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Influence of particle size distribution on rheology and particle packing of silica-based suspensions
Powder Technology 139 (2004) 69 – 75 www.elsevier.com/locate/powtec
Influence of particle size distribution on rheology and particle packing of silica-based suspensions S.M. Olhero, J.M.F. Ferreira* Department of Ceramics and Glass Engineering, CICECO, University of Aveiro, Aveiro 3810-193, Portugal Received 1 July 2001; received in revised form 13 August 2003; accepted 20 October 2003
Abstract The effect of particle size, particle size distribution and milling time on the rheological behaviour and particle packing of silica suspensions was investigated using slurries containing total solids loading of 46 vol.%. Three silica powders with different average particle sizes (2.2, 6.5 and 19 Am), derived from dry milling of sand, and a colloidal fumed silica powder with 0.07 Am were used. Different proportions of colloidal fumed silica powder were added to each of the coarser silica powders and the mixtures were ball-milled for different time periods. The influence of these factors and of the particle size ratio on the rheological behaviour of the suspensions and densities of green slip cast bodies was studied. The results show that the flow properties of slips are strongly influenced by the particle size distribution. The viscosity of suspensions increases with the addition of fine particles, imposing some practical limitations in terms of volume fraction of fines that can be added. On the other hand, increasing the size ratio enhanced the shear thinning character of the suspensions, while decreasing the size ratio led to an accentuation of the shear thickening behaviour. For all mixed suspensions, green densities increased with increasing milling time, due to size reduction of silica powders and a more efficient deagglomeration of fumed silica. Increasing amounts of fumed silica led to a first increase of particle packing up to a maximum, followed by a decreasing trend for further additions. Good relationships could be observed between rheological results and packing densities. D 2003 Elsevier B.V. All rights reserved. Keywords: Rheology; Particle size distribution; Particle packing; Green density
1. Introduction The homogeneity of particle packing in the green bodies of a ceramic compact is a key factor for the improvement of the sintering behaviour and the final properties of the material. This target is better achieved when colloidal shaping techniques are used to consolidate the bodies [1,2]. Colloidal methods enable the modification and control interaction forces between particles, to destroy or eliminate particle agglomerates, and to achieve an intimate mixing of two or more different powders to produce uniform and reliable ceramic bodies. The rheology and processing ability of the suspensions and the particle packing also depend on other relevant factors such as particle size and particle size distribution [3 – 6]. It is generally believed that the presence of coarse particles in the suspensions confer a shear-thick-
* Corresponding author. E-mail address: [email protected] (J.M.F. Ferreira). 0032-5910/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2003.10.004
ening behaviour, while the compaction efficiency increases with extended particle size distributions [7,8]. However, this concept cannot be generalised for all the systems. In fact, bimodal particle size distributions can enable significant decreases in viscosity for a given solids loading, or improvements of the solids volume fraction while maintaining a given viscosity level [9 – 11]. This is the reason why industrial dispersions, e.g., inks and paints are not monodisperse, but result from mixtures of different particle sizes. Other benefits of using mixtures of different sized particles might be related to the control of shrinkage, density and homogeneity of the microstructure of green and sintered bodies [12,13]. The surface chemistry of the particles is another relevant factor in colloidal processing. Previous theoretical and experimental works have demonstrated the influence of the interparticle forces on suspensions’ viscosity and packing ability of the particles during slip casting [10,14 – 16]. Recently, Zaman and Moudgil [17] used binary mixtures of silica powders to show the effect of the magnitude of
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electrostatic repulsive forces on viscosity. They concluded that long-range repulsive forces impart to the suspensions higher viscosity values compared with short-range interactions. Other authors [14,18] drew similar conclusions concerning monomodal or bimodal systems. These findings point out the mutual interferences among different factors, such as particle size and particle size distribution, solids loading and the type and amount of dispersant used to stabilise the suspensions. Since it is important to discriminate the role of each experimental variable in a given process, constant solids loading and a complete absence of dispersant were used in the present work. The aim is to understand the relationships between, particle size distribution and size ratio, and the rheological behaviour of the suspension as well as their packing ability either in suspension or in green bodies consolidated by slip casting. Basically, bimodal suspensions containing mixtures of a sand powder (coarse, intermediate sized, or fine) + fumed silica, in several proportions, were prepared by different times of ball milling. The effects of the proportions of fumed silica, milling time and size ratio on rheological behaviour and green densities were studied at their natural pH.
