Modeling the Effects of Hydrolyzed Aluminum and Solution Chemistry on Flocculation Kinetics Raymond D. Letterman" Department of Civil Engineering, Syracuse University, Syracuse, New York 132 10
Dharmarajan R. Iyer O'Brien and Gere Engineers, Inc., Syracuse, New York 13221
w Computer programs are available that allow self-consistent calculations to be made simultaneously for solution and surface chemical equilibria. One of these programs, an augmented version of MINEQL, employs the GouyChapman-Stern-Grahame model of the electrical double layer to account for the distribution of charge and potential at the solid solution interface. In this study the modified program has been used to predict the effects of solution and suspension variables on flocculation efficiency when aluminum salt coagulants are used. Electrophoretic mobility measurements and constant pH titrations with the surface complexingsulfate ion have been used to determine intrinsic surface ionization and complexation constants for the aluminum sites. Expressions that relate the modelpredicted electrical double-layer characteristics of the aluminum-treated particles and the amount of aluminum hydroxide coating on the particles to the efficiency of flocculation are also employed. For the simple system tested, model predictions of relative flocculation efficiency are in reasonable agreement with batch flocculation results. Introduction
In this study a computer program that allows self-consistent calculations to be made simultaneously for surface and solution chemistry equilibria was used to predict, for aluminum salt coagulants, the effect of solution and suspension variables on flocculation process efficiency. The program MINEQL (I)with modifications by Davis et al. (2) was used to predict the electrical double-layer characteristics of the treated particles as a function of the amount of adsorbed aluminum hydrolysis products and the solution chemistry. An analysis by van de Ven and Mason (3) of interparticle forces for particle interactions in simple shear flow was used in conjunction with a flocculation rate equation by Saffman and Turner (4) to relate the model-predicted electrical double-layer characteristics of the particles and the volume concentration of the aluminum hydroxide precipitate to the initial rate of orthokinetic flocculation. The overall model as presented represents a critical assembling of various submodels as well as an effort to develop a conceptual framework which helps explain the action of hydrolyzing metal coagulants. Magnitudes of model parameters were estimated by using independent experiments that involved electrophoretic mobility mea0013-936X/85/0919-0673$01.50/0
surements, constant pH titrations with the surface complexing sulfate ion, and floc density measurements. Whenever it was possible, these quantities were compared, for the sake of discussion, with reasonably appropriate literature values. After calibration the model was used to predict the effect of aluminum sulfate dosage and pH on relative flocculation efficiency, and the results were compared with batch flocculation data. Flocculation Rate Equation. According to Saffman and Turner (4)the collision frequency between i and j size particles in homogeneous, isotropic turbulence is given by
Iij = 1.294ninj(ai + aj)3(e/u)1/2
(1)
where ni, ai and nj, aj are the number concentration and radius of i and j size particles, respectively. The quantity E is the local rate of energy dissipation per unit mass of fluid and u is the kinematic viscosity. Okamoto et al. (5) measured local rates of energy dissipation in mechanically agitated vessels and concluded that the space mean value of the energy dissipation rate, (e), is approximately equal to P/ (Vp,) where P/ V is the power input to the fluid by the impeller per unit volume of fluid and pw is the fluid density. Substituting P/(Vp,) for e in eq 1 and then G for [P/(Vp)]1/2yields
( I i j ) = 1.294ninj(ai + aj)3G
(2)
where (Iij) is the average collision frequency for the entire vessel. In the case of a discrete particle size spectrum the rate of formation of particles of size w by collisions of particles of size i and j is given by Y2
C CIij)
i+j=w
The rate of loss of particles of size w by collision with any other size particle is
5 (Iiw)
i=l
and the net rate of generation of particles of size w is given by
0 1985 American Chemical Soclety
m
(3) Environ. Sci. Technol., Vol. 19, No. 8, 1985 673
where n, is the number concentration of size w particles. Substitution of eq 2 into eq 3 and the assumption that all the particles are nearly the same size, a, i.e., a; = aj a, = a, yield dn/dt = -5.176n2a3G
(4)
where n is the total number concentration of particles, i.e., the sum of all singlets, doublets, triplets, etc. If it is assumed that the total particle volume concentration, 4, where
4
N
Y33"a3n
(5)
is conserved in the aggregation process, then combining eq 4 and 5 gives dn/dt = -(3.88/~)4Gn
(6)
The total particle volume concentration of the aluminum salt treated suspension is assumed to be equal to the sum of the volume concentration of the uncoated primary particles and the volume concentration of sorbed aluminum hydrolysis products, i.e.
