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Langmuir 2002, 18, 1974-1984
Aggregation Mechanisms of Latex of Different Particle Sizes in a Controlled Shear Environment C. Selomulya,† G. Bushell,† R. Amal,*,† and T. D. Waite‡ Centre for Particle and Catalyst Technologies, School of Chemical Engineering and Industrial Chemistry, UNSW, Sydney, NSW 2052, Australia, and School of Civil and Environmental Engineering, UNSW, Sydney, NSW 2052, Australia Received May 10, 2001. In Final Form: November 23, 2001 Latex particles with diameters of 60, 380, and 810 nm, respectively, were sheared in a controlled shear environment of circular couette flow after being destabilized by the addition of MgCl2. The evolution of aggregate size and structure, as well as a measure of aggregate mass, was monitored with use of a particle size analyzer (Coulter LS230) operating on the principle of small-angle light scattering. The aggregates of different primary particle sizes displayed distinct behavior in attaining steady state under similar shear conditions, notably at low to moderate shear rates (G e 100 s-1). Restructuring of aggregate structure was favored over fragmentation for aggregates composed of 60- and 380-nm particles, whereas fragmentation and reaggregation were the main mechanism in governing the final floc size and structure for aggregates made up from 810-nm particles. Also presented in this study is a dimensional analysis that yields a correlation between a floc factor (consisting of floc size and structure) and an aggregation factor, which encompasses the fluid properties, applied shear, number concentration and size of primary particles, as well as the estimated bonding force between particles. This relationship provides a better appreciation of other significant aggregation parameters, apart from the shear level and aggregate size, which are often ignored in the more conventional manners of presenting data from flocculation processes.
Introduction The properties of aggregates or flocs produced from the flocculation step before solid-liquid separation are crucial in determining the overall efficiency of water or wastewater treatment processes. The size distribution is clearly important, because it will determine whether the flocs are suitable for a particular separation process such as filtration or sedimentation. Another vital property is the aggregate strength, because an inability to withstand the separation process without being significantly altered may result in a reduction in the extent of solids capture. Currently, little is known regarding the floc strength or its relationship with the floc size,1 and the available data relating the two properties generally depend on the chemical and mixing conditions operative during floc production.2-4 Measurements of floc strength have been attempted by exposing the flocs to known stresses5 and by micro-mechanical measurement of the floc binding strength via its rupture force.6 Although these techniques can provide an indication of the aggregate strength in a particular system, they lack practicality, especially if a need exists to monitor and then control the floc properties during the flocculation process. An alternative approach of assessing the floc strength is to relate it to the floc structure, a characteristic that can be quantified with methods such as static light scattering7 and image * To whom correspondence should be addressed. † School of Chemical Engineering and Industrial Chemistry. ‡ School of Civil and Environmental Engineering. (1) Boller, M.; Blaser, S. Water Sci. Technol. 1998, 37(10), 9-29. (2) Tambo, N.; Hozumi, H. Water Res. 1979, 13, 421-427. (3) Smith, D. K. W.; Kitchener, J. A. Chem. Eng. Sci. 1978, 33, 16311636. (4) Peng, S. J.; Williams, R. A. J. Colloid Interface Sci. 1994, 166, 321-332. (5) Bache, D. H.; Johnson, C.; McGilligan, J. F.; Rasool, E. Water Sci. Technol. 1996, 36(4), 49-56. (6) Yeung, A. C. K.; Pelton, R. J. Colloid Interface Sci. 1996, 184, 579-585.
analysis.8,9 It has been widely acknowledged that the structures of a range of aggregate types can be characterized by using the concept of fractal morphology, first introduced by Mandelbrot.10 This includes flocs of gold, latex, silica,11 and hematite7 particles, and bacterial aggregates.12 This manner of assessing the structure provides an indication of aggregate compactness. Because the overall floc strength depends on both the binding forces between primary particles and the number of bonds3, increasing compactness implies that the flocs should be stronger because of a greater number of interparticle contacts per cross-sectional area. However, the floc strength may also be gauged by the limiting size, which is the maximum size to which the flocs can grow under a certain shear field.13 For example, large flocs with relatively loose structures can be formed when polymers are used to aid floc growth. In that event, polymer bridging creates much stronger bonds than would otherwise be the case in, say, electrolyte-induced aggregation. Thus, both size and structure must be considered when evaluating the floc strength. The chemical composition of the coagulating particles and their surface chemistry are likewise crucial because they influence the particle-particle interactions and the strength of the attachment, and consequently, the overall strength of the flocs. It is also important to understand the mechanisms by which the flocs reach steady state, because they affect the (7) Amal, R.; Gazeau, D.; Waite, T. D. Part. Part. Syst. Charact. 1994, 11, 315-319. (8) Clark, M. M.; Flora, J. R. V. J. Colloid Interface Sci. 1991, 147, 407-421. (9) Serra, T.; Casamitjana, X. J. Colloid Interface Sci. 1998, 206, 505-511. (10) Mandelbrot, B. B. The Fractal Geometry of Nature; Freeman: San Francisco, 1982. (11) Lin, M. Y.; Lindsay, H. M.; Weitz, D. A.; Ball, R. C.; Klein, R.; Meakin, P. Nature 1989, 339, 360-362. (12) Guan, J.; Amal, R.; Waite, T. D. Environ. Sci. Technol. 1998, 32, 3735-3742. (13) Gregory, J. Water Sci. Technol. 1997, 36(4), 1-13.
