Hydrodynamics of CNT dispersion in high shear dispersion mixers

Transcription

1 Korea-Australia Rheology Journal, Vol.26, No.4, pp (November 2014) DOI: /s Hydrodynamics of CNT dispersion in high shear dispersion mixers Young Min Park 1, Dong Hyun Lee 1, Wook Ryol Hwang 1, *, Sang Bok Lee 2 and Seung-Il Jung 3 1 School of Mechanical Engineering, Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju , Korea 2 Korea Institute of Materials Science, Changwon , Korea 3 Future Industry R&D Center, DH Holdings, Gwangmyeong , Korea (Received June 12, 2014; final revision received October 19, 2014; accepted October 20, 2014) In this work, we investigate the carbon nanotube (CNT) fragmentation mechanism and dispersion in high shear homogenizers as a plausible dispersion technique, correlating with device geometries and processing conditions, for mass production of CNT-aluminum composites for automobile industries. A CNT dispersion model has been established in a turbulent flow regime and an experimental method in characterizing the critical yield stress of CNT flocs are presented. Considering CNT dispersion in ethanol as a model system, we tested two different geometries of high shear mixers blade-stirrer type and rotor-stator type homogenizers and reported the particle size distributions in time and the comparison has been made with the modeling approach and partly with the computational results. Keywords: turbulent dispersion, CNT dispersion, homogenizer, CNT/aluminum composites, CFD 1. Introduction There has been an ever-demanding need for development of light-weighted structural materials in automobile industries to enhance the fuel efficiency of vehicles. One of promising alternatives replacing current steel-based structural components is the aluminum composites, since the aluminum density about 2.7 g/cm 3 is just roughly 35% of the density of steel. But at the same time the tensile modulus of Aluminum (~70 GPa for 1100-O) is again of 35% of that of normal steel and moreover its yield strength is roughly 100 MPa, which is far below as the standard structural material (Davis et al., 1982). In this regard, incorporation of the aluminum composites with reinforcement is necessary particularly with fibrous nano fillers such as carbon nanotubes (CNT). Advanced functionality and reliability of CNT-aluminum composites requires careful processing method particular in dispersion to realize desired strength enhancement. Dispersion of CNT in a liquid is often performed by roll-mills or sonication by ultrasound waves and related topics are reviewed elsewhere (e.g., Huang and Terentjev, 2012). However these conventional techniques are not preferred or even inadequate for the aluminum based CNT composites primarily due to the fact that the processing temperature of the aluminum is about 720 o C and that the wettability between carbon and aluminum is significantly poor with the contact angle 157 o with the interfacial energy up to 0.93 N/m (Brandes and Brook, 1992; Naidich, 1981). In addition, a scalable dispersion process should be employed to be applied to large scale casting and continuous *Corresponding author: wrhwang@gnu.ac.kr casting in automobile industries. Therefore we choose a mechanical dispersion technique using high shear homogenizers. There are distinct advantages in this particular approach: turbulence dispersion mechanism is still there at high temperature; non-wettability concern such as the fisheye formation can be avoided in strong turbulence; and finally controllable scale-up can be performed with the homogenizer. We remark that the presence of the turbulence due to very high shear rate is a distinctive feature of the present work, whose mechanism for dispersion is far different from that of the moderate high speed laminar mixer, such as shown in Choi et al. (2013). Homogenizers such as rotor-stators is characterized by a high-speed rotor in close proximity to a stator and it is called a high-shear mixing device due to very high shear rate of the order of 10 4 ~10 5 /s and thereby high energy dissipation (Paul et al., 2004). Calabrese et al. (2000) performed the drop size measurement in a rotor-stator device and the result has been correlated with a class of hydrodynamic models accounting for drop interaction with turbulence at various length scale. Utomo et al. (2008) investigated flow characteristics of a