2. Experimental procedure 2.1. Materials and slip preparation and characterisation Three commercial silica powders, P10 (coarse), P500 (intermediate sized) and P600 (fine) with mean particle sizes of 19, 6.5 and 2.2 Am, respectively, were prepared by dry ball-milling and supplied by Sibelco Portuguesa. A fumed silica powder (Aldrich Chemical), hereafter designated by FS, with a mean size of 0.07 Am (after 10 min in an ultrasonic bath), was also used as a raw material. Particle size analyses of these powders were performed using a laser diffraction instrument (Coulter LS 230, UK). The zeta potential of the FS particles was analysed by using a Doppler Electrophoretic Light Scattering Analyser (Coulter DELSA 440, UK). Experimentally, the suspensions were prepared by first adding the FS particles in to water under ultrasonic and mechanical stirring. Then, the other powders (coarse, intermediate or fine) were progressively added and kept under stirring for further 30 min. The suspensions were transferred to polyethylene ball mill containing silicon nitride balls as grinding media (diameter = 15 mm). Deagglomeration/milling was performed for 10 and 20 h of milling to test the rheological behaviour of suspensions and particle size distributions. These characteristics were compared with those of non-deagglomerated suspensions. Rheological measurements were carried out with a rotational controlled stress rheometer (Carri-med 500 CSL, UK). The measuring configuration adopted was a concentric coaxial cylinder and flow measurements were performed in the shear rates range from about 0.1 to 550 s 1. Before
starting a measurement, pre-shearing was performed at high shear rate for 1 min followed by a rest of 90 s in order to transmit the same rheological history to whole suspension being tested. 2.2. Preparation and characterisation of green bodies Slip casting experiments were carried out in order to gather complementary information on packing ability of the different suspensions. Three samples (F = 28 mm and thickness = 0.5 mm) were consolidated by unidirectional slip casting from each suspension after different milling times (0, 10 and 20 h). After demoulding, the bodies were placed into an oven at 120 jC for 24 h for complete drying and the green densities were measured by the mercury immersion method using the Archimedes principle.
3. Results and discussion The coarser silica powders tended to sediment during zeta potential measurements. Measurements could be performed on a fine fraction of P600, fractionated by sedimentation, which behaved likewise to FS. Because of that, only the results of FS are presented in Fig. 1. It can be seen that the isoelectric point (pHiep) is located between pH 2– 3, in good agreement with other reported values for this oxide [19,20]. Furthermore, at the natural pH of the suspensions, pH 5.5– 6, the zeta potential reaches a negative value of about 25 mV, which is high enough to electrostatically stabilise the systems [21]. The effects of milling time and the amount of FS added to the coarse, intermediate and fine silica sand powders on the flow curves are displayed in Figs. 2 – 4. The results show that the slips containing the coarse sand powder exhibit a shear thinning behaviour, which is enhanced with increasing amounts of fumed silica in the mixture and decreases with increasing milling time (Fig. 2). On the other hand, Fig. 4 shows that the suspensions containing the fine sand powder exhibit a shear thickening behaviour, which becomes more
Fig. 1. Zeta potential versus pH for FS particles dispersed in a 10 3 M KCl solution.
S.M. Olhero, J.M.F. Ferreira / Powder Technology 139 (2004) 69–75
Fig. 2. Flow curves (up branches) for the suspensions of the coarser sand powder (P10) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
accentuated with increasing amounts of FS added and less pronounced with increasing milling time. The slips containing the intermediate sized sand powder, P500, present different behaviours depending on the amount of FS present (Fig. 3). At 5% FS a slightly thickening behaviour is observed, which gradually changes towards a shear thinning behaviour with increasing amounts of FS up to 15%. These results are somewhat surprising, since it is usually accepted that the presence of coarse particles in a suspension tends to impart a shear thickening effect, especially for high solid volume fractions [22,23]. On the other hand, it is believed that the presence of increasing amounts of very fine particles would enhance the shear thinning characteristics of the slips. However, Fig. 4 shows an opposite trend. The rheological model that better describes the results presented in Figs. 2– 4 is the Herschel –Buckley: r ¼ r0 þ Kp c˙n
ð1Þ
where, r is the shear stress, r0 is the yield stress, Kp is the plastic viscosity coefficient, c˙ is the shear rate and n is the shear rate index. Figs. 5 and 6 display the shear rate index,
Fig. 3. Flow curves (up branches) for the suspensions of the intermediate sand powder (P500) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
71
Fig. 4. Flow curves (up branches) for the suspensions of the finer sand powder (P600) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
n, as a function of milling time (for 10 wt.% FS), or as a function of the added amount of FS (for 10 h milling time), respectively. It can be seen that n < 1 for suspensions containing P10 and slightly increases with milling time, while n>1 for P600 and decreases with milling time. In the case of P500 n z 1 and its value is practically unchanged with increasing milling time. For a fixed milling time, n>1 for P600 and increases with the amount of FS, while an opposite situation is observed in the case of P10. For suspensions with P500 the shear rate index decreases with increasing the amount of FS passing from shear thickening to pseudoplastic behaviour. These results are in close agreement with those presented in Figs. 2 –4. Using PVC dispersions, Collins et al. [24] found that a broadening of the size distribution of the particles led to a decrease in the shear thickening effect at high shear rates and that this change was more prominent when the size distribution was broadened by the addition of coarse particles. The shear thinning behaviour is often associated with the slurry structure. When the attractive forces between particles prevail, collisions among them will lead to the formation of agglomerates. At low shear rates, liquid is immobilised in void spaces within flocs and the floc network. As the shear rate is increased, the flocs and floc network break down and
Fig. 5. Shear rate index, n, as a function of milling time for a fixed amount (10 wt.%) of FS.
