Aggregation and Disruption Mechanisms of Nanoparticulate

Mar 1, 2008 - Aggregation and Disruption Mechanisms of Nanoparticulate Aggregates. 2. Dispersion of Aggregates Using a Motionless Mixer...
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Ind. Eng. Chem. Res. 2008, 47, 2401-2413

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Aggregation and Disruption Mechanisms of Nanoparticulate Aggregates. 2. Dispersion of Aggregates Using a Motionless Mixer I. N. Seekkuarachchi† and H. Kumazawa* Department of Chemical Process Engineering, UniVersity of Toyama, Toyama 930-8555, Japan

A novel motionless mixer named Ramond supermixer (RSM) was used to disperse nanoparticle suspensions under the various process conditions. Commercially available nanoparticles, fumed silica (SiO2) of primary particle diameter (d0) ranging from 7 to 30 nm, zirconia (ZrO2) of d0 ) 12 nm, and titanium oxide (TiO2) of d0 ) 21 nm, were dispersed either in an ion-exchanged water or in aqueous ethylene glycol solutions. The smaller the d0, the harder it is to disperse the aggregates. Zeta potential was largely dependent on d0 and became independent of process variables and, hence, of aggregate diameter. By evaluation of energy barrier values, the aggregation during disruption was found to be negligible. Aggregate disruption was predominant at the viscous subrange. By balancing mechanical energy with turbulent disruptive energy, a mechanistic model was developed for aggregate disruption. The analysis of fractal dimension showed that nanoaggregates are made up by orthokinetic cluster-cluster collision. Fractal dimensions are invariant throughout the disruption process. The rheological measurements further confirmed the evaluated fractal dimensionality. Introduction Motionless mixers have widely been known in industry for the mixing of liquids, especially for highly viscous materials and to enhance heat and mass transfer. High performance with less energy, continuous operation, minimum space requirement, low maintenance cost, trouble-free operation, etc. make motionless mixers applicable to liquid-liquid mixing. Though the application of motionless mixers in solid dispersion in liquid media has been envisaged for more than 30 years, less information has been determined on their behavior and capabilities, and much of the work has been limited to free-flowing particles.1 Recent studies gave evidence of their beneficial features in solid dispersion in liquid media, but they were limited to simple particle analysis.2,3 Most of the existing studies have focused on describing process improvements such as the ways of getting high yields, process debottlenecking, etc. No information has been determined on their behavior and applications in dispersing solid-liquid dispersions, especially those with nanoparticles. The method for effectively dispersing nanoparticle aggregates with the aid of motionless mixers will be an indispensable alternative to high-energy homogenizers. In Part I,23 we focused on the kinetics of aggregation and disruption of nanosuspensions. Here, in Part II‡, the dispersion mechanisms of such suspensions using a novel motionless mixer named Ramond supermixer (Environmental Science Technology Corporation, Japan, called RSM hereafter) were investigated. Particle-size distribution, hydrodynamic mean diameter (dm), zeta potential (ζ), and suspension viscosity were investigated under the various combinations of operation variables: primary particle diameter (d0), sort of particle, dispersed-phase volume fraction (φ), continuous-phase viscosity (ηc), liquid velocity (VL), number of mixing units (N), and number of passages through RSM (n). A mechanistic model for the dispersion of aggregates with negligible simultaneous aggregation was developed by balancing the turbulent disruptive energy stress with the * Corresponding author. Phone/Fax: +81-76-445-6859. E-mail: [email protected]. † Fujifilm Corporation, R&D Management HeadQ., Production Eng. & Dev. Center, 577, Ushijima, Kanagawa 258-8577, Japan. Tel: 046586-1305. Fax: 0465-86-1023. E-mail: isuru_seekkuarachchi@ fujifilm.co.jp.

Figure 1. Internal arrangement of Ramond supermixer.

mechanical strength of the aggregate. The concept of fractal dimensionality was used to illustrate the aggregation behavior of particles. The mechanistic model was constructed under the viscous subrange, where the dispersion through the surface erosion becomes predominant. Suspension viscosity was also measured, and the static shear stress-shear rate relationship was correlated according to the Casson model. The concept of yield stress was employed to confirm the fractal dimension dimensionality obtained in the mechanistic model. Experimental Apparatus and Procedures Internal arrangement of Ramond supermixer is shown in Figure 1. This motionless mixer is composed of a series of diskshaped units up to 10, placed inside the casing of 36 mm in

10.1021/ie0714955 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/01/2008

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Figure 4. Influences of d0 on dm and dm/d0 for SiO2 at various n at φ ) 0.2, VL ) 0.373 m‚s-1, N ) 10, and ηc ) 1 mPa‚s.

Figure 2. Scattering curve I(q) versus q for SiO2, ZrO2, and TiO2 at various N, VL, and n.

Figure 3. Relationship between dg and dm for SiO2, ZrO2, and TiO2 at various n.

internal diameter and 300 mm in length. Each disk-shaped unit is separated by an O-ring. Each unit is composed of a pair of diverging and converging elements, and the configuration of either diverging or converging element is illustrated in Figure 1. On the surfaces of diverging and converging elements, groups of hexagonal cells of 2.2 mm in depth are arranged compactly like a honeycomb. Both elements have the same configuration. The liquid enters from the central part (through 10 mm diameter (D1) with metal thickness 2.5 mm), spreads in the radial directions to the circumference (D2), and then gathers toward the center. Such a configuration facilitates a large number of dispersions. Traditional motionless mixers suffer from limitations of producing high local turbulence, and in order to achieve such dispersions, a large number of mixing units are needed. The flow behavior inside RSM gives considerably high turbulence and eliminates the above limitations to a higher extent. The mean cross-sectional area for liquid flow in a mixing unit, Alm, was obtained as the logarithmic mean of cross-sectional areas for flows at internal and circumference sides (πD1H and πD2H, respectively),

(

Alm ) πH

D2 - D1

ln(D2/D1)

)

) 1.34 × 10-4 m2

(1)

