Chemical Engineering Science 90 (2013) 10–16

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Chemical Engineering Science

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Complete CNT disentanglement–dispersion–functionalisationin a pulsating micro-structured reactor

Paul Michelis a,n, John Vlachopoulos b

a Institute of Mechanics of Materials and Geostructures S.A., IMMG SA, 22 Askiton Street, 15236 Penteli, Greeceb McMaster University, Department of Chemical Engineering, Hamilton, Ontario, Canada L8S 4L7

H I G H L I G H T S

c CNT disentanglement–dispersion–distribution is fully attained by a micro-reactor.c Also, functionalisation, leading to homogenised reinforcement, is complete.c Disentanglement–functionalisation are attained with negligible CNT attrition.c The reactor generates an extensional-shear-spiralling flow and is easy up-scalable.

a r t i c l e i n f o

Article history:

Received 24 August 2012

Received in revised form

15 November 2012

Accepted 3 December 2012Available online 12 December 2012

Keywords:

Chemical reactors

Dispersion

Mixing

Agglomeration

Carbon nanotubes

Functionalisation

09/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.ces.2012.12.003

esponding author. Tel.: þ30 210 8046477.

ail address: immg@otenet.gr (P. Michelis).

a b s t r a c t

Disentanglement, dispersion of CNTs without attrition and efficient interfacial interaction with polymer

chains are a major challenge in developing CNT/polymer composites. In the present device the mixture

of highly viscous polyphosphoric acid (PPA) and entangled MWCNTs fills a hollow cylinder where a

perforated piston, encasing micro-grids, is axially translating, oscillating and simultaneously rotating.

This generates an extensional-shear-spiralling flow, magnified in the entrance/exit zone of the grid

micro-openings, the smallest having diameter of 40 mm. The reciprocating action forces the agglom-

erates to cross the grid many times, while the oscillation reduces effectively the clogging of the grid.

Flow micro-splitting and recombination, across millions of micro-openings in a time dependent regime,

facilitated erosion and collision mechanisms to prevail, leading to a gradual CNT deagglomeration–

dispersion without CNT attrition. The resulting high multi-directional-rotational flow generated the

conditions for efficient functionalisation.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

A significant challenge in developing high performance polymer/CNT composites is the introduction of individual CNTs in a polymermatrix fully dispersed, functionalised, aligned and straightened(Hilding et al., 2003). This is a prerequisite for strong interfacialinteractions and therefore load transfer across the CNT–matrix inter-face. However, as-supplied CNTs (�3.66�1012 mm�3) are initiallyentangled and form agglomerates held together by steric interactionsas well as by Van der Waals forces. The extraordinary surface-to-volume ratio of as-supplied CNTs (�140 m2/cm3) make their disen-tanglement and dispersion extremely difficult (Delsman et al., 2005),particularly when one aims at eliminating attrition as well.

Using CNTs as a reinforcing component in polymer compositesrequires the ability to modify the nature of CNT’s walls in order to

ll rights reserved.

control the interfacial interactions between the CNT and the polymerchains. These interactions govern the load-transfer efficiency from thepolymer to CNT and the optimum procedure is to introduce covalentattachment of functional groups of the polymer to the CNT wall.Molecular dynamics simulations indicate that if only 1% of the carbonatoms of the CNTs form reactive bridges with a polymer matrix, asignificant improvement in mechanical properties of the polymer–CNT composite can be observed (Frankland et al., 2002). In addition,the covalent CNT functionalisation is an effective way to preventre-aggregation of separated CNTs.

Stirring and ultrasonication are used extensively for CNTdisentanglement, dispersion and functionalisation. Both techniquesdevelop flow patterns non-homogeneously distributed in themixture. Stirring is characterised by a shear flow, which in manyapplications is not achieving sufficient mixing, it is time consumingand when it becomes intense turbulence develops only alongperipheral zones, which may impart structural damage to CNTsdepending on exposure time and power level (Hilding et al., 2003;Suslick 1990; Sutherland and Tan, 1970). Ultrasonic waves develop

Fig. 1. Entangled CNTs, as received.

P. Michelis, J. Vlachopoulos / Chemical Engineering Science 90 (2013) 10–16 11

low shear forces and are associated with violent (microsecond timescale) collapse of cavitation bubbles, generating high local tempera-ture and high pressure (500 Atm) (Suslick 1990). Depending on theconditions, ultrasonic treatment of CNTs in methylene chloridecauses a considerable amount of defects, including buckling, bendingand dislocations (Lu et al., 1996).

CNT melt-mixing with polymers is more problematic sincemelt viscosity is several orders of magnitude higher than solutionviscosity and residence time is limited by polymer degradationand operational concerns. Recently, an accurate method to deter-mine CNT attrition, during melt mixing with polycarbonate,confirmed shortening of CNTs up to 30% for the products NanocylNC7000 and Baytubes C150HP (Krause et al., 2011). Three-rollcalendering was reported to achieve homogeneous dispersion ofCNTs in epoxy matrix but recent examination (Fu et al., 2009) ofthe CNTs length revealed severe reduction from �15 mm to�1.5 mm. The same extent of CNT length reduction (from�10 mmto�0.5 mm) was measured when CNT was melt mixed withpolyamide 6 (PA6) in a Brabender mixing machine with optimumblade geometry for the application (Logakis et al., 2009).Kasaliwal et al. (2010) carried out an analysis of agglomeratedispersion mechanism of CNTs during melt mixing in polycarbo-nate using a microcompounder (conical, corotating twin extruder)and concluded that no complete dispersion of the nanotubescould be achieved.

Recently, flow in micro-channels was proposed to promote themixing process, in which the mixing of the reactants usuallyoccurs in 10–500 mm wide channels (Luo et al., 2006). The smallchannel dimensions lead to a large surface area-to-volume ratioand also to increased driving forces for mass transport and heat.The sudden fluid flow expansion/contraction at the entrance/exitof microchannels and micro-orifices can generate adequate andcontrollable shear/extensional stresses, capable to reduce themixing time to reach milliseconds (Kumar et al., 2011). However,the narrow flow channels limit the flow rate and an efficientprocess to scale up to mass production has not yet been achieved.

In the present work, the development and validation of amicrostructured, active, reactor