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Fig. 6. Shear rate index, n, as a function of the added amount of FS at a fixed milling time (10 h).
Fig. 8. Particle size distributions (cumulative percent greater than, CPGT) of suspensions of sand powder P500 and FS (5% and 10%) before and after 20 h of ball milling.
the entrapped liquid is released and a more ordered structure in the flow direction is formed. However, such explanation does not give a complete picture of the results observed in the present work. In fact, the formation of agglomerates is more likely to occur in the case of fine and attractive particles. Furthermore, the systems that present the shear thinning characteristics are precisely those containing the coarser particles. Moreover, the shear thickening behaviour appears in the systems composed by the finer sandy particles. From the previous discussion, it seems clear that the concept to explain the rheological behaviours observed cannot be based only on the size of particles. The particle size distributions would play the most relevant role in the present situation, since they directly influence the packing ability of the powders in suspension. This view is in agreement with that reported by Greenwood et al. [22] who showed that a reduction in viscosity was strongly dependent on the particle size ratio. For all the suspensions the viscosity was lower after ball milling than only after stirring. This can be attributed to the deagglomerating effect and to the obtaining of a more favourable particle size distribution. The less resistance offered by the suspensions to flow means that the packing fraction of the systems was improved. The sand P10 has a broader particle size distribution (Figs. 7 and 8) and would
pack better in suspension compared with the sand P600 which presents a narrow particle size distribution (Fig. 9). During milling, it was observed that the particle size distribution of the mixtures containing the coarser sand powder narrows, while those containing the finer one broadens. This seems reasonable, since the coarser particles are more prone to be broken during milling than the finer ones. On the other hand, the milling action will also destroy the agglomerates of FS. The efficiency of this deagglomeration process would depend on the size of interstitial pores among the coarser particles present in the mixture, since larger interstices can accommodate larger FS agglomerates. Therefore, it seems likely that the deagglomeration efficiency of FS would be higher in the case of P600. This, coupled with the expected less efficient milling action expected on its own particles, explains the broadening effect observed. In fact, the comparison of Figs. 7 and 9 reveals that the effects of milling on particle size distribution are mostly observed on the coarse and fine extremities of PSDs for the mixtures containing P10 and P600, respectively. As reported in the experimental procedure, FS was the first powder added to distilled water during suspensions’ preparation. It was observed that a gel-like structure was
Fig. 7. Particle size distributions (cumulative percent greater than, CPGT) of suspensions of sand powder P10 and FS (5% and 10%) before and after 20 h of ball milling.
Fig. 9. Particle size distributions (cumulative percent greater than, CPGT) of suspensions of sand powder P600 and FS (5% and 10%) before and after 20 h of ball milling.
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Table 1 Green densities of slip cast bodies from suspensions of sand powders and FS powder obtained at different milling times FS (%)
5 10 15
P600 (g/cm3)
P500 (g/cm3)
P10 (g/cm3)
0h
10 h
20 h
0h
10 h
20 h
0h
10 h
20 h
0.66 0.67 0.63
0.67 0.68 0.63
0.69 0.70 0.64
0.62 0.63 0.60
0.63 0.64 0.62
0.64 0.65 0.64
0.62 0.62 0.62
0.64 0.63 0.62
0.66 0.63 0.63
The accuracy associated at all measurements is within F 0.005 g/cm3.