The final suspension obtained in the stirred tank equipped with Ramond stirrer was transferred to a temperature-controlled reservoir maintained at 298 K. The suspension was then continuously fed into RSM by a three-stroke, high-pressure plunger pump (model KC70-13A, Hatsuda Kougyou Ltd, Japan). No alternations of aggregate size distributions compared to that in the stirred vessel were observed in the reservoir. Sensors of differential pressure transducers (DP15, Validyne Engineering Co.) were attached to the points 30 mm away from the top and bottom plates of the mixer, and the pressure drop was recorded. Samples were collected from the immediate exit of the mixer and kept sealed until the measurement. Commercially available nanoparticles, fumed silica (SiO2) of d0 ) 7, 12, 20, 30 nm, zirconia (ZrO2) of d0 ) 12 nm, and titanium oxide (TiO2) of d0 ) 21 nm (Degussa Co., Germany), were used as received. The particles were preliminarily dispersed either in an ion-exchanged water or in an aqueous ethylene glycol solution (Wako Pure Chemicals Industries Ltd., Japan), using Ramond stirrer (Environmental Science Technology Corporation, Nagoya, Japan) in a vessel of 2 L capacity. The rotation speed of the stirrer (ω) was varied from 500 to 1500 rpm, and at each speed, mixing was continued until the mean aggregate size became constant. Thus, the aggregation of nanoparticles was considered to be completed before being fed into RSM, and no aggregation was found during the feeding process. The configuration of Ramond stirrer is similar to a mixing element (i.e., half unit) of RSM, which is composed of one diverging element with external diameter 0.036 m. The volumetric flow rate of liquid (QL) through RSM was adjusted at 5 × 10-5 to 1.58 × 10-4 m3‚s-1 (corresponding superficial liquid velocity (VL) ranged from 0.373 to 1.19 m‚s-1) with 8.33 × 10-6 m3‚s-1 intervals. The pressure drop through the mixer was measured with differential pressure transducers (DP15, Validyne Engineering Co.). The number of units (N) was fixed at N ) 1, 2, 3, 4, 6, 8, and 10, and the number of passages through the RSM (n) was adjusted at 1-20. Continuous-phase (disperse medium) viscosity (ηc) was varied from 1.0 to 50.0 mPa‚s, and the dispersed-phase volume fraction (φ) was varied from 0.01 to 0.3. Particle-size distribution and zeta potential were measured using zeta size nanoseries (NanoZS, Malvern Instruments, U.K.). The aggregation rates were obtained by measuring transmission light intensity. Suspensions were characterized using ultra-small-angle X-ray scattering (USAXS) by Nanostar (Bruker AXS, provided by MAC Science, Japan). A rotational viscometer (B8L, Tokyo Keiki, Japan) was used to make rheological measurements. A rotational viscometer (B8L, Tokyo Keiki, Japan) was used to make rheological measurements, and apparent viscosity obtained at a shear rate of 35.8 s-1 at 298 K was used in the model. The measurement techniques are described in detail in Part I.23 All the experiments were carried out at 25 °C ((1 °C).

Ind. Eng. Chem. Res., Vol. 47, No. 7, 2008 2403 Table 1. λ, Umax and Uk Values Obtained at Each n for SiO2 at N ) 10, VL ) 0.373 m‚s-1, O ) 0.1, and ηc ) 1 mPa‚s n 1 3 5 10 15 20

λ, nm 150 e λ e 190 138 e λ e 180 110 e λ e 158 98 e λ e 139 79 e λ e 119 69 e λ e 100

Umax, J 10-18

Uk, J 10-18

1× e Umax e 5 × 9 × 10-19 e Umax e 8 × 10-18 6 × 10-19 e Umax e 1.5 × 10-18 3 × 10-19 e Umax e 8 × 10-19 1.2 × 10-19 e Umax e 5 × 10-19 8 × 10-20 e Umax e 1 × 10-19

Results and Discussion Calculation of Fractal Dimension. The scattering curves, I(q) versus q, for SiO2, ZrO2, and TiO2 at different N, VL, and n for φ ) 0.1 and ηc ) 1.0 mPa‚s are given in Figure 2. Here, suspensions obtained at ω ) 1300 rpm are compared (n ) 0). At any experimental condition, the power-law regime was observed for the entire range of q. From the slope of the curve, β was calculated and found to be β ) 1.75-1.8. No change of β was observed due to turbulent mixing in RSM. This indicated that aggregates are stiff with stronger hydrodynamic forces between primary particles. Thus, dispersion does not alter the fractal aggregate structure, which indicates that reaggregation and reconfiguration by bond deformation under turbulent flow is negligible. Aggregate reaggregation and deformation largely result in increasing β, while constant β was found for disruption of aggregates by surface erosion.4

10-20

8× e Umax e 4 × 10-20 2 × 10-20 e Umax e 4 × 10-20 7 × 10-21 e Uk e 4.5 × 10-21 4.5 × 10-21 e Uk e 2.8 × 10-21 1 × 10-21 e Uk e 8 × 10-22 5 × 10-22 e Uk e 6 × 10-21

Figure 3 depicts the relationship between hydrodynamic mean diameter dm obtained by DLS and diameter of gyration (dg) obtained by USAXS. Diameter of gyration was ∼10% higher than mobility diameter (dg/dm ) 1.1). At any experimental condition, similar observations were obtained. This observation is similar to that with n ) 0, presented in Part I. Turbulent dispersion does not alter the relationship. Energy Dissipation Rate in RSM. The energy dissipation rate per unit mass of liquid and unit pass (w,MM) was obtained for RSM as follows:

w,MM ) (∆P)MMQL/VMMNFs

(2)

The void volume of mixer unit (VMM) was determined by water displacement, and the correlation of pressure difference with process variables was expressed as ∆PMM ) 0.270 ×

Figure 5. Influence of d0 on the particle-size distribution at VL ) 0.373 m‚s-1, N ) 10, and ηc ) 1 mPa‚s. Broken line represents the distribution of the feed into RSM.

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Figure 6. Influence of φ on dm and |ζ| at N ) 10, n ) 1, and ηc ) 1 mPa‚s and for SiO2 at various d0 and VL ) 0.373 m‚s-1, and for ZrO2 and TiO2 at various VL.