rotor-stator mixer computationally and reported that about 70% of energy is dissipated near the mixing head and jet velocity scales with the rotor speed N, while the energy dissipation scales with N 3. Kamiya et al. (2010) proposed the homogenization coefficient, based on the power number, the flow number and shear frequency between rotor blades and stator holes to assess the homogenization effect for different rotor-stator combinations. As a part of the continuous development of light-weighted CNT-aluminum structural composites, we present a modeling approach for CNT in ethanol as a model dispersion 2014 The Korean Society of Rheology and Springer 347

2 Young Min Park, Dong Hyun Lee, Wook Ryol Hwang, Sang Bok Lee and Seung-Il Jung system in this work, putting all other complexity aside, and two different geometries of high shear homogenizers are tested in experiments and reported the particle size distributions in time. The comparison has been made with the modeling approach and partly with the computational results. 2. Hydrodynamic Modeling on CNT Dispersion The CNT flocs are primarily bonded by itself due to the strong van der Waals force and understanding the critical stress to break a CNT floc is essential in development of the hydrodynamic dispersion modeling. Start et al. (2006) measured the critical yield stress of multiwalled CNT suspended in a polymeric solution in a microfluidic trap that generates a (nearly) planar elongational flow and they reported a correlation between aggregate size and the critical elongational stress for fragmentation. The area of CNT floc A inf has been shown to scale with S 0.45, where S is the critical yield stress, and small fragments of µm are found very robust. Non-uniformity in floc composition is responsible for decreasing floc strength with aggregate size (Kusters, 1991). Let us rewrite the correlation of Start et al. (2006) for further development: S ~ d 4.4 (1) where d is the floc diameter. It would be worthwhile to mention the limitation of Eq. (1) in this work: Eq. (1) describes CNT breakup in a laminar elongational flow, which is very different from turbulence breakup in homogenizers, where shear and pressure fluctuation should be taken into account. Typical approach in deriving turbulence dispersion models are presented in Kusters (1991) for particle clusters and Calabrese et al. (2000) for droplets. In this work, we follow their approaches in high shear homogenizers, by substituting the expression in Eq. (1) relating CNT floc size to its yield strength S into the turbulent breakup criteria. Dispersion in turbulent flows is significantly different from that in laminar flows. Turbulent flow is characterized by various scales of eddy motions from the largest rotor scale to the Kolmogorov scale and by the successive energy transfer within eddies to smaller scale one, until it vanishes due to viscous dissipation at the Kolmogorov scale. Although there are various geometries of mixers from baffled agitators to ultrasound sonicators, the small scale turbulence structure that determines ultimate size of dispersed droplets or particles is independent of the device geometry, which allows the development of mechanistic analysis coupled with similarity arguments to develop correlations for the mean drop/particle size (Paul et al., 2003). The small scale turbulence structure that is related with the dispersed drop/particle size is likely isotropic, which means that the turbulent stress can be estimated by the isotropic turbulence theory with the energy cascade spectrum in the inertial subrange. The idea adopted in this work is that the eddy scales of the same as or smaller than the ultimate dispersed particle size influences the final dispersed state; the larger eddies will convect particle clusters (Calabrese et al., 2000). Then the turbulence stress is estimated simply by integrating the energy spectrum, E(k)=1.5ε 2/3 k 5/3, which is universally scaled with given turbulent energy disspation rate ε, over the relevant eddy length scales. (The symbol k indicates the wave number or the inverse of the eddy size.) Another mechanism that is related with the particle dispersion is that in the viscous subrange where no more eddy is present. This scenario needs to be considered, when the final dispersed size appears smaller than the predicted Kolmogorov scale. Let us first consider