Fig. 10. Equilibrium viscosity curves for the suspensions of the finer sand powder (P600) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
obtained, which was accentuated with increasing amounts of FS. The gel-like structure tended to be destroyed with the addition of the coarser sand powders, since introduction of coarse particles will imply the division of the starting gel into small portions. For the mixtures containing 15% FS it was impossible to add the whole amount of FS to the water due to the strong gel features of the suspensions. Further addition of FS was only possible after adding some of the coarser component, which improved the fluidity of the system. The presence of a gel-like structure would enhance the shear thinning character of the system. The portions in which a gel structure was divided would depend on the size of the particles introduced, being larger in the case of P10. This might contribute to the shear thinning behaviour observed with the coarser powder mixtures. In the case of P600, the FS gel should be divided into too small portions for the intrinsic shear thinning character to become appreciable. In
fact, Fig. 10 shows that the shear thinning behaviour is confined to the very low shear rates and is followed by a shear thickening effect for intermediate shear rates and a trend to Newtonian flow behaviour in the highest shear rate region. The shear-thinning behaviour was explained above and is schematically represented in Fig. 11A for small deformations. Higher deformations in a high packed system with a narrow PSD imply particle rearrangements and increasing average distances between layers of particles. Capillary forces oppose to the flow and the suspension thickens (Fig. 11B). With the shear rate further increasing, there could be a gradual alignment of particle layers in the flow direction and the viscosity would decrease, as observed. This interpretation is supported by the recent studies of the rheology of calcium carbonate suspensions in aqueous polysaccharides matrices, reported by Lapasin et al. [25,26]. They have found that under low shear stress conditions, the rheological properties of filled gels are strictly governed by those of the polymeric matrices, and that the addition of particles partially destroys the weak gel structures. Under high shear stress conditions, the hydrodynamic effects due
Fig. 11. Schematic illustration of the causes determining the shear-thinning and shear-thickening behaviours.
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to the presence of particles control the rheological characteristics of the suspensions. The results of the slip casting experiments from slurries with different amounts of FS and milling times are reported in Table 1. It can be seen that the green density increases with increasing milling time for all the mixtures tested. This is in agreement with the rheological results discussed above. When the packing ability of particles increases the viscosity of the slurry decreases. Further, a more favourable PSD would enable higher green densities to be obtained. This also explains why green density increases when the amount of FS increases from 5% to 10% for the mixtures containing P500 and P600. This suggests that FS would occupy the interstitial voids among the coarser particles. A further increase in FS to 15% led to a diminution of green density. Therefore, the proportion between coarse/fine components that lead to maximum packing densities is considerably lower compared with those already reported for other bimodal systems, which usually corresponds to about 70/30 for size ratios according to the Furnas model [27,28]. This can be understood since the FS particles are very small and their apparent size in suspension is expected to increase significantly [29]. In the case of P10, the maximum packing density is observed at 5% FS. This is likely due to a more extensive segregation phenomena of particles (sedimentation and clogging effect) during slip casting due to the larger particle size ratio between the components [30].
4. Conclusions The results presented and discussed in this study showed that for given solids loading, the viscosity (shear stress) of the suspensions increases with increasing amounts of the fine component (FS), as expected. However, in contrast with the common knowledge, the suspensions containing the coarser sand powder exhibit shearthinning behaviour while those containing the finer sand powder show shear thickening. These characteristics are even accentuated with increasing amounts of FS. These results could be explained in terms of a gel-like structure formed by FS particles in aqueous media, which is more extensively destroyed (subdivided) by the introduction of the coarser component particles, and in terms of size ratio. The same factors and particle segregation phenomena determine the green packing density of compacts prepared by slip casting.
Acknowledgements This work is supported by FCT (Portuguese Foundation for Science and Technology) in the frame of the Praxis XXI programme.