106VL2.08N0.815 (Pa). Since the power raised to VL is >2, it can be easily assumed that the flow inside the mixer is in fully turbulence.5 Effects of Operation Variables on Hydrodynamic Mean Diameter, Zeta Potential, and Geometric Standard Deviation. The effects of operation variables on hydrodynamic mean diameter, zeta potential, and geometric standard deviation of the particle-size distribution of suspensions passing through RSM are discussed below in the respective subsections. These suspensions were initially obtained by stirring at ω ) 1300 rpm. Effect of Primary Particle Diameter. The variations of hydrodynamic mean diameter dm and diameter ratio dm/d0 with d0 at different φ and n for N ) 10, VL ) 0.373 m‚s-1, and ηc ) 1 mPa‚s are shown in Figure 4. Similar observations as in Figure 7 of part I were observed. At any φ and n, similar variations were observed. The results indicate that the smaller the primary particle diameter is, the harder it is to disperse them. For the entire experimental range, dm/d0 ranged from 8 to 13 for d0 ) 7 nm, from 5 to 9 for d0 ) 12 nm, and from 4 to 6 for d0 g 20 nm. Higashitani et al.,6,7 who studied the dispersion of aggregates formed with micrometer-size polystyrene latex (PSL) particles of 0.59-1.27 µm, by contractile flow in orifice and ultrasonification, observed a similar leveling-off at large particle diameters. They simply related such leveling-off to the balance between the aggregate strength and the hydrodynamic drag

Figure 7. Influence of φ on the particle-size distribution at VL ) 0.373 m‚s-1, N ) 10, n ) 1, and ηc ) 1 mPa‚s.

Ind. Eng. Chem. Res., Vol. 47, No. 7, 2008 2405 Table 2. λ, Umax, and Uk Values Obtained at Each d0 for SiO2 at N ) 10, n ) 1, VL ) 0.373 m‚s-1, and ηc ) 1 mPa‚s d0, nm

λ, nm

Umax, J

Uk, J

7 12 20 30

135 e λ e 145 159 e λ e 180 175 e λ e 188 188 e λ e 202

1 × 10-18 e Umax e 4 × 10-18 3 × 10-18 e Umax e 6 × 10-18 5 × 10-18 e Umax e 8.5 × 10-18 4 × 10-18 e Umax e 9.6 × 10-18

7 × 10-20 e Uk e 9.7 × 10-20 6 × 10-20 e Uk e 8 × 10-20 5 × 10-20 e Uk e 7 × 10-20 4 × 10-20 e Uk e 6 × 10-20

force. In the present study, a decrease of aggregate strength with an increase of d0 was observed; therefore, such a balance does not seem viable. Here, the turbulent microscale (λ) varies with d0 at each n as follows: at n ) 1, λ ) 150-190 nm; n ) 3, λ ) 138-180 nm; n ) 5, λ ) 110-158 nm; n ) 10, λ ) 98-139 nm; and n ) 15, λ ) 79-119 nm. Except at n ) 1 and d0 ) 30 nm, d0 < λ; thus, viscous subrange prevails. The variations of the average values Umax and Uk (calculated by eqs 12-15 in part I) with d0 at each n are given in Table 1. At all the conditions, Umax > UK. Rc,v (calculated by eq 5 in Part I) decreases from 0.07 to 0.01 with increasing d0 from 7 to 30 nm. A 4% increase of Rc,v with ZrO2 as compared to SiO2 was obtained at the same d0 ) 12 nm, and the degree of increase with TiO2 was just 2%. The influence of d0 on the particle-size distribution at VL ) 0.373 m‚s-1, N ) 10, and ηc ) 1 mPa‚s at different n and φ is shown in Figure 5. The broken line represents the particulatesize distribution of the feed into RSM (i.e., n ) 0). About 60% decrease in aggregate diameter by just passing through the mixer (n ) 1) was observed at any φ. As d0 increased, the particlesize distributions shifted to larger particle-size range. The distributions exhibited a bimodal one at n ) 1; log-normal distributions were obtained at any d0 for n ) 10 and φ ) 0.05. For n ) 10 and φ ) 0.2, distributions slightly deviated from log-normal ones. Similarly, at small n and large φ, the distributions are more or less bimodal, whereas at large n, the distributions became log-normal even under large φ. To compare the polydispersity of the distributions obtained under the various process conditions, the geometric standard deviation of the particle-size distribution (σg) was calculated. σg increased from 1.14 to 1.39 at n ) 1, φ ) 0.05, and at n ) 1, φ ) 0.2, σg increased from 1.46 to 1.78 as d0 increased from 7 to 30 nm. For the similar range of d0 and for true log-normal conditions shown in Figure 5c, σg increased from 1.02 to 1.05, representing narrow distributions. Though the distributions shown in Figure 5d are apparently bimodal, σg varied from 1.08 to 1.20, representing comparatively narrow distributions. Effects of Sort of Particle and Dispersed-Phase Volume Fraction. Figure 6 was drawn in order to illustrate the effects of sort of particle and φ on dm and ζ. For SiO2, plots were drawn at different d0, whereas for ZrO2 and TiO2, plots were drawn at different VL. At d0 ) 12 nm, the aggregates obtained with ZrO2 particles were slightly larger (ca. 5%) than those with SiO2 and the same as those with TiO2 as compared with SiO2 of d0 ) ca. 20 nm. For any sort of particle, dm slightly decreased with increasing φ. With increasing φ, the packing density within the network of suspension increases. The abrasion between aggregates becomes effective; thus, a reduction in aggregate diameter with an increase of φ occurs. A common observation of increase of particle diameter with φ, due to the suppression of turbulent intensity with increasing φ, is not applicable here. For the purpose of comparison, the absolute value of ζ was taken. For SiO2, a large dependency of |ζ| on d0 was obtained; |ζ| ) 33-36 mV for d0 ) 7 nm, |ζ| ) 28-32 mV for d0 ) 12 nm, |ζ| ) 26-28 mV for d0 ) 20 nm, and so on. An increase of d0, resulting in comparatively less stable suspensions, but it should be noted that all the suspensions obtained are stable against sedimentation for weeks. For ZrO2 and TiO2, |ζ| ) 52-

