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Aggregation Behavior of Latex Particles in Shear Flow Confined between Two Parallel Plates Yosuke Kikuchi,† Hirotsugu Yamada,† Hiromi Kunimori,† Takao Tsukada,*,† Mitsunori Hozawa,† Chiaki Yokoyama,† and Masaki Kubo‡ Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Katahira 2-1 -1, Aoba-ku, Sendai 980-8577, Japan, and Department of Chemical Engineering, Tohoku University, Aoba Aramaki, Aoba-ku, Sendai 980-8579, Japan Received August 6, 2004. In Final Form: January 25, 2005 In this study, the aggregation and breakup behaviors of latex particles in shear flow confined between two parallel plates were investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the effects of shear rate and the gap width between two parallel plates on the size and structure of the aggregates in the steady state, the distributions of the projected cross-sectional area and perimeter-based fractal dimension of the aggregates were measured. As a result, the average size of the aggregates decreases as shear rate increases and the gap width decreases due to the hydrodynamic effect acting on the aggregates. The size distributions of the aggregates become narrow as the gap width decreases. In addition, the fractal dimension, that is, the structure of the aggregates, was almost independent of shear rate and the gap width and approximately 1.2, which suggests that the aggregates are relatively compact.
Introduction The study of aggregation and breakup behaviors of fine particles under shear stress conditions is important for the understanding of product behavior in fine-particle manufacturing and polishing processes using abrasives slurries. Many experimental studies have been carried out to investigate the effect of shear flow on the size distributions and structures of particle aggregates. Vadas et al.1 developed a hydraulically driven traveling microtube apparatus with the aim of tracking the movements and interactions of individual latex particles of 2-µm diameter and aggregates in Poiseuille water flow through capillary tubes of 50-75-µm radii. They revealed that the formation and redistribution of aggregates with respect to size and geometry during downward flow in the tube depend on the magnitude of velocity gradient in the tube. Hunter and Frayne2 investigated the relationship between average aggregate radius rav and shear rate γ through shearing experiments on poly(methyl methacrylate) particles of 119-nm radius and reported that the average slope of the log(γ)-log(rav) plot is -0.42 ( 0.03 and does not appear to depend on the ζ potential of the particle. Spicer et al.3 investigated the effects of impeller type and shear rate on aggregate size and structure during the shear-induced aggregation of polystyrene latex particles in a stirred tank and suggested that the fractal dimension characterizing the aggregate structure is independent of shear rate in the steady state. Serra et al.4 and Serra and Casamitjana5 studied the aggregation and breakup behaviors of particles * Corresponding author. Tel: +81-22-217-5650. Fax: +81-22217-5651. E-mail:
[email protected]. † Institute of Multidisciplinary Research for Advanced Materials, Tohoku University. ‡ Department of Chemical Engineering, Tohoku University. (1) Vadas, E. B.; Goldsmith, H. L.; Mason, S. G. J. Colloid Interface Sci. 1973, 43, 630-648. (2) Hunter, R. J.; Frayne, J. J. Colloid Interface Sci. 1980, 76, 107115. (3) Spicer, T. P.; Keller, W.; Pratsinis, S. E. J. Colloid Interface Sci. 1996, 184, 112-122. (4) Serra, T.; Colomer, J.; Casamitjana, X. J. Colloid Interface Sci. 1997, 187, 466-473.
