# Estimating the Shear Resistance of Flocculated Kaolin Aggregates: Effect of Flocculation Time, Flocculant Dose, and Water Quality

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Aggregate Characterization

^{−1}approximately) for 30 min at pH 8 to keep the particles dispersed before flocculation. Stirring was then reduced to 200 rpm (G = 273 s

^{−1}). After 1 min, the flocculant was added in doses of 8 to 89 g/t. The evolution of the average size of flocs was analyzed for 6 min. The strength of the aggregates was evaluated by increasing the mixing intensity. For this, the flocculation tests were repeated at the standard agitation of 200 rpm, but after a determined flocculation time, which was considered to be in the range of 30–120 s, the mixing intensity was increased to promote shear fragmentation. Independent tests were performed by applying shear rate increments from the initial G = 273 s

^{−1}(0 to 1516 s

^{−1}).

#### 2.3. Shear Rate

#### 2.4. Sedimentation Tests

^{3}cylinders (35 mm internal diameter). Then, each cylinder with its content was slowly inverted three times (each cylinder inversion took ~4 s) and then placed on a flat surface to determine the sedimentation rate classically (the change in the liquid–solid interface was recorded over 10 min).

#### 2.5. Fractal Dimension

_{p}is the average size of primitive particles, d

_{agg}is the average size of aggregates after some flocculation time, in this work both d

_{p}and d

_{agg}are approximated by the squared-weighted mean chord length, ρ

_{s}and ρ

_{l}are, respectively, the densities of solid and liquid phases, g is the acceleration of gravity, μ is the fluid viscosity, ${\phi}_{s}$ is the solid fraction, and D

_{f}is the mass fractal dimension. Many of these parameters remain constant across experiments, for example, ρ

_{s}, ρ

_{l}, μ, ${\phi}_{s}$, and d

_{p}. While the hindered sedimentation rate was experimentally determined after flocculation as described above. ${D}_{f}$ was calculated from Equation (4) using the standard method of least squares.

## 3. Results

#### 3.1. Aggregation with Flocculant

^{−1}. Once the flocculant is added, the growth of the aggregates is practically instantaneous, and it only takes a few seconds to reach a maximum size. Subsequently, shear fragmentation causes a continuous reduction in the size of the aggregates until reaching a stable size. The average size of aggregates shows an increasing trend with the doses studied; for example, at 13 g/t in seawater, a size peak of 115 µm is reached, while at 89 g/t the peak is at 300 µm. A saline system can favor or harm flocculation. The final result depends on the competition of two mechanisms propitiated by the presence of cations, that is, (i) better flocculant adsorption via cationic bridges and (ii) electrostatic shielding of the active sites in the flocculant, leading to polymer curling. The results in Figure 2 show better flocculation in industrial water than in seawater, indicating that the high concentration of cations in seawater causes a significant increase in polymer curling, limiting its ability to form hydrogen bonds and thus its effectiveness as a flocculant. Figure 3 shows unweighted and squared-weighted chord length distributions (CLD) for the kaolin suspension at 4 wt%, using seawater at polyacrylamide doses of 13, 34, and 89 g/t and industrial water at 89 g/t. The chosen mixing time is 55 s, just before applying an increase in shear rate.

^{−1}, while with 89 g/t the peak occurs at 200 µm with a frequency of just over 160 s

^{−1}. The unweighted distribution is illustrative of the particle growth process when the flocculant dose increases. At any of the flocculant doses tested, the distribution is markedly bimodal. At 13 g/t of flocculant, the distribution shows similar size frequencies of fine and coarse particles, centered, respectively, at 4 and 40 µm. The flocculant captures only a few fines at this low dosage to form larger aggregates. At the highest rate of 34 g/t, the flocculant can capture many fines (about 4 µm) to form aggregates of just over 100 µm. Then, the frequency of fine particles drops dramatically to just under 300 s

^{−1}. The frequency of coarse agglomerates also decreases to about 300 s

^{−1}. The coarse ones consume fines, and the more they consume, the lower their number. At the highest dose tested of 89 g/t, the effectiveness of the flocculant is very high because it captures practically all the fines, whose frequency decreases to less than 50 s

^{−1}, forming a few agglomerates that reach a peak size of 110 µm although with the lowest frequency, just over 200 s

^{−1}. The coiling effect of the polymer chains at high salt in seawater ceases to be a limiting factor for flocculation when the flocculant dose is high enough.