10.1021/la010702h CCC: $22.00 © 2002 American Chemical Society Published on Web 02/21/2002
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resultant floc properties. The processes to which the flocs are exposed include aggregation, fragmentation, and in some cases, rearrangement of their structure. Improved comprehension of aggregate behavior should enable better manipulation of floc properties. For example, increased floc density may be achieved by encouraging restructuring through application of specific shear regimes.13 In this study, the evolution of latex aggregate properties under controlled shear is monitored by using small-angle static light scattering. The data obtained are interpreted in terms of various processes considered to be operative during the floc transformation to their equilibrium state. Relationships between the floc characteristics, the properties of the aggregating particles, and the shear field are verified through the use of dimensional analysis. Theory Measurement of Floc Size and Structure from Light Scattering. Size distribution measurement by the particle size analyzer (Coulter LS230) is undertaken by fitting the aggregate scattering patterns with the patterns predicted by the built-in optical model to obtain an equivalent volume-based size distribution, assuming spherical particles. The average floc size is taken as the mean of this size distribution (d[4,3]). The true size will be significantly different from this estimate if the particle shapes are very nonspherical (i.e., very elongated, highly crystalline, or perhaps, fractal).14 A better approximation of the aggregate size is the root-mean-square of the mass squared-weighted radius of gyration (RG′_), which can be estimated from the scattering data without a presumption of the particle or aggregate shape. Nonetheless, a comparison of RG′_ and d[4,3] displayed similar trend and magnitude for the latex aggregation systems both in the current study and in previous work,15 indicating that the optical model assumption of spherical particles is adequate for measuring size in this particular system. Hence, we used the d[4,3] given by the Coulter LS230 as the measure of aggregate size (d) in this study. In addition to the size estimation, static light scattering can be used to acquire information regarding the floc structure in terms of its mass (or number) fractal dimension (dF).7,11 The scattered intensity from aggregates of small, nonabsorbing primary particles with low refractive indices can be approximated by Rayleigh-GansDebye (RGD) theory. This leads to a relationship between the measured scattered intensity of aggregate clusters [I(q)] and the momentum transfer (q)11
I(q) ∝ q-dF
(1)
where
q)
θ 4πn sin λ 2
(2)
and n is the refractive index of the fluid, λ is the wavelength in vacuo of the laser light used, and θ is the scattering angle. This q-dF dependence with the scattered intensity is valid in a range of length scales much larger than the primary particles and much smaller than the aggregate11 (14) Sorensen, C. M. In Handbook of Surface and Colloid Chemistry; Birdi, K. S., Ed.; CRC Press: New York, 1997; p 533. (15) Selomulya, C.; Amal, R.; Bushell, G.; Waite, T. D. J. Colloid Interface Sci. 2001, 236(1), 67-77.
1 1 ,q, Raggregate Rparticle
(3)
This regime is recognized as the fractal regime, where the mass fractal dimension (dF) reflects the internal structure of the fractal clusters. The mass fractal dimension describes the space-filling ability of the aggregate, and it can vary from 1 (a linear aggregate) to 3 (a compact or space-filling form). As the length scale corresponding to the q value approaches the aggregate size (q = 1/Raggregate), the q-dF relationship begins to be influenced by the edge of the aggregate, and the structure can no longer be determined in this q region.11 At even lower q, the scattering intensity is free from the effects of aggregate structure. The intensity is then only a function of the cluster size (RG′) in the form of the root-mean-square of the mass squared-weighted radius of gyration of each aggregate (RGi).16,17
I(q) 1 ) 1 - (qRG′)2 3 I(0)
(
RG′ )
)
x
∑i mi2RGi2 ∑i
(4)
(5)
mi2
This regime is known as the Guinier regime where I(0) is the intensity at q ) 0 and mi is the mass of each aggregate. For fractal flocs of monodisperse particles, I(0) is proportional to the average mass (Mw) of an aggregate or the average number of particles in an aggregate (N),14 because all particles in an aggregate scatter in phase as qf0.
