of interception, is the ratio of the size of suspended particle to the size of collector and NGaccounts for gravity eect. These quantities
are listed in the ®rst section.
By applying the clean-bed ®ltration model and a mass balance of particles over a dierential packed-bed volume, the experimental collision eciency (aexp) can be related to the initial (clean-bed)
removal, (C/C0)0, as follows (Elimelech and
O'Melia, 1990): aexp ÿln C=C00 4ac 3 1 ÿ eLZr 2 where ac is the radius of the collector, e is the
porosity of the ®lter bed, L is the column depth and Z is the single-collector eciency. The clean bed removal eciency, (C/C0)0, is the value taken
at the time corresponding to a complete break-through curve of an inert tracer.
MATERIALS AND METHODS
The experimental set-up consisted a stock sample tank with stirrer, pump, ®lter column, and fraction collector. The ®lter column, a 21 mm i.d. 10 cm acrylic column with two adjustable bed supports, was packed with 2-mm glass beads. These glass beads were ®rst cleaned by soak-ing in the hot 10 g/l Alconox detergent solution for at least 2 h and then rinsing a few times with de-ionized water. Thereafter, glass beads were again soaked in 5 N nitric acid for at least 12 h and then ®nally were rinsed with de-ionized water. All de-ionized water used for glass-ware washing and solution preparation was obtained from a Milli-Q system (Millipore). The porosity of the media used in this study was measured to be 0.379 by the volu-metric method, and the column speci®cations are given in Table 1. Algae and kaolin suspensions were fed to the col-umn by a peristaltic pump at a volumetric ¯ow rate of 2.1 ml/min (the corresponding average residence time was 6.54 min).
The algae species, Selenastrum capriconutum, used in this study is one of the six freshwater algae which have been suggested by APHA et al. (1992) for the bioassay. Algae was incubated in a 50-ml nutrient medium suggested by Miller et al. (1978) for about 4 days in a shaker at 248C. This growth medium contained six major com-ponents including 25.5 mg NaNO3, 5.7 mg MgCl2 6H2O,
4.41 mg CaCl2 H2O, 14.7 mg MgSO4 7H2O, 1.04 mg
K2HPO4 and some trace elements (e.g. B, Mn, Zn, Co,
Cu, Mo, Fe) per liter de-ionized water. About 7.4 106
cells/ml of algae particles were obtained after a 4-day incu-bation period. 30 mg/l of kaolin suspension was prepared for each column ®ltration experiment.
Two approaches to measure particle size have been con-ducted in this study. One was measured by a particle size analyzer (PSA) with automatic image scanner (Galai Production LTD, Israel) and the other was directly observed through scanning electric microscopy (SEM) (Hitachi S-2300, Japan). The results from PSA indicated that average Feret's diameters for kaolin and algae par-Table 1. Parameters used for ®ltration model calculations
Parameter Value Column length (m) 0.1 Column i.d. (m) 0.021 Media size (dc) (m) 0.002 Porosity (e) 0.397 Kaolin diameter (dp) (m) 4.3 10ÿ6 Algae diameter (dp) (m) 5.0 10ÿ6
Kaolin speci®c gravity 2.67
Algae speci®c gravity 1.09
Temperature (8C) 25 Fluid viscosity, m [(Ns)/m2] 8.94 10ÿ4 Fluid density (kg/m3) 997 Approach velocity, U (m/s) 1.01 10ÿ4 Gravitational acceleration, g (m/s2) 9.8 Boltzmann constant (J/K) 1.38048 10ÿ23
Hamaker constant [J (1020)] (estimated value) H
water=3.7, Hglass=6.5, Hkaolin=10, Halgae=3.0
ticles were 3.921.71 and 4.221.33, respectively. Because Selenastrum cells are crescent-shaped, we, therefore, used the equation: [long diameter (a) short diameter (b)]1/3to
calculate the diameter equivalent to a spheric particle (d). The results from the measurement through SEM showed that kaolin had a diameter from 4 to 5 mm and Selenastrum cells had lengths ranging from 6 to 8 mm and widths from 2 to 3 mm. The average equivalent diameters for kaolin and algae particles then can be calculated to be 4.6 and 5.0 mm, respectively. In this study, we chose these two values from SEM measurement, not from PSA, for later calculations.