in Couette flow using a two-concentric-cylinder system with an inner cylinder rotating at constant speed and revealed that there are three different regimes for the dependences of shear stress and particle concentration on final aggregate diameter and that the transition between the two of them corresponds to that from laminar to turbulent flows. They also investigated the structure of aggregates under shear flow on the basis of fractal dimension, which indicates the high compactness of the aggregates and does not depend on shear rate. Berre et al.6 investigated the mass and size distributions of aggregates formed under a low shear rate by collisions between hydrated colloids of 1.09-µm diameter under marginal stability conditions and revealed that the particle concentration and ionic strength induce aggregate formation in different ways and that the fractal dimension of the aggregates becomes relatively small due to the existence of a preferential orientation of the aggregates at a low shear rate. Selomulya et al.7 used a small-angle light scattering technique to monitor the aggregate size and structure in the shear-induced aggregation of latex particles with different diameters in a circular Couette flow, and revealed that the restructuring of aggregate structures is favored for relatively small particles, for example, those of 60- and 380-nm diameters, whereas fragmentation and reaggregation were the main mechanisms governing the final aggregate size and structure for relatively large aggregates. Nazmul et al.8,9 studied the aggregation and breakup of asphaltenes in an organic solvent under Couette flow and revealed that an increase in applied shear rate leads to increases in aggregation and fragmentation rates, thereby reducing the steady(5) Serra, T.; Casamitjana, T. J. Colloid Interface Sci. 1998, 206, 505-511. (6) Berre, F. L.; Chauveteau, G.; Pefferkorn, E. J. Colloid Interface Sci. 1998, 199, 13-21. (7) Selomulya, C.; Bushell, G.; Amal, R.; Waite, T. D. Langmuir 2002, 18, 1974-1984. (8) Nazmul, H.; Rahmani, G.; Masliyah, J. H.; Dabros, T. AIChE J. 2003, 49, 1645-1655. (9) Nazmul, H.; Rahmani, G.; Dabros, T.; Masliyah, J. H. Chem. Eng. Sci. 2004, 59, 685-697.
10.1021/la048011j CCC: $30.25 © 2005 American Chemical Society Published on Web 03/04/2005
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Figure 1. Schematic diagram of the experimental apparatus.
state average aggregate size and the characteristic relaxation time required to achieve a steady state. Also, they modeled such an aggregation behavior using a population balance approach. In previous studies including some of the abovementioned ones, a light scattering technique was often used for characterizing the microstructure of aggregates. However, such a method reflects the average microstructure in an indirect way, and direct information on the dynamic behavior of the aggregates cannot be obtained on the micrometer scale. Recently, the direct observations of aggregates under shear flow using video microscopy or laser scanning confocal microscopy (CLSM) have been attempted. Hamberg et al.10 observed the aggregation behavior of protein-coated latex particles under shear flow generated by a four-roll mill using CLSM, as well as the viscosity measurement of the suspensions. They demonstrated the relationship between the aggregation structure type and the viscosity of the dispersions. Hoekstra et al.11 investigated the effect of shear flow on the structure of reversibly aggregated two-dimensional suspensions at an air-aqueous liquid interface using video microscopy and revealed that shear flow induces anisotropy, which was explained by a mechanism based on the directional dependence of the breakup and aggregation phenomena of flocs. Moreover, Tolpekin et al.12 studied the behavior of an aggregating suspension in shear flow using CLSM, in which 920-nm-diameter silica spheres were dispersed in a methanol/bromoform solvent and poly(ethylene glycol) was added to induce weak particle aggregation, and demonstrated that aggregate size is determined by the competition between cohesive forces caused by the polymer and rupture forces caused by the flow. However, there have been few studies on the aggregation and breakup behaviors of particles in shear flow confined between two parallel plates. The aggregation of particles may be suppressed by a confined space, and the flow field (10) Hamberg, L.; Walkenstrom, P.; Stading, M.; Hermansson, A. M. Food Hydrocolloids 2001, 15, 139-151. (11) Hoekstra, H.; Vermant, J.; Mewis, J. Langmuir 2003, 19, 91349141. (12) Tolpekin, V. A.; Duits, M. H. G.; van den Ende, D.; Mellema, J. Langmuir 2004, 20, 2614-2627.