^{−1}(vs. 250 s

^{−1}in seawater) with a peak size of 115 µm (vs. 110 µm in seawater). This result reveals that the polymer coiling effect in industrial water is less than in seawater. This effect on flocculation may be more dominant than the salt bridges that are more frequent in seawater.

#### 3.2. Settling Rate

#### 3.3. Fractal Dimension

#### 3.4. Resistance of Aggregates

^{−1}), U is the difference between the maximum aggregate rupture at an infinite shear rate (ΔG → ∞) and the rupture degree at the base agitation of 273 s

^{−1}(ΔG = 0), and B is the constant of flocs rupture due to the increase in agitation, whose inverse is considered a characteristic shear rate for the disintegration that should be useful as an indicator of the resistance of aggregates.

^{−1}. The resistance increases steadily up to 90 s of mixing, reaching a maximum value of $R$ = 424 s

^{−1}. After this maximum, a longer mixing time leads to a decrease in aggregate strength, $R$ = 400 s

^{−1}. The smaller structures that are obtained with extended mixing are less prone to breakage and in the case studied here, they dominate the behavior above 100 s of flocculation, a condition in which the aggregates present stable size and structure.

^{−1}is obtained, which increases monotonically with the dose until it reaches a value slightly higher than $R$ = 400 s

^{−1}with 55 g/t of flocculant, and tends to settle after $R$ = 445 s

^{−1}with 89 g/t of flocculant. The flocculant dose is a critical aspect in the formation of the aggregates since it determines the number of polymer molecules available in the suspension to join the particles. Therefore, for a fixed surface area, an increase in polymer molecules is expected to generate a greater number of particle–flocculant bonds or a more intricate particle network. This explains the increasing aggregate strength in Figure 9 with flocculant dosages increasing from 8 to 55 g/t. At higher doses, 89 g/t, the resistance does not change significantly despite having a greater number of polymer molecules. In this case, it should be considered that the large aggregates are more prone to breakdown, which limits the value of the resistance.

^{−1}in industrial water and only $R$ = 276 s

^{−1}in seawater. At 89 g/t of flocculant, the resistance is $R$ = 552 s

^{−1}in industrial water and only $R$ = 446 s

^{−1}in seawater. Furthermore, the increase of flocculant dose in the same type of water leads to a greater resistance of the aggregates in industrial water than in seawater. When the dose increases from 21 to 89 g/t in industrial water, the resistance increases in 202 s

^{−1}, while in seawater, it increases only in 170 s

^{−1}. These results of the effect of salinity on the strength of kaolin aggregates were anticipated by Jeldres et al. recently [25]. The resistance of kaolin aggregates in freshwater without salt reaches a characteristic shear of $R$ = 530 s

^{−1}, while in saltwater 0.1 M NaCl, the resistance reaches a modest $R$ = 320 s

^{−1}. These authors observed that an increase in salinity generates aggregates that are more prone to fragmentation due to several factors. For example, changes in the aggregation modes of the primary particles, coiling of the flocculant chains due to a reduced repulsion between anionic functional groups, and changes in the particle–flocculant interactions due to a prevalence of the train configuration in the adsorption mode of the flocculant.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Evolution of the average size of aggregates of kaolin particles (chord length) before and after the addition of flocculant in different doses in seawater (SW) and industrial water (IW).

**Figure 3.**Unweighted (

**a**) and squared-weighted (

**b**) size distribution of kaolin suspensions with different doses of flocculant in SW and IW after three minutes of flocculation at 200 rpm immediately before increasing shear rate.

