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Concentration dependence of yield stress and dynamic moduli of kaolinite suspensions Yuan Lin, Nhan Phan-Thien, Jason Boon Ping Lee, and Boo Cheong Khoo Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.5b00536 • Publication Date (Web): 12 Apr 2015 Downloaded from http://pubs.acs.org on April 15, 2015
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Concentration dependence of yield stress and dynamic moduli of kaolinite suspensions Yuan Lin,†,‡ Nhan Phan-Thien,∗,†,‡ Jason Boon Ping Lee,† and Boo Cheong Khoo†,‡ Department of Mechanical Engineering, National University of Singapore, Singapore 117576, and NUS-Keppel Corporate Laboratory, National University of Singapore, Singapore 117576 E-mail:
[email protected] Abstract The concentration dependence of yield stress and dynamic moduli of kaolinite suspensions is studied. Complex electrostatic interactions between kaolinite platelets promote a more liquid-like behavior, with clay particles changing from attractive interactions to a face-face repulsive interaction as the mass fraction of clay particles increases. A yield stress model is developed based on the repulsive interaction between diskshaped particles, which yields a good prediction of experimental observations when repulsive face-face interaction is dominant. The critical concentration when attractive interaction changes completely to face-face repulsive interaction is estimated from the theory. Four regions are identified in the variation of yield stress as a function of the concentration. ∗
To whom correspondence should be addressed National University of Singapore ‡ National University of Singapore †
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Introduction Understanding the rheology of suspensions of clay minerals is important in deep-sea seabed harvesting of polymetallic nodules, as well as in transportation and discharging of mining tailings. 1,2 The rheology of clay slurries is related to the strength and property of inter-particle forces between particles, which include DLVO and non-DLVO forces. The DLVO forces are the van der Waals and electrostatic double layer forces; the non-DLVO forces are induced by absorbed additives including bridging, steric, charged patch and hydrophobic ones. The rheology of aqueous clay suspension has been studied by many researchers. 3–10 The most important rheological parameter that reflects the existence of a network and inter-particle forces in clay suspension is arguably the yield stress, τy . Laxton and Berg 4 investigated the relationship between τy and the zeta potential ζ for a laptonite suspension and a suspension of kaolinite and bentonite mixture. They found that the behavior of these suspensions can be described by the DLVO theory with the assumption that electrostatic interaction is attractive. Teh et al. 3 studied the yield stress behavior of kaolinite suspensions with various pH values (thus ζ), at different concentrations of citric acid, by which they attempted to relate τy to the electrostatic inter-particle forces. Small amplitude oscillatory shear (SAOS) tests have also been carried out to study the behavior of clay suspensions. SAOS experiment is a useful method that allows probing the structure of the materials without damaging it. Michot et al. 8 and Paineau et al. 9 used this method to investigate the degree of gelation of nontronite and smectite suspensions, respectively. They pointed out that a typical gel-like feature is that G′ is much larger than G′′ and both G′ and G′′ exhibit a limited frequency dependence. In a study on laponite suspensions, Cocard et al. 6 showed that at the gel point, G′ and G′′ have about the same power-law frequency dependence, with a power-law exponent ∆ = 0.55. Kaolinite is a hydrated aluminum silicate with composition Al2 O3 · 2SiO2 · 2H2 O. Kaolinite particles are thin, roughly hexagonal platelets. It is commonly understood that the surfaces of the kaolinite particle carry permanent negative charges due to substitution of 2 ACS Paragon Plus Environment
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Figure 1: Schematic illustration of the edge-face and face-face structure in kaolinite suspensions. Al3+ for Si4+ in the silica face and M g 2+ for Al3+ in the alumina face. The charges carried at the edges are positive in an acidic medium and negative in an alkaline medium. Depending on the balance between electrostatic interactions and van der Waals forces, the kaolinite platelets may form edge-edge (E-E), edge-face (E-F) and face-face (F-F) structures, which would result in different gelating behaviors and consequent settling processes. The E-F and F-F structures are schematically shown in Fig. 1. In recent years, it has been found by atomic force microscopy (AFM) surface force measurement that the charges carried by alumina and silica faces in the kaolinite platelet also depend on the pH of the suspension. 11–13 The silica face is negatively charged at pH > 4, while the alumina face is positively charged at low pH and negatively charged at high pH. The charge at the kaolinite edge surface is found to be negative at pH = 4 ∼ 9 14 in contrast to the previous studies. As a result, a different F-F (silica face-alumina face) attractive interaction at low pH is proposed, which promotes E-F attractive interactions (edge-silica face and edge-alumina face) and induces the card-house structure. 14 To date, most studies on kaolinite suspensions focus on low mass fractions, where attractive interactions prevail in acidic condition. These interactions are reduced when the pH is adjusted to values larger than 7, resulting in negligible yield stress values. 3,15,16 With increasing pH values, the settling behavior also changes significantly, from settling as a gel to settling individually as flocs. 17–20 In this paper, we study the concentration dependent behavior of gelation of kaolinite suspension, in particular its yield stress and dynamic moduli. The evolution of electrostatic 3 ACS Paragon Plus Environment
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interactions between kaolinite particles with the mass fraction is investigated.