55 and 26-29 mV, respectively, for the entire experimental range. A slight increase of |ζ| with increasing φ was obtained. For SiO2, as φ increases from 0.01 to 0.3, λ varies as given in Table 2. For ZrO2, as φ increases from 0.01 to 0.3, λ varies as follows: at VL ) 0.497 m‚s-1, λ ) 176-142 nm; VL ) 0.621 m‚s-1, λ ) 165-130 nm; VL ) 0.870 m‚s-1, λ ) 158-119 nm; and VL ) 1.119 m‚s-1, λ ) 145-100 nm. Similarly, for the entire range, dc,dm < λ. For SiO2, as φ increases from 0.01 to 0.3, Umax and UK decrease as given in Table 2. This data were obtained at VL ) 0.373 m‚s-1. An increase of VL from 0.373 to 1.119 m‚s-1 resulted in an increase of Umax and UK in 5% and 2%, respectively. Similar degree of variation was obtained with other sorts of particles. It was found that Umax > UK. The effects of φ on the particle-size distributions for SiO2 and ZrO2 at d0 ) 12 nm and for SiO2 and TiO2 at d0 ) 20 and 21 nm, respectively, are shown in Figure 7. With SiO2, for any process conditions, the distributions are in a true log-normal nature at φ < 0.1. As φ increases, the distributions become more bimodal in nature. At low N and n, regardless of other process variables, the distributions are mostly bimodal. Like in Figure 5c, at large N and n and low φ, the distributions became lognormal for any sort of particle, whereas for ZrO2 and TiO2, the distributions remain bimodal even at low φ for low N and n. As φ increased from 0.01 to 0.3, σg increased for the conditions drawn in this figure as follows: in Figure 7a from 1.02 to 1.41, in Figure 7b from 1.02 to 1.54, in Figure 7c from 1.08 to 1.61, and in Figure 7d from 1.09 to 1.59. It was observed that there was no significant effect of the sort of particle on σg.

Figure 8. Influence of ηc on dm and |ζ| at VL ) 0.373 m‚s-1, N ) 10, and n ) 1, and for SiO2 at various d0 and φ ) 0.1, and for ZrO2 and TiO2 at various φ.

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Figure 9. Influence of ηc on the particle-size distribution at φ ) 0.1, VL ) 0.373 m‚s-1, N ) 10, and n ) 1.

Effect of Continuous-Phase Viscosity. The effects of ηc on dm and ζ at VL ) 0.373 m‚s-1, N ) 10, n ) 1, and for SiO2 at various d0 and φ ) 0.1, as well as for ZrO2 and TiO2 at various φ, are shown in Figure 8. A continuous and rapid decrease of dm with increasing ηc was observed. The suspensions studied here were limited to the low viscosity range (i.e., ηc e 50 mPa‚ s). For any sort of particles, a similar rapid decrease of dm with increasing ηc was observed. ζ was independent of ηc, where it depended on d0, only for SiO2 as shown above. To illustrate the effect of ηc on the particle-size distributions, Figure 9 was drawn at φ ) 0.1, VL ) 0.373 m‚s-1, N ) 10, and n ) 1. Other conditions were the same as in Figure 7. Bimodal distributions were obtained at ηc e 3 mPa‚s, and as ηc increased, the distributions became log-normal. Even at low n for any process conditions, sharp log-normal distributions were obtained for ηc g 10 mPa‚s. As ηc increased from 1 to 20 mPa‚s, σg decreased for conditions drawn in this figure as follows: in Figure 9a from 1.39 to 1.02, in Figure 9b from 1.48 to 1.03, in Figure 9c from 1.41 to 1.02, and in Figure 9d from 1.49 to 1.03; for ηc g 20 mPa‚s, σg remained constant at 1.02. Here also, dc,dm < λ. An increase of ηc resulted in ca. 2% of variation in Umax and UK. Stabilization that was achieved by delaying the drainage time of interfacial film between two approaching particles was studied recently in the emulsion field. The same concept can be applied to nanosuspensions as well. Small molecules of ethylene glycol intervene between approaching particles or aggregates, and an

increase of continuous-phase viscosity at any particular energy input extends the microfilm drainage time, thus reducing the collision frequency. Therefore, aggregation or coalescence frequency is reduced, resulting in stable suspensions as shown in this figure. Effect of Number of Mixing Units. Figure 10 depicts the variation of dm at VL ) 0.373 m‚s-1, φ ) 0.1, ηc ) 1 mPa‚s, and for SiO2 at various d0 and n ) 1, as well as for ZrO2 and TiO2 at various n. As N increased from 2 to 3, a rapid decrease of dm was observed at any experimental conditions, and for N g 3, the effect of N was rather low. With an increase of N, the mixing length became longer, which gave rise to high pressure drops. The energy dissipation was enhanced, resulting in greater aggregate disruption. At the same time, due to high turbulence, aggregates were susceptible for more collisions and, thus, collision frequency increased. This resulted in some particle aggregation. The balance of these two effects could have resulted in deterioration of the influence of N on aggregate diameter, as shown in the figure. Some researchers, studying emulsions, found that the effect of N on the droplet size diminished with an increase of N and there existed a maximum of N to obtain effective droplet distruption.8,9 This can be attributed to the reduction of driving force for the droplet disruption, which is the difference between the local average droplet diameter and the equilibrium diameter. Passing the feed suspension through the mixer with N ) 2 resulted in a reduction of dm by ca. 60%. As N further increased from 2 to 3, the dispersion of aggregates

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Figure 10. Influence of N on dm at VL ) 0.373 m‚s-1, φ ) 0.1, and ηc ) 1 mPa‚s and for SiO2 at various d0 and n ) 1, and for ZrO2 and TiO2 at various n.

reached a dynamic equilibrium stage, and an increase of surface area available for dispersion by superimposing N resulted in no remarkable effect. In our previous paper studying micrometer and submicrometer emulsions with the same mixer, we obtained a continuous reduction of droplet diameters with an increase of N.5 In nanosuspensions, the resulting aggregates were strong enough to avoid further breakage due to the turbulent forces, thus reaching a dynamic equilibrium at such low N. |ζ| exhibited no dependency on N. The influence of N on the particle-size distributions at the same conditions as in Figure 10 except VL ) 0.621 m‚s-1 is shown in Figure 11 for different sorts of particles. N ) 0 represents the passing of feed suspension through the mixer with no elements. No significant differences between size distributions at N ) 0 and feed suspension were observed, suggesting piping and measurement valves should have no effect on dispersion. As N increased, the distributions were shifted to smaller diameter range. For N g 4, the distributions could be described by almost log-normal function. As N increased from 2 to 10, σg decreased as follows for conditions drawn in this figure: in Figure 11a from 1.41 to 1.07, in Figure 11b from 1.51 to 1.11, in Figure 11c from 1.43 to 1.08, and in Figure 11d from 1.53 to 1.18. At N g 6, large n and VL, log-normal distributions were obtained under any process conditions. Though dm remained unchanged with an increase of N, σg varied, resulting in sharp log-normal distributions. Effect of Liquid Velocity. The variations of dm with VL at φ ) 0.1, N ) 10, n ) 1, ηc ) 1 mPa‚s, and for SiO2 at various d0 and N ) 10, as well as for ZrO2 and TiO2 at various N, are shown in Figure 12. A rapid decrease of dm was observed with increased VL. The increase of VL results in a higher turbulent intensity, which enhances the aggregate disruption. On one hand, such an increase of turbulence could enhance the collision frequency between particles or small fragments, which might lead to an increase of dm with increasing VL. These two opposite effects are counterbalanced, and eventually the coalescence frequency decreased with increasing velocity. This led to a

