7. Implications and Future Work
7.1. Filtration Methods vs. Light Scattering Techniques
In the membrane filtration method, a filter of a certain cutoff size is used. For practical purposes, one filter size of 0.45μm is commonly used, although a range of 0.01 to 100μm filters is reported in filtration measurements in the literature. The procedure for iron determination in the estuarine zone by the filtration method is summarized as follows. A river water sample is first filtered, and the amount of iron in the filtrate is measured (by colorimetric or spectrophotometric methods). The iron determined is defined as “dissolved iron”. The filtered river water is then mixed with seawater (simulating the estuarine mixing zone), allowed to settle and subsequently filtered. The iron remaining in the filtrate is measured and the amount of iron removed is determined.
In the filtration method, the collected mass on a filter corresponds to the mass of aggregated particles as a result of changing ionic strength and time. The basis of the light scattering technique, however, is the change in the number concentration and the size of the particles. The rate of change in the mass concentration of the filtrable particles can be related to the change in number concentration by assuming a certain shape and the size distribution for the filtrable particles.
7.1.1
ExperimentalProcedure
An experiment based on the filtration procedure was designed and carried out in
this research as a case study. A nuclepore filter of pore size 0.1μm was used since sin
glet particles go through the filter, but aggregates of two or more particles in general do not. Preliminary experiments showed that monodispersed particles completely pass the filter with a recovery of at least 95%. The filtrate iron mass concentration can be determined by dissolving the oxide in acid, and then measuring the total iron by atomic absorption spectrophotometry. For a quick and simple measurement, a calibration curve was made using a spectrophotometer at λ = 364nm for different hematite mass concentrations. Figure 7.1 shows a linear relationship between the total extinction of light and hematite mass concentration. Preliminary experments showed that in the presence of 0.01M NaCl, the stability ratio of hematite at pH 11 is about 20 (see Fig. 4.5). If the initial particle number concentration is 3 × 109 cm-3 the coagulation characteristic time is 15 minutes.
Based on these estimates, the filtration experiment was carried out as follows.
Approximately 3 mg/1 of hematite particles were dispersed in a beaker at pH 11.
NaCl was introduced into the suspension to make the final ionic strength 0.013M. At 5 minute intervals 10ml of suspension was withdrawn, filtered, and the concentration of hematite in the filtrate was determined.
7.1.2 Results
and
InterpretationThe results of the filtration experiment are presented in Fig. 7.2, where the amount of material remaining in the filtrate (normalized with respect to the initial concen
tration) is plotted against time. The figure shows that in the first 5 minutes of the experiment about 40% of the colloidal hematite particles are removed. The iron re
moval is entirely due to the coagulation of colloidal particles. The removal process slows down as the experiment progresses. The behavior of colloidal hematite removal resembles the filtration results presented by Mayer (1982), who showed the filtrable iron fraction as a function of time when river water and seawater were mixed.
The results of the filtration study presented in Fig. 7.2 are in terms of mass
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Fe2O3 (mg∕l) e
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Figure 7.1: Calibration curve used to determine hematite mass concentration from total light extinction at wavelength A = 364nm.
concentration. The conversion of a mass concentration to a number concentration is readily made since hematite particles are approximately spherical in shape and monodispersed. The evolution of the particle size distribution as a result of co
agulation of initially monodispersed particles is given by Smoluchowski’s simplified equations (Sec. 2.1). The mass of a particle of diameter d, with density p, can be calculated from πd3ρ∣Q and the number concentration can be converted to a mass concentration. Fig. 7.3 shows the hematite mass fraction as a function of time of a hematite suspension undergoing coagulation. This plot is related to the variation of number concentration with time shown in Fig. 2.1. Although the total number concentration is reduced by coagulation, the total mass concentration is conserved.
The hematite mass remaining in the filtrate (i.e., what passes through the 100nm fil
ter) at the time of filtration corresponds to the mass of singlets. The experimentally determined number of singlets remaining as a function of time is compared with that predicted by theory in Fig. 7.3, in which the data points are derived from the filtration
Figure 7.2: Mass fraction remaining in filtrate plotted as a function of time for a hematite suspension of 3.62 mg∕l. The ionic strength is 1.3×10-2M, and the pH is 11.0.
results of Fig. 7.2. In Fig. 7.3 time is normalized by dividing by the characteristic coagulation time, r, of 15 minutes. The data points at the initial stage of coagulation (t∕τ <1) follow the predicted mass concentration of singlets fairly well. At times exceeding the coagulation characteristic time, the experimental results deviate from the theoretical prediction. The underlying assumption in interpretating the filtration results is that the total mass is conserved, but in reality, the total mass may not be conserved due to the mass loss to the wall of the container. This loss may be cumulative over time which may provide an explanation for the observed deviation in the hematite mass fraction from the theory at longer experimental time.
Nevertheless, the results of the initial stage filtration experiment are sufficient for comparison with the results obtained by the light scattering method, since the coag
ulation rate constants were derived from the initial light scattering data (Sec. 4.1).
For the experimental conditions pertaining (3.62mg∕l, pH=ll, (NaCl)=0.013M), the
Figure 7.3: Mass fraction as a function of normalized time. The dotted line and the short dashed line represent the mass fraction of singlets and doublets, respectively.
The solid line is the sum of these two fractions. The total mass, shown by a long dashed line, is conserved during coagulation. The open circles are data from Fig. 7.2.
fast diffusion controlled time scale is of the order of 40 seconds. The longer actual coagulation time of 15 minutes is due to the repulsion between particles during their encounter. Comparison of these time scales yields a stability ratio of 20. This is the same value as that derived from coagulation data by the light scattering technique.
Using a simple monodispersed hematite suspension, the stability ratio obtained from the light scattering method agrees well with the result from the filtration method.
Hence, it is concluded that the initial filtration results of field studies can be inter
preted on the basis of coagulation kinetics determined by light scattering techniques.