Experimental
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Figure 2: (a) Particle size distribution and (b) SEM images of Kaolinite clay used in the experiment. The distance between two nearest dots in (b) is 5µm. A commercial kaolinite clay (Kaolin (Malaysia) Sdn. Bhd) was used in our experiment. The moisture content of the clay sample is below 1.5%. The clay particle size distribution as measured by a Mastersizer (Malvern, wet method) is shown in Fig. 2(a). The morphology of the particles was investigate by a Hitachi S4300 scanning electron microscope (SEM) as 4 ACS Paragon Plus Environment
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shown in Fig. 2(b). Note that because clay particles form flocs, the particle distribution may reflect only the flocs size rather than the individual platelets size. Kaolinite suspensions were made by mixing clay samples with deionized water using a magnetic stirrer for 30 mins. Suspensions were then sealed and kept at rest for 24 hrs before they were re-homogenized and tested. The natural pH of the suspension varies with the concentration of clay from 4.95 to 5.3 with changing mass fraction. Samples were adjusted to a desired pH using an appropriate amount of 1M NaOH solution. The ionic strength of the suspension was adjusted by dissolution of an appropriate amount of NaCl. A controlled-stress HAAKE MARS III rotational rheometer from Thermo Scientific was used for rheological measurements, with a 35mm diameter cone-plate geometry. Each sample loaded was tested only once to minimize errors caused by water evaporation from the suspension. In small amplitude oscillatory shear (SAOS) tests, the stress was kept well bellow the yield stress of the suspension, therefore, the response is linear viscoelastic. For the rheological tests on the sediment bed, clay suspensions were allowed to settle for two days to ensure complete settling. The samples were then taken from the top part of the sediment bed (around 5mm below the interface of the sediment bed and the supernatant) using a pipette. A pre-shearing with shear rate of 102 s−1 and a shearing time of 30s (shear strain 3 × 103 ) was applied before measurements were taken. The experimental temperature was kept at 25◦ C. The settling tests of kaolinite suspension were carried out in 50ml measuring cylinders with diameter of 21.52mm. The initial height of the suspension column is 77mm. The procedure is similar to the one used by Nasser and James. 17 The time evolution of the position of the interface between the settling gel and the supernatant clear water was recorded until the equilibrium position was reached.
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Results and discussion The kaolinite suspension is a non-Newtonian fluid with a yield stress behavior. As shown in Fig. 3, the shear rate increases rapidly when the applied stress exceeds a certain critical stress, below which the deformation is negligibly small and the data scattering in this range mainly reflect the solid gel-like behavior. The yield stress, τy , is defined as the critical stress where the shear rate starts increasing significantly with shear stress. From our data, the yield stress τy increases with increasing concentration. Due to electrostatic interactions between clay particles, the clay suspension forms a gel which resists to flow. For suspensions below 5wt% in our experiment, no yield stress can be measured, indicating that there is a critical concentration below which gelation cannot occur. Although some degree of gelation is observed at 5wt%, τy cannot be measured reliably because the settling of the gel is fast (this will be discussed later). The microstructure formed by kaolinite platelets in the gel with changing concentration is of great interest here. In SAOS tests for suspensions with concentration of 10wt%, it is observed that the storage modulus, G′ , is much larger than the loss modulus, G′′ and at low frequency range, both G′ and G′′ are roughly independent of the frequency as shown in Fig. 4(a). This is a typical gel behavior. 8 With increasing concentration, however, at low frequency, G′ and G′′ becomes more dependent on the frequency and G′′ approaches G′ (for the 28.5wt%). The phase angle, δ, defined as tanδ = G′′ /G′ increases accordingly as shown in Fig. 4(b). These indicate that the suspension becomes more viscous with increasing concentration of kaolinite particles. We may therefore suspect that the gel structure in suspensions at high concentrations may be different from those at low concentrations: gels formed by kaolinite particles are more solid-like at low concentrations while become more liquid-like with increasing concentrations. For kaolinite suspensions at low concentration, gelation caused by the attractive interactions between particles is often considered to be dominant at low pH. In order to analyze gelation mechanisms for clay suspensions at different concentrations, the pH of the suspen6 ACS Paragon Plus Environment
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Figure 3: (a) Shear rate versus shear stress curves, (b) yield stress as a function of mass fraction for kaolinite suspensions at various concentrations and at natural pH value (pH ≈ 5). The error bars indicate the data scattering from different runs; the red solid line shows the theoretical prediction (Eq. 7).