Zeta (z) potentials of algae and kaolin particles were measured with a zeta meter (System 3.0, Zeta-Meter, U.S.A.). Algae suspensions used for z potential and col-umn experiments were prepared by diluting the broth with de-ionized water. The concentration of the background electrolyte (NaClO4) was adjusted to give a wide range
from 0.001 to 0.1 M. The pHs of the colloidal suspensions in column experiments were adjusted to 3, 5, 6, 7, 8 and 9 with 0.1 and 0.01 N HClO4and NaOH. Prior to each
ex-perimental run, the entire system was ®lled with a given concentration of NaClO4 solution with the up¯ow mode
for at least 30 min. Experiments were carried out at room temperature (23±258C) with downward vertical ¯ow at 2.1 ml/min (approach velocity = 1.01 10ÿ4m/s). The
®l-trate was collected by the fraction collector at a 2-min interval from 0 to 40 min. The collected ®ltrate of kaolin was analyzed by UV (420 nm). The quantity of algae in the ®ltrate was numerated by the coulter counter (Coulter electronics, U.S.A.).
RESULTS AND DISCUSSION
Surface properties of algae and kaolin particles The z potentials of algae and kaolin in dierent ionic strength as a function of pH are presented in Figs 1 and 2, respectively. It appears that the z
potentials of both algae and kaolin decrease with increasing NaClO4 concentrations. The increase in
ionic strength enhances the electrical-double-layer compression, thereby resulting in a decrease in repulsive force and z potential. When the pH is lower than 6, the z potential of algae increase nega-tively. When the pH is higher than 6, the z potential remains the same regardless of pH variation. This phenomenon can be explained by the ionization of N-functional groups on the algal surface. Protein molecules, which consist essentially of a-amino acids linked by peptide (-CONH-) linkages, are the major component of the algal membrane. The sur-face charge of algae originates from the ionization of N- and C-functional groups of the amino acids. All naturally occurring N-functional groups may form a stable ®ve-member ring chelated with Ca2+
and Mg2+provided by the nutrient, thereby
result-ing in the neutralization of the amino groups, and leaving the carboxyl groups as the major charged sites on the algae surface. Because of the pKavalues
of carboxyl groups of amino acids, from 1.71 to 3.0 (Smith and Martell, 1976), 99% of the -COOH groups ionize to -COOÿgroup when pH = pK
a+2
(i.e. pH = 5±6), and thus explains the results in Fig. 1. The z potential of kaolin increases negatively with pH as indicated in Fig. 2. The surface hydroly-sis of kaolin is very similar to that of the oxide sur-face.
Breakthrough curves
The breakthrough curves of column ®ltration are presented as C/C0, C and C0 are the euent and
in¯uent concentrations of particles, respectively, with respect to time. 10 min was required to com-plete breakthrough, which was the duration used
for the clean-bed removal of the breakthrough curve described in Fig. 3. The breakthrough curve of the inert tracer (Clÿ) exhibits a characteristic
Fig. 2. z potentials of kaolin as a function of pH with various concentrations of NaClO4.
Fig. 3. Breakthrough curve of an inert tracer Clÿ. Experimental conditions were as follows: volumetric
sigmoidal shape, which is caused by the dispersion of tracer molecules in the inlet and the outlet of column.
The breakthrough curves of algae and kaolin particles at dierent NaClO4 concentrations are
presented in Figs 4 and 5. As observed, the removal eciencies, 1 ÿ C/C0, of both algae and kaolin
increase with NaClO4 concentrations. This ®nding
agreed with the DLVO theory. The total interaction energy and the height of the energy barrier of the reaction decrease as the concentration of NaClO4in
the suspension increases, since the van der Waals interaction is independent of the solution chemistry. Figure 4 also indicates that the removal of algae particles is very low (C/C0close to 1) in the dilute
salt concentrations. It infers that the repulsive force between algae and the collector is very signi®cant compared to the van der Waals force.