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and volume ratio on the viscosity of bimodal suspensions of polymer lattices, J. Colloid Interface Sci. 191 (1997) 11 – 21. I. Wagstaff, C.E. Chaffey, Shear thinning and thickening rheology, J. Colloid Interface Sci. 59 (1977) 53 – 62. E.A. Collins, D.J. Hoffmann, P.L. Soni, Rheology of PVC dispersions—effect of particle size and particle size distribution, J. Colloid Interface Sci. 71 (1) (1979) 21 – 29. A. Zupancic, U. Florjancic, R. Lapasin, M. Zumer, The effect of CaCO3 concentration on the rheological behaviour of filled weak gel systems, in: B. de Lindio, Cuen Srl Napoli (Eds.), Proceedings of the Eurorheo 99-3, Southern European Conference on Rheology, Sangineto, 1999, p. 130. R. Lapasin, A. Zupancic, Eurorheo 99-3; Rheology of calcium carbonate suspensions in welan and rhamsan aqueous matrices,
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in: B. de Lindio, Cuen Srl Napoli (Eds.), Proceedings of the Southern European Conference on Rheology, Sangineto, 1999, p. 143. C.C. Furnas, The Relations Between Specific Volume Voids, and Size Composition in System of Broken Solids of Mixed Size, Report of Investigations no. 2894, Department of Commerce-Bureau of Mines, 1928 (Oct.). D.C.C. Lam, M. Nakagawa, Packing particles (Part 2)—effect of extra pore volume on packing density of mixtures of monosized spheres, J. Ceram. Soc. Japan 101 (1993) 1204 – 1208. K. Higashitani, M. Kongo, S. Hatade, Effect of particle size on coagulation rate of ultrafine colloidal particles, J. Colloid Interface Sci. 142 (1991) 204 – 213. J.M.F. Ferreira, Role of the clogging effect in the slip casting process, J. Eur. Ceram. Soc. 18 (1998) 1161 – 1169.
Influence of particle size distribution on rheology and particle packing of silica-based suspensions S.M. Olhero, J.M.F. Ferreira* Department of Ceramics and Glass Engineering, CICECO, University of Aveiro, Aveiro 3810-193, Portugal Received 1 July 2001; received in revised form 13 August 2003; accepted 20 October 2003
Abstract The effect of particle size, particle size distribution and milling time on the rheological behaviour and particle packing of silica suspensions was investigated using slurries containing total solids loading of 46 vol.%. Three silica powders with different average particle sizes (2.2, 6.5 and 19 Am), derived from dry milling of sand, and a colloidal fumed silica powder with 0.07 Am were used. Different proportions of colloidal fumed silica powder were added to each of the coarser silica powders and the mixtures were ball-milled for different time periods. The influence of these factors and of the particle size ratio on the rheological behaviour of the suspensions and densities of green slip cast bodies was studied. The results show that the flow properties of slips are strongly influenced by the particle size distribution. The viscosity of suspensions increases with the addition of fine particles, imposing some practical limitations in terms of volume fraction of fines that can be added. On the other hand, increasing the size ratio enhanced the shear thinning character of the suspensions, while decreasing the size ratio led to an accentuation of the shear thickening behaviour. For all mixed suspensions, green densities increased with increasing milling time, due to size reduction of silica powders and a more efficient deagglomeration of fumed silica. Increasing amounts of fumed silica led to a first increase of particle packing up to a maximum, followed by a decreasing trend for further additions. Good relationships could be observed between rheological results and packing densities. D 2003 Elsevier B.V. All rights reserved. Keywords: Rheology; Particle size distribution; Particle packing; Green density
1. Introduction The homogeneity of particle packing in the green bodies of a ceramic compact is a key factor for the improvement of the sintering behaviour and the final properties of the material. This target is better achieved when colloidal shaping techniques are used to consolidate the bodies [1,2]. Colloidal methods enable the modification and control interaction forces between particles, to destroy or eliminate particle agglomerates, and to achieve an intimate mixing of two or more different powders to produce uniform and reliable ceramic bodies. The rheology and processing ability of the suspensions and the particle packing also depend on other relevant factors such as particle size and particle size distribution [3 – 6]. It is generally believed that the presence of coarse particles in the suspensions confer a shear-thick-
* Corresponding author. E-mail address: [email protected] (J.M.F. Ferreira). 0032-5910/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2003.10.004
ening behaviour, while the compaction efficiency increases with extended particle size distributions [7,8]. However, this concept cannot be generalised for all the systems. In fact, bimodal particle size distributions can enable significant decreases in viscosity for a given solids loading, or improvements of the solids volume fraction while maintaining a given viscosity level [9 – 11]. This is the reason why industrial dispersions, e.g., inks and paints are not monodisperse, but result from mixtures of different particle sizes. Other benefits of using mixtures of different sized particles might be related to the control of shrinkage, density and homogeneity of the microstructure of green and sintered bodies [12,13]. The surface chemistry of the particles is another relevant factor in colloidal processing. Previous theoretical and experimental works have demonstrated the influence of the interparticle forces on suspensions’ viscosity and packing ability of the particles during slip casting [10,14 – 16]. Recently, Zaman and Moudgil [17] used binary mixtures of silica powders to show the effect of the magnitude of
70
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electrostatic repulsive forces on viscosity. They concluded that long-range repulsive forces impart to the suspensions higher viscosity values compared with short-range interactions. Other authors [14,18] drew similar conclusions concerning monomodal or bimodal systems. These findings point out the mutual interferences among different factors, such as particle size and particle size distribution, solids loading and the type and amount of dispersant used to stabilise the suspensions. Since it is important to discriminate the role of each experimental variable in a given process, constant solids loading and a complete absence of dispersant were used in the present work. The aim is to understand the relationships between, particle size distribution and size ratio, and the rheological behaviour of the suspension as well as their packing ability either in suspension or in green bodies consolidated by slip casting. Basically, bimodal suspensions containing mixtures of a sand powder (coarse, intermediate sized, or fine) + fumed silica, in several proportions, were prepared by different times of ball milling. The effects of the proportions of fumed silica, milling time and size ratio on rheological behaviour and green densities were studied at their natural pH.