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Figure 4: (a) Dynamic moduli and (b) phase angle as a function of frequency for kaolinite suspensions at different concentrations and with natural pH value (pH ≈ 5).
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sions are altered from around 5 to 8 using NaOH solution. With pH = 8, the edges and faces of the kaolinite particles are both carrying a negative charge, resulting in a repulsive force between edge and face, and the gelation by a card-house structure due to the attractive interaction in an acidic suspension can no longer exist. For a 10wt% suspension at pH = 7.09, it is found that the yield stress is still comparable to that at pH = 5.27 as shown in Fig. 5(a). However, at pH = 8.01, no yield stress can be measured (τy = 0). No gelation behavior is observed until a higher concentration is achieved during settling. As a result, we can infer that the gelation of 10wt% suspension at pH ≈ 5 is caused by the electrostatic attractive interactions between particles. For 20wt% suspension, it can be seen in Fig. 5(b) that there is a very slight decrease in τy at pH = 7.97 compared to the one at pH = 5.01. Since the yield stress in the 20wt% suspension is quite insensitive to pH values, it may be concluded that at pH ≈ 5, the yield behavior at such concentration is not caused by the electrostatic attractive interactions in contrast to when the concentration is 10wt%. In SAOS tests, shown in Fig. 6, we found that G′ and G′′ decrease notably compared to τy when pH is adjusted from 5.01 to 8. However, as shown in the inset of Fig.6, the phase angle is nearly independent of the pH. The transition from the card-house structure to the more compact F-F structure in a gel has been observed in the settling process of kaolinite suspensions. 17,19 The F-F structure, which is the main structure in the sediment bed, is formed by the collapse of the card-house structure under its own weight during settling. The settling experiment as well as the SAOS experiment on the sediment bed (from settling of the homogenous suspension) have also been carried out at pH ≈ 5. From Fig. 7(a) and for the sediment bed from a 10wt% suspension in which the card-house structure prevails as discussed previously, both G′ and G′′ increase compared to the initial suspension shown in Fig. 4(a). The difference between G′ and G′′ becomes smaller compared to the one in the homogenous suspension. These changes may be due to the transition from the card-house structure to the F-F structure. Since a similar behavior has been found with increasing mass fraction of the suspension as shown in Fig.
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Figure 5: Changes of the shear rate versus shear stress curves with the shift of pH for suspensions with the mass fraction of (a) 10wt% and (b) 20wt%.
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Figure 6: Dynamic moduli as a function of frequency for suspensions with different pH and with mass fraction of 20wt%. The inset shows the phase angle as a function of frequency. 4(a), we consider that the increase in G′′ towards G′ with increasing concentration is an indication of the transition from the card-house structure to the F-F structure. At higher concentrations where F-F interaction is considered to dominate, no significant change of G′ and G′′ can be observed after settling. In Fig. 7(b), the settling becomes much slower in the suspension of 10wt% compared to 5wt% because of the high fraction of F-F structures in the 10wt% suspension. Similar to the transition during settling, we consider that the transition to the F-F structure with increasing concentration is caused by the packing effect at high volume fraction of particles. In gels formed by F-F interactions, the nature of the interactions can be either attractive or repulsive. By increasing the concentration of electrolyte, Nasser and James 17 found that the previously dispersed low-concentration kaolinite suspensions at pH ≥ 7 form gels again. Since at high electrolyte concentrations, the electrical double layer is compressed and the electrostatic repulsive interaction is reduced, they proposed that gelation is formed by particle attractions caused by van der Waals and other attractive colloidal forces. Paineau 11 ACS Paragon Plus Environment
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Figure 7: (a) Dynamic moduli as a function of frequency for sediment bed after settling of kaolinite suspensions; (b) the height of the interface of the sediment bed and supernate as a function of time for kaolinite suspensions. The pH of the suspension is unmodified (pH ≈ 5).
