Polymers 2022 , 14 , 3309
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flocculants tested (CPAM, BEKP and cationic celluloses), 0.1 wt % of aqueous suspensions were prepared and kept under magnetic stirring. For the flocculation experiment, 15 mL of the PCC suspension was added to the equipment dispersion unit vessel containing 700 mL of distilled water, resulting in a PCC concentration of around 0.02 wt % (a laser-obscuration level of nearly 30% [32]) and a pH of 9. The pump speed was set to 1400 rpm. In an initial test, after the stabilization of the PCC median size, a certain amount of flocculant (1 mg of flocculant/g of PCC) was added to the measuring vessel every single minute until a maximum of 15 mg of flocculant was reached (15-min test). Although this procedure is not typical in flocculation studies, and although that one minute between the subsequent additions of flocculant is not enough time for all the flocculation steps (mixing, adsorption, reconformation and aggregation) to occur, it has proven to be a faster and more efficient way of screening those flocculants that offer the best potential. This method was also previously used with synthetic flocculant to access the optimum dosage [32]. Additionally, this strategy is quite common when prescreening flocculants for flocculation in effluent treatment, wherein offline tests with the continuous addition of consecutive doses of the flocculant are conducted (jar tests) [40], in order to optimize the flocculant dosage, the difference being that, in that case, the normal strategy does not involve the simultaneous measurement of the particle size. For the samples presenting the best performance in the previous test, a second study was conducted to study the evolution in the size of the flocs over time for a fixed concentra- tion of flocculant. In this test, after the addition of the PCC, a certain amount of flocculant (1, 2, 4, 8 or 10 mg/g of PCC) was added to the PCC suspension at once. The evolution of the size of the flocs was measured every minute for 15 min. All the measurements were performed in triplicate. A test with only PCC (no addition of flocculant), wherein the size was monitored for 15 min, was performed for comparison. The minimum flocculant dosage considered in this study (1 mg/g of PCC) was based on the typical values used in a papermill for the flocculation of mineral fillers. Other authors have tested similar dosages of bioflocculants for the flocculation of distinct minerals. As an example, Sirviö et al. [25] tested dosages of up to 9 mg/g of mineral, while Aguado et al. [15] tested the addition of 20 mg/g of mineral. Higher dosages, of up to 500 mg/g of mineral, were tested by Campano et al. [41]. 2.5. Mass Fractal Dimension of the PCC Flocs Besides the mean size and size distribution, LDS also allows us to infer the structure of the formed flocs by means of mass fractal dimensions (d F ) [31,42,43]. The d F expresses the degree to which primary particles fill the space within the nominal volume occupied by an aggregate; this can be used as an indication of the fluffiness/density of the flocs (Equation (1)): m(R) ∝ R d F (1) The mass (m) of any fractal aggregate is directly proportional to its radius (R), raised to the exponent, d F [44]. Ad F value tending to 1 indicates a more stringy and less dense floc structure, while a value approaching 3 suggests stronger and denser flocs [42]. According to the Rayleigh–Gans–Debye (RGB) theory, the d F can be calculated from the negative slope of the log-log plot of the scattered light intensity versus the scattering wave vector (q) (Equation (2)) [35,44]:
q= (4 π n 0 / λ 0 )sin( θ /2)
(2)
n 0 is the refractive index of the dispersant medium (1.33 for water), θ is the scattering angle (between 0.01 ◦ and40.6 ◦ for the Mastersizer 2000 equipment) and λ 0 is the incident light wavelength in vacuo (630 nm). The validity of the RGB theory is based on the assumption that the elementary units scatter light independently, this being more appropriate for sub-micron spherical particles
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