4 =Ms/p
+ 4-41
Table I. Equations Used To Calculate Flocculation Efficiency
(7)
where @ and p are the mass concentration and density of the primary particles. The magnitude of 4N is assumed to be proportional to the molar concentration of aluminum retained on the primary particles, MA1. The magnitude of the proportionality constant is assumed to depend on the extent of the aluminum hydrolysis product (AHP) coating. The extent of the coating is described by using the dimensionless parameter, pMA1,which is given by
(Id) a = 0.5[6Q, ( ~ n , , ) ] ' / ~
grated after the substitution of the right-hand side of eq 10 for k'(MA1),the result is
(
(9)
)-
In e@MA'+ 1 l ] M A 1 (11) PM-4' k[ The effects of the field forces of particle-particle interaction (double-layer repulsion or attraction and van der Waals attraction) and hydrodynamic forces on the collision process are included in the coagulation rate equation by the use of what is usually termed, somewhat inappropriately, a collision efficiency factor, a. The magnitude of a ranges from near zero when repulsive hydrodynamic and double-layer forces are controlling to a value slightly greater than one when only attractive forces are present. With a included eq 6 becomes dn/dt = (-3.88/1r)a@Gn (12) Studies by van de Ven and Mason (3) and Zeichner and Schowalter (8) examined (using trajectory analysis) the effects of hydrodynamic forces as well as van der Waals attraction and electrostatic repulsion on the efficiency of doublet formation for the interaction of equal spheres in simple shear flow. According to van de Ven and Mason at low shear rates, low ionic strength (I< 0.01), and negligible double-layer repulsion the magnitude of a is given approximately by 1 \ 0.18 a
In eq 8 r is the amount of sorbed aluminum at complete coverage (in moles per unit area) and A? is the specific surface area of the uncoated primary particles. Complete coverage, which corresponds to OMM1 1, is the condition where the surface chemical properties of the composite particles are described solely by the sorbed AHP. to M A are The equations used in this study to relate
(le) (If)
1
BMM = M I(rA?@)
0.08
(-)
A 362a3p
where A is the Hamaker constant, 2 is the shear flow velocity gradient, a is the particle radius, and p is the absolute viscosity. Hagashitmi et al. (9) used Zeichner and Schowalter's (8) results to derive a similar equation. In order to apply eq 13 in a description of flocculation in turbulent fluid motion, it is assumed, as suggested by Spielman (IO), that 2 can be replaced by G where, as in the case of eq 6
and
According to eq 10 when M N > 0, k'(MA1)N k. Equation 10 was chosen because it is simple and the general relationship it establishes between k'(MA1)and M N is intuitively reasonable and consistent with the observed effect of the amount of aluminum hydroxide precipitate on floc density as observed by Lagvankar (6) and Tambo and Watanabe (7). At surface coverages less than complete (@Ma< 1)the density of the aluminum hydroxide coating is relatively high, and as the coverage increases, the density decreases and eventually approaches a constant minimum value. In other words as M A increases, the coating is assumed to become less like a very thin, tightly bound layer of microcrystals and more like the characteristic, low-density gel structure of aluminum hydroxide precipitate. When eq 9 is inte674
Envlron. Scl. Technol., Vol. 19, No. 8, 1985
The magnitude of a is determined by the surface potential of the particles (3). At low shear rates and with values of the surface potential tending toward zero, a is given by eq 13. As the surface potential is increased, eq 13 continues to apply until a critical potential is reached at which double-layer repulsion and hydrodynamic forces in combination become great enough to essentially prevent close interaction and a abruptly decreases to zero. The program MINEQL was used to determine MN and the surface potential (actually the diffuse layer potential, $,-J of the aluminum salt treated particles as a function of variables such as the aluminum sulfate concentration and the solution pH. Table I summarizes the equations which were used to calculate the flocculation efficiency parameter, n/no. Equation l a in Table I is the integrated form of eq 12, and eq l e is obtained from eq 5. The quantity no is the initial number concentration of the primary
particles and S/dC is the critical diffuse layer potential. Calculation of $d and MA’Using the MINEQL Program. The computer program MINEQL (1)can be used to solve for the composition of complex chemical systems which may involve solution species as well as precipitating or dissolving solids. Davis et al. (2)using the site binding model of Yates et al. (11)expanded the MINEQL program to include the effect of the electrical double layer on ionization and electrolyte binding (complexation) reactions for surface functional groups. These investigators applied what is effectively the Gouy-Chapman-Stern-Grahame (GCSG) model of the electrical double layer. In this scheme H+ and OH- are considered to react in an inner adsorption layer (effectively in the solid) while specifically sorbed ions are in a layer adjacent to the surface. Two different capacitances are assumed for the inner and outer regions of the compact (sorbed) layer. The governing equations consist of two sets. The first describes the thermodynamic, stoichiometric, and electrostatic constraints on surface, Stern, and diffuse layer charge, and the second expresses the constraints imposed by the model chosen for the electrical double-layer structure. For a complete explanation and detailed derivations of the basic equations the reader is referred to Davis et al. (2) and James and Parks (12). Two assumptions can be made concerning the distribution of sites on a surface with two different types of surface functional groups. One assumption, described by James and Parks (12), assumes that one type of site is interspersed uniformly with the other type of site, and therefore, the speciation of all sites is related to one set of electrical double-layer properties. This condition has been labeled a mixed-site distribution (13, 14). According to the other assumption, called the patch site distribution (13, 14),the dual site surface is modeled by using two sets of electrical double-layer equations, one set for areas covered exclusively by site “A” and the other set for areas covered by site “B”. The electrical double layers for the two types of sites have a common dependence on the characteristics of the bulk solution and are used to calculate the net electrical double-layer properties of the entire dual-site surface. In this study, the patch site distribution model was assumed to apply when a primary particle is partially coated by aluminum hydrolysis products. The area concentration of exposed primary particle surface, AS, is assumed to decrease linearly with the amount of aluminum on the primary particle surface, MA1,i.e., for @MA’< 1
AS = A,SMS(l- @MA’)
(15)
and for @MA1 2 1