I(0) ∝ Mw ∝ N
(6)
The values of RG′_and I(0) can be obtained by simply fitting the Guinier equation at the portion of the scattering curve where qRG′_, 1.16 The measure of fractal dimension can be estimated from the absolute slope of I(q) versus q by fitting a straight line through the fractal regime section of the scattering plot. This procedure of obtaining information from the aggregate scattering patterns is not significantly affected by the presence of polydisperse flocs having a relatively narrow size distribution typical of an aggregation process.18 The technique of quantifying floc structure from their fractal dimensions should be used with caution, however, because many aggregates do not exhibit fractal characteristics, and the applicability of the RGD theory is limited.19 In addition, aggregate restructuring may take place when the flocs are exposed to shear. The structural rearrangement would occur on the larger length scale, because the aggregate strength decreases with increasing size, whereas the hydrodynamic forces experienced by the flocs increase with the aggregate length scale.20 Hence, the slope of the scattering pattern of a restructured aggregate would be higher at low q (large (16) Bushell, G.; Amal, R. J. Colloid Interface Sci. 2000, 221, 186194. (17) Guinier, A.; Fournet, G. Small Angle Scattering of X-rays; John Wiley & Sons: New York, 1955. (18) Lawler, D. F. Water Sci. Technol. 1997, 36, 15-23. (19) Farias, T. L.; Ko¨ylu¨, U ¨.O ¨ .; Carvalho, M. G. Appl. Opt. 1996, 35, 6560-6567. (20) Bushell, G.; Yan, Y. D.; Woodfield, D.; Raper, J.; Amal, R. Adv. Colloid Interface Sci., in press.
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and no sudden change or discontinuity should occur in the flow pattern from laminar to turbulent regimes.24 Still, the presence of these vortices promotes mixing in circumferential, radial, and axial directions, and results in measured torque greater than predicted for a particular shear rate. The stability criteria for Newtonian fluids in terms of the Taylor number (Ta) of the flow25 are
Fω1(R2 - R1)3/2R11/2 µ Ta < 41 Laminar couette flow 41 < Ta < 400 Laminar flow with Taylor vortices Ta > 400 Turbulent flow (8)
Ta )
[
Figure 1. Scattering pattern of a restructured aggregate displaying higher slope at lower q, indicating a more compact structure at larger length scale of the aggregate.
length scale) compared with that at high q (Figure 1). In other words, the aggregate structure is no longer fractal, because uniform mass scaling with the aggregate length scale is not observed. Nevertheless, we can still obtain the information regarding the change in aggregate structure at large length scale because the structure at small length scale is usually unchanged from its original structure. In this study, we refer to the slope of the scattering patterns over the q range of 1.0 × 10-4 to 5.0 × 10- nm-1 as the scattering exponent (SE) rather than the floc fractal dimension, in view of both the possibility of restructuring effects and the uncertainty concerning the validity of the RGD approximation. The scattering exponent should still, however, provide an indication of the compactness of the aggregates. Estimation of Shear Rate in a Couette Flow. The aggregation was performed in a couette-type flow, with flow generated in the gap between two concentric cylinders, with rotating inner cylinder and a stationary outer cylinder. When the gap is sufficiently narrow (i.e., ratio of gap width, h, to the outer cylinder radius, R2, is e0.05), the shear profile created in the gap will be similar to that produced between two parallel plates.21 Hence, the shear is distributed more uniformly and, in turbulence, is more isotropic22 than that produced by other equipment such as a mixing tank. The average shear rate (G) within the gap when the inner cylinder is rotating at an angular frequency of Ω1 ()ω1 × 60/2π, where ω1 is the rotation rate in s-1) and the flow between cylinders is laminar21 is
G)
2ω1R1R2 (R22 - R12)
(7)
where R1 and R2 are the radii of the inner and outer cylinders, respectively. This approximation is valid when the flow between the cylinders is stable and negligible gravity or end effects exist. Instability of flow occurs above a particular speed when the inertial forces from inner cylinder rotation cause the formation of a small axisymmetric cellular secondary flow, better known as Taylor cells or vortices.21 The characteristic vortex structure can still be retained in the flow at up to 500 times this rate,23 (21) Macosko, C. W. In Rheology Principles, Measurements, and Applications; Macosko, C. W., Ed.; VCH Publishers Inc.: New York, 1994; pp 181-235. (22) Pandya, J. D.; Spielman, L. A. Chem. Eng. Sci. 1983, 38(12), 1983-1992.