reduction of particle diameters with increasing liquid velocity, as shown in this figure. Also, no dynamic equilibrium as with N was observed here. Though dm decreased with increasing VL, |ζ| was completely independent of VL. Accordingly, the aggregate diameter was less effective on |ζ|. The influence of VL on particle-size distribution at φ ) 0.1, N ) 10, n ) 1, and ηc ) 1 mPa‚s is shown in Figure 13. For VL e 0.621 m‚s-1, bimodal distributions were obtained. As VL increased, sharp log-normal distributions were obtained. As VL increased from 0.373 to 0.870 m‚s-1, σg decreased as follows for conditions drawn in this figure: in Figure 13a from 1.39 to 1.02, in Figure 13b from 1.49 to 1.03, in Figure 13c from 1.41 to 1.03, and in Figure 13d from 1.51 to 1.03; in VL g 0.994 m‚s-1, σg remained constant at 1.02. Similarly, log-normal distributions with σg ) 1.02 were obtained at VL g 0.994 m‚s-1 and any process conditions. Effect of Number of Passages Through RSM. Figure 14 depicts the variations of dm with n, at the same conditions as in Figure 12 and at VL ) 0.621 m‚s-1. An increase of n resulted in a considerable decrease of dm, and for n > 10, the effect leveled off. In other words, supply of energy beyond n ) 10 resulted in no effect on aggregate dispersion. A dynamic equilibrium stage was attained at n ) 10, and a further energy by increasing n was applied only to maintain the dynamic stage. A similar effect was observed for any sorts of particles. At large n and N and lower VL, log-normal distributions with σg < 1.05 were obtained, whereas at large n, N, and VL, the distributions can be described by a log-normal function with constant σg at 1.02. The distributions with n e 3 are most bimodal. |ζ| showed no dependency on n. Calculation of Disruption Rates. The degree of aggregation (Φ), defined in Part I, was determined from transmitting light intensity measurements. dΦ/dt can be assumed to be equivalent to simultaneous aggregation and disruption rates. The residence time in the mixer (t) was calculated as t ) (VMMN/AlmVL)‚n. The influences of VL on the relationship between Φ and t for SiO2 at φ ) 0.1and ηc ) 1 mPa‚s are shown in Figure 15. Here, t is calculated by varying N at constant n (n ) 1) for the top figure and by varying n at constant N (N ) 10) for the bottom figure. The data were plotted, and the lines were drawn, according to eq 8 in Part I, since viscous subrange prevails under aggregate disruption. At the initial stage, the process is solely dominated by aggregate disruption. Then an equilibrium is reached, where the rate of aggregation due to collision of small aggregates and the rate of disruption are balanced. The data and rate equations tally within an error of (5%. With the increase of VL, the equilibrium stage is achieved, at different residence times. It is interesting to note that these time limits correspond to the values of N and n that produced leveling-off with the variation of dm. For example, in Figure 10, dm became independent of N for N > 3. The time limits obtained in the top part of Figure 15 correspond to N ) 3 at each VL. Similarly, the effects of N and n on dm, shown in Figures 10 and 14, respectively, directly interrelated to the time limits in Figure 15. Figure 16 was drawn to show the effects of φ and ηc on the Φ-t relationship at N ) 10 and VL ) 1.119 m‚s-1. Variations of t are due to n. Disruption rates increased with the increase of φ, and especially at φ g 0.2, a considerable rise was observed. The increase of ηc resulted in an decrease of Φ, which is similar to the relationship between dm and ηc. Correlation of dm, σg, and |ζ| with Process Variables. The dependencies of process variables on dm, σg, and |ζ| were interpreted as the following correlations (MRC ) 98%).

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Figure 11. Influence of N on the particle-size distribution at φ ) 0.1, VL ) 0.621 m‚s-1, n ) 1, and ηc ) 1 mPa‚s.

For SiO2 at d0 e 20 nm and n e 10,

dm ) 30.0 × 10-9d00.3φ-0.04ηc-0.08VL-0.52N-0.05n-0.17 (m) (3) The proportionality constant for ZrO2 and TiO2 is estimated to be 31.5 × 10-9. The aggregate diameter largely depends on the size of the primary particle and the liquid velocity, and the effects of φ and N are trivial. Aggregates obtained with ZrO2 and TiO2 at almost the same d0 as SiO2 resulted in slightly larger aggregates. The effect of φ and ηc on dm is the same as that in mechanical stirring (eq 18 in part I). For any sort of particle at VL < 0.994 m‚s-1 and n e 10,

σg ) 1.3d00.15φ-0.20ηc-0.09VL-0.25N-0.09n-0.08

(4)

Like the effect of process variables on dm, large effects of primary particle size and liquid velocity were observed. Comparatively, a large effect of φ on σg was observed. Similarly, the following correlation for |ζ| was obtained for the entire experimental range,

|ζ| ) 6.0 × 10-2d0-0.25φ0.02 (V)

(5)

This is equivalent to the data obtained under the mechanical stirring (eq 19 in Part I). Mechanistic Model for Aggregate Disruption in RSM. For an isotropic turbulent flow lying in the viscous subrange, the

Figure 12. Influence of VL on dm at φ ) 0.1, N ) 10, n ) 1, and ηc ) 1 mPa‚s and for SiO2 at various d0 and N ) 10, and for ZrO2 and TiO2 at various N.