Column ®ltration experiments of kaolin and algae suspensions were also carried out in various pH in the presence of 0.01 M NaClO4 as a
back-ground electrolyte. The eects of pH on the ®ltration of kaolin and algae particles are illustrated in Figs 6 and 7, respectively. Figure 6 indicates that better removal eciency of kaolin suspensions is
found at lower pH values. It can be explained by the pH eect on z potentials as shown in Fig. 2. The larger removal eciency that kaolin suspen-sions have therefore at lower pH values is probably due to the reduced repulsive force between particles and collectors. However, a quite dierent phenom-enon has been found in the algae suspensions as shown in Fig. 7. At acidic condition (pH<6), the removal eciencies decrease with increasing pH, with no apparent change beyond pH 6. This ®nding is consistent with the pH dependence of z potentials as shown in Fig. 1.
Model parameters
Several uncertainties are involved in determining the single collector eciency for algae and kaolin ®ltration. One is the average diameter of particles. When the particle size is smaller than 1 mm, which is the size of the Brownian particle, the mechanism of the particle transport is dominated by diusion. Therefore a decrease in the size of the Brownian particle will result in a better collector eciency in the deep ®lter. As for non-Brownian particles, transport is controlled by gravity, ¯uid drag and interception in the deep ®lter. Therefore, larger
particles will result in better collector eciency. In this study, the average diameters of algae and kaolin are measured to be 5.0 and 4.3 mm, respect-ively, with a particle size analyzer as described previously.
The second uncertainty is the density of the particle (rp). The speci®c gravity of kaolin was
determined as 2.67 from the gravity test. On the other hand, it is dicult to determine the density of algae due to its natural buoyancy in the suspension. Little information is available on the range of buoy-ant densities of algae in aquatic systems. However, it may be assumed that most algae in water have near neutral buoyancy, judged from their slow settling velocities. Algae, being a biological entity, contain mostly water. When suspended in solution, they are capable of adjusting their water content in order to ¯oat in the medium freely. As a result, they don't have an exact density. This has been mentioned by Ronald (1991) in his study of model-ing the movement of bacteria through a sandy aqui-fer using colloid ®ltration theory. When clean-bed ®ltration theory was applied to bacterial deposition in porous media, Martin et al. (1992) mentioned the same diculty and adopted 1.04, 1.10 and 1.13 as
the density of bacteria. Since algae behave the same as the bacteria in water, it is reasonable to assume that they have similar densities, which is approxi-mately 1. In the calculation of single ®lter collection eciency, we have used dierent densities, namely 1.05, 1.07 and 1.09, to study their eect on collision attachment.
The last uncertainty is the value of Hamaker con-stant. Other appropriate values for the calculation of collision eciency were adopted from the related work (Hough and White, 1980). The values of par-ticle-water-collector have been calculated by using the Hamaker approach as listed in Table 1 pre-viously.
Experimental collision eciencies
In theory, the collision eciency approaches unit when colloidal interactions are dominated by depo-sition. If not, their collision eciencies would drop. In this study, experimental collision eciencies (denoted as aexp) can be calculated from the results
of column ®ltration experiments. The stability curves, the logarithm of aexp vs the logarithm of
electrolyte concentration, of kaolin and algae ®ltration are presented in Figs 8 and 9. A gradual Fig. 5. Breakthrough curves of kaolin with various concentrations of NaClO4at pH 6.
Fig. 6. Breakthrough curves of kaolin with various pH in the presence of 0.01 M NaClO4.
increase in the collision eciency with increasing NaClO4 concentration is observed. As the
electro-lyte concentration increases, the diuse layer is compressed and therefore more colloidal particles complete the attachment process successfully. Figure 8 also points out that at the same electrolyte concentration, smaller collision eciencies occur at kaolin suspensions of higher pH. Surface charges of kaolin particles in the water develop as a result of chemisorption of water splitting into H+ and
OHÿduring adsorption to form a hydroxylated
sur-face. At higher pH, OHÿ ions are adsorbed in
excess onto the hydroxylated surface, thereby result-ing in more negative charges on the kaolin surface. This situation of more negative charges, therefore, causes higher energy barrier and smaller collision eciency between two particles or the particle and collector.