AS = 0 (16) The magnitude of Ah, the area concentration of the sorbed aluminum hydroxide, is the difference between the total area concentration of the composite particle, AT, and As, or AAI = AT - AS (17) The expression used to relate AT to C#IA1, the volume concentration of the aluminum hydroxide coating, was derived by integrating the left side of d4A1= Adr, (18) from dA1= 0 to c # and ~ ~ ~the right side from A = A,SMS to AT. It was assumed that spherical geometry applies and A = no4rr,2where r, is the radius of the composite particle. The result of the integration is
+
AT = [(A,Si@)3/2 6rnoC#IA1]2/3
(19) The effective diffuse layer charge, tfd, for a composite particle is calculated by using an area-weighted average of the diffuse layer charges for the component patches (ads and adA1), i.e. a d = (adSAS adAIAh)/AT (20)
+
where AS,Ah, and AT are obtained from eq 11,15-17, and 19 and ads and adA’are calculated by solving the equations listed in the Appendix using the MINEQL program. It was assumed that the molar concentration of aluminum in the AHP coating, MA’,is equal to the total concentration of aluminum hydroxide precipitate predicted by the solution/precipitate chemistry part of MINEQL. The validity of this rough approximation will be discussed later. The effective diffuse layer potential, S/d, upon which the determination of a (Table I, eq ICand Id) was then based, is determined by substituting a d from eq 20 in a GouyChapman type relationship given by
zeS/d - ( 8 e ~ k T ) sinh ~/~ 2kT where e is the background electrolyte concentration, E is the dielectric constant of the solution, k T is the product of Boltzmann’s constant and absolute temperature, e is the charge of an electron, and z is the valence of the electrolyte ions. Determination of Model Parameters. The data used to test model predictions were obtained in batch flocculation/sedimentation experiments. The suspensions were prepared with kaolin clay, and the aluminum salt coagulant was aluminum sulfate (alum). The background electrolyte was NaC1. To model the electrical double-layer properties of kaolin and kaolin partially coated with aluminum hydrolysis products, it was assumed that the surface charge on kaolin arises from the ionization of aluminum (AlOH) and silanol (SiOH) groups and that the mixed site distribution assumption applies. The total site density, N?, was assumed to consist of an aluminum site fraction, and a silanol site fraction, fsiN,S. In the batch flocculation experiments the NaCl background electrolyte was present at concentrations less than M. Calculations made by using intrinsic surface complexation constants from James and Parks (12) indicated that the presence of complexes such as SiO-Na+ and AIOHztCl- was negligible over the pH range studied. The formation of A10Hz+S02-and A.IOHztHSO, was included in model calculations due to the presence of significant amounts of sulfate from the aluminum sulfate and the well-documented affinity of sulfate species for the aluminum hydroxide surface. The set of equations which describes the surface reactions is given in the Appendix. To solve the equations listed in the Appendix (along with eq 11,1517, and 19) for ads and adh using the MINEQL program, values must be specified that characterize the kaolin particles (AsS, N:, f ~ ’ fsi, , no,and p ) , the aluminum hydroxide coating (MA,NSN,r, and k),the surface ionization and complexation reactions (Kalint,KaZint, KsOpint,KHsorint,&lint, and Kbzint),the electrical double layer (Cl and C J , and the background electrolyte concentration, e. The magnitudes used in this study are discussed in the following sections and are listed in Table 11. K b l i n t and Kbpt. The intrinsic surface ionization equilibrium constants for the silanol group, Kblintand Kbpt, were determined (13, 14) by fitting, under dilute solution conditions ( I < 0.001 M) and therefore with ad =
fa:,
e,
Environ. Sci. Technoi., Vol. 19, No. 8, 1985
675
Table 11. Magnitudes of Model Parameters
symbol
parameter
Kaolin Clay specific surface area A?, m2/g mass concentration @, mg/L N?, sites/m2 total surface site density fraction of total sites which are fAl A1 sites fraction of total sites which are fsi silanol sites initial number concentration no, per L particle density P, g/cm3 Aluminum Hydroxide Coating molar concentration of A1 in the coating NBA.', sites/m2 aluminum surface site density r , mol/mZ moles of A1 in the coating per unit area of particles at complete coating k, L/mol proportionality constant-amount of A1 in coating and volume concentration of the coating MAl
magnitude 23 50
1 x 1017 0.3
0.7 4 x 1013 2.7 calculated using MINEQL 8 x 101s 9 x 10-6 120
Table 111. Titration Experiments Used To Determine K S O ~ Zand - ~ ' KHS04-int ~ at Constant pH 5.00 & 0.01
Intrinsic Equilibrium Constants-Surface Reactions pKaPt aluminum site ionization 5.7 pKaPt aluminum site ionization 11.5 pKblint silanol site ionization -1.0 1.0 pKbPt silanol site ionization pK~o,z-~"~ Al site complexation with Sod2- -7.0 ~ K H s ~ ~A1-site ~ complexation ~ ~ with HSOC -15.6 bF/cm2 Cz, pF/cm2 C1,
C
Electrical Double Layer inner integral capacitance outer integral capacitance
20
Background Electrolyte background electrolyte concentration
calculated usine MINEQL
140
negligible specific adsorption of the supporting electrolyte ions, MINEQL predicted values of the diffuse layer potential, $d, to measured [potential vs. pH data for silica particles (Min-U-Sil). The values obtained are pKblint= -1.0 and pKbzint = 1.0. pKbpt is significantly different than the magnitude listed by James and Parks (12) for a-SiOz. When the value from James and Parks, pKbzht= 7.2, was used with their referenced value of the surface site density for silica, NSsi = 5 X lo8 sites/m2, model predicted values of !)d were significantly more negative than the measured { potentials, and instead of decreasing from an isoelectric pH (pHiep)of about zero and approaching a constant negative value at about pH 5, the !)d results exhibited a decreasing trend throughout the pH interval from 2 to 12. It is possible that this disagreement between the calculated and measured potentials is due to differences in particle source material. James and Parks (12) have noted the surface properties of silica vary considerably with particle source and suspension preparation. Calculations made by using the surface complexation constant for sodium ion on silica given by James and Parks (12) indicated that including this factor did not explain the discrepancy. Kalht,Kdht, and NaM.The intrinsic surface ionization equilibrium constants, Ka1" and KdM, and the surface site for a particle completely coated by aluminum density, NsM, hydrolysis products, were determined by using a procedure similar to that used to obtain Kblintand Kbpt (13, 14). Under a dilute background electrolyte condition, MINEQL-predicted values of !)d were fitted to measured [ potential vs. pH data for silica particles which were completely coated by aluminum hydrolysis products. The results are pKalht = 5.7, pKdht = 11.5, and N," = 8 X l0ls sites/m2. These are in agreement with values listed by 676
Environ. Sci. Technol., Vol. 19, No. 8, 1985
Flgure 1. (Curves A and A') Model-predictedand measured volume of 0.1 N HNO, required to maintain pH 5 f 0.05 during titration of a suspension of aluminum hydroxide coated silica particles with 0.5 M Na,SO, solution. (Curves B and B') Model-predicted diffuse layer potential and measured {potential vs. volume of 0.5 M Na,SO, titrant.