around the aggregates may be completely different from the simple shear flow. The study of aggregation behavior in a confined space is important in the understanding of the size and structure of aggregates in crystallization and separation processes in a microchannel, filtration of particle suspensions, and polishing processes such as a chemical mechanical polishing. In this study, the aggregation behavior of latex particles in shear flow confined between two parallel plates was investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the effects of the shear rate and the gap width between two plates on the size and structure of the aggregates, the distributions of the projected cross-sectional area and perimeter-based fractal dimension of the aggregates were measured. Experimental Section Experimental Apparatus and Procedure. To observe the aggregation and breakup behaviors of latex particles in shear flow confined between two parallel plates, the experimental apparatus shown in Figure 1 was constructed, where the upper plate is a silicon wafer of 100-mm diameter and 0.5-mm thickness attached to a rotational axis in a vacuum and the lower one is a stationary circular glass plate of 150-mm diameter and 0.5mm thickness placed on a stainless steel susceptor. The upper silicon wafer also serves as a reflector to keep the view fairly bright. The distance between the two plates was adjusted in the range from 30 to 100 µm and the rotation rate of the upper plate in the range from 0.14 to 1.92 rpm. Consequently, the shear rates from 20 to 80 s-1 were achieved at a position 40 mm from the central axis. For each plate distance, an observation position was set 40 mm from the central axis and 15-25 µm above the lower glass plate surface. The inclination of the upper plate surface to the lower one was within 4.3 × 10-3 deg in all the experiments. In the experiments, first, the distance between the two plates was adjusted to 200 µm, and the prepared suspension was poured over the edge of the wafer using a pipet. Then, the suspension spontaneously flowed into the gap between the two plates due to capillary force. After confirming the lack of bubbles in the suspension, the distance between the two plates was immediately adjusted to a set value and the upper wafer was rotated at a given rate; then, the aggregation and breakup behaviors of the latex particles were observed from below through a window set on the stainless steel susceptor using a laser scanning confocal
Latex Particle Aggregation in Confined Shear Flow
Figure 2. Force-distance curve based on the DLVO theory. microscope of 632.8 nm (1LM15H, Lasertec Co., Ltd.). All the experiments were carried out in an air bath at 298 K. The images of latex particles recorded using a charge-coupled device camera were captured on a personal computer. From these images, the distributions of the size and projected area of the aggregates and their average values were analyzed using WinROOF (MITANI Co., Ltd.). Sample Preparation. A suspension of polystyrene latex particles of 2 µm ((1%) diameter (Polysciences., Inc.) was used in all the experiments, where uniform microspheres are suspended in distilled water, the volume fraction of solids is 0.025, and the particle specific gravity is 1.055 g/cm3. An aliquot of the latex particle suspension was diluted by adding aqueous solutions of NaCl and glycerol to form a suspension with a final solid concentration of 2.0 × 10-3 or 4.0 × 10-3 volume fraction in a 0.2 mol/dm3 NaCl aqueous solution. Here, glycerol was added so that the density of the suspension well approximated that of the latex particles, and consequently the sedimentation of particles was avoided during the experiment. In addition, the aggregated particles in the suspension were sonicated using an ultrasonic homogenizer (Sonifier 450, Branson Co., Ltd.) to ensure the monodispersion of the latex particles before the experiment. The zeta potential of the latex particles in the 0.2 mol/dm3 NaCl aqueous solution with glycerol was measured using an electrophoretic light scattering spectrophotometer (ELS-6000, Otsuka Electronics Co., Ltd.) and was found to be -28.4 ( 0.4 mV. Figure 2 shows the force-distance curve for the present system based on the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, by which we can understand the balance between two opposite forces, that is, electrostatic repulsion and van der Waals attraction. Here, an assumed value of the Hamaker constant, 1.3 × 10-20 J,13 was used as well as the measured value of surface potential. It is inferred that the present system shows a reaction-limited aggregation and that two particles aggregate if they overcome the slight potential barrier due to shear flow. For the present study using primary particles of 2-µm diameter, the Peclet number was found to be more than 150, which ensures that the aggregation due to Brownian movement can be neglected compared with the shear-induced aggregation.
Results and Discussion Figure 3 shows the micrograph of the latex particle aggregates in shear flow confined between two parallel plates 70 min after rotating the upper plate, where the shear rate is 80 s-1, the gap width between the two plates is 30 µm, and the volume fraction of the particles is 2 × 10-3. The circled aggregates in the figure are moving and rotating due to shear flow, while the obscure aggregates consisting of singlets, doublets, or triplets are those adhering onto the upper or lower plates. From the figures, it is found that the present apparatus with a confocal scanning laser microcope shown in Figure 1 is a powerful tool for ensuring the high-resolution direct observation of the aggregation behavior of latex particles in shear flow
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Figure 3. Micrograph of the latex particle aggregates in shear flow confined between two parallel plates for a shear rate of 80 s-1, gap width of 30 µm, and volume fraction of particles of 0.002.