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Figure 13. Influence of VL on the particle-size distribution at φ ) 0.1, N ) 10, n ) 1, and ηc ) 1 mPa‚s.

maximum aggregate diameter can be obtained by balancing the mechanical strength of aggregate and the turbulent disruptive stress:10,11

σ)

( )( )

πFp w 4 d 6A ν m,max

(6)

Rumpf and Rumpf and Schubert proposed the following equation for σ.12,13

σ)

KψFA πdp2

(7)

For nonspherical polydispersed particles, it is shown that the aggregate internal structure is critically dependent on the mean aggregate size, and the strength is obviously decreased with the increase of size. Such an aggregate is considered to be consisted of a relatively weak outer layer made up of loosely bonded primary particles and a strong internal layer from densely packed particles. Shamlou et al.14 suggested that the coordination number (K) should be replaced by Ψ as K is proportional to Ψ1.2. This implies that σ is proportional to Ψ2.2FA/πdp2. Solid concentration within aggregate (Ψ) can be represented with fractal dimension (β). Simulation studies of aggregation processes suggested that β could be defined according to the mode of aggregation, such as β ) 1.75 for aggregation via orthokinetic

cluster-cluster collisions, β ) 2.5 for aggregation via particleparticle collisions, etc., which is discussed in detail in Part I. Ψ can be simply written in terms of β,15

ψ ∝ (β/β + 2)β/2(β/3)(dm/dp)β-3

(8)

Also, the cross-sectional area of rupture (A) can be considered proportional to dm2Ψ2/3. dm,max represents the particle diameter at 99.9% of the size distribution of number basis, and for the present study, dm,max ) 3dm. By substituting the above expressions, eq 6 can be reduced to

dm3β-11 )

()

π 2F p dp3β-7 w β/2 -3 6FA ((β/β + 2) β/3) υ

(9)

For the entire experimental range except at n e 10, dm was proportional to (w/ν)-0.17 within an error of (2%. dm became proportional to (d0)0.3, which was compatible with eq 3, and similar compatibility could be found with respect to other process variables. Back-calculation for β gave a value approximately equal to 1.75, suggesting that nanoaggregates should be formed with orthokinetic cluster-cluster collision but not with particle-particle collision. This further confirms the experimental values obtained by USAXS. The above model was developed by assuming negligible aggregation during motionless mixing. Calculation of Umax and

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Figure 16. Influence of (a) φ at ηc ) 1 mPa‚s and (b) ηc at φ ) 0.1 on the relationship between Φ and t at N ) 10 and VL ) 1.119 m‚s-1.

Figure 14. Influence of n on dm at φ ) 0.1, VL ) 0.621 m‚s-1, N ) 10, and ηc ) 1 mPa‚s and for SiO2 at various d0 and N ) 10, and for ZrO2 and TiO2 at various N.

Figure 15. Influence of VL on the relationship between Φ and t at different (a) N and (b) n and at φ ) 0.1 and ηc ) 1 mPa‚s.

UK values for the entire experimental range showed that Umax > UK. Rc,v was found to be a maximum of 0.08. Thus, aggregation can be easily neglected and the above model conforms to the data. Suspension Viscosity. Static shear stress measurements were made for suspensions obtained under stirring and passing through RSM, in order to understand the relationship between particle diameter and suspension viscosity. Stirring data were discussed here for easy comparison with RSM. The diagrams of shear stress (τ) versus shear rate (γ) for suspensions obtained under stirring at ω ) 1300 rpm and ηc ) 1 mPa‚s at different d0 of SiO2 are shown in Figure 17. At any d0, suspensions exhibited shear thinning behavior where the apparent viscosity depended on γ. The apparent viscosity decreased with an

Figure 17. Influence of φ on the relationship between τ and γ for stirring at ω ) 1300 rpm and ηc ) 1 mPa‚s.

increase of γ and reached a constant value in the range of γ g 35.8 s-1. A pronounced effect of φ on the τ-γ relationship was observed. The apparent viscosity drastically increased with increasing φ. It has been widely believed that the shear thinning is due to ordering of the aggregates into layers or strings, which ultimately reduces the energy dissipation under shear. The porous particulate structure can be distorted partially and, again, presumably leads to a decrease in the energy dissipation. An increase of φ resulted in forming a more dense structure, but the leveling-off effect of γ was obtained at the same value. In order to illustrate the effect of ηc on the τ-γ relationship, Figure 18 was drawn for the same stirring conditions as those in Figure 17, except at φ ) 0.1. A slight increase of apparent viscosity

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Figure 18. Influence of ηc on the relationship between τ and γ and for stirring at ω ) 1300 rpm and φ ) 0.1.

Figure 20. Influence of ηc on the relationship between τ and γ for mixing in RSM at φ ) 0.1, N ) 10, VL ) 0.621 m‚s-1, and n ) 1.

Figure 21. Relationship between ηs and dm with φ as a parameter at the entire experimental range for SiO2, ZrO2, and TiO2.

Figure 19. Influence of φ on the relationship between τ and γ for mixing in RSM at ηc ) 1 mPa‚s, N ) 10, VL ) 0.621 m‚s-1, and n ) 1.

with ηc was observed. It is obvious that the viscosity of the continuous particulate network increases with increasing continuous-phase viscosity; thus, the entire network viscosity increases. Figures 19 and 20 were drawn for RSM at N ) 10, VL ) 0.621 m‚s-1, and n ) 1. Again, a greater effect of φ on the

τ-γ relationship was obtained, but the apparent viscosities were much less than those with initial aggregates. For φ e 0.02, the suspensions exhibited Newtonian flow behavior, and the shear thinning behavior was obtained with increasing φ. The apparent viscosities became independent of γ beyond γ ) 35.8 s-1. Figure 21 illustrates the effect of ηc on the τ-γ relationship. This figure shows that the suspensions with ηc g 20 mPa‚s exhibited Newtonian behavior, whereas the suspensions with low continuous-phase viscosity did true shear thinning behavior. A completely opposite effect of ηc during the aggregate