initial solution (1) total initial volume 50 mL (2) Aluminum, 1 X M, as A1(N03)3 (3) background electrolyte 0.01 M NaNO, (4) Min-U-Si15, 500 mg/L (1.1 m2/L) titrant concentrations (1) nitric acid, 1.0919 N (2) potassium hydroxide, 1.0303 N (3) sodium sulfate, 0.5 M titrant volumes added: summary (step 1) 0.462 mL of HN03 solution to pH 2 (step 2) 0.57 mL of KDH solution to pH 5 (step 3) 0.153 mL of HNO, solution to maintain pH at 5.00 f 0.01 during addition of 1.05 mL of NaZSO4solution in small increments
James and Parks (12) for a-A1203. This agreement is reasonable given that many oxide particles appear to form an outer shell of a porous, amorphous phase through hydrolysis and adsorption (possibly surface precipitation) of hydrolysis products (15). Also the isoelectric pH of hydrous a-A1203(-9.1) is similar to that of freshly precipitated aluminum hydroxide (16, 17). KsOpintand K H s O ~ - ~ The ~ ~ . intrinsic complexation constants for sulfate adsorbed on aluminum hydroxide, K s o ~ and % ~K~o,-'"~, ~ were determined by using the MINEQL program, and the results of experiments in which aluminum hydroxide coated silica particles were titrated with sodium sulfate solution at constant pH (13). The cumulative amount of nitric acid required to maintain a constant pH and the electrophoretic mobility of the particles were measured as the sulfate solution was added. It was observed that as the amount of sulfate added increases, the total amount of HNO, needed to maintain a constant pH eventually approaches an asymptote and the [ potential decreases. The titration results for pH 5, a total aluminum concentration of 1 X M, an ionic strength of 0.01 (from NaN03), and 500 mg/L of Min-U-Si1 5 are plotted in Figure 1. The experimental conditions are summarized in Table 111. The magnitudes of KSOpintand KHSOfntwere determined by simulating the surface reactions AlOH H+ + A10H2+S042(22)
+
and AlOH using the
+ 2H+ +
MINEQL
+ A10H2+HS04-
(23)
program. KS04~-int and KHS0T were
I
- I
I
I
2
B
I I I I William and Williams (19)data -Model predided c m e
I1
X
80
c
I
I
I
I
I
I
t
I
1
1 1 1 -
-808 I 0
2
4
6
8
IO
1 2 1 4
PH
Figure 2. Model-calculated diffuse layer potential and measured { potentials (79) vs. pH for kaolin clay.
varied by trial and error until the simulated acid volume required and +d vs. sulfate added curves were in approximate agreement with the experimental acid volume required and the { potential results plotted in Figure 1. The model with these intrinsic constants also yields predictions that are in agreement with pH 6 electrophoretic mobility results, Le., +d = { potential = 0 at a total surface concentration of 1 X M. Initially the set of reactions simulated, eq 22 and 23, included 2(A10H) + 2H+ + S042- (A10H2+)2S042- (24) which is based on the assumption that the surface specie (A10H2+)2S042-described by Hohl et al. (18) is significant. I t was determined, however, that the model predictions could not be matched with the acid volume required and the {potential results using a single set of parameters when eq 24 was included. N,S, f A l , and fsi. Current models of the electrical double layers of clays usually include two types of charge, a fixed surface charge associated with isomorphic substitution of cations in the crystal lattice and a smaller pH-dependent charge arising from ionization of AlOH and SiOH groups on the particle edges. However, as noted by James and Parks (12),some investigators have been successful using ionization models exclusively. In this study an ionization model was used to fit predicted values of +d vs. pH to measured t potential vs. pH data for kaolin. The { potential data were obtained from a paper by Williams and Williams (19). A reasonable fit of Williams and Williams (19) potential data was obtained by using N : = l X lo1' sites/m2, f A = 0.3, and fsi = 0.7 (see Figure 2). N : is the total site density, and fA1 and fsi are the fractions of the total sites which are aluminum and silanol groups, respectively. Values of +d were calculated by using the MINEQL program, the mixed-site distribution assumption, and the set of equations given in the Appendix. The previously determined equilibrium constants for aluminum and silanol surface sites (Kapt,Kapint,&lint, and &Zint) were used in the calculations (see Table 11). C1and C P The integral capacitances for the inner and outer parts of the Stern layer, C1 and Cz, are variable parameters which are not directly accessible to experimental determination. Davis et al. (2) and James et al. (20) following Yates et al. (11) assigned C2the value 20 pF/cm2 because, they noted, it is consistent with experimental values of the compact layer capacitance for HgH 2 0 and Ag-AgI-H20 systems. The inner layer capaci-
-60 I
0
l
l
l
l
l
l
l
l
l
l
2 4 6 8 1 O I ADSORBED ALUMINUM, (moies/m2)xl06
r
l
l
2
Figure 3. Measured { potential vs. surface aluminurn concentration for Min-U-SI1 5 particles at pH 5.