confined between two parallel plates. In this work, the projected cross-sectional area and periphery length of the aggregates were measured from a photograph of the aggregates shown in Figure 3. Here, it was first judged which aggregates were moving between the two parallel plates but not adhering onto the plates, by comparing a given frame of photographs with the previous and next ones. Then, because the projected cross section of an aggregate was considered to consist of a number of circles with a given area of 2 × 2π/4 µm2, the periphery of the aggregate was approximated by the arcs, where the periphery was judged being based on the contrast to the background in the photograph. Subsequently, both the periphery length and the area surrounded by the periphery were evaluated using WinROOF. Figure 4 shows the time evolution of the average projected cross-sectional area of the latex particle aggregates, that is, aggregate formation (and breakup), at the shear rate of 80 s-1 and the gap width of 30 µm, at which the volume fraction of the particles is 2 × 10-3. In the present system, the aggregation is induced by an increase in collision frequency due to the shear flow between the two plates but not by Brownian coagulation, because of the relatively large primary particles of 2-µm diameter. In Figure 4, aggregate size increases with time t, and then the steady-state size of the aggregates is reached at approximately t ) 50 min. Although the aggregation is dominant in the early stage, at larger t, the breakup and aggregation become equally significant, and, thus, the steady state is maintained. Here, the experimental aggregation rate in the early stage was compared with the simplified expression derived on the basis of the Smoluchowski theory for shear-induced aggregations,14 that is,
( )
d(Nt/N0) 4φγ Nt )dt π N0
where Nt is the number concentration of aggregates, t is time, γ is the shear rate, and φ is the volume fraction of particles. As a result, the experimental aggregation rate evaluated in the early stage (t ) 0-3 min), -0.225 min-1, was in fair agreement with -4φγ/π in the above equation, -0.204 min-1, where Nt in the experiment was the number of the aggregates between the two plates counted with (13) Parsegian, V. A.; Weiss, G. H. J. Colloid Interface Sci. 1981, 81, 285-289. (14) Swift, D. L.; Friedlander, S. K. J. Colloid Sci. 1964, 19, 621647.
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Figure 4. Time evolution of the average projected cross-sectional area of latex particle aggregates for a shear rate of 80 s-1, gap width of 30 µm, and volume fraction of particles of 0.002.
time and N0 was the number of aggregates just before the upper wafer was rotated. In Figure 4, the distributions of the projected crosssectional area of the aggregates are also shown in the form of a histogram and a cumulative distribution curve obtained by averaging over each time interval. The relative number frequency of each class of projected area is calculated using j+1
frequency (Aj - Aj+1) )
ni/nT ∑ i)j
where the numerator is the number of aggregates whose projected cross-sectional area is in the range from Aj to Aj+1 and nT is the total number of aggregates. At the start, the area distributions of aggregates indicate the higher fraction of aggregates with a relatively small projected area. Then, with time, the distributions shift to a larger projected area and become broad, and the steady-state size is reached. Here, the reason the initial distribution is not monodispersed despite the initial preparation of a sample using a homogenizer is the unavoidable aggregation of particles during the adjustment of the width of the gap between two plates. Following the results of the time evolution of aggregation shown in Figure 4, the effects of the gap width and shear rate on the distributions of the projected cross-sectional area of particle aggregates mentioned below were investigated on the basis of the results obtained 70 min after rotating the upper plate, at which the elapsed time is considered to be sufficiently long to reach the steady state. Figure 5 shows the effect of shear rate γ on the distributions of the projected cross-sectional area of the latex particle aggregates for the two widths of the gap between two plates, (a) h ) 100 µm and (b) h ) 30 µm. Here, strictly speaking, the actual shear rate and gap width differ from those in the figures and fall within a certain range, for example, 27-35 µm for h ) 30 µm, because the adjustment to the set values was experimentally difficult. Therefore, the values in all the figures discussed below are target values to adjust and not actual values. For both widths, the average values of the projected area of the aggregates Aav decrease and the size distribu-