2. Experimental procedure 2.1. Materials and slip preparation and characterisation Three commercial silica powders, P10 (coarse), P500 (intermediate sized) and P600 (fine) with mean particle sizes of 19, 6.5 and 2.2 Am, respectively, were prepared by dry ball-milling and supplied by Sibelco Portuguesa. A fumed silica powder (Aldrich Chemical), hereafter designated by FS, with a mean size of 0.07 Am (after 10 min in an ultrasonic bath), was also used as a raw material. Particle size analyses of these powders were performed using a laser diffraction instrument (Coulter LS 230, UK). The zeta potential of the FS particles was analysed by using a Doppler Electrophoretic Light Scattering Analyser (Coulter DELSA 440, UK). Experimentally, the suspensions were prepared by first adding the FS particles in to water under ultrasonic and mechanical stirring. Then, the other powders (coarse, intermediate or fine) were progressively added and kept under stirring for further 30 min. The suspensions were transferred to polyethylene ball mill containing silicon nitride balls as grinding media (diameter = 15 mm). Deagglomeration/milling was performed for 10 and 20 h of milling to test the rheological behaviour of suspensions and particle size distributions. These characteristics were compared with those of non-deagglomerated suspensions. Rheological measurements were carried out with a rotational controlled stress rheometer (Carri-med 500 CSL, UK). The measuring configuration adopted was a concentric coaxial cylinder and flow measurements were performed in the shear rates range from about 0.1 to 550 s 1. Before
starting a measurement, pre-shearing was performed at high shear rate for 1 min followed by a rest of 90 s in order to transmit the same rheological history to whole suspension being tested. 2.2. Preparation and characterisation of green bodies Slip casting experiments were carried out in order to gather complementary information on packing ability of the different suspensions. Three samples (F = 28 mm and thickness = 0.5 mm) were consolidated by unidirectional slip casting from each suspension after different milling times (0, 10 and 20 h). After demoulding, the bodies were placed into an oven at 120 jC for 24 h for complete drying and the green densities were measured by the mercury immersion method using the Archimedes principle.
3. Results and discussion The coarser silica powders tended to sediment during zeta potential measurements. Measurements could be performed on a fine fraction of P600, fractionated by sedimentation, which behaved likewise to FS. Because of that, only the results of FS are presented in Fig. 1. It can be seen that the isoelectric point (pHiep) is located between pH 2– 3, in good agreement with other reported values for this oxide [19,20]. Furthermore, at the natural pH of the suspensions, pH 5.5– 6, the zeta potential reaches a negative value of about 25 mV, which is high enough to electrostatically stabilise the systems [21]. The effects of milling time and the amount of FS added to the coarse, intermediate and fine silica sand powders on the flow curves are displayed in Figs. 2 – 4. The results show that the slips containing the coarse sand powder exhibit a shear thinning behaviour, which is enhanced with increasing amounts of fumed silica in the mixture and decreases with increasing milling time (Fig. 2). On the other hand, Fig. 4 shows that the suspensions containing the fine sand powder exhibit a shear thickening behaviour, which becomes more
Fig. 1. Zeta potential versus pH for FS particles dispersed in a 10 3 M KCl solution.