**Figure 4.**Sedimentation rate of kaolin suspensions with different doses of flocculant in SW and IW at a shear rate of 200 rpm.

**Figure 5.**Fractal dimension of kaolin suspensions with different doses of flocculant in SW and IW at a shear rate of 200 rpm.

**Figure 6.**Evolution of the average size of aggregates of kaolin in suspensions with different doses of flocculant in SW and IW at a shear rate of 200 rpm (black dots) and after several increments of shear rate (color dots). The curves with increased shear show three stages, pre-flocculation (primary particles remain free), flocculation (particle size first increases sharply by aggregation and then decreases smoothly with time), and disaggregation (particle size decreases abruptly as shear is increased). (

**a**–

**c**) correspond to 13, 34, and 89 g/t of flocculant in seawater, respectively, while (

**d**) corresponds to 89 g/t of flocculant in industrial water.

**Figure 7.**Percentage of maximum rupture (at an infinite time) of aggregates of kaolin in solutions with different doses of flocculant in SW and IW for each increase in agitation from the base of G = 273 s

^{−1}(200 rpm).

**Figure 8.**Effect of flocculation time on the resistance of kaolin aggregates (R) flocculated in SW with 89 g/t of flocculant.

**Figure 9.**Effect of the flocculant dose on the resistance of kaolin aggregates (R) flocculated in SW after 60 s flocculation time.

**Figure 10.**Effect of water type on the resistance of kaolin aggregates (R) flocculated at two doses of flocculant after 60 s flocculation time.

Ion | Concentration (g/L) | Method |
---|---|---|

${\mathrm{Na}}^{+}$ | 10.9 | Atomic absorption spectrometry |

${\mathrm{Mg}}^{2+}$ | 1.38 | Atomic absorption spectrometry |

${\mathrm{Ca}}^{2+}$ | 0.4 | Atomic absorption spectrometry |

${\mathrm{K}}^{+}$ | 0.39 | Atomic absorption spectrometry |

${\mathrm{Cl}}^{-}$ | 19.6 | Argentometric method |

${\mathrm{HCO}}^{3-}$ | 0.15 | Acid–base volumetry |

Parameter | Value | Unit of Measurement |
---|---|---|

${\mu}_{sus}$ | 0.004 | kg/(m·s) |

${N}_{p}$ | 0.6 | |

$D$ | 0.08 | m |

$W$ | 0.04 | |

${\rho}_{s}$ | 2600 | kg/${\mathrm{m}}^{3}$ |

${\rho}_{w}$ | 1000 | kg/${\mathrm{m}}^{3}$ |

$V$ | 0.25 | L |

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## Share and Cite

**MDPI and ACS Style**

Pérez, K.; Toro, N.; Jeldres, M.; Gálvez, E.; Robles, P.; Alvarado, O.; Toledo, P.G.; Jeldres, R.I.
Estimating the Shear Resistance of Flocculated Kaolin Aggregates: Effect of Flocculation Time, Flocculant Dose, and Water Quality. *Polymers* **2022**, *14*, 1381.
https://doi.org/10.3390/polym14071381

**AMA Style**

Pérez K, Toro N, Jeldres M, Gálvez E, Robles P, Alvarado O, Toledo PG, Jeldres RI.
Estimating the Shear Resistance of Flocculated Kaolin Aggregates: Effect of Flocculation Time, Flocculant Dose, and Water Quality. *Polymers*. 2022; 14(7):1381.
https://doi.org/10.3390/polym14071381

**Chicago/Turabian Style**

Pérez, Kevin, Norman Toro, Matías Jeldres, Edelmira Gálvez, Pedro Robles, Omar Alvarado, Pedro G. Toledo, and Ricardo I. Jeldres.
2022. "Estimating the Shear Resistance of Flocculated Kaolin Aggregates: Effect of Flocculation Time, Flocculant Dose, and Water Quality" *Polymers* 14, no. 7: 1381.
https://doi.org/10.3390/polym14071381