tance, C1, has been used as an adjustable parameter, and values in the range 60-140 pF/cm2 have been found to give reasonable agreement between model predicted and experimental observations. A sensitivity analysis was conducted (13) to determine the effect of the magnitudes of the capacitances on the model-predicted values of +d for pure silica and A1(OH)3 coated particles. C1and C2 were varied over the ranges 10-40 and 70-280 pF/cm2, respectively. The maximum effect of varying C1or C2 over these ranges on +d was less than 5%, and therefore, C1 = 140 pF/cma and C2 = 20 MF/cm2 were used exclusively in this study because these magnitudes had been applied successfully in previous work by Davis et al. (2). r . The magnitude of r, the moles of aluminum sorbed per unit area of primary particle surface at complete coverage, was estimated by using aluminum uptake and electrophoretic mobility measurements (13). An example of results obtained for silica particles and target pH values of 5 and 6 is plotted in Figure 3. According to Figure 3 as the amount of A1 on the surface of the particles increases, the { potential increases linearly from the negative value of the silica particles to the positive value of the aluminum hydroxide coating. The { potential reaches its maximum positive values (64 mV for pH 5 and 44 mV for pH 6) at a surface aluminum concentration of approximately 9 X lo* mol/m2, and therefore, this value was assumed to be equal to r. Wiese and Healy (21) determined that the amount of sorbed aluminum required to change the isoelectric pH of Ti02from 5.8 to 9.1 (the value for the aluminum hydroxide coating) was approximately 7 X lo4 mol/m2. They assumed that this quantity represents incipient complete coverage by surface-precipitated aluminum hydroxide. Their value compares reasonably with the magnitude of r used in this study. k. The magnitude of k,the proportionality constant in eq 10 and 11, was estimated by using floc density measurements. According to eq 11 when the particles are coated by a thick layer of precipitate, i.e., @MA'>> 1, c$~' = kM4,and the floc density, pf, can be related to the mass and volume concentrations of the primary particles (I@, @) and hydroxide precipitate (m', kMA)by the expression pf =
(e + m ? / ( @ + kMM)
(25)
Substituting in eq 25 the expression m' = kMA1p' where Environ. Sci. Technol., Vol. 19, No. 8, 1985
677
Table IV. Equilibrium Constants Used in the Solution Chemistry Part of the MINEQL Program log (equilibrium constant)
reaction AP+ + SO?- * Also4+ AP+ + 2S042- + A1(S0,2-)2A13+ HzO A1(OH)2t + H+ A13+ 2H20 * A1(OH)2++ 2H+ A13++ 4H20 -+Al(OH)[ + 4Ht HC + SO-: + HSO,
3.02 4.92 -4.99 -10.13
+ +
-21.57 1.99
aluminum hydroxide solubility
1% K*p 8.77
[A13+l[Htl-3= K.,
Figure 4. Floc buoyant density vs. silica to alumlnum ratio In the aggregated suspension.
p' is the mass density of the hydroxide precipitate and assuming that kMA1>> @ yield Pf =
Ms
+ P'
If the mass density of water, pw, is subtracted from both sides of eq 26, the result is
Ms
Pf - Pw = kMAl+ (P' - Pw) 0
According to eq 27, a plot of pf - pw vs. W / M Mwill have, at low values of @/MA, a slope equal to l/k and a y axis intercept of p' - pw, the buoyant density of the aluminum hydroxide precipitate matrix. The floc density data used in this study were obtained by Sricharoenchaikit (22) using a technique similar to one reported by Lagvankar and Gemmell (6). Solutions of known density were prepared by dissolving different weights of sucrose in 1 L volumes of distilled water. Single flocs were carefully pipetted from the flocculated suspension to the sucrose solutions. A trial and error procedure was used to find the solution in which a floc was neutrally buoyant. When it was found, the floc was assigned the density of that solution. A silica powder, Min-U-Si1 30, was used as a source of primary particles. To vary the quantity Ms/MA1,flocs were formed by using various combinations of silica powder and aluminum nitrate. The sulfate concentration was 3 X 10" M, the ionic strength was approximately 0.01 M, and the pH was 6. The flocs were formed during a 15-min period of low-intensity mixing after the addition of the sulfate to the aluminum nitrate treated suspension. A supernatant aluminum concentration measurement indicated that under these conditions essentially all the aluminum added was precipitated and apparently associated with the floc particles. Figure 4 is a plot of the measured floc buoyant density, pf - pw, vs. @/MAL. A number of additional points have been plotted by using data obtained by Tambo and Watanabe (7). These investigators measured floc settling velocity by a photographic technique and calculated the floc density using Stoke's law. Tambo and Watanabe's points are in reasonable agreement with those obtained in this study. The data points plotted in Figure 4 (excluding those from Tambo and Watanabe) were fitted with a straight line by the method of least squares. The slope of this line 678 Environ. Sci. Technol., Vol. 19, No. 8, 1985
I
2
3
4
5
6
7
8
C, x IO' (maler/t) Flgure 5. Surface alumlnum concentration and {potential vs. filtrated aluminum concentration for Min-U-Si1 5 particles at pH 5.