dispersion in inertial subrange where floc size is much larger than the Kolmogorov scale of turbulence, which seems to be a plausible mechanism. In this regime, the breakup criteria can be written in terms of the turbulence stress τ acting on the scale d of the floc size: τ ρε 2/3 d 2/3 S (2) where ρ is the fluid density and ε is the turbulence energy dissipation rate. Then one gets the following expression for the maximum particle size d max : d max ~ ρ 1/5 ε 2/15 ~ ρ 1/3 N 2/5 D 4/15 (3) where D is the rotor size. For CNT flocs less than 10 µm which is hardly fragmented according to Start et al. (2006), one can introduce a constant yield stress S and the maximum particle size d max can be expressed in this case d max = ---- S 3/2 1 --, i.e. d. (4) ρ ε max ~ ( N 3 D 2 ) 1 On the other hand, it is also possible to have fragmentation in viscous subrange when CNT flocs smaller than the Kolmogorov scale is observed, though it is a bit questionable to occur in practical dispersion. In the viscous subrange, the shear stress, a driving force for dispersion, is expressed as τ = (2/15ρμε) 1/2 with the μ being the kinematic viscosity of a fluid, and the maximum particle size is then scaled as follows: d max ~ ( ρμε) ~ ( ρμ) N D (5) Assuming that d max would scale with the mean floc size, the experimental measurement may reveal the correct breakup criteria. It is interesting to recognize that the critical yield stress modeling for CNT flocs in turbulence flows might be identified by extremely careful experiments. We remark that floc yield strength in a laminar uniform shear/elongation may differ from that in turbulence especially in 348 Korea-Australia Rheology J., Vol. 26, No. 4 (2014)

3 Hydrodynamics of CNT dispersion in high shear dispersion mixers inertial subrange where pressure fluctuation governs. Let us begin with a power-law correlation A inf ~S a in this case. The factor a is negative, since flocs are generally non-uniform in composition resulting in decreasing floc strength with size, as mentioned earlier. Following the previous procedures, one gets the maximum particle size in terms of the factor a: 3a 23 d max ~ ρ ( a) a ε 3 a a ~ ρ 23 ( a) a a N 3 a D 3 a. (6) At least in theory, one can find the factor a of the critical yield stress model by mean floc size measurements with respect to the rotor speed N or rotor scale D, though it has been failed in the current work unfortunately. Before closing this section, we would like to emphasize that the dispersion mechanisms that yields ultimate particle size in two different rotor geometries in this work or more exactly in any turbulent dispersion devices are essentially the same in the theoretical viewpoint. The dispersion mechanism in the inertial subrange or in the viscous subrange is universal, except for the laminar flow. Dispersion performance is determined by the maximum turbulence energy dissipation rate and its distribution due to the geometry. The distribution is important, since it determines how many particles will experience the maximum energy dissipation, turbulence stress and eddies. 3. Experiments Fig. 1. (Color online) Two types of high shear mixers: (a) the blade-stirrer type (Heungbo Neo II); (b) the two-stage rotor-stator type (Heungbo Neo V). Figures on the bottom are geometries used for numerical simulations where only one fourth of the geometry is along with the applied boundary condition in numerical simulations. We performed experiment for CNT in ethanol as a model dispersion system particularly to reduce wettability concern. A commercially available CNT (MWCNT CM- 95, Hanwha Nanotech, Korea) with the diameter nm, the length µm and the density g/cm 3 has been employed. As shown in Fig. 1, two types of high shear mixers are used. One is a blade-stirrer type (Neo II, Heungbo Tech Co., Korea), with a single axial discharge (up-pumping) rotor of the diameter D = m in a stator with eight circular holes at the exit. The gap between rotor and stator ranges from mm (for only small volumes of the narrowest region) to the order of the rotor radius. The other is a rotor-stator type (Neo V) from the same company with a two-stage radial discharge rotor of the diameter D=0.022 m in a two-stage stator. The gap between rotor and stator in this case is almost constant around 0.5 mm. The blade-stirrer type (Neo II) is known as a moderate dispersion