Figure 9 shows the experimental stability curves of algae at various pHs. It is observed that, in the pH ranging from 3 to 9, the result is similar to that of kaolin ®ltration, where the aexp value increases
with electrolyte concentrations. For algae ®ltrations at the same electrolyte concentration, the aexpvalue
at pH 3 is larger than that at a pH above 6, with no signi®cant change beyond pH 6. This phenom-enon can be described by the variation of z poten-tials with the pH. This is the major reason why the interaction energy between the algae and the collec-tor is almost independent of pH, which results in a similar aexpvalue.
SUMMARY
A semi-empirical approach for predicting col-lision eciencies of algae and kaolin particles for the colloid deposition in porous media is presented. The chemical system of suspensions was changed by adjusting the electrolyte concentrations and pH. The results reveal that the experimental collision eciencies of both algae and kaolin particles appear to be proportional to the electrolyte concentrations as well as inversely proportional to the z potentials of the particles. Kaolin ®ltration with higher operating-pH results in larger experimental collision eciency. However, the experimental collision e-ciencies for algae ®ltration decrease with an increase Fig. 8. Experimental stability curves of kaolin with various pH. The logarithm aexpis plotted as a
in pH up to pH 6 and no signi®cant change beyond pH 6.
AcknowledgementsÐThe authors wish to express their gratitude for the technical assistant given by Professor C. Y. Chen and his research group in our institute. We also wish to mention our sincere gratitude to Union Chemical Laboratory, ITRI for the assistance in particle size analysis.
REFERENCES
APHA, AWWA and WEF (1992) Standard Methods for the Examination of Water and Wastewater, 18th edn. Amirtharajah A. and Wetstein D. P. (1980) Initial
degra-dation of euent quality during ®ltration. J. AWWA 72, 518±524.
Elimelech M. and O'Melia C. R. (1990) Kinetics of depo-sition of colloidal particles in porous media. Environ. Sci. Technol. 24, 1528±1536.
Elimelech M. (1992) Predicting collision eciencies of col-loidal particles in porous media. Water Res. 26, 1±8. Hough D. B. and White L. R. (1980) The calculation of
Hamaker constants from Lifshitz theory with appli-cations to wetting phenomena. Adv. Colloid Interface Sci. 14, 3±41.
Litton G. M. and Olson T. M. (1993) Colloid deposition rates on silica bed media and artifacts related to
collec-tor surface preparation methods. Environ. Sci. Technol. 27, 185±193.
Martin R. E., Edward J. B. and Linda M. H. (1992) Application of clean-bed ®ltration theory to bacterial deposition in porous media. Environ. Sci. Technol. 26, 1053±1058.
Mau R. E. (1992) Particle transport in ¯ow through por-ous media: Advection, longitudinal dispersion and ®l-tration. Ph.D. Dissertation, California Institute of Technology.
Miller W. E., Green J. C. and Shiroyama T. (1978) The Selenastrum capricornutum printz algal assay bottle test. Experimental design, application, and data interpretation protocol. EPA-600/9-78-018.
O'Melia C. R. (1985) Particles, pretreatment and perform-ance in water ®ltration. J. Environ. Eng. 111, 874±890. Rajagopalan R. and Tien C. (1976) Trajectory analysis of
deep-bed ®ltration with the sphere-in-cell porous media model. AIChE J. 22, 523±533.
Ronald W. H. (1991) Use colloid ®ltration theory in mod-eling movement of bacteria through a contaminated sandy aquifer. Environ. Sci. Technol. 25, 178±185. Smith R. M. and Martell A. E. (1976) Critical Stability
Constants. Plenum Press, New York.
Yao K. M., Mohammad T. H. and O'Melia C. R. (1971) Water and waste water ®ltration: concepts and appli-cations. Environ. Sci. Technol. 5, 1105±1112.
Fig. 9. Experimental stability curves of algae with various pH. The logarithm aexpis plotted as a