mol/L, and the y intercept is 0.005 g/cm3. The reciprocal of the slope yields k = 120 L/mol of Al(0H)3precipitate. This value was used in eq 11. M M . At the present time there are no models that can be used to quantitatively predict the adsorption of hydrolyzed Al(II1). Existing models for the adsorption of hydrolyzed metal ions, e.g., James and Healy (23) and the site-binding approach (12),must assume a certain limiting surface coverage or total site density, and this limit can be much less than the surface coverages observed when adsorption experiments are conducted; e.g., see Hahn and Stumm (24). James (25) has stated recently that one of the challenging problems that remains to be answered is whether the (aluminum hydroxide) coating forms by surface condensation of simple ionic species or by surface condensation of hydrolyzed species, including polymers, or whether it is due to adhesion of colloidal hydroxides formed in the solution (i.e., heterocoagulation). In this study, the molar concentration of adsorbed aluminum, MA',was assumed to be equal to the total concentration of aluminum hydroxide precipitate predicted by the solution precipitate chemistry part of MINEQL. In estimating MA( any effects of the silica surface on the solubility product for aluminum hydroxide (23) or the uptake of thermodynamically stable, soluble aluminum hydrolysis products (for example, at low pH) were not included. Table IV lists the equilibrium constants used with MINEQL to calculate MA'. According to Figure 5 from Sricharoenchaikit (22) and similar adsorption isotherms by Hahn and Stumm (24), the assumption of quantitative adsorption of precipitate becomes increasingly approximate as the particle surface i s 8.3 X
area concentration decreases. For example, in the case of a total aluminum concentration of 2 X M and a primary particle surface area concentration of 5 m2/L, quantitative adsorption of the precipitate formed at pH 5 leads to a surface A1 concentration of approximately 4 X lo* mol/m2 while the value obtained from the isotherm plot in Figure 5 is 3.3 X lo* mol/m2, a difference of about 20%. However, when the surface area concentration is decreased to 1.4 m2/L, quantitative adsorption of precipitate gives a surface Al concentration of 1.4 X lo4 mol/m2, and the adsorption isotherm plot yields 6.7 X 1Pmol/m2, a difference of over 50%. It should be noted that Figure 5 pertains only when the positive coating of aluminum hydroxide stabilizes the suspension of primary particles. When aluminum hydrolysis takes place under conditions that lead to the formation of a flocculent hydroxide precipitate (or unstable coated primary particles) (16),essentially all the aluminum hydroxide formed in the system eventually becomes associated with the aggregating primary particles (22). In other words, although the assumption of quantitative uptake of precipitate may not lead to an accurate estimate of the initial rate of flocculation, it may give a reasonable, although rough, indication of the state of the suspension and the kinetics of flocculation after the initial period is completed, and primary particles have become associated with the flocculent, initially unadsorbed, hydrolysis products. MS, A ?, no,and p. The mass concentration of kaolin clay used in the batch flocculation experiments, @, was 50 mg/L. It was estimated that the specific surface area of the kaolin, A?, was 23 m2/g and that the initial number concentration, no,and density, p, were 4 X 1013particles/L and 2.7 g/cm3, respectively. Batch Flocculation Experiments. The batch flocculation data used to test model predictions were from a thesis by Ames (26). A brief description of the materials and procedure used by Ames is given below. The experimental suspension was prepared by dispersing kaolin clay in distilled water. The stock aluminum sulfate solution contained 10 g of A12(S04)3.18H20/L.A 0.1 N solution of reagent-grade NaOH was used for the initial pH adjustment. The flocculation reactor was a cylindrical, 1-L fully baffled vessel with a flat plate impeller. The energy dissipation rate-impeller rotational speed relationship for this configuration has been presented by Andreu-Villegas and Letterman (27). Coagulant addition by syringe and pH adjustment were accomplished during an initial 2-min mixing period. The impeller rotational speed was 170 rpm (G = 500 s-I). Initial mixing was followed by 60 min of low-intensity mixing (26 rpm, G = 20 s-l). When required, pH adjustment using 0.01 N NaOH was continued a t regular intervals during the low-intensity mixing step. The pH recorded was the value measured a t the conclusion of the low-intensity mixing period. Mixing was preceded by a 30-min sedimentation period. At the conclusion of this step, 400 mL of supernatant were withdrawn from the vessel by using a siphon inserted to middepth. The turbidity of this sample was measured by using a Hach Model 2100 turbidimeter. The instrument was calibrated frequently by using standard formazin dispersions. The turbidity of the kaolin suspension before treatment was 39 NTU, and this quantity was used to calculate the fraction of the turbidity remaining after sedimentation. The temperature of the suspensions was 22-24 "C.
