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De-agglomeration of goethite nano-particles using ultrasonic comminution device
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Powder Technology 187 (2008) 1 – 10 www.elsevier.com/locate/powtec
De-agglomeration of goethite nano-particles using ultrasonic comminution device P. Ding, A.W. Pacek ⁎ School of Engineering, Chemical Engineering, the University of Birmingham, Birmingham, B15 2TT, UK Received 25 January 2007; received in revised form 6 December 2007; accepted 20 December 2007 Available online 3 January 2008
Abstract The effect of power input, solid content and ionic strength of liquid on the kinetics of de-agglomeration of acicular goethite nano-particles in ultrasonic comminution device has been investigated. It has been found that the pattern of de-agglomeration is independent of power input. Initially large aggregates are broken by fragmentation and as the process progresses the primary particles are gradually eroded from the surface of those large aggregates. The breakage of large aggregates was described by size-energy model and the model describing the generation of primary particles was developed. The increase of solid concentrations in the suspension (up to 20 wt.%) leads to an increase of the efficiency of both breakage of large aggregates and formation of fine particles. The ionic strength and solid concentration have practically no effect on mechanism of de-agglomeration but they affect the morphology and rheology of the suspensions of goethite nano-powder. © 2008 Elsevier B.V. All rights reserved. Keywords: Goethite nano-particles; De-agglomeration; Ultrasonic comminution; Solid concentration; Ionic strength; Rheology
1. Introduction Goethite (hydrous ferric oxide α-FeOOH) powder of acicular nano-particles morphology is commonly used in pigments, catalysts, coatings and flocculants [1]. In a majority of applications, it has to be dispersed in liquids to give homogenous, stable dispersions and the aggregates inherently present in dry nano-powders have to be broken into a single nano-particles. It is well known that dispersion of even moderate amount of goethite based pigments in aqueous solutions is difficult and expensive step in the paints manufacture [2]. There are three interconnected properties of nano-particles/ liquid suspensions strongly affecting the quality of products: structure, stability and rheology. All those properties are usually determined when nano-powder is dispersed in the liquid and are strongly affected by both the pH and the concentration of the nano-powder. Recently Blakey and James [3] reported that goethite suspensions are stable at pH = 3 but at natural pH of 7 ⁎ Corresponding author. E-mail address: [email protected] (A.W. Pacek). 0032-5910/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.12.016
flocculation occurs even at solid volume fraction as low as 1% vol% v/v. It has been also reported that pH and solid concentration strongly affect rheology of laterite suspensions [4], nickel laterite suspensions [5] and polymer latex suspensions [6,7]. Whilst there is some information in open literature on the rheology of suspensions of goethite nano-particles [3] there is practically none on the kinetics and mechanism of dispersion of goethite nano-powder in liquids. Kinetics of de-aggregation of silica and titania nano-powders was investigated by Kusters et al. [8,9] who proposed a simple model relating break-up rate of large aggregates to specific energy input and postulated that large aggregates of titania nano-powder are broken by both erosion and fracture. Recently Pacek et al. [10] investigated the kinetics and mechanisms of dispersion of silica nano-powder (nano-particles size of the order of 12 nm) and found that the size of large aggregates is reduced by erosion of primary aggregates (of the order of 100 nm) from their surface. Those primary aggregates could not be broken into separate nanoparticles even at very high energy input. In many industrial applications, de-agglomeration of nanopowders in different suspensions is often carried out by
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energy released during collapse of bubbles is reduced and the efficiency of the ultrasonication is also reduced [12]. Whilst the ultrasonication is one of the most efficient methods of deaggregation, understanding of the mechanisms of breakage of the aggregates formed from irregularly shaped nano-particles and the effect of energy input and solid load on the kinetics of deagglomeration is still rather limited. To fill this gap the effect of ultrasound energy input, solid concentration and ionic strength on the kinetics of de-aggregation of goethite nano-powder and rheology of resulting suspensions has been investigated and the results are discussed below. 2. Experimental 2.1. Materials Dry goethite nano-powder of bulk density of 4000 kg m− 3 was purchased from BASF. The structure of dry powder (as supplied) and the morphology of single nano-particles was analysed using a scanning transmission electron microscope (STEM). The analysis revealed needle shaped primary nanoparticles of approximately 100 nm length shown in Fig. 1a. In dry powder those particles tend to adhere to each other to form aggregates with the size from tens to hundreds of microns. The structure of those large aggregates is shown in Fig. 1b. 2.2. Experimental rig and procedure Fig. 1. Morphology of goethite particles: (a) single nano-particles after ultrasonication for tr = 800 s at average energy dissipation rate of 500 kW m− 3, (b) dry nano-powder.
ultrasonication. In this method the aggregates are broken by the action of local, high velocity liquid jets (up to 100 m/s) and pressure gradients up to 20 GPa/cm [11]. It has been reported that as the viscosity of suspension increases the amount of mechanical
Experimental rig shown in Fig. 2 consists of an ultrasonic processor (Dr. Hielscher Gmbh, Germany) working at 24 kHz connected to a jacketed stirred vessel via peristaltic pump. The stirred vessel of diameter 0.05 m and height of 0.1 m was fitted with the pitched blade turbine impeller of diameter of 0.025 m. The total volume of the rig was 350 ml and the volume of the flow cell was 80 ml. Prior to dispersion experiments ultrasound power input was estimated by operating the rig as a crude calorimeter
Fig. 2. Experimental rig: 1 — ultrasonic head (UP200S), 2 — sonotrode (S14D), 3 — flow cell, 4 — stirred vessel, 5 — impeller, 6 — pH probe, 7 — thermocouple, 8 — peristaltic pump.
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Fig. 3. Zeta potential of goethite nano-particles, solid concentration 0.01 wt.%, (○) distilled water only, (▲) 0.01 M NaCl solution, (■) 0.1 M NaCl solution.
and by measuring the temperature increase at different amplitudes and cycles of ultrasound over a fixed time interval using water as the working fluid. In all experiments the same procedure was followed. Required mass of goethite powder was dispersed in water in a stirred vessel at impeller speeds ranging from 650 to 1050 rpm depending on concentrations of dry nano-powder. pH was adjusted to one of the following values 3, 5, 6, 7, 10 or 12 using hydrogen chloride and sodium hydroxide and at each pH zeta potential was measured using ZetaMaster (from Malvern Instruments). The suspension was then circulated at flow rate of 10 ml/s through ultrasonic device. Small samples of suspension were withdrawn after different processing time and the particle size distributions were measured using Mastersizer 2000 (Malvern Instruments, UK). All de-agglomeration experiments were carried out at constant suspension temperature (20 °C) and at pH = 3. As the total volume of the dispersion in the experimental rig was 350 ml and the volume of the flow cell where the powder was exposed to the ultrasound was 80 ml, the specific energy input was calculated from: E¼
P tr Vcell
3
on the particles surface which is usually quantified by zeta potential. The zeta potential at different pH and salt concentration was measured using ZetaMaster and the results are shown in Fig. 3. The measured values of zeta potential indicate iso-electric point at pH = 8.9 that is in the range between 8.4 and 9.5 reported in the literature [3,14]. Whilst the strong dependence of zeta potential on pH was expected, the lack of the effect of salt on zeta potential was less obvious. Theoretically, presence of salt changes the ionic strength of the liquid therefore it should also affect zeta potential. However, Blakey and James [3] measured zeta potential of synthetic goethite powder in salt solutions and reported that to up 0.01 M salt does not affect zeta potential. At 0.1 M salt they observed the reduction of very high values of zeta potential (above 50 mV) but the lower values (below 40 mV) were practically not affected. Our results also indicate that zeta potential up to 40 mV is not affected by the presence of salt. In general, at zeta potential higher than |30 mV| the majority of solid/liquid suspensions [13] are stable as at this charge the
ð1Þ
and the mean residence time tr in the cell was calculated from: tr ¼
tt 1þ
Vt Vc Vc
¼ tt
Vc c0:23 tt : Vt
ð2Þ
The total ultrasonic energy input was controlled by adjusting ultrasound power input between 28 and 60 W and by varying processing time between 2 and 80 min what corresponds to the variation of the mean residence time in the cell between 27 s and 18 min. 3. Results and discussion 3.1. Zeta potential The kinetics of de-aggregation and the stability of a suspension of nano-particles is strongly affected by the charge
Fig. 4. Aggregate size distributions in salt free 5 wt.% goethite suspension: (a) transient size distributions at specific power input of 500 kW m− 3; (b) distributions at the same total energy input (200 MJ m− 3) but different specific power input.
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volume of primary nano-particles/small aggregates increases but the size of nano-particles does not change (see first mode in Fig. 4a). Considering the shape of single goethite nano-particle (see Fig. 1a) it is difficult to judge whether particles corresponding to the first mode (median of the order of 100 nm) are single, needle shaped nano-particles of the length of 100 nm or whether several of those nano-particles adhered to each other along the longest edges and formed aggregates also of the order of 100 nm. The aggregates' volume distributions measured at the same total energy input of 200 MJ m− 3 but at different specific power input shown in Fig. 4b practically overlap indicating that the total energy input controls breakage of the large aggregates. The bimodal transient size distributions cannot be analysed in terms of the mean sizes, therefore the analysis of both modes was carried out separately. The second mode was analysed in terms of transient median diameters of the large aggregates and the first mode was analysed in terms of cumulative volume fraction of primary particles. The experimental median diameters of large aggregates (corresponding to the second mode of volume distributions in Fig. 4a) shown as a function of processing time at different specific power input in Fig. 5a are rather scattered. These data can be collapsed into a straight line (within engineering accuracy, Fig. 5b) in log–log coordinates if diameters are
Fig. 5. Median diameters of the large aggregates in salt free 5 wt.% goethite suspension corresponding to second mode of transient distributions at different power input (○) — 354 kW m− 3, (◊) — 500 kW m− 3, (▽) — 750 kW m− 3 (a) as a function of mean residence time; (b) as a function of specific energy input.
electrostatic repulsive forces are sufficiently strong to overcome attractive van der Waals forces. Fig. 3 indicates that the suspensions of goethite nano-powder should be stable at pH b 3 and at pH N 12. In this range of pH the repulsive electrostatic forces should enhance de-agglomeration. Therefore the effect of energy input, solid concentration and ionic strength on deaggregation was investigated at pH = 3. 3.2. The effect of energy input on kinetics of de-aggregation Typical transient volume distribution functions of the aggregates in the suspension at specific power input of 500 kW m− 3 are shown in Fig. 4a and the volume distributions at the same energy density but at different power inputs are compared in Fig. 4b. The transient aggregates' volume distributions shown in Fig. 4a indicate that the kinetics and the mechanism of de-aggregation of goethite nano-powder at pH= 3 is similar to the de-aggregation of silica nano-powder [10] e.g. large aggregates of initially dry powder are gradually broken by erosion of single nano-particles/ primary aggregates (of the order of 100 nm) from their surface. As the time progresses the size of large aggregates decreases and the
Fig. 6. Cumulative volume fraction of the nano-particles in the first mode: (○) — 354 kW m− 3, (▽) — 500 kW m− 3, (□) — 750 kW m− 3: (a) as a function of mean residence time; (b) as a function of specific energy input.
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related to specific energy input according to an empirical sizeenergy model [9,10]:
Table 1 Parameters in Eq. (8) and the regression coefficients
d50 ¼ C Ea :
Specific power input [kW/m3]
β ⁎ 103 [−]
td [s]
r2
354 500 650
2.3 3.2 4.5
56.5 54.4 28.1
0.9856 0.9857 0.9932
ð3Þ
This model has been used to describe different types of breakage processes ranging from grinding of solid particles [15,16] where α of the order of 0.7 was reported to liquid/liquid emulsification in a different types of high shear mixers where α of the order of 0.4 [17] was reported. Breakage of large goethite aggregates investigated in this work can also be described by this model. The empirical constant α calculated by non-linear regression from experimental data shown in Fig. 5b is the order of 0.68 with a regression coefficient of 0.971. The first mode of transient volume distributions was analysed in terms of cumulative volume fractions of primary particles (or aggregates smaller than 350 nm) and the results are summarised in Fig. 6. Fig. 6a shows that the rate of formation of fine particles decreases with the processing time indicating erosion type of de-agglomeration and it can be described by: dyðt Þ ¼ bð1 yðt ÞÞ dt
ð4Þ
where experimental constant β depends on the type and strength of the aggregates Kusters et al. [8,9]. They solved Eq. (4) with the initial condition: y ð 0Þ ¼ 0
ð5Þ
and obtained the following expression for transient cumulative volume fraction of primary particles: yðt Þ ¼ 1 exp ðb t Þ:
ð6Þ
Eq. (6) indicates that the theoretical cumulative volume fraction of fine particles passes through the origin of the y, t coordinate systems. Experimental results shown in Fig. 6 and the results of batch de-agglomeration of silica nano-powder [18] clearly indicate that the fine particles appear after certain processing time. Very similar results were also reported by Kusters et al. [9]. These observations imply that before erosion commences a certain amount of energy has to be supplied to the aggregates and that requires a certain processing time. However, in the experimental arrangement used in this work samples were taken from stirred vessel not from the flow cell (see Fig. 2) therefore the delay time can result both from the circulation time and from the time necessary to form initial cracks in the aggregates. These results were incorporated into the theoretical model by assuming that the fine particles appear after a certain delay time td and by modifying the initial condition accordingly: yðtd Þ ¼ 0:
ð7Þ
Eq. (4) was integrated with initial condition (7) giving: yðt Þ ¼ 1 exp ½bðt td Þ
ð8Þ
where both β and td are system specific constants which were calculated from experimental data and the results are summarised in Table 1. For all values of the specific power input the proposed model fits experimental data very well up to the volume fraction of fine particles of the order of 0.8. As the specific power input increases the delay time is reduced and the erosion constant β increases indicating that at higher specific energy input erosion is faster. However, the experimental times necessary for complete breakage of all aggregates into primary nano-particles are considerably shorter than the times predicted by the model. This is an inherent feature of the model (both physical and mathematical) which assumes that erosion is proportional to surface area e.g. as the surface decreases with time (total number of aggregates stay constant) the rate of erosion also decreases and complete erosion can only be achieved (theoretically) after infinitely long time. Clearly the complete model of deagglomeration would have to account for a simultaneous erosion and fracture. 3.3. Effect of solid concentration on kinetics of de-agglomeration The effect of the solid concentration on de-agglomeration kinetics has been investigated at the specific power input of 500 kW/m3. Cumulative size distributions at different solid concentrations after different processing times are compared in Fig. 7. At all investigated solid concentrations the transient distributions (Fig. 7a and b) are bimodal with the median of the first mode of the order 100 nm being practically time independent and the median of the second mode decreasing with time from approximately 20 μm to 2 μm. Whilst, as shown by the first mode, the generation of primary particles is practically independent of solid content, the cumulative volume fraction of aggregates larger than 350 nm (second mode) depends on solid concentration and this dependence is stronger at lower total energy input (short processing time) than at higher total energy input (longer processing time). After sufficiently long processing time when all large aggregates are broken (see Fig. 7c), the cumulative distributions of primary nano-particles at 5 wt.%, 10 wt.% and 20 wt.% of solid are practically identical. The effect of solid content on de-agglomeration kinetics has also been analysed in terms of the reduction of median diameter of the second mode using size-energy model and in terms of the cumulative volume fraction of primary particles in the first mode. The results are summarised in Fig. 8.
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Fig. 8. The effect of goethite concentration in salt free suspensions on (a) median diameter of large aggregates and (b) cumulative volume fraction of fine particles at energy dissipation rate 500 kW m− 3.
The exponent in the size-energy model increases as the solid concentration increases indicating that the breakage rate (understood here as a time gradient of median diameter) also increases. Also the delay time increases with the solid concentration and the erosion efficiency is highest at the highest solid load. These results can be explained by more efficient utilisation of ultrasound energy in more concentrated suspension as shown in Fig. 9 where the median diameters and cumulative volume fractions are plotted as a function of specific energy input (energy input per mass of solid). Fig. 7. Cumulative size distributions at different solid concentrations in salt free suspensions: (a) and (b) transient, (c) steady state. (○) — 1 wt.%, (▽) — 5 wt.%, (□) — 10 wt.%, (◊) — 20 wt.%.
The transient median diameters of the large aggregates can be related to processing time via size-energy model: dav ¼ C Ea ¼ C Pa t a ¼ C1 t a :
Table 2 Coefficients in Eqs. (8) and (9) at different solid concentrations of goethite powder in suspension Solid content
ð9Þ
Experimental constants C1 and α calculated by non-linear regression from experimental data shown in Fig. 8a are summarised in Table 2. Fig. 8 and Table 2 indicate that the reduction rate of median diameter is higher at higher solid content.
Breakage of large aggregates
Cumulative volume fraction of primary particles
Coefficients in Eq. (9)
Coefficients in Eq. (8)
[wt.%]
C1 [m sα]
α [−]
r2
β ⁎ 103 [−]
td [s]
r2
1 5 10 20
40.4 62.8 103.6 159.3
0.59 0.66 0.72 0.81
0.8940 0.9624 0.8525 0.9742
3.64 2.967 3.068 3.068
49.69 53.20 55.26 57.28
0.9967 0.9941 0.9952 0.9805
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diameter) and to lesser extent by erosion. Only after the size of large aggregates falls in the range 0.5–5 μm does erosion becomes the dominant mechanism. This can be seen from Fig. 5 and also from Fig. 8 where after approximately 250 sec (aggregate size of the order of 2 μm) the experimental median diameters are practically the same for all concentrations of solid. Kusters et al. [9] reported that in batch de-aggregation of silica nano-powder at solid load up to 50% w/w the cumulative size distributions at different solid content were identical and that the breakage rate was independent of solid concentration, whereas as discussed above our results clearly show that there is a dependence between the solid load and de-aggregation rate. This difference can be explained by: a) different type of nanoparticles and/or (b) by different level of energy input. Kusters et al. [9] investigated breakage at specific power input of 62.5 kW/m3 whereas the results discussed above were obtained at a specific energy input of 500 kW/m3. 3.4. Effect of ionic strength on kinetics of de-agglomeration The ionic strength of the suspension was modified by the addition of salt at two different concentrations: 0.01 M and 0.1 M. The addition of salt did not affect zeta potential as discussed in
Fig. 9. The median diameters of the large aggregates (a) and cumulative volume fractions of small particles (b) at different solid contents in salt free suspensions as a function of specific energy. (●) — 1 wt.%, (○) — 5 wt.%, (▼) — 10 wt.%, (△) — 20 wt.%.
Fig. 9 shows that whilst the reduction rate of large aggregates is practically independent of solid content (all lines in Fig. 9a are practically parallel) breakage of aggregates in a concentrated suspensions starts at much lower specific energy input than in a diluted suspension. Also the volume fraction of primary particles at the same specific energy increases with the solid concentration. This clearly indicates that in the investigated range of solid load the efficiency of energy utilisation during de-agglomeration increases with the solid load which can be explained by the mechanism of breakage in the ultrasound systems. In such systems only aggregates which are close to collapsing cavities are broken by the forces resulting from large pressure gradients and/or from high velocity liquid jets generated by collapsing cavities. As the length scales of both types of forces are rather small (water is incompressible) only the aggregates close to collapsing cavities can be broken whereas the energy from the cavities collapsing far away from aggregates dissipates into heat. As the concentration of solid increases the number of the aggregates in a close proximity to collapsing cavities also increases therefore the efficiency of energy utilisation increases what explains the results shown in Fig. 9. It is also possible that as the solid content increases the size and the number of large aggregates present in the suspension after premixing also increases and initially those large aggregates might be broken also by fracture (very fast reduction of median
Fig. 10. Median diameters of large aggregates (a) and cumulative volume fraction of primary particles (b) in a 5 wt.% goethite suspension at specific power input of 500 kW m− 3: (○) — in distilled water, (▽) — in 0.01 M NaCl solution, (□) — in 0.1 M NaCl solution.
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constant α = 0.69, the delay time 53.6 s, erosion constant β of 0.00326). The identical values of the constants characterising erosion and breakage in the presence and in the absence of salt (at different ionic strength) are in agreement with the identical values of zeta potential discussed in Section 3.1 and confirm that ionic strength does not affect the mechanism of breakage during ultrasonication. This might be explained by very high specific ultrasound energy input so even if there were some changes in the repulsive inter-particle forces at such a high energy input they would be very difficult to detect. 3.5. Effect of solid content and ionic strength on the rheology of goethite suspension The flow curves at different concentration of solid were measured using a controlled stress rheometer AR 1000 (TA Instruments, UK) and the results are summarised in Fig. 11a. At all concentrations of solid the suspensions were nonNewtonian and the apparent viscosity was increasing with solid concentration. The viscosity of the suspensions at medium to high solid concentrations can be calculated from the Kreiger– Dougherty (K–D) equation [19]. / ½g/m g ¼ g0 1 /m
Fig. 11. Effect of solid concentrations on viscosity of goethite suspensions: (a) the flow curves, (b) viscosity as a function of solid concentrations, (●) — 1 wt.%, (○) — 5 wt.%, (▼) 10 wt.%, (△) — 20 wt.%.
Section 3.1. The transient volume distribution functions were also not affected by the presence of salt and were practically identical as the volume distributions shown in Fig. 7. The transient median diameters of the large aggregates and transient cumulative size distributions of primary particles shown in Fig. 10 are practically the same in the presence of salt and in the salt free suspension giving the same values of constants in Eqs. (8) and (9) (breakage
ð10Þ
where φm is the volume fraction of solid at maximum packing at which viscosity is equal to infinity. For several solid/liquid suspensions the product [η]φm is of the order of 2 [20] and Eq. (10) can be rearranged to give a simple relation between the viscosity of suspension and a solid volume fraction, so called MPQK equation [21–24]: rffiffiffiffiffi g0 / ¼1 : ð11Þ /m g It has been reported that Eq. (11) can be used with a wide range of solid/liquid suspensions up to 60 vol.% of solid [25]. Fig. 11b shows that in the investigated case MPQK equation fits the
Fig. 12. Flow curves (a) of 5 wt.% goethite powder suspended in: (○) — distilled water, (▽) — 0.01 M NaCl solution, (□) — 0.1 M NaCl solution and morphology (b) of suspension containing 0.1 M salt at pH = 3. The height of the image is equal to 136 μm.
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experimental data only up to approximately 3 vol.% (10 wt.%) of goethite nano-powder. At 5 vol.% (20 wt.%) there is a considerable deviation between the experimental results and the results predicted from Eq. (11). As Eq. (11) was derived for the solid suspensions where the particles interact only via liquid continuous phase (pure hydrodynamic interaction) the results shown in Fig. 11b indicate that in goethite suspension at pH= 3 the attractive or repulsive inter-particles forces cannot be ignored when considering the effect of concentration on the rheological properties. The addition of salt had relatively strong effect on the rheology and, at higher concentration, on morphology of suspension. The flow curves for salt free suspension and for suspensions containing different amount of salt as well as morphology of the suspension at the highest salt concentration are shown in Fig. 12. At 0.01 M salt the suspension was very weakly nonNewtonian with average apparent viscosity 3 times higher than viscosity of salt free suspension. At this salt concentration the flocculation of nano-particles was not observed. As the salt concentration was increased to 0.1 M the suspension became non-Newtonian and strongly shear thinning. This change of rheology can be explained by the change of morphology and flocculated structures observed under optical microscope are shown in Fig. 12b. The analysis of several images taken at the same magnification indicate presence of a single spherical aggregates of the order of 2 μm (see Fig. 1a for single nano-particles) which tend to flocculate further into much larger, irregular flocks. Neither small aggregates nor large flocks were detected in the images of salt free suspension or in the images of the suspension containing 0.01 M salt. The increase of ionic strength leads to the reduction of Debye length from 3.04 nm at 0.01 M salt to 0.96 nm at 0.1 M salt. According to Isrealachvili [26]: 1 0:304 ¼ pffiffiffi j c
ð12Þ
therefore the electrostatic repulsive force is reduced by half: el F0:1 exp ðj1 xÞ c½ exp ð xÞ½ exp ðj1 þ j2 Þc0:5 exp ð xÞ: c el exp ðj2 xÞ F0:01
ð13Þ The above analysis carried out within DLVO model does not take into account structural forces between surfaces [14,27] which strongly depend on the type of surface hydroxyl groups. One might expect that at such low pH those forces might play substantial part in aggregation of goethite nano-particles, but the detail analysis of such complex phenomena is well outside the scope of this work. Recently Blakey et al. [3] investigated the stability and rheology of the suspension of synthetic goethite nano-particles of similar size and shape to the nano-particles used in this work and found that at low pH and volume fraction of 1% the suspension is non-viscous what is similar to our results. They also reported the aggregation/flocculation but postulated that this was due to the different faces of irregular nano-particles having different electrostatic charges. This
9
suggestion might also be valid in our case. Clearly the relation between inter-particle forces, morphology and rheology in the suspension of goethite nano-particles in aqueous solutions is far from obvious and further work relating inter-particle forces to structure and rheological behaviour is necessary. 4. Conclusions This study has revealed that the mechanism of breakage of goethite aggregates built from acicular nano-particles of 100 nm length is similar to the mechanism of breakage of silica aggregates built from nearly spherical particles [10]. In both cases large aggregates of single modal size distributions are initially broken by fracture and at higher energy density, the erosion of primary particles/primary aggregates has been observed. This kinetics leads to bimodal volume distributions that cannot be analysed in terms of an average size. Therefore, a new method was used where both modes were analysed separately, breakage of large aggregates was analysed within size-energy law with the power index of 0.68 and a model describing generation of fines has been developed. This approach allows detailed description of deagglomeration and accounts for experimentally observed delay time. The increase of solid concentration from 1% to 20 wt.% leads to the reduction of energy input per unit mass of solid necessary for complete de-agglomeration, or in other words as the solid load increases the de-agglomeration energy efficiency increases. In the investigated range of parameters (pH, temperature) the suspensions of goethite nano-powder were Newtonian and the apparent viscosity was well correlated with goethite concentration up to 10 wt.% of solid by MPKQ equation [22]. Only at the highest solid concentration viscosity was higher than predicted by MPKQ equation what might be explained by needle shape of the particles. Increase of ionic strength caused by addition of salt lead to the increase of the viscosity of suspensions but did not affect the kinetics of de-agglomeration. At 0.1 M salt and 0.01 volume fraction of goethite nano-powder the suspension becomes nonNewtonian and shear thinning. These results indicate that the addition of salt leads to partial agglomeration and formation of irregular structures what would suggest the reduction of repulsive forces in the presence of salt. However, the zeta potential was not affected by the presence of salt, what indicates that electrostatic repulsive forces were not affected by the presence of salt. It is possible that non-DLVO forces are affected by presence of salt and this hypothesis is currently investigated. Acknowledgements This work is a part of PROFORM (“Transforming Nanoparticles into Sustainable Consumer Products Through Advanced Product and Process Formulation” EC Reference NMP4-CT2004-505645) project which is partially funded by the 6th Framework Programme of EC. The contents of this paper reflect only the authors' view. The authors gratefully acknowledge the useful discussions held with other partners of the Consortium:
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Bayer Technology Services GmbH; BHR Group Limited; Centre for Computational Continuum Mechanics (C3M); Karlsruhe University, Inst. of Food Process Eng; Loughborough University, Department of Chemical Eng; Poznan University of Technology, Inst. of Chemical Technology and Eng; Rockfield Software Limited; Unilever UK Port Sunlight, Warsaw University of Technology, Department of Chemical and Process Eng. References [1] E. Matijevic, P. Scheiner, Ferric hydrous oxide sols. 3. Preparation of uniform particles by hydrolysis of Fe(Iii)-chloride, Fe(Iii)-nitrate, and Fe(Iii)perchlorate solutions, Journal of Colloid and Interface Science 63 (1978) 509–524. [2] J.O. Stoffer, M. Fahim, Ultrasonic dispersion of pigment in water based paints, Journal of Coatings Technology 63 (1991) 61–68. [3] B.C. Blakey, D.F. James, The viscous behaviour and structure of aqueous suspensions of goethite, Colloids and Surfaces. A, Physicochemical and Engineering Aspects 231 (2003) 19–30. [4] K.S. Avramidis, R.M. Turian, Yield stress of laterite suspensions, Journal of Colloid and Interface Science 143 (1991) 54–68. [5] I.N. Bhattacharya, D. Panda, P. Bandopadhyay, Rheological behaviour of nickel laterite suspensions, International Journal of Mineral Processing 53 (1998) 251–263. [6] P. Ding, A.W. Pacek, K. Abinhava, S. Pickard, M.R. Edwards, A.W. Nienow, A process for the manufacture of chemically produced toner (CPT). I. Evolution of structure and rheology, Industrial & Engineering Chemistry Research 44 (2005) 6004–6011. [7] P. Ding, A.W. Pacek, K. Abinhava, S. Pickard, M.R. Edwards, A.W. Nienow, A process for the manufacture of chemically produced toner (CPT). II. Effect of operating conditions, Industrial & Engineering Chemistry Research 44 (2005) 6012–6021. [8] K.A. Kusters, S.E. Pratsinis, S.G. Thoma, D.M. Smith, Ultrasonic fragmentation of agglomerate powders, Chemical Engineering Science 48 (1993) 4119–4127. [9] K.A. Kusters, S.E. Pratsinis, S.G. Thoma, D.M. Smith, Energy-size reduction laws for ultrasonic fragmentation, Powder Technology 80 (1994) 253–263. [10] A.W. Pacek, P. Ding, A.T. Utomo, Effect of energy density, ph and temperature on de-aggregation in nano-particles/water suspensions in high shear mixer, Powder Technology 173 (2007) 203–210. [11] M. Aoki, T.A. Ring, J.S. Haggerty, Analysis and modelling of the ultrasonic dispersion technique, Advanced Ceramic Materials 2 (1987) 209–212. [12] J.O. Stoffer, M. Fahim, Ultrasonic dispersion of pigment in water based paints, Journal of Coatings Technology 63 (1991) 61–68. [13] K. Holmberg, Handbook of Applied Surface and Colloid Chemistry, vol. 1–2, John Wiley & Sons, Chichester, 2002. [14] R.M. Cornell, U. Schwertmann, The Iron Oxides, Structure, Properties, Reactions, Occurrence and Uses, VCH, Weinheim, 1996. [15] M.W. Gao, E. Forssberg, Prediction of product size distributions for a stirred ball mill, Powder Technology 84 (1995) 101–106. [16] S. Mende, F. Stenger, W. Peukert, J. Schwedes, Mechanical production and stabilization of submicron particles in stirred media mills, Powder Technology 132 (2003) 64–73. [17] H. Karbstein, H. Schubert, Developments in the continuous mechanical production of oil-in-water macro-emulsions, Chemical Engineering and Processing 34 (1995) 205–211.
[18] P. Ding, A.W. Pacek, De-agglomeration of silica nano-particles in presence of surfactants, Proceedings of 1st International Conference on Industrial Processes of Nano and Micro Products, 3–4 April, Publisher BHR Group Limited, London, UK, 2007, pp. 67–76. [19] I.M. Krieger, T.J. Dougherty, A mechanism for non-Newtonian flow in suspensions of rigid spheres, Transactions of the Society of Rheology 3 (1959) 137–152. [20] H.A. Barnes, J.F. Hutton, K. Walters, An Introduction to Rheology, Elsevier, Amsterdam0-444-87469-0, 1989. [21] S.H. Maron, P.E. Pierce, Application of ree-eyring generalized flow theory to suspensions of spherical particles, Journal of Colloid Science 11 (1956) 80–95. [22] D. Quemada, Rheology of dispersed systems — new viscosity– concentration law for concentrated solutions and suspensions, Comptes Rendus Hebdomadaires des Seances de l Academie des Sciences. Serie B 281 (1975) 173–176. [23] D. Quemada, Rheology of concentrated disperse systems and minimum energy-dissipation principle. 1. Viscosity–concentration relationship, Rheologica Acta 16 (1977) 82–94. [24] T. Kitano, T. Kataoka, T. Shirota, An empirical-equation of the relative viscosity of polymer melts filled with various inorganic fillers, Rheologica Acta 20 (1981) 207–209. [25] H.A. Barnes, The rheology of filled viscoelastic systems: a review, Rheology Reviews 2003, British Society of Rheology, ISBN: 0-95389048-1, 2003, pp. 1–36. [26] J. Israelachvili, Intermolecular & Surface Forces, Academic Press Limited, 1992. [27] N.V. Churaev, B.V. Derjaguin, Inclusion of structural forces in the theory of stability of colloids and films, Journal of Colloid and Interface Science 103 (1985) 542–553.
Glossary c: C: C1: d50: E: P: Vcell: Vt: r2: td: tr: tt: y: α: β: κ: η: ϕ: ϕm: η0: [η]:
ion concentration [mol/l] constant constant Median diameter of aggregates [m] specific energy input [MJ m− 3] power input [W] volume of flow cell [m3] volume of experimental rig [m3] coefficient of determination [−] delay time in Eq. (8) [s] mean residence time in flow cell [s] total processing time [s] cumulative volume fraction of fine particles [−] constant [−] constant [−] inverse Debye length [m− 1] viscosity of suspension [Pa s] volume fraction of solid [−] volume fraction of maximum packing solid [−] viscosity of Newtonian continuous phase [Pa s] intrinsic viscosity [Pa s]
Powder Technology 187 (2008) 1 – 10 www.elsevier.com/locate/powtec
De-agglomeration of goethite nano-particles using ultrasonic comminution device P. Ding, A.W. Pacek ⁎ School of Engineering, Chemical Engineering, the University of Birmingham, Birmingham, B15 2TT, UK Received 25 January 2007; received in revised form 6 December 2007; accepted 20 December 2007 Available online 3 January 2008
Abstract The effect of power input, solid content and ionic strength of liquid on the kinetics of de-agglomeration of acicular goethite nano-particles in ultrasonic comminution device has been investigated. It has been found that the pattern of de-agglomeration is independent of power input. Initially large aggregates are broken by fragmentation and as the process progresses the primary particles are gradually eroded from the surface of those large aggregates. The breakage of large aggregates was described by size-energy model and the model describing the generation of primary particles was developed. The increase of solid concentrations in the suspension (up to 20 wt.%) leads to an increase of the efficiency of both breakage of large aggregates and formation of fine particles. The ionic strength and solid concentration have practically no effect on mechanism of de-agglomeration but they affect the morphology and rheology of the suspensions of goethite nano-powder. © 2008 Elsevier B.V. All rights reserved. Keywords: Goethite nano-particles; De-agglomeration; Ultrasonic comminution; Solid concentration; Ionic strength; Rheology
1. Introduction Goethite (hydrous ferric oxide α-FeOOH) powder of acicular nano-particles morphology is commonly used in pigments, catalysts, coatings and flocculants [1]. In a majority of applications, it has to be dispersed in liquids to give homogenous, stable dispersions and the aggregates inherently present in dry nano-powders have to be broken into a single nano-particles. It is well known that dispersion of even moderate amount of goethite based pigments in aqueous solutions is difficult and expensive step in the paints manufacture [2]. There are three interconnected properties of nano-particles/ liquid suspensions strongly affecting the quality of products: structure, stability and rheology. All those properties are usually determined when nano-powder is dispersed in the liquid and are strongly affected by both the pH and the concentration of the nano-powder. Recently Blakey and James [3] reported that goethite suspensions are stable at pH = 3 but at natural pH of 7 ⁎ Corresponding author. E-mail address: [email protected] (A.W. Pacek). 0032-5910/$ - see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2007.12.016
flocculation occurs even at solid volume fraction as low as 1% vol% v/v. It has been also reported that pH and solid concentration strongly affect rheology of laterite suspensions [4], nickel laterite suspensions [5] and polymer latex suspensions [6,7]. Whilst there is some information in open literature on the rheology of suspensions of goethite nano-particles [3] there is practically none on the kinetics and mechanism of dispersion of goethite nano-powder in liquids. Kinetics of de-aggregation of silica and titania nano-powders was investigated by Kusters et al. [8,9] who proposed a simple model relating break-up rate of large aggregates to specific energy input and postulated that large aggregates of titania nano-powder are broken by both erosion and fracture. Recently Pacek et al. [10] investigated the kinetics and mechanisms of dispersion of silica nano-powder (nano-particles size of the order of 12 nm) and found that the size of large aggregates is reduced by erosion of primary aggregates (of the order of 100 nm) from their surface. Those primary aggregates could not be broken into separate nanoparticles even at very high energy input. In many industrial applications, de-agglomeration of nanopowders in different suspensions is often carried out by
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energy released during collapse of bubbles is reduced and the efficiency of the ultrasonication is also reduced [12]. Whilst the ultrasonication is one of the most efficient methods of deaggregation, understanding of the mechanisms of breakage of the aggregates formed from irregularly shaped nano-particles and the effect of energy input and solid load on the kinetics of deagglomeration is still rather limited. To fill this gap the effect of ultrasound energy input, solid concentration and ionic strength on the kinetics of de-aggregation of goethite nano-powder and rheology of resulting suspensions has been investigated and the results are discussed below. 2. Experimental 2.1. Materials Dry goethite nano-powder of bulk density of 4000 kg m− 3 was purchased from BASF. The structure of dry powder (as supplied) and the morphology of single nano-particles was analysed using a scanning transmission electron microscope (STEM). The analysis revealed needle shaped primary nanoparticles of approximately 100 nm length shown in Fig. 1a. In dry powder those particles tend to adhere to each other to form aggregates with the size from tens to hundreds of microns. The structure of those large aggregates is shown in Fig. 1b. 2.2. Experimental rig and procedure Fig. 1. Morphology of goethite particles: (a) single nano-particles after ultrasonication for tr = 800 s at average energy dissipation rate of 500 kW m− 3, (b) dry nano-powder.
ultrasonication. In this method the aggregates are broken by the action of local, high velocity liquid jets (up to 100 m/s) and pressure gradients up to 20 GPa/cm [11]. It has been reported that as the viscosity of suspension increases the amount of mechanical
Experimental rig shown in Fig. 2 consists of an ultrasonic processor (Dr. Hielscher Gmbh, Germany) working at 24 kHz connected to a jacketed stirred vessel via peristaltic pump. The stirred vessel of diameter 0.05 m and height of 0.1 m was fitted with the pitched blade turbine impeller of diameter of 0.025 m. The total volume of the rig was 350 ml and the volume of the flow cell was 80 ml. Prior to dispersion experiments ultrasound power input was estimated by operating the rig as a crude calorimeter
Fig. 2. Experimental rig: 1 — ultrasonic head (UP200S), 2 — sonotrode (S14D), 3 — flow cell, 4 — stirred vessel, 5 — impeller, 6 — pH probe, 7 — thermocouple, 8 — peristaltic pump.
P. Ding, A.W. Pacek / Powder Technology 187 (2008) 1–10
Fig. 3. Zeta potential of goethite nano-particles, solid concentration 0.01 wt.%, (○) distilled water only, (▲) 0.01 M NaCl solution, (■) 0.1 M NaCl solution.
and by measuring the temperature increase at different amplitudes and cycles of ultrasound over a fixed time interval using water as the working fluid. In all experiments the same procedure was followed. Required mass of goethite powder was dispersed in water in a stirred vessel at impeller speeds ranging from 650 to 1050 rpm depending on concentrations of dry nano-powder. pH was adjusted to one of the following values 3, 5, 6, 7, 10 or 12 using hydrogen chloride and sodium hydroxide and at each pH zeta potential was measured using ZetaMaster (from Malvern Instruments). The suspension was then circulated at flow rate of 10 ml/s through ultrasonic device. Small samples of suspension were withdrawn after different processing time and the particle size distributions were measured using Mastersizer 2000 (Malvern Instruments, UK). All de-agglomeration experiments were carried out at constant suspension temperature (20 °C) and at pH = 3. As the total volume of the dispersion in the experimental rig was 350 ml and the volume of the flow cell where the powder was exposed to the ultrasound was 80 ml, the specific energy input was calculated from: E¼
P tr Vcell
3
on the particles surface which is usually quantified by zeta potential. The zeta potential at different pH and salt concentration was measured using ZetaMaster and the results are shown in Fig. 3. The measured values of zeta potential indicate iso-electric point at pH = 8.9 that is in the range between 8.4 and 9.5 reported in the literature [3,14]. Whilst the strong dependence of zeta potential on pH was expected, the lack of the effect of salt on zeta potential was less obvious. Theoretically, presence of salt changes the ionic strength of the liquid therefore it should also affect zeta potential. However, Blakey and James [3] measured zeta potential of synthetic goethite powder in salt solutions and reported that to up 0.01 M salt does not affect zeta potential. At 0.1 M salt they observed the reduction of very high values of zeta potential (above 50 mV) but the lower values (below 40 mV) were practically not affected. Our results also indicate that zeta potential up to 40 mV is not affected by the presence of salt. In general, at zeta potential higher than |30 mV| the majority of solid/liquid suspensions [13] are stable as at this charge the
ð1Þ
and the mean residence time tr in the cell was calculated from: tr ¼
tt 1þ
Vt Vc Vc
¼ tt
Vc c0:23 tt : Vt
ð2Þ
The total ultrasonic energy input was controlled by adjusting ultrasound power input between 28 and 60 W and by varying processing time between 2 and 80 min what corresponds to the variation of the mean residence time in the cell between 27 s and 18 min. 3. Results and discussion 3.1. Zeta potential The kinetics of de-aggregation and the stability of a suspension of nano-particles is strongly affected by the charge
Fig. 4. Aggregate size distributions in salt free 5 wt.% goethite suspension: (a) transient size distributions at specific power input of 500 kW m− 3; (b) distributions at the same total energy input (200 MJ m− 3) but different specific power input.
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volume of primary nano-particles/small aggregates increases but the size of nano-particles does not change (see first mode in Fig. 4a). Considering the shape of single goethite nano-particle (see Fig. 1a) it is difficult to judge whether particles corresponding to the first mode (median of the order of 100 nm) are single, needle shaped nano-particles of the length of 100 nm or whether several of those nano-particles adhered to each other along the longest edges and formed aggregates also of the order of 100 nm. The aggregates' volume distributions measured at the same total energy input of 200 MJ m− 3 but at different specific power input shown in Fig. 4b practically overlap indicating that the total energy input controls breakage of the large aggregates. The bimodal transient size distributions cannot be analysed in terms of the mean sizes, therefore the analysis of both modes was carried out separately. The second mode was analysed in terms of transient median diameters of the large aggregates and the first mode was analysed in terms of cumulative volume fraction of primary particles. The experimental median diameters of large aggregates (corresponding to the second mode of volume distributions in Fig. 4a) shown as a function of processing time at different specific power input in Fig. 5a are rather scattered. These data can be collapsed into a straight line (within engineering accuracy, Fig. 5b) in log–log coordinates if diameters are
Fig. 5. Median diameters of the large aggregates in salt free 5 wt.% goethite suspension corresponding to second mode of transient distributions at different power input (○) — 354 kW m− 3, (◊) — 500 kW m− 3, (▽) — 750 kW m− 3 (a) as a function of mean residence time; (b) as a function of specific energy input.
electrostatic repulsive forces are sufficiently strong to overcome attractive van der Waals forces. Fig. 3 indicates that the suspensions of goethite nano-powder should be stable at pH b 3 and at pH N 12. In this range of pH the repulsive electrostatic forces should enhance de-agglomeration. Therefore the effect of energy input, solid concentration and ionic strength on deaggregation was investigated at pH = 3. 3.2. The effect of energy input on kinetics of de-aggregation Typical transient volume distribution functions of the aggregates in the suspension at specific power input of 500 kW m− 3 are shown in Fig. 4a and the volume distributions at the same energy density but at different power inputs are compared in Fig. 4b. The transient aggregates' volume distributions shown in Fig. 4a indicate that the kinetics and the mechanism of de-aggregation of goethite nano-powder at pH= 3 is similar to the de-aggregation of silica nano-powder [10] e.g. large aggregates of initially dry powder are gradually broken by erosion of single nano-particles/ primary aggregates (of the order of 100 nm) from their surface. As the time progresses the size of large aggregates decreases and the
Fig. 6. Cumulative volume fraction of the nano-particles in the first mode: (○) — 354 kW m− 3, (▽) — 500 kW m− 3, (□) — 750 kW m− 3: (a) as a function of mean residence time; (b) as a function of specific energy input.
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related to specific energy input according to an empirical sizeenergy model [9,10]:
Table 1 Parameters in Eq. (8) and the regression coefficients
d50 ¼ C Ea :
Specific power input [kW/m3]
β ⁎ 103 [−]
td [s]
r2
354 500 650
2.3 3.2 4.5
56.5 54.4 28.1
0.9856 0.9857 0.9932
ð3Þ
This model has been used to describe different types of breakage processes ranging from grinding of solid particles [15,16] where α of the order of 0.7 was reported to liquid/liquid emulsification in a different types of high shear mixers where α of the order of 0.4 [17] was reported. Breakage of large goethite aggregates investigated in this work can also be described by this model. The empirical constant α calculated by non-linear regression from experimental data shown in Fig. 5b is the order of 0.68 with a regression coefficient of 0.971. The first mode of transient volume distributions was analysed in terms of cumulative volume fractions of primary particles (or aggregates smaller than 350 nm) and the results are summarised in Fig. 6. Fig. 6a shows that the rate of formation of fine particles decreases with the processing time indicating erosion type of de-agglomeration and it can be described by: dyðt Þ ¼ bð1 yðt ÞÞ dt
ð4Þ
where experimental constant β depends on the type and strength of the aggregates Kusters et al. [8,9]. They solved Eq. (4) with the initial condition: y ð 0Þ ¼ 0
ð5Þ
and obtained the following expression for transient cumulative volume fraction of primary particles: yðt Þ ¼ 1 exp ðb t Þ:
ð6Þ
Eq. (6) indicates that the theoretical cumulative volume fraction of fine particles passes through the origin of the y, t coordinate systems. Experimental results shown in Fig. 6 and the results of batch de-agglomeration of silica nano-powder [18] clearly indicate that the fine particles appear after certain processing time. Very similar results were also reported by Kusters et al. [9]. These observations imply that before erosion commences a certain amount of energy has to be supplied to the aggregates and that requires a certain processing time. However, in the experimental arrangement used in this work samples were taken from stirred vessel not from the flow cell (see Fig. 2) therefore the delay time can result both from the circulation time and from the time necessary to form initial cracks in the aggregates. These results were incorporated into the theoretical model by assuming that the fine particles appear after a certain delay time td and by modifying the initial condition accordingly: yðtd Þ ¼ 0:
ð7Þ
Eq. (4) was integrated with initial condition (7) giving: yðt Þ ¼ 1 exp ½bðt td Þ
ð8Þ
where both β and td are system specific constants which were calculated from experimental data and the results are summarised in Table 1. For all values of the specific power input the proposed model fits experimental data very well up to the volume fraction of fine particles of the order of 0.8. As the specific power input increases the delay time is reduced and the erosion constant β increases indicating that at higher specific energy input erosion is faster. However, the experimental times necessary for complete breakage of all aggregates into primary nano-particles are considerably shorter than the times predicted by the model. This is an inherent feature of the model (both physical and mathematical) which assumes that erosion is proportional to surface area e.g. as the surface decreases with time (total number of aggregates stay constant) the rate of erosion also decreases and complete erosion can only be achieved (theoretically) after infinitely long time. Clearly the complete model of deagglomeration would have to account for a simultaneous erosion and fracture. 3.3. Effect of solid concentration on kinetics of de-agglomeration The effect of the solid concentration on de-agglomeration kinetics has been investigated at the specific power input of 500 kW/m3. Cumulative size distributions at different solid concentrations after different processing times are compared in Fig. 7. At all investigated solid concentrations the transient distributions (Fig. 7a and b) are bimodal with the median of the first mode of the order 100 nm being practically time independent and the median of the second mode decreasing with time from approximately 20 μm to 2 μm. Whilst, as shown by the first mode, the generation of primary particles is practically independent of solid content, the cumulative volume fraction of aggregates larger than 350 nm (second mode) depends on solid concentration and this dependence is stronger at lower total energy input (short processing time) than at higher total energy input (longer processing time). After sufficiently long processing time when all large aggregates are broken (see Fig. 7c), the cumulative distributions of primary nano-particles at 5 wt.%, 10 wt.% and 20 wt.% of solid are practically identical. The effect of solid content on de-agglomeration kinetics has also been analysed in terms of the reduction of median diameter of the second mode using size-energy model and in terms of the cumulative volume fraction of primary particles in the first mode. The results are summarised in Fig. 8.
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Fig. 8. The effect of goethite concentration in salt free suspensions on (a) median diameter of large aggregates and (b) cumulative volume fraction of fine particles at energy dissipation rate 500 kW m− 3.
The exponent in the size-energy model increases as the solid concentration increases indicating that the breakage rate (understood here as a time gradient of median diameter) also increases. Also the delay time increases with the solid concentration and the erosion efficiency is highest at the highest solid load. These results can be explained by more efficient utilisation of ultrasound energy in more concentrated suspension as shown in Fig. 9 where the median diameters and cumulative volume fractions are plotted as a function of specific energy input (energy input per mass of solid). Fig. 7. Cumulative size distributions at different solid concentrations in salt free suspensions: (a) and (b) transient, (c) steady state. (○) — 1 wt.%, (▽) — 5 wt.%, (□) — 10 wt.%, (◊) — 20 wt.%.
The transient median diameters of the large aggregates can be related to processing time via size-energy model: dav ¼ C Ea ¼ C Pa t a ¼ C1 t a :
Table 2 Coefficients in Eqs. (8) and (9) at different solid concentrations of goethite powder in suspension Solid content
ð9Þ
Experimental constants C1 and α calculated by non-linear regression from experimental data shown in Fig. 8a are summarised in Table 2. Fig. 8 and Table 2 indicate that the reduction rate of median diameter is higher at higher solid content.
Breakage of large aggregates
Cumulative volume fraction of primary particles
Coefficients in Eq. (9)
Coefficients in Eq. (8)
[wt.%]
C1 [m sα]
α [−]
r2
β ⁎ 103 [−]
td [s]
r2
1 5 10 20
40.4 62.8 103.6 159.3
0.59 0.66 0.72 0.81
0.8940 0.9624 0.8525 0.9742
3.64 2.967 3.068 3.068
49.69 53.20 55.26 57.28
0.9967 0.9941 0.9952 0.9805
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diameter) and to lesser extent by erosion. Only after the size of large aggregates falls in the range 0.5–5 μm does erosion becomes the dominant mechanism. This can be seen from Fig. 5 and also from Fig. 8 where after approximately 250 sec (aggregate size of the order of 2 μm) the experimental median diameters are practically the same for all concentrations of solid. Kusters et al. [9] reported that in batch de-aggregation of silica nano-powder at solid load up to 50% w/w the cumulative size distributions at different solid content were identical and that the breakage rate was independent of solid concentration, whereas as discussed above our results clearly show that there is a dependence between the solid load and de-aggregation rate. This difference can be explained by: a) different type of nanoparticles and/or (b) by different level of energy input. Kusters et al. [9] investigated breakage at specific power input of 62.5 kW/m3 whereas the results discussed above were obtained at a specific energy input of 500 kW/m3. 3.4. Effect of ionic strength on kinetics of de-agglomeration The ionic strength of the suspension was modified by the addition of salt at two different concentrations: 0.01 M and 0.1 M. The addition of salt did not affect zeta potential as discussed in
Fig. 9. The median diameters of the large aggregates (a) and cumulative volume fractions of small particles (b) at different solid contents in salt free suspensions as a function of specific energy. (●) — 1 wt.%, (○) — 5 wt.%, (▼) — 10 wt.%, (△) — 20 wt.%.
Fig. 9 shows that whilst the reduction rate of large aggregates is practically independent of solid content (all lines in Fig. 9a are practically parallel) breakage of aggregates in a concentrated suspensions starts at much lower specific energy input than in a diluted suspension. Also the volume fraction of primary particles at the same specific energy increases with the solid concentration. This clearly indicates that in the investigated range of solid load the efficiency of energy utilisation during de-agglomeration increases with the solid load which can be explained by the mechanism of breakage in the ultrasound systems. In such systems only aggregates which are close to collapsing cavities are broken by the forces resulting from large pressure gradients and/or from high velocity liquid jets generated by collapsing cavities. As the length scales of both types of forces are rather small (water is incompressible) only the aggregates close to collapsing cavities can be broken whereas the energy from the cavities collapsing far away from aggregates dissipates into heat. As the concentration of solid increases the number of the aggregates in a close proximity to collapsing cavities also increases therefore the efficiency of energy utilisation increases what explains the results shown in Fig. 9. It is also possible that as the solid content increases the size and the number of large aggregates present in the suspension after premixing also increases and initially those large aggregates might be broken also by fracture (very fast reduction of median
Fig. 10. Median diameters of large aggregates (a) and cumulative volume fraction of primary particles (b) in a 5 wt.% goethite suspension at specific power input of 500 kW m− 3: (○) — in distilled water, (▽) — in 0.01 M NaCl solution, (□) — in 0.1 M NaCl solution.
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constant α = 0.69, the delay time 53.6 s, erosion constant β of 0.00326). The identical values of the constants characterising erosion and breakage in the presence and in the absence of salt (at different ionic strength) are in agreement with the identical values of zeta potential discussed in Section 3.1 and confirm that ionic strength does not affect the mechanism of breakage during ultrasonication. This might be explained by very high specific ultrasound energy input so even if there were some changes in the repulsive inter-particle forces at such a high energy input they would be very difficult to detect. 3.5. Effect of solid content and ionic strength on the rheology of goethite suspension The flow curves at different concentration of solid were measured using a controlled stress rheometer AR 1000 (TA Instruments, UK) and the results are summarised in Fig. 11a. At all concentrations of solid the suspensions were nonNewtonian and the apparent viscosity was increasing with solid concentration. The viscosity of the suspensions at medium to high solid concentrations can be calculated from the Kreiger– Dougherty (K–D) equation [19]. / ½g/m g ¼ g0 1 /m
Fig. 11. Effect of solid concentrations on viscosity of goethite suspensions: (a) the flow curves, (b) viscosity as a function of solid concentrations, (●) — 1 wt.%, (○) — 5 wt.%, (▼) 10 wt.%, (△) — 20 wt.%.
Section 3.1. The transient volume distribution functions were also not affected by the presence of salt and were practically identical as the volume distributions shown in Fig. 7. The transient median diameters of the large aggregates and transient cumulative size distributions of primary particles shown in Fig. 10 are practically the same in the presence of salt and in the salt free suspension giving the same values of constants in Eqs. (8) and (9) (breakage
ð10Þ
where φm is the volume fraction of solid at maximum packing at which viscosity is equal to infinity. For several solid/liquid suspensions the product [η]φm is of the order of 2 [20] and Eq. (10) can be rearranged to give a simple relation between the viscosity of suspension and a solid volume fraction, so called MPQK equation [21–24]: rffiffiffiffiffi g0 / ¼1 : ð11Þ /m g It has been reported that Eq. (11) can be used with a wide range of solid/liquid suspensions up to 60 vol.% of solid [25]. Fig. 11b shows that in the investigated case MPQK equation fits the
Fig. 12. Flow curves (a) of 5 wt.% goethite powder suspended in: (○) — distilled water, (▽) — 0.01 M NaCl solution, (□) — 0.1 M NaCl solution and morphology (b) of suspension containing 0.1 M salt at pH = 3. The height of the image is equal to 136 μm.
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experimental data only up to approximately 3 vol.% (10 wt.%) of goethite nano-powder. At 5 vol.% (20 wt.%) there is a considerable deviation between the experimental results and the results predicted from Eq. (11). As Eq. (11) was derived for the solid suspensions where the particles interact only via liquid continuous phase (pure hydrodynamic interaction) the results shown in Fig. 11b indicate that in goethite suspension at pH= 3 the attractive or repulsive inter-particles forces cannot be ignored when considering the effect of concentration on the rheological properties. The addition of salt had relatively strong effect on the rheology and, at higher concentration, on morphology of suspension. The flow curves for salt free suspension and for suspensions containing different amount of salt as well as morphology of the suspension at the highest salt concentration are shown in Fig. 12. At 0.01 M salt the suspension was very weakly nonNewtonian with average apparent viscosity 3 times higher than viscosity of salt free suspension. At this salt concentration the flocculation of nano-particles was not observed. As the salt concentration was increased to 0.1 M the suspension became non-Newtonian and strongly shear thinning. This change of rheology can be explained by the change of morphology and flocculated structures observed under optical microscope are shown in Fig. 12b. The analysis of several images taken at the same magnification indicate presence of a single spherical aggregates of the order of 2 μm (see Fig. 1a for single nano-particles) which tend to flocculate further into much larger, irregular flocks. Neither small aggregates nor large flocks were detected in the images of salt free suspension or in the images of the suspension containing 0.01 M salt. The increase of ionic strength leads to the reduction of Debye length from 3.04 nm at 0.01 M salt to 0.96 nm at 0.1 M salt. According to Isrealachvili [26]: 1 0:304 ¼ pffiffiffi j c
ð12Þ
therefore the electrostatic repulsive force is reduced by half: el F0:1 exp ðj1 xÞ c½ exp ð xÞ½ exp ðj1 þ j2 Þc0:5 exp ð xÞ: c el exp ðj2 xÞ F0:01
ð13Þ The above analysis carried out within DLVO model does not take into account structural forces between surfaces [14,27] which strongly depend on the type of surface hydroxyl groups. One might expect that at such low pH those forces might play substantial part in aggregation of goethite nano-particles, but the detail analysis of such complex phenomena is well outside the scope of this work. Recently Blakey et al. [3] investigated the stability and rheology of the suspension of synthetic goethite nano-particles of similar size and shape to the nano-particles used in this work and found that at low pH and volume fraction of 1% the suspension is non-viscous what is similar to our results. They also reported the aggregation/flocculation but postulated that this was due to the different faces of irregular nano-particles having different electrostatic charges. This
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suggestion might also be valid in our case. Clearly the relation between inter-particle forces, morphology and rheology in the suspension of goethite nano-particles in aqueous solutions is far from obvious and further work relating inter-particle forces to structure and rheological behaviour is necessary. 4. Conclusions This study has revealed that the mechanism of breakage of goethite aggregates built from acicular nano-particles of 100 nm length is similar to the mechanism of breakage of silica aggregates built from nearly spherical particles [10]. In both cases large aggregates of single modal size distributions are initially broken by fracture and at higher energy density, the erosion of primary particles/primary aggregates has been observed. This kinetics leads to bimodal volume distributions that cannot be analysed in terms of an average size. Therefore, a new method was used where both modes were analysed separately, breakage of large aggregates was analysed within size-energy law with the power index of 0.68 and a model describing generation of fines has been developed. This approach allows detailed description of deagglomeration and accounts for experimentally observed delay time. The increase of solid concentration from 1% to 20 wt.% leads to the reduction of energy input per unit mass of solid necessary for complete de-agglomeration, or in other words as the solid load increases the de-agglomeration energy efficiency increases. In the investigated range of parameters (pH, temperature) the suspensions of goethite nano-powder were Newtonian and the apparent viscosity was well correlated with goethite concentration up to 10 wt.% of solid by MPKQ equation [22]. Only at the highest solid concentration viscosity was higher than predicted by MPKQ equation what might be explained by needle shape of the particles. Increase of ionic strength caused by addition of salt lead to the increase of the viscosity of suspensions but did not affect the kinetics of de-agglomeration. At 0.1 M salt and 0.01 volume fraction of goethite nano-powder the suspension becomes nonNewtonian and shear thinning. These results indicate that the addition of salt leads to partial agglomeration and formation of irregular structures what would suggest the reduction of repulsive forces in the presence of salt. However, the zeta potential was not affected by the presence of salt, what indicates that electrostatic repulsive forces were not affected by the presence of salt. It is possible that non-DLVO forces are affected by presence of salt and this hypothesis is currently investigated. Acknowledgements This work is a part of PROFORM (“Transforming Nanoparticles into Sustainable Consumer Products Through Advanced Product and Process Formulation” EC Reference NMP4-CT2004-505645) project which is partially funded by the 6th Framework Programme of EC. The contents of this paper reflect only the authors' view. The authors gratefully acknowledge the useful discussions held with other partners of the Consortium:
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Glossary c: C: C1: d50: E: P: Vcell: Vt: r2: td: tr: tt: y: α: β: κ: η: ϕ: ϕm: η0: [η]:
ion concentration [mol/l] constant constant Median diameter of aggregates [m] specific energy input [MJ m− 3] power input [W] volume of flow cell [m3] volume of experimental rig [m3] coefficient of determination [−] delay time in Eq. (8) [s] mean residence time in flow cell [s] total processing time [s] cumulative volume fraction of fine particles [−] constant [−] constant [−] inverse Debye length [m− 1] viscosity of suspension [Pa s] volume fraction of solid [−] volume fraction of maximum packing solid [−] viscosity of Newtonian continuous phase [Pa s] intrinsic viscosity [Pa s]