mixer with the relatively wide particle size distribution but is easy in manufacturing particularly with the graphite for high temperature environment in aluminum melt. On the other hand, the two-stage rotorstator type (Neo V) is believed to show better dispersion characteristics with narrow particle size distribution though it is hard to manufacture with the graphite for its complex geometry. Viscosity measurement for CNT-ethanol suspension has been carried out with an oscillatory rheometer (Physica MCR 301, Germany) with the double-gap concentric cylinder unit. In addition, floc size distribution has been measured with a laser diffraction particle analyzer (Fritsch Analysette 22, Germany). Presented in Fig. 2 are the particle size distributions of the blade-stirrer type (Neo II) for 1 wt% CNT suspension in ethanol with N=2000 rev/min and 4000 rev/min at three different elapsed times: 10 min, 30 min and 60 min. The Reynolds numbers, defined as Re = ρnd 2 /μ, are and 33000, respectively. For N = 2000, no dispersion has been observed and even agglomeration appears due to floc collision in dense suspension (Fig. 2a), which indicates that the maximum turbulence stress over the fluid volume in this case does not overcome the critical yield stress of 100 µm CNT flocs. On the other hand, further increase of the rotor speed up to N = 4000, dispersion of CNT flocs occurs and gradual reduction in the mean floc size can be observed (Fig. 2b). The number density of flocs of µm size increases monotonically in time and the number Korea-Australia Rheology J., Vol. 26, No. 4 (2014) 349

4 Young Min Park, Dong Hyun Lee, Wook Ryol Hwang, Sang Bok Lee and Seung-Il Jung Fig. 2. (Color online) CNT floc size distributions for 1 wt% CNT suspension in ethanol from the blade-stirrer type (Neo II) with (a) N = 2000 rev/min and (b) 4000 rev/min at three different dispersion time: 10 min, 30 min and 60 min. Fig. 3. (Color online) CNT floc size distributions for 1 wt% CNT suspension in ethanol from the two-stage rotor-stirrer type (Neo II) with (a) N = 2000 rev/min and (b) 4000 rev/min at three different dispersion time: 10 min, 30 min and 60 min. mean diameter of flocs d mean reduces gradually: 56 µm in 10 mins, 45 µm in 30 mins and 33 µm in 60 mins. (The operation time in experiments is limited to one hour due to excessive heat generation in the homogenizer.) Plotted in Fig. 3 are experimental particle size distributions from the two-stage rotor-stator type homogenizer (Neo V) with the same conditions as the previous experiments for direct comparison of the dispersion characteristics. In contrast to the previous blade-stirrer type, it shows efficient dispersion already with N = 2000 (Re = 10500) in Fig. 3a: the number mean floc diameter is reduced in time in the order of 50 µm, 41 µm and 39 µm at 10, 30 and 60 min, respectively. The number density of flocs of size µm keeps increasing in time. For a higher rotor speed N=4000 (Re=21000) in Fig. 3b, the number mean diameter of flocs reduces from 37 µm at 10 mins to 30 µm at 30 mins; and then elevates up to 39 µm in 60 min. It is interesting to see that the optimal dispersion is observed after 30 minute operation and it has been turned out to be deteriorated later on. In addition, another peak in the distribution appears near 50 µm. Excessive high shear rate in this case seems to be responsible for enhanced floc coalescence due to increase in collision frequency. The largest number density of flocs is found near 20 µm, which is smaller than the two previous cases. In Fig. 4, we presented the mean floc size in terms of the rotor speed from the above two experimental data at 60 min. Notice that the slope in a log-log plot for the two different homogenizers appears very similar, which implies that hydrodynamic dispersion mechanisms in both cases may be identical. The data in Fig. 4 can be directly compared with the previous dispersion model in Eq. (6) and the least-square fitting yields the correlation between the mean drop size and the rotor speed: d~n In comparison with the factors in Eqs. (3)-(5), the most likely dis- Fig. 4. (Color online) The number mean floc size as a function of the rotor speed for the two different homogenizers with CNT suspension of 1 wt% in ethanol. 350 Korea-Australia Rheology J., Vol. 26, No. 4 (2014)