Figure 6. Fraction of turbidity remaining (data from ref 26) and model-calculated n / n , vs. pH for AI,(S0.,)B~18H,0 = 100 (curve A) and 25 mg/L (curve B) (kaolin surface modeled using surface area concentration of 1.2 m2/L and a 30%/70% mixture of Ai and Si sites).
Results and Discussion Panels A and B of Figure 6 contain experimental values of fraction turbidity remaining and model-calculated values of n/noplotted vs. pH for aluminum sulfate (A12(S04)318H20)concentrations of 25 and 100 mg/L, respectively. In the model calculations it was assumed on the basis of a number of studies (16,28,29) that have reported abrupt changes in suspension stability at particle electrophoretic mobilities in the range 11- 2 pm s-l V-l cml that the critical diffuse layer potential, gdC, is 0.020 V . Since Ames (26) did not use a background electrolyte in the batch flocculation experiments and he did not report the amount of base added for pH adjustment, it was necessary to calculate, by using the MINEQL program, the amount of base required to maintain a given target pH. The amount of base was then used in calculating the corresponding ionic strength. To calculate n/noby using eq l a in Table I, it was assumed on the basis of Ames (26) experimental conditions that the dimensionless product Gt for the batch experiments was equal to 72 000. It is apparent in Figure 6 that while there is approximate agreement between the model calculated and experimental results, the model predicts significantly more abrupt transitions between regions of stability and flocculation, particularly for 25 mg/L alum. The reasons for this discrepancy are difficult to determine because of the many uncertainties involved in the interpretation of residual turbidity data. Also van de Ven and Mason's (3) analysis indicates that the critical potential is a function of the size of the colliding particles; therefore, a heterodispersed suspension such as the kaolin of these experiments is probably best described by a distribution of critical potentials rather than a single value. Figure 7 is a log [All-pH stability diagram based on a set of plots that includes the model-calculated and experimental curves of Figure 6. The regions shown in Figure 7 were delineated by locating, on graphs such as Figure 6, the pH values that correspond to n/no = 0.5 for each aluminum sulfate concentration. Envlron. Sci. Technol., Vol. 19,
No. 8, 1985 679
I
I
I --0--
Appendix The following equations were used in the surface chemistry model. The following equations were used for kaolin. surface charge density
I I I Kaolin 5 0 m g l L Ames,126)JorTest Res& Model pediclions
-
-3.-
aoS = (F/As)([A10H2+] + [A10H2+S042-]+
[AIOH2+HS04-]+ [SiOH2+1- [SiO-I - [AlO-])
Stern layer charge density
- [A10H2+HS04-])
a? = (F/AS)(-2[A10H2+S0:-] 3
4
5
6
7
8
9
10
pn
Flgure 7. Model-predicted and experimental stability regions for 50 mg/L kaolin clay. Curves plotted by using graphs whlch Include those in Flgure 6. Aluminum added as aluminum sulfate.
total surface site concentration SF = AsN?/N, total A1 site concentration fAIS,S
In region I of Figure 7, protonation of the surface results in a relatively low value of $d and a is therefore greater than zero. However, because there is minimal uptake of aluminum, only the kaolin particles contribute to 4, and n/nois relatively low. In region I1 sorption of positive aluminum hydrolysis products on the negative particles leads to charge neutralization and a > 0. When the primary particle volume concentration, W/p,is relatively high, region I1 may also appear as a narrow band between region I and region 111. Region I11 corresponds to restabilization of the particles by the positive coating of aluminum hydrolysis products. Above and to the right of region 111, the aluminum hydroxide coated particles are destabilized by the specific adsorption of sulfate and, as the pH approaches 9, ionization of the aluminum hydroxide surface. This region, labeled region IV, is often referred to as the “sweep floc” region. Flocculation is relatively efficient in region IV because of the contribution of the aluminum hydroxide coating to the total particle volume concentration, 4. In region V most of the aluminum is dissolved as AI(OH),, and interaction of aluminum species with the silica surface is minimal. Overall the regions delineated by the computer model are in general agreement with Ames (26) experimental results.
= [AlOH2+]
+ [A10H2+S042-]+ [AlOH2+HS04-] + [AlO-] + [AlOH]
total Si site concentration
fSiSF= [SiOH2+]+ [SiOH] + [SiO-] GCSG electrical double-layer model equations
mass action expressions for site binding reactions [A10H2+]= [AlOH][H’] exp( g -e$0)
/Kapt
[A10H2+S042-]=
Conclusions
The results obtained in this study provide evidence that computer programs which allow self-consistentcalculations to be made simultaneously for solution and surface chemical equilibria, e.g., MINEQL, have potential for predicting the effect of the hydrolyzing metal coagulant concentration and certain solution and suspension variables on flocculation efficiency. Titrations that involve the measurement of the amount of acid or base required to maintain a constant pH while a surface complexing ion is added to the suspension have utility in the determination of surface reaction equilibrium constants. Electrophoretic mobility measurements can also be used in model calibration. The results obtained pertain only to very simple systems; i.e., S042- and HS04- are the only complexing anions. Additional work is needed to include the competitive interaction of additional adsorbing anions such as fluoride and bicarbonate (as well as adsorbing cations) with the surfaces. A better understanding of the uptake of aluminum hydrolysis products by colloidal surfaces is needed before the model has significant practical value for this purpose. 680
Environ. Sci. Technol., Vol. 19, No. 8, 1985
[A10H2+HS04-J=
\
I
[AlOH][H+][HS04-] exp
e+pS - e+oS KHSOIint
(
[SiOH2+]= [SiOH][H+] exp -i:’)/Kbpt [SiO-] = [SiOH] ex.(
%>,,.