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Fig. 2. Flow curves (up branches) for the suspensions of the coarser sand powder (P10) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
accentuated with increasing amounts of FS added and less pronounced with increasing milling time. The slips containing the intermediate sized sand powder, P500, present different behaviours depending on the amount of FS present (Fig. 3). At 5% FS a slightly thickening behaviour is observed, which gradually changes towards a shear thinning behaviour with increasing amounts of FS up to 15%. These results are somewhat surprising, since it is usually accepted that the presence of coarse particles in a suspension tends to impart a shear thickening effect, especially for high solid volume fractions [22,23]. On the other hand, it is believed that the presence of increasing amounts of very fine particles would enhance the shear thinning characteristics of the slips. However, Fig. 4 shows an opposite trend. The rheological model that better describes the results presented in Figs. 2– 4 is the Herschel –Buckley: r ¼ r0 þ Kp c˙n
ð1Þ
where, r is the shear stress, r0 is the yield stress, Kp is the plastic viscosity coefficient, c˙ is the shear rate and n is the shear rate index. Figs. 5 and 6 display the shear rate index,
Fig. 3. Flow curves (up branches) for the suspensions of the intermediate sand powder (P500) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
71
Fig. 4. Flow curves (up branches) for the suspensions of the finer sand powder (P600) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
n, as a function of milling time (for 10 wt.% FS), or as a function of the added amount of FS (for 10 h milling time), respectively. It can be seen that n < 1 for suspensions containing P10 and slightly increases with milling time, while n>1 for P600 and decreases with milling time. In the case of P500 n z 1 and its value is practically unchanged with increasing milling time. For a fixed milling time, n>1 for P600 and increases with the amount of FS, while an opposite situation is observed in the case of P10. For suspensions with P500 the shear rate index decreases with increasing the amount of FS passing from shear thickening to pseudoplastic behaviour. These results are in close agreement with those presented in Figs. 2 –4. Using PVC dispersions, Collins et al. [24] found that a broadening of the size distribution of the particles led to a decrease in the shear thickening effect at high shear rates and that this change was more prominent when the size distribution was broadened by the addition of coarse particles. The shear thinning behaviour is often associated with the slurry structure. When the attractive forces between particles prevail, collisions among them will lead to the formation of agglomerates. At low shear rates, liquid is immobilised in void spaces within flocs and the floc network. As the shear rate is increased, the flocs and floc network break down and
Fig. 5. Shear rate index, n, as a function of milling time for a fixed amount (10 wt.%) of FS.
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Fig. 6. Shear rate index, n, as a function of the added amount of FS at a fixed milling time (10 h).
Fig. 8. Particle size distributions (cumulative percent greater than, CPGT) of suspensions of sand powder P500 and FS (5% and 10%) before and after 20 h of ball milling.
the entrapped liquid is released and a more ordered structure in the flow direction is formed. However, such explanation does not give a complete picture of the results observed in the present work. In fact, the formation of agglomerates is more likely to occur in the case of fine and attractive particles. Furthermore, the systems that present the shear thinning characteristics are precisely those containing the coarser particles. Moreover, the shear thickening behaviour appears in the systems composed by the finer sandy particles. From the previous discussion, it seems clear that the concept to explain the rheological behaviours observed cannot be based only on the size of particles. The particle size distributions would play the most relevant role in the present situation, since they directly influence the packing ability of the powders in suspension. This view is in agreement with that reported by Greenwood et al. [22] who showed that a reduction in viscosity was strongly dependent on the particle size ratio. For all the suspensions the viscosity was lower after ball milling than only after stirring. This can be attributed to the deagglomerating effect and to the obtaining of a more favourable particle size distribution. The less resistance offered by the suspensions to flow means that the packing fraction of the systems was improved. The sand P10 has a broader particle size distribution (Figs. 7 and 8) and would
pack better in suspension compared with the sand P600 which presents a narrow particle size distribution (Fig. 9). During milling, it was observed that the particle size distribution of the mixtures containing the coarser sand powder narrows, while those containing the finer one broadens. This seems reasonable, since the coarser particles are more prone to be broken during milling than the finer ones. On the other hand, the milling action will also destroy the agglomerates of FS. The efficiency of this deagglomeration process would depend on the size of interstitial pores among the coarser particles present in the mixture, since larger interstices can accommodate larger FS agglomerates. Therefore, it seems likely that the deagglomeration efficiency of FS would be higher in the case of P600. This, coupled with the expected less efficient milling action expected on its own particles, explains the broadening effect observed. In fact, the comparison of Figs. 7 and 9 reveals that the effects of milling on particle size distribution are mostly observed on the coarse and fine extremities of PSDs for the mixtures containing P10 and P600, respectively. As reported in the experimental procedure, FS was the first powder added to distilled water during suspensions’ preparation. It was observed that a gel-like structure was
Fig. 7. Particle size distributions (cumulative percent greater than, CPGT) of suspensions of sand powder P10 and FS (5% and 10%) before and after 20 h of ball milling.
Fig. 9. Particle size distributions (cumulative percent greater than, CPGT) of suspensions of sand powder P600 and FS (5% and 10%) before and after 20 h of ball milling.