tions become narrow as γ increases. Particularly, the dependence of γ for h ) 100 µm is strong. The increase in γ enhances the breakup of aggregates due to shear force in the aggregation/breakup until the steady state is reached; the larger the size of the aggregates, the more significant the hydrodynamic effect on the aggregates. Figure 6 shows the effect of the widths of the gap between the two plates h on the distributions of the projected cross-sectional area of the latex particle aggregates for γ ) 40 s-1. From the figures, it is found that particle aggregation is markedly suppressed and the size distribution also becomes narrow as the gap width between the two plates decreases. This is considered to be due to the enhanced hydrodynamic stress acting on the aggregates which are placed in the confined space between the two plates. To summarize the results of the effects of shear rate and the gap width between two parallel plates on the average size of the aggregates mentioned above, the relationships between shear rate γ and (a) the equivalent diameter of the aggregates dav and (b) its scaled one with gap width h are shown in Figure 7, where dav is evaluated using 2(Aav/π)1/2. The aggregate size dav decreases with γ, and its dependence becomes stronger as h increases. Also, the smaller the gap width, the smaller the aggregates. In addition, Figure 7b suggests that the ratio of the average size of the aggregates to the gap width increases as h decreases, and the aggregate size is approximately one third the gap width for h ) 30 µm. The issue remains that the suppression of the aggregations accompanied by the decrease in the gap width between the two plates might be attributed to the reduction in the actual particle concentration between the plates due to adherence of the particles to the lower and upper plates during the adjustment of the gap width and the observation experiment. In particular, the effect of the adherence of particles is more significant for a smaller gap width. Therefore, another experimental observation of the aggregation behavior of latex particles in shear flow confined between two parallel plates was carried out, in which the upper silicon substrate was entirely covered by a thin film of SiO2 and the particle concentration was doubled, that is, 4 × 10-3 volume fraction. Because the
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Figure 5. Effect of shear rate on the distributions of projected cross-sectional area of latex particle aggregates for two gap widths between two plates at 70 min after rotating the upper plate.
Figure 6. Effect of gap width between two plates on the distributions of projected cross-sectional area of latex particle aggregates for γ ) 40 s-1.
surface of the silicon wafer was found to be much easier for the latex particles to adhere to than the glass plate surface, the coating with SiO2, which has the characteristics nearer that of the glass plate than the silicon wafer, was tested. Consequently, the particle concentration in the suspensions obviously increased. Figure 8 shows the distributions of the projected cross-sectional area of the aggregates in the form of a histogram and a cumulative distribution curve when h is 30 µm and γ is 20 s-1. Compared with Figure 5b, the distributions are almost the same. Therefore, it is clear that the suppression of aggregation is caused by the confined space between
two plates rather than by a decrease in particle concentration. Aside from the size of the particle aggregates, to investigate the effects of the shear rate and the gap width between two plates on the structure of aggregates during aggregation, the fractal dimension of the aggregates, a perimeter-based fractal dimension defined by the following equation for Dp, was evaluated.
log P ) (Dp/2) log A + C Here, A and P are the projected cross-sectional area and
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Figure 7. Effects of shear rate and gap width between two parallel plates on the average size of aggregates.
Figure 8. Distributions of projected cross-sectional area of aggregates for a shear rate of 20 s-1and gap width of 30 µm, where the upper silicon wafer was entirely covered with SiO2.
perimeter of an aggregate, respectively, and C is a constant. Dp ranges from 2, corresponding to a perfect linear aggregate, to 1, corresponding to a perfectly spherical aggregate. The relationships between P and A revealed that the fractal dimension Dp for every γ and h is approximately 1.2 as shown in Figure 9 and does not depend on the shear rate and the gap width between two plates. From the results, we can expect that particle aggregates in the present system have a nearly spherical projected area and are, thus, very compact. This fractal dimension and its independence of shear rate are almost the same as those reported by Spicer et al.3 and Serra and Casamitjana.5 Conclusions In this study, the aggregation behavior of latex particles in shear flow confined between two parallel plates was investigated using an in situ observation apparatus with a laser scanning confocal microscope. To investigate the
Figure 9. Effects of shear rate and gap width between two parallel plates on fractal dimensions of aggregates.
effects of shear rate and the gap width between two plates on the size and structure of the aggregates, the distributions of the projected cross-sectional area and perimeterbased fractal dimension of the aggregates were measured. As a result, the average size of the aggregates decreases as the shear rate increases and the gap width decreases due to the hydrodynamic effect acting on the aggregates. The size distribution of the aggregates becomes narrow as the gap width decreases. In addition, the fractal dimension, that is, the structure of the aggregates, is almost independent of the shear rate and the gap width and is approximately 1.2, suggesting that the aggregates are relatively compact. Acknowledgment. This work was funded partially by a Grant-in-Aid for Scientific Research (No. 10171969) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and partially by the Hosokawa Powder Technology Foundation. LA048011J