5 Hydrodynamics of CNT dispersion in high shear dispersion mixers persion mechanism might be the turbulent dispersion in inertial subrange with the factor 0.4. In addition, from Eq. (6), one can determine the factor a in the expression of the critical yield stress of CNT flocs and by simple manipulations one gets A inf ~S a (a = 0.43), which is close to the factor 0.45 of Start et al. (2006) for a laminar planar elongational flow. At least from this result, one might conclude that the critical yield strength in turbulence would be not much different from that in a laminar flow. However, it would be worthwhile to mention some limitations and assumption in this analysis: floc size distribution is not the final one and effects of the agglomeration cannot be neglected. In addition, the number mean floc diameter is assumed to scale linearly with the maximum floc size. The viscosity dependence on shear rate has been also measured for CNT dispersed ethanol in Fig. 5. The shear viscosity is critical in setting up the processes such as casting and the continuous casting of CNT dispersed aluminum melt. Viscosity measurement was only possible for well dispersed mixtures: for the blade-stirrer type (Neo II) and the rotor-stator type (Neo V), N should be larger than 5000 rev/min and 4000 rev/min, respectively. Fig. 5 shows the highly shear thinning behavior such that the power-law index is close to 1 particularly in a low shear regime. Another interesting point is that the zero shear viscosity is reduced as the dispersion time increases. This might be related with the change in floc size distribution, temperature rise due to energy dissipation, or even effective floc swelling due to impregnation of fluid into porous flocculation, etc. In the actual CNT-aluminum suspension, the relative shear viscosity, i.e. viscosity normalized by the medium viscosity, is expected to behave in a similar way as in Fig. 5, which invokes strongly suppressed fluidity in low shear process such as in the continuous casting or even in casting near the end of cavity or near the top of the riser. 4. Numerical Simulations The corresponding CFD simulation has been performed using a commercial software (ANSYS CFX v.12) with the standard k ε turbulence model with the frozen rotor method to obtain instantaneous velocity fields. The simulation geometries for both types of homogenizers are already presented in Fig. 1 with the corresponding boundary conditions. The number of elements are about for the blade-stirrer type (Neo II) and for the rotor-stator type (Neo V). The working fluid is either aluminum melt at 720 o C or CNT dispersed ethanol (1 wt%) and in the latter case the viscosity value has been interpolated from shear-dependent viscosity data in Fig. 5, which yields around 4-6 mpa s. This brutal approach for the viscosity is inevitable to employ the two equation turbulence model: flow and orientation dependent viscosity model cannot be incorporated. Fig. 6 presents the smallest local Kolmogorov scale in computational domains as a function of the Reynolds number for the two different homogenizers with both CNT in ethanol (1 wt%) and aluminum melt. The Kolmogorov scale in the rotor-stator type (Neo V) always appears smaller than that in the blade-stirrer type (Neo II). In case of CNT suspension in ethanol, the Kolmogorov scale η subject to the experimental condition ranges from 6 to 10 µm. In spite of the limitation in the viscosity prediction, the Kolmogorov scale in this case seems to be much smaller than the floc size µm of the highest number density in experiments, which may partly support the argument that the most likely dispersion mechanism might be the Fig. 5. (Color online) The shear viscosity of CNT suspension in ethanol (1 wt%) with respect to the rotor speed and dispersion time for two different homogenizer types. Fig. 6. (Color online) The smallest Kolmogorov scale with respect to the Reynolds number for both CNT in dispersed in ethanol and aluminum melt for two different homogenizers. Korea-Australia Rheology J., Vol. 26, No. 4 (2014) 351