[H+l The following equations were used for sorbed aluminum hydrolysis products. surface charge density goA1 = @‘/AA’)([AlOH2+]
+ [A10H2+S042-]+ [AlOH2+HS04-]- [AlO-J)
Stern layer charge density noA1= (F/AA’)(-2[A10H2+S042-]- [AlOHZ+HS04-])
total surface site concentration
StAl= ( A M N / ’ / N , )= [A10H2+]+ [A10H2+S042-]+ [AlOH2+HS04-] + [AlO-] + [AlOH] GCSG electrical double-layer model equations adA1 =
- ( 8 ~ e k T ) l / sinh ~
[A10H2+]= [AlOH][H+] ex.(
[AlO-] = [AIOH] exp( [H+l
zeqdA’
2kT
g-e*0) / K a p t g)Kapt
[A10H2+S042-]=
[A10H2+HS04-]=
[AlOH][H+][HS04-] exp
KH,q04-int
Registry No. Aluminum hydroxide, 21645-51-2.
Literature Cited (1) Westall, J. C.; Zachary, J. L.; Morel, F. M. M. ”MINEQL-A
(2) (3) (4) (5) (6)
Computer Program for the Calculation of Chemical Equilibrium Composition of Aqueous Solutions”. Department of Civil Engineering, Massachusetts Institute of Technology, 1976, Note 18. Davis, J. A,; James, R. 0.;Leckie, J. 0. J. Colloid Interface Sci. 1978, 63, 480. van de Ven, T. M. G.; Mason, S. G. J. Colloid Interface Sci. 1976, 57, 505. Saffman, P. G.; Turner, J. S. J. Fluid Mech. 1956,1, 16. Okamoto, Y.; Nishikawa, M.; Hashimoto, K. Int. Chem. Eng. 1981, 21, 88. Lagvankar, A.; Gemmell, R. S. J.-Am. Water Works Assoc. 1968, 60, 1040.
(7) Tambo, N.; Watanabe, Y. Water Res. 1979, 13, 409. (8) Zeichner, G. R.; Schowalter, W. R. J. Colloid Interface Sei. 1979, 71, 237. (9) Higashitani, K.; Miyafusa, S.; Matsuda, T.; Matsumo, Y. J. Colloid Interface Sci. 1981, 77, 21. (10) Spielman, L. Sci. Basis Flocculation,Proc. NATO Adv. Study Inst. 1977, Part I (Chapter 3). (11) Yates, E. D.; Levine, S.; Healy, T. W. J. Chem. SOC., Faraday Trans. 1 1974, 70, 1807. (12) James, R. 0.;Parks, G. A. Surf. Colloid Sci. 1982,12, 119. (13) Iyer, D. R. Ph.D. Dissertation, Syracuse University, Syracuse, NY, 1984. (14) Letterman, R. D.; Iyer, D. R. In “Solid-Liquid Separation”; Gregory, J., Ed.; Ellis Horwood, Ltd.: Chichester, England, 1984. (15) Perram, J. W.; Hunter, R. J.; Wright, H. J. L. Aust. J. Chem. 1974, 27, 461. (16) Letterman, R. D.; Vanderbrook, S. G.; Sricharoenchaikit, P. J.-Am. Water Works Assoc. 1982, 74, 44. (17) Matijevic, E.; Mangravite, F.; Cassell, E. A. J. Colloid Interface Sci. 1971, 35, 560. (18) Hohl, H.; Sigg, L.; Stumm, W. In “Particulates in Water”; Kavanaugh, M. C.; Leckie, J. O., Eds.; American Chemical Society: Washington, DC, 1980; Publication 189, 1. (19) Williams, D. J. A.; Williams, K. P. J. Colloid Interface Sci. 1978, 65, 79. (20) James, R. 0.;Davis, J. A.; Leckie, J. 0. J. Colloid Interface Sci. 1978, 65, 331. (21) Wiese, G. R.; Healy, T. W. J. Colloid Interface Sci. 1975, 51, 434. (22) Sricharoenchaikit, P. Ph.D. Dissertation, Syracuse University, Syracuse, NY, 1984. (23) James, R. 0.; Healy, T. W. J. Colloid Interface Sci. 1972, 40, 53. (24) Hahn, B. H.; Stumm, W. In “Adsorption from Aqueous Solutions”; Gould, R. F., Ed.; American Chemical Society: Washington, DC, 1968; Publication 79, 91; J. Colloid Interface Sei. 1968, 28, 134. (25) James, R. 0. In “Adsorption of Inorganics at Solid-Liquid Interfaces”; Anderson, M. A,; Rubin, A. J., Eds.; Ann Arbor Science: Ann Arbor, MI, 1981. (26) Ames, R. S. Thesis, Illinois Institute of Technology, 1976. (27) Andreu-Villegas, R.; Letterman, R. J. Env. Eng. Diu. (Am. SOC.Civ. Eng.) 1976, 102, 251. (28) Black, A. P.; Chen, C. J.-Am. Water Works Assoc. 1967, 59, 1173. (29) Black, A. P.; Hannah, S. A. J.-Am. Water Works Assoc. 1961, 53, 438.
Received for review November 29, 1982. Revised manuscript received February 28,1985. Accepted April 22,1985. This study was supported in part by a research grant from the Allied Corp., Morristown, NJ.
Environ. Sci. Technol., Vol. 19, No. 8, 1985 681
