15 Prediction of Suspension Turbidities from Aggregate Size Distribution
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G O R D O N P. T R E W E E K James M . Montgomery, Consulting Engineers, Inc., 555 East Walnut Street, Pasadena, C A 91101 JAMES J. M O R G A N Environmental Engineering Science Department, California Institute of Technology, 1201 East California Boulevard, Pasadena, C A 91125 The turbidity of a coagulating, but noncoalescing, suspen sion cannot be determined directly because of interference between scattered waves and phase shifts in transmitted waves. This research developed a "coalesced-sphere" light scattering model which was applied to a noncoalescing, coagulating system to predict, within reasonable limits, the suspension turbidity. The application of the coalesced -sphere model for aggregates in the Mie scattering regime allows the calculation of the turbidity per size interval caused by particulates in the coagulated suspension. Knowl edge of the turbidity fraction can lead to improved design of phase-separation devices, such as water and wastewater filters, so they remove the portion of the size distribution that contributes most significantly to the overall suspension turbidity.
T n general, the removal of particulate matter i n water and wastewater via coagulation/flocculation with cationic polymers occurs i n three steps: 1. Destabilization—modification of the surface properties of the singlet particles so that interparticle repulsion is re duced and collision effectiveness is enhanced (coagula tion). 0-8412-0499-3/80/33-189-329$05.75/0 © 1980 American Chemical Society
Kavanaugh and Leckie; Particulates in Water Advances in Chemistry; American Chemical Society: Washington, DC, 1980.
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PARTICULATES I N W A T E R
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2. Transport—movement of the particles into adhesive con tacts via perikinetic (Brownian) or orthokinetic motion resulting in aggregate growth (flocculation). 3. Phase separation—removal of particle aggregates from the suspending medium. More than 20 techniques have been used by prior investigators to evaluate flocculant effectiveness in accomplishing these steps, but aside from the efforts of TeKippe and H a m (4), little has been done to correlate the measurements taken by these different techniques. Many of the experimental techniques (settling velocity, residual scattering intensity, settled turbidity, refiltration rate) currently employed rely solely on measuring the final phase separation of particulate matter from the suspension. W h i l e these methods record the end result of successful coagulation and flocculation, the preceding steps are not followed quan titatively. In addition, measurement of phase separation alone tends to bias the investigator toward improvement of the physical parameters of the system at the expense of possible chemical alterations which would enhance earlier destabilization stages. This research involves a quantitative study to evaluate the effective ness of relative scattering intensity measurements (l9o%Ti8o°) in recording the coagulation-flocculation of a suspended biocolloid, E. coli, via the addition of a cationic polymer, polyethyleneimine ( P E I ) . To accomplish this goal, the changes in the scattering intensity must be correlated with changes in the particle size distribution. The assumption was made (and verified) that the aggregates of the singlet cells could be treated, for light scattering purposes, as coalesced spheres. Using the coalescedsphere model for aggregates in the M i e scattering regime allows the calculation of the turbidity caused by the aggregated singlets in each size interval in the coagulated suspension. Particle Size Distributions Via Electronic Particle Counters A direct quantitative measure of change in aggregate diameter can be achieved via the electronic particle counting and sizing technique. Flocculation data recorded by this technique were used as the basis against which data taken by light scattering were compared. The intrica cies of measuring particle size distributions in aggregating suspensions via electronic particle counters have been presented i n the works of Birkner and Morgan (1,2); H a m and Christman (3); TeKippe and H a m (4); Camp ( 5 , 6 ) ; Hannah, Cohen, and Robeck (7); and Treweek (8,14). Light Scattering by Aggregated Particles Light scattered from coagulating systems can be evaluated by one of three theories: Rayleigh, Rayleigh-Debye, or Mie, depending on the size
Kavanaugh and Leckie; Particulates in Water Advances in Chemistry; American Chemical Society: Washington, DC, 1980.
Downloaded by EAST CAROLINA UNIV on January 2, 2018 | http://pubs.acs.org Publication Date: November 1, 1980 | doi: 10.1021/ba-1980-0189.ch015
15.
T R E W E E K AND MORGAN
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Suspension Turbidities
regime of the aggregates. The Rayleigh theory for particles with d less than A/10 treats both singlets and aggregates as Rayleigh scatterers i n which an aggregate of k spheres, each of volume v, is equivalent to a single Rayleigh sphere of volume kv. F o r such an aggregate, the light scattered is k times greater than from k single spheres. The second theory, a Rayleigh-Debye-type treatment derived by Benoit, Ullman, DeVries, and Wippler ( 9 ) , evaluates the scattering properties of aggregates whose constituent particles have: (1) refractive indices close to those of the suspending medium and (2) negligible "phase shift" at any point i n the aggregate. The third interpretation, based on M i e theory, is used for larger particles without restriction on the index of refraction. Since bac teria cells are obviously larger than Rayleigh spheres (d > A/10), only the latter two interpretations w i l l be discussed further. Rayeigh-Debye Scattering. I n the analysis by Benoit et a l . ( 9 ) , primary particles within an aggregate scatter light which interferes i m mediately with that scattered by its aggregate neighbors. The intensity of light scattered at an angle ^ by an aggregate of k monodisperse spheres randomly positioned to the incident light beam is expressed as: /,,(*) = k / ( * ) [ i + ( 2 / f c M * ( * ) ]
(l)
1
where J i ( ^ ) is the intensity of light scattered at an angle ^ by a single primary sphere (Rayleigh-Debye or M i e theory) and A (V) is a form factor that is a function of the geometry of the aggregate and of the scattering angle Benoit et al. (9) analogized the aggregate form factor A (V), which accounts for the interference between light waves scattered by particles within an aggregate, to the Rayleigh-Debye form factor P(&), which accounts for scattering interference between the various scattering centers within the same particle. The form factors and hence the scattering properties of aggregates depend on the geometrical arrangement of par ticles within the aggregates. Because an infinite number of arrangements of singlets is possible i n a coagulating system, a precise evaluation of A (