6 Young Min Park, Dong Hyun Lee, Wook Ryol Hwang, Sang Bok Lee and Seung-Il Jung (Neo V) is found to dissipate roughly 5 times larger energy than the blade-stirrer type (Neo II), which confirms the larger Kolmogorov scales in the former cases in Fig. 6, as η scales with ε 1/4 and ε behaves in the same manner as the power draw per unit mass. 5. Conclusions Fig. 7. (Color online) Dependence of the flow rate as a function of the rotor speed for both CNT in dispersed in ethanol and aluminum melt for two different homogenizers. turbulent dispersion in inertial subrange expressed in Eqs. (3) and (6). Plotted in Fig. 7 is the flow rate Q in terms of the rotor speed with both CNT in ethanol (1 wt%) and aluminum melt for the two different homogenizers. The flow rate per unit area on the exit Q/D 2 is found to scale linearly with the rotor tip velocity ND, which indicates that the dispersion process is scalable in terms of the productivity. This controllable scalability in flow rate and thereby in dispersion time is of great importance in practice and renders one of the major advantages in using the homogenizer for CNT dispersion in aluminum melt, since fast dispersion is necessary to avoid possible degradation of CNT in a hot aluminum melt. Finally the power draw per unit mass is presented in Fig. 8 as a function of the rotor speed. All data set shows the mean energy dissipation rate scales with N x with x similar to 3 or less, which is consistent with the measurement reported in Calabrese et al. (2000). The rotor-stator type Fig. 8. (Color online) Power draw as a function of the rotor speed for both CNT in dispersed in ethanol and aluminum melt for two different homogenizers. We present experimental and numerical studies on CNT dispersion in ethanol by high shear mixing devices as a simple model system to investigate the CNT dispersion characteristics, motivated by an ever-demanding need for CNT-aluminum composites in automobile industries. Two different geometries of homogenizers, say the blade-stirrer and rotor-stator types, have been investigated. Experimental measurement of floc size distribution has been correlated with the hydrodynamic CNT floc dispersion models and reported that the turbulent dispersion in inertial subrange seems to be the most likely route for dispersion. We also reported highly shear-thinning behavior in CNT suspension and the elevated zero shear viscosity. Numerical results include the Kolmogorov scale, the flow rate and the power draw for both the homogenizers with CNT suspension in ethanol and aluminum melt. Acknowledgments This work has been supported by the National Research Foundation of Korea funded by the Ministry of Education (NRF-2013R1A1A2A ) and by the Ministry of Trade, Industries and Energy, Korea, via the WPM Project (Nano Carbon Composite Materials). References Brandes, E.A. and G.B. Brook, 1992, Smithells Metals Reference Book (7 th ed.), Butterworth-Heinemann, Boston, MA. Calabrese, R.V., M.K. Francis, V.P. Mishra, and S. Phongikaroon, 2000, Measurement and Analysis of Drop Size in a Batch Rotor-Stator Mixier, in Proceedings of 10 th European Mixing Conference on Mixing, edited by van den Akker and Derksen, Elsevier. Choi, J.H., Y.W. Nam, and J.S. Hong, 2013, Microfluidic study on CNT dispersion during breakup of aqueous alginic acid drop in continuous PDMS phase, Korea-Aust. Rheol. J. 25, 1-8. Davis, H.E., G.E. Troxell, and G.F.W. Hauck, 1983, The Testing of Engineering Materials (4 th ed.), McGraw-Hill, New York, NY. Huang, Y.Y. and E.M. Terentjev, 2012, Dispersion of Carbon Nanotubes: Mixing, Sonication, Stabilization, and Composites Properties, Polymers 4, Kamiya, T., S.H. Sasaki, Y. Toyama, K. Hynyu, M. Kaminoyama, K. Nishi, and R. Misumi, 2010, Evaluation Method of Homogenization Effect for Different Stator Configurations of Internally Circulated Batch Rotor-Stator Mixers, J. Chem. Eng. Jap. 43, Korea-Australia Rheology J., Vol. 26, No. 4 (2014)

7 Hydrodynamics of CNT dispersion in high shear dispersion mixers Kusters, K.A., 1991, The Influence of Turbulence on Aggregation of Small Particles in Agitated Vessels, Ph.D Thesis, Eindhoven University of Technology. Naidich, J.V., 1981, The Wettability of Solids by Liquid Metals, Prog. Surf. Membr. Sci. 14, Paul, E.L., V.A. Atiemo-Obeng, and S.M. Kresta, 2003, Handbook of Industrial Mixing: Science and Practice, pp , Wiley, Hoboken, NJ. Start, P.R., S.D. Hudson, E.K. Hobbie, and K.B. Migler, 2006, Breakup of carbon nanotube flocs in microfluidic trap, J. Colloid Interf. Sci. 297, Utomo, A.T., M. Baker, and A.W. Pacek, 2008, Flow Pattern, Periodicity and Energy Dissipation in a Batch Rotor-Stator Mixer, Chem. Eng. Res. Des. 86, Korea-Australia Rheology J., Vol. 26, No. 4 (2014) 353