]
where F and µ are the density and dynamic viscosity of the suspension, respectively. The gap shear rate for turbulent flow can be estimated by directly measuring the torque (M) on the inner cylinder, which is related to the energy dissipation rate () according to the next equation26
M)
Lm ηω1
(9)
where L and m are the height and mass of liquid in the gap, respectively. The coefficient η is an efficiency factor because the power input is not entirely dissipated by turbulence. Muhle26 proposed the efficiency to be ∼60% for the core of the flow, where the flocs are experiencing hydrodynamic stresses, whereas the rest of the energy is converted to heat within the boundary layers. The average shear rate is then estimated from
G)
xν
(10)
where ν is the kinematic viscosity of the suspension. This estimation is particularly useful in determining shear rate when the flow within the gap is not fully laminar and eq 7 is not particularly accurate. Experimental Section Surfactant-free monodisperse polystyrene latex primary particles with mean diameters (measured by transmission electron microscopy) of 60 ( 5 nm (purchased from IDC), 380 ( 10 nm, and 810 ( 15 nm (both prepared by the method of Goodwin et al.27), and solids volume fractions (φo) of 3.83 × 10-6, 3.74 × 10-5, and 3.76 × 10-5, respectively, were used in this study. The number concentrations (no) of the particles corresponding to these volume fractions were 3.4 × 1016/m3, 1.3 × 1015/m3, and 1.4 × 1014/m3, respectively. The volume fractions were chosen to satisfy the requirement for sample obscuration of the light-scattering instrument, while simultaneously providing an adequate number of particles in suspension to allow the kinetics of aggregation to be monitored. The latex suspensions were ultrasonified before any of the experiments to ensure that no aggregates were present. Each suspension was then fully destabilized with 0.05 M MgCl2 at pH 9.15 ( 0.05 by mixing equal volumes of primary particle suspension and salt solution to give the concentrations indicated (23) Smith, G. P.; Townsend, A. A. J. Fluid Mech. 1982, 123, 187217. (24) Moore, C. M. V.; Cooney, C. L. AIChE J. 1995, 41(3), 723-727. (25) Powell, R. L. In Rheological Measurement; Collyer, A. A.; Clegg, D. W., Eds.; Elsevier Applied Science Publishers Ltd.: Essex, 1988; pp 247-298. (26) Muhle, K. In Coagulation and Flocculation Theory and Applications; Dobias, B., Ed.; Marcel Dekker Inc.: New York, 1993; Vol. 47, pp 355-390. (27) Goodwin, J. W.; Hearn, J.; Ho, C. C.; Ottewill, R. H. Colloid Polym. Sci. 1974, 252, 464.
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Figure 2. Schematic of experimental setup. above. The mixture was immediately poured into the gap of the couette device via gravity flow to minimize any disruption to the suspension. The preparation process took less than 5 min and the presence of any aggregates that may have been formed in the interim would not have been expected to significantly influence the overall aggregate behavior observed during these experiments. The schematic of the experimental setup is shown in Figure 2. The inner cylinder is made from poly(vinyl chloride) and has a diameter of 292 mm. The outer cylinder is constructed from Plexiglas and the diameter of the cylinder inner wall is 302 mm, giving a gap width of 5 mm. The height of the liquid within the gap is 724 mm, and the sample volume is estimated to be 3.4 L. The design of the apparatus gives a sufficiently narrow gap (h/R2 ) 0.03 < 0.05). Any end effects caused by shear flow at the bottom of the cylinder are also minimized by ensuring that the ratio between the depth of the liquid and the gap width is greater than 100.28 A stepper motor, connected to a speed controller, is used to rotate the inner cylinder. The torque on the inner cylinder is measured by an inline torque transducer, which is placed on the shaft connecting the motor and the cylinder. The inner cylinder was rotated at selected speeds between 10 and 60 rpm. Laminar couette flow ceases to exist for this configuration when the rotation is higher than 3 rpm (Ta > 41), and thus instabilities were always present for the range of the speeds studied. The average shear rates were estimated from eq 7 and then compared with those obtained from the measured energy dissipation through direct torque measurement, assuming an efficiency of 60% as proposed by Muhle.26 The shear rates calculated by these two methods were similar for up to 30 rpm (G ∼100s-1), where the Taylor number for this configuration is