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Table 1 Green densities of slip cast bodies from suspensions of sand powders and FS powder obtained at different milling times FS (%)
5 10 15
P600 (g/cm3)
P500 (g/cm3)
P10 (g/cm3)
0h
10 h
20 h
0h
10 h
20 h
0h
10 h
20 h
0.66 0.67 0.63
0.67 0.68 0.63
0.69 0.70 0.64
0.62 0.63 0.60
0.63 0.64 0.62
0.64 0.65 0.64
0.62 0.62 0.62
0.64 0.63 0.62
0.66 0.63 0.63
The accuracy associated at all measurements is within F 0.005 g/cm3.
Fig. 10. Equilibrium viscosity curves for the suspensions of the finer sand powder (P600) with different amounts of FS (total solid loading 46 vol.%) and different milling times.
obtained, which was accentuated with increasing amounts of FS. The gel-like structure tended to be destroyed with the addition of the coarser sand powders, since introduction of coarse particles will imply the division of the starting gel into small portions. For the mixtures containing 15% FS it was impossible to add the whole amount of FS to the water due to the strong gel features of the suspensions. Further addition of FS was only possible after adding some of the coarser component, which improved the fluidity of the system. The presence of a gel-like structure would enhance the shear thinning character of the system. The portions in which a gel structure was divided would depend on the size of the particles introduced, being larger in the case of P10. This might contribute to the shear thinning behaviour observed with the coarser powder mixtures. In the case of P600, the FS gel should be divided into too small portions for the intrinsic shear thinning character to become appreciable. In
fact, Fig. 10 shows that the shear thinning behaviour is confined to the very low shear rates and is followed by a shear thickening effect for intermediate shear rates and a trend to Newtonian flow behaviour in the highest shear rate region. The shear-thinning behaviour was explained above and is schematically represented in Fig. 11A for small deformations. Higher deformations in a high packed system with a narrow PSD imply particle rearrangements and increasing average distances between layers of particles. Capillary forces oppose to the flow and the suspension thickens (Fig. 11B). With the shear rate further increasing, there could be a gradual alignment of particle layers in the flow direction and the viscosity would decrease, as observed. This interpretation is supported by the recent studies of the rheology of calcium carbonate suspensions in aqueous polysaccharides matrices, reported by Lapasin et al. [25,26]. They have found that under low shear stress conditions, the rheological properties of filled gels are strictly governed by those of the polymeric matrices, and that the addition of particles partially destroys the weak gel structures. Under high shear stress conditions, the hydrodynamic effects due
Fig. 11. Schematic illustration of the causes determining the shear-thinning and shear-thickening behaviours.
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to the presence of particles control the rheological characteristics of the suspensions. The results of the slip casting experiments from slurries with different amounts of FS and milling times are reported in Table 1. It can be seen that the green density increases with increasing milling time for all the mixtures tested. This is in agreement with the rheological results discussed above. When the packing ability of particles increases the viscosity of the slurry decreases. Further, a more favourable PSD would enable higher green densities to be obtained. This also explains why green density increases when the amount of FS increases from 5% to 10% for the mixtures containing P500 and P600. This suggests that FS would occupy the interstitial voids among the coarser particles. A further increase in FS to 15% led to a diminution of green density. Therefore, the proportion between coarse/fine components that lead to maximum packing densities is considerably lower compared with those already reported for other bimodal systems, which usually corresponds to about 70/30 for size ratios according to the Furnas model [27,28]. This can be understood since the FS particles are very small and their apparent size in suspension is expected to increase significantly [29]. In the case of P10, the maximum packing density is observed at 5% FS. This is likely due to a more extensive segregation phenomena of particles (sedimentation and clogging effect) during slip casting due to the larger particle size ratio between the components [30].
4. Conclusions The results presented and discussed in this study showed that for given solids loading, the viscosity (shear stress) of the suspensions increases with increasing amounts of the fine component (FS), as expected. However, in contrast with the common knowledge, the suspensions containing the coarser sand powder exhibit shearthinning behaviour while those containing the finer sand powder show shear thickening. These characteristics are even accentuated with increasing amounts of FS. These results could be explained in terms of a gel-like structure formed by FS particles in aqueous media, which is more extensively destroyed (subdivided) by the introduction of the coarser component particles, and in terms of size ratio. The same factors and particle segregation phenomena determine the green packing density of compacts prepared by slip casting.
Acknowledgements This work is supported by FCT (Portuguese Foundation for Science and Technology) in the frame of the Praxis XXI programme.
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