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et al. 9 found that the interaction between smectite particles is repulsive, with G′ decreasing with increasing electrolyte concentration. Sakairi et al. 21 developed a simple yield stress model taking into account the face-face repulsive interaction. Gupta et al. 11,12 pointed out that the electrostatic attractive interactions between the silica and alumina faces of two particles at pH < 6 may induce a pH-dependent F-F attractive structure. However, this is not supported by our data in which we found that the yield behavior of the kaolin suspension at high concentration is insensitive to the change of pH, as shown in Fig.5(b). In Fig.4(b), the phase angle increases with increasing concentration, which indicates that the gel becomes weaker (more liquid-like) at high concentrations. This may also indicate that at high concentrations, the strong electrostatic attractive interactions are replaced by F-F interactions which are relatively weak for gelation. As shown in Fig. 8(a), τy decreases when the concentration of N aCl is increased in our kaolinite suspension at high mass fraction. As increasing the ionic strength suppresses the repulsive electrostatic interaction, we infer that the F-F interaction of the kaolinite suspension at low ionic strength, which controls the gelation, is a repulsive electrostatic interaction. For the dynamic moduli, as shown in Fig.8(b), we observe that at low frequency, with increasing ionic strength, G′ decreases, and the phase angle increases. At a high mass fraction where the repulsive F-F interaction dominates in the suspension, the increase of the phase angle may be a direct indication of the reduction of the repulsive F-F interaction. In Fig.6, we find that the phase angle is nearly independent of pH. Considering that τy is insensitive to pH, we may also deduce that τy is mainly controlled by the F-F repulsive interaction. However, the dynamic moduli decrease notably with pH compared to τy , which may be caused by other pH dependent electrostatic interactions (such as edge-edge interactions). A yield stress model which connects τy to ζ as well as the volume fraction ϕ of clay particles has been proposed. 3,4 The bulk yield stress, τy , is proportional to the interparticle
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Figure 8: (a) Shear rate versus shear stress curves and (b) Dynamic moduli as a function of frequency for 20wt% kaolinite suspensions with various ionic strength. The inset shows the phase angle as a function of frequency. Curves of 0M indicates the rheological behavior of the kaolinite suspensions with natural ionic strength. The pH of the suspension is unmodified (pH ≈ 5).
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force times the number of particle contacts per unit area, which scales as ϕ2 /a2 , 22
τy ∼
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1 ]. 1 − exp(−κD)
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δ , αD + δ
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we propose that We dominates everywhere except when D is of O(1)nm where the particles should fall into an infinitely deep van der Waals primary minimum (attractive “well”). 22 Therefore, WvdW is considered to be negligible at large D. The F-F structure collapses when the stress applied overcomes the repulsive potential We (D) between particles. Combining Eqs. 1, 2, 4 and 5, we obtain the yield stress for an aqueous clay suspension, −2
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ϕ2 [ρc−1 + (1 − ρ)] = τ , 0 exp[κδα−1 (ϕ−1 − 1)] − 1 exp[κδα−1 ρ(c−1 − 1)] − 1
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where c is the mass fraction of clays in suspension and τ0 = 2πε0 εψs2 /aκ−1 is a constant stress coefficient, or equivalently, −2
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[ρc−1 + (1 − ρ)] , exp[Bρ(c−1 − 1)] − 1
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where A is a constant, which acts as a scaling factor since the bulk yield stress is proportional to the inter-particle force times the number of particle contacts per unit area (cf., Eq.1). A is also a correction factor because the kaolin platelets are regarded as spheres with an effective radius a, and the electrostatic potential, ψs is approximated by the zeta potential as adopted in Eq. 4. B = δ/ακ−1 , and ρ ≈ 2.6g/cm3 is the density of the clay particles. Aτ0 and B are considered as parameters to be determined experimentally. Fig. 3(b) shows the fitting of Eq. 7 to the experimental results, in which Aτ0 = 88.4P a and B = 0.11. The fitting is quite good for 0.2 < c < 0.4, while it deviates slightly from experimental values when c ≤ 0.2. Eq. 7 is only available at the concentration range where the gelation is caused mostly by the F-F repulsive interactions. As discussed previously, at c = 0.1, pH ≈ 5, the gel is mainly induced by the card-house structure, τy is expected to have a different origin from those assumed in deriving Eq. 7. Eq. 7 predicts a τy of the order of 10−2 P a at c = 0.1, which is also different from our experimental results shown in Fig. 5(a) (at pH = 8, gelation cannot occur and τy = 0). This may be explained by the fact that at c = 0.1 and pH = 8, the gel cannot be stabilized by the repulsive F-F interaction and thus cannot be described by the theory 16 ACS Paragon Plus Environment
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developed here. With c ≥ 0.4, the measured yield stress is much larger than the theoretical prediction based on the F-F repulsive interactions alone. It is proposed that with decreasing D(ϕ) at high ϕ, the gel structure controlled by the F-F repulsive interactions is no longer stable since the F-F attractive interactions caused by van der Waals potential, WvdW , may play a role. The gel structure at c ≥ 0.4 will need further investigations. The critical volume fraction, ϕc (or critical mass fraction cc ), at which the transition of gelation from attractive interactions to completely F-F repulsive interactions takes place, can be estimated. It is proposed that the transition occurs when repulsive interactions are inevitable for a clay platelet in the system. That is, the separation between the platelets is of the same order of the Debye length, D(ϕc ) ≈ κ−1 . From the parameter B, we obtain δ/ακ−1 = 0.11 and combing with Eq. 5, we have ϕc ≈ 0.1 (cc ≈ 0.22). It is also noted that at c < 0.22, when c approaches 0.22, the repulsive interaction could also dominate and control the rheological behavior (e.g., c = 0.2 as shown in Fig. 5(b) and Fig. 8). We find that the microstructure (thus the yield stress) of the kaolinite suspension as a function of concentration can be divided into four regions as shown in Fig. 3(b): (I) in very dilute suspension (c < 0.05), no gelation occurs and thus there is no yield stress; (II) approximately with c ≥ 0.05, a gelation caused by electrostatic attractive interactions and the card-house structure resulting in a yield stress. In this region, the fraction of FF repulsive interactions increases continuously with increasing c; (III) when c ≥ 0.22, the gelation caused by attractive interactions changes completely to a gelation stabilized by repulsive F-F interactions. In this region, τy can be estimated by Eq. 7; and (IV) with c ≥ 0.4, τy is considerably larger than estimated by Eq. 7. It may be that the repulsive gel becomes unstable because of the rising attractive van der Waals forces, leading to a different gel structure.
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Conclusion The concentration dependence of yield stress, and dynamic moduli (G′ and G′′ ) of aqueous kaolinite suspensions has been studied. With increasing mass fraction of kaolinite particles, gelation by attractive interactions at low mass fractions changes to gelation by face-face interactions. The gelation by face-face interactions is stabilized by repulsive electrostatic force between the faces of the disk-shaped particles. From a DLVO theory that is based on attractive interparticle forces, a modified model based on repulsive electrostatic force between platelet faces has been developed. The model was found to predict well the yield stress as a function of the mass fraction at the concentration range where the face-face repulsive interactions are dominant. The critical concentration where a complete transition from the attractive interactions to the face-face repulsive interaction take place can be estimated. Four regions are identified in the variation of yield stress as a function of the concentration.
Acknowledgement The authors thank the National Research Foundation, Keppel Corporation and National University of Singapore for supporting this work done in the Keppel-NUS Corporate Laboratory. The conclusions put forward reflect the views of the authors alone, and not necessarily those of the institutions within the Corporate Laboratory.
Supporting Information Available This material is available free of charge via the Internet at http://pubs.acs.org/.
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Table of Contents Graphic, Concentration dependence of yield stress and dynamic moduli of kaolinite suspensions, Yuan Lin, Nhan Phan-Thien, Jason Boon Ping Lee, and Boo Cheong Khoo
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