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disruption process compared to the stirring process was observed, whereas in the former, the apparent viscosity drastically decreased with an increase of ηc. The exact reason for such observation is unclear, but it can be closely related to the reduction of aggregate diameter with increasing ηc. As the aggregate diameter decreased, the viscosity severely decreased. This will be discussed later. Nevertheless, in the stirring process, ηc gave only a slight effect of aggregate diameter. The rheological behavior, mainly the effect of φ, of nanosuspensions has been studied recently because of their importance in production processes. Al2O3 nanoparticles suspended in pure water with different pH values showed shear thinning behavior for φ e 0.16, like in our case.15 An apparent transmission from shear thinning to shear thickening was observed when the shear rate exceeded a critical value, and it was suggested to be due to the transformation of packing structure to the threedimensional structure from a fixed arranged two-dimensional structure.15,16 The arranged structure obtained in the present study was much more stable against shear stress, so such an effect was not noticeable. Several empirical rheological models, which are the twoparameter power-law, Bingham plastic, and Casson models and the three-parameter Herschel-Bulkley and Sisko models, are found in the literature to illustrate the effect of various factors on the τ-γ relationship.17 Shear thinning suspensions obtained in the present study for both stirring and aggregate disruption processes were correlated according to the above five models. The best fitting was obtained with the Casson model, which describes the τ-γ relationship.

τ ) (τy0.5 + ηsγ0.5)2

(10)

The yield stress (τy) represents the minimum stress needed to overcome interparticle attractions, so that individual particles or fragments at rest are able to slide over adjacent particles or fragments and allow flow to occur.18 It should be noted that this term is used as a model parameter rather than a true material property; however, such an analysis is overly important to understand rheological properties of suspensions. τy obtained under both processes within the entire experimental range was strongly influenced by φ, such that τy was proportional to φ3.16 with an error of (5%. For porous particulate structures, Shih et al. proposed the following formula for the relationship between τy and φ in terms of β, assuming van der Waals attractions to be predominant.20

τy ) (1 - C1κζ2)(HA/24s1.5)(1/dD-1.5)φm

(11)

The exponent m was defined as m ) (D + X)/(D - β). m equals 3.15 (error of (5%). The Euclidean dimension (D) and the fractal dimension of the backbone of the aggregates (X) can be assumed to be 3 and 1, respectively, for all sorts of particles.19-21 The value of β obtained from the above expression was closely equal to 1.75, which was the same value obtained by the fractal dimensionality analysis under the mechanistic model. Therefore, the fractal dimensionality obtained from the rheological data was confirmed by that predicted by fractal dimension analysis. The relationship between dm and suspension viscosity (ηs) obtained from eq 10 was plotted in Figure 21, as a parameter of φ. At any φ, a rapid decrease of ηs with the decrease of dm was obtained. A similar effect was obtained for any sort of particles. As the disruption of aggregates seems continuous, a network of densely packed structure with small aggregates is formed. Such a structure is less influenced by the shear stress

during viscosity measurements; thus, a considerably low viscosity was gained. The following correlation was obtained for the entire study (MRC ) 99%).

ηs ) C2dm10φ1

(12)

Here, C2 varies from 2.5 to 2.8, depending on the sort of particle, and it should be noted that C2 is independent of d0 and the other process variables. Conclusion A novel motionless mixer named Ramond supermixer (RSM) was used to disperse aggregated nanoparticle suspensions under various process conditions. Suspensions were initially obtained by mechanical stirring in a stirred vessel. Commercially available nanoparticles, fumed silica (SiO2) of primary particle diameter d0 ) 7-30 nm, zirconia (ZrO2) of d0 ) 12 nm, and titanium oxide (TiO2) of d0 ) 21 nm, were dispersed either in an ion-exchanged water or in an aqueous ethylene glycol solution. Dispersed-phase volume fraction (φ), dispersion medium viscosity (ηc), number of mixing units (N), liquid velocity (VL), and number of passages (n) through the RSM were varied in a wide range. The aggregate mean diameter (dm) largely depended on d0 and VL and weakly depended on φ and N. The smaller the d0, the harder it is to disperse the aggregates. Zeta potential was largely dependent on d0 and became independent of process variables and, hence, of aggregate diameter. The combinations of process variables were evaluated in order to obtain sharp distributions, with the aid of geometric standard deviation of the particle-size distribution. Pressure drop across the mixer was found to be proportional to VL2.08; thus, fully turbulent mixing was assumed. In RSM, the dispersion process occurred in a viscous subrange. The evaluation of maximum energy barrier, etc. showed that the aggregation within RSM could be neglected. Thus, only the aggregate disruption occurred. By balancing the mechanical energy with the turbulent disruptive energy at the maximum possible aggregate diameter, a mechanistic model was developed. The analysis of fractal dimension by ultra-small-angle X-ray scattering gave a value of ca. 1.75, which was equal to the feed in to the RSM. This indicated that reaggregation and reconfiguration by bond deformation under turbulent flow are negligible. Aggregates were made up from the orthokinetic cluster-cluster collision. Aggregate disruption occurred by surface erosion. For the dispersion process, dm became proportional to w-0.17, where w is the energy dissipation rate per unit mass. The static shear stress measurements were made to understand the effect of process variables on rheological behavior of suspensions. Shear thinning suspensions were obtained during stirring for any φ and ηc. φ revealed a prominent effect on the apparent viscosity. For the aggregate disruption process within RSM, suspensions became Newtonian at low φ and large ηc. The effect of ηc on apparent viscosity during stirring and disruption was reversed. The shear stress-shear rate relation was discussed according to the Casson model. The strong correlation between yield stress and φ was obtained. Rheological data were used to reconfirm the value of fractal dimension. Nomenclature A ) cross-sectional area of rupture, m2 C1, C2 ) constants appearing in eqs 11 and 12, respectively D ) euclidean dimension, m

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D1, D2 ) internal and external diameters of the mixing unit, respectively, as shown in figure 1, m dc ) collision model diameter, m d0 ) primary particle diameter, m dm ) hydrodynamic mean diameter, m di ) particle diameter, m dg ) geometric mean diameter defined by ln dg ) ∑ ni ln di/ ∑ni d ) average droplet diameter, defined by d ) ∑ dini FA ) force of attraction between particles or aggregates, N H ) depth of hexagonal cells of the mixing unit and the thickness of metal plate as shown in figure 1, m I ) scattering intensity, mm-1 K ) coordination number given in eq 7 l ) macroscale of turbulence, m MRC ) multiple regression coefficient m ) exponent raised to φ appearing in eq 11 N ) number of mixing units n ) number of passages through RSM q ) scattering wave vector, nm-1 QL ) liquid flow rate through RSM, m3‚s-1 s ) surface separation between particles, m T ) absolute temperature, K t ) residence time within RSM, s UK, Umax ) kinetic collision energy and maximum energy, respectively, J V ) cumulative volume fraction of particles, % VL ) superficial liquid velocity through RSM, m‚s-1 VMM ) void volume of the mixer unit, m3 V ) kinematic viscosity of continuous phase, m2‚s-1 X ) fractal dimension of the backbone of the aggregates Greek Letters Rc ) collision efficiency β ) fractal dimensionality γ ) static shear rate, s-1 (∆P)MM ) pressure drop across RSM, Pa w ) energy dissipation rate per unit mass of liquid, W‚kg-1 ζ ) zeta potential, V ηc ) continuous-phase viscosity, mPa‚s ηs ) viscosity of suspension defined by eq 10, mPa‚s λ ) turbulent microscale, m Fc ) density of continuous phase, kg‚m-3 Fp ) density of primary particle, kg‚m-3 σ ) aggregate strength, Pa σg ) geometrical standard deviation of the droplet-size distribution defined by ln σg ) x∑[ni(lndi-lndg)2]/∑ni τ ) static shear stress, Pa τt ) turbulent stress, N‚m-2 τy ) yield stress, Pa Ψ ) solid concentration with aggregate, wt % φ ) dispersed-phase volume fraction Φ ) degree of aggregation Subscripts c ) collision max ) maximum

MM ) motionless mixer (RSM) v ) viscous subrange Literature Cited (1) Gyenis, J. Motionless Mixers in Bulk Solids TreatmentssA Review. Kona 2002, 20, 9. (2) Bauman, I. Solid-Solid Mixing with Static Mixers. Chem. Biochem. Eng. 2001, 15 (4), 159. (3) Gyenis, J.; Ulbert, Zs.; Szepvogyi, J.; Tsuji, Y. Discrete Particle Simulation of Flow Regimes in Bulk Solids Mixing and Conveying. Powder Technol. 1999, 104, 248. (4) Wengeler, R.; Wolf, F.; Dingenouts, N.; Nirschl, H. Characterizing Dispersion and Fragmentation of Fractal, Pyrogenic Silica Nanoagglomerates by Small-Angle X-ray Scattering. Langmuir 2007, 23, 4148. (5) Seekkuarachchi, I. N.; Kumazawa, H. Characteristics of Micrometer and Submicrometer Size O/W Emulsions Produced by Ramond Supermixer. Chem. Eng. Commun. 2006, 193, 1333. (6) Higashitani, K.; Tanise, N.; Yoshiba, A.; Kondo, A.; Murata, H. Dispersion of Coagulated Particle by Contractile Flow to Orifice. J. Chem. Eng. Jpn. 1992, 25 (5), 502. (7) Higashitani, K.; Yoshiba, A.; Tanise, N.; Murata, H. Local Structure Analysis of the Mineral Core of Reverse Micelles in Dispersion in Hydrocarbons. Colloids Surf., A 1993, 81, 167. (8) Al Taweel, A. M.; Walker, L. D. Liquid Dispersion in Static In-line Mixers. Can. J. Chem. Eng. 1983, 61, 527. (9) Joshi, P.; Nigam, K. D. P.; Nauman, E. B. The Kenics Static Mixer: New Data and Proposed Correlations. Chem. Eng. J. 1995, 59, 265. (10) Levich, V. G. Physicochemcial Hydrodynamics; Prentice Hill: New York, 1962. (11) Wengeler, R.; Nirschl, H. Turbulent Hydrodynamic Stress Induced Dispersion and Fragmentation of Nanoscale Agglomerates. J. Colloid Interface Sci. 2007, 306, 262. (12) Rumpf, H. The Strength of Granules and Agglomerates. In Agglomeration; Knepper, W. A., Ed.; Interscience: New York, 1962; p 480. (13) Rumpf, H.; Schubert, H. The Behavior of Agglomerates under Tensile Strain. J. Chem. Eng. Jpn. 1974, 7, 294. (14) Shamlou, P. A.; Gierczycki, A. T.; Tichener-Hooker, N. J. Breakage of Flocs in Liquid Suspensions Agitated by Vibrating and Rotating Mixers. Chem. Eng. J. 1996, 62, 23. (15) Hiemenz, P. C.; Rajagopalan, R. Principles of Colloid and Surface Chemistry, third ed.; Dekker: New York, 1997. (16) Tseng, W. J.; Wu, C. H. Aggregation, Rheology and Electrophoretic Packing Structure of Aqueous Al2O3 Nanoparticle Suspension. Acta Mater. 2002, 50, 3757. (17) Tseng, W. J.; Lin, K. C. Rheology and Colloid Structure of Aqueous TiO2 Nano Particle Suspensions. Mater. Sci. Eng. 2003, A355, 186. (18) Turian, R. M.; Ma, T. W.; Hsu, F. L. G.; Sung, D. J. Characterization, Settling, and Rheology of Concentrated Fine Particulate Mineral Slurries. Powder Technol. 1997, 93, 219. (19) Casson, N. Rheology of Dispersed Systems; Pergamon: New York, 1959. (20) Shih, W. Y.; Shih, W.-H.; Aksay, I. A. Elastic and Yield Behavior of Strongly Flocculated Colloids. J. Am. Ceram. Soc. 1999, 82, 616. (21) Grant, M. C.; Russel, W. B. Distinguishing Between Dynamic Yielding and Wall Slip in a Weakly Flocculated Colloidal Dispersion. Phys. ReV. E 1993, 47, 2606. (22) Shih, W.-H.; Shih, W. Y.; Kim, S.-I.; Liu, J.; Aksay, I. A. Scaling Behavior of the Elastic Properties of Colloidal Gels. Phys. ReV. A: Gen. Phys. 1990, 42, 4772. (23) Seekkuarachchi, I. N.; Kumazawa, H. Aggregation and Disruption Mechanisms of Nanoparticulate Aggregates Using a Motionless Mixer. I. Kinetics of Simultaneous Aggregation and Disruption. Ind. Eng. Chem. Res. 2008, 47.

ReceiVed for reView November 3, 2007 Accepted November 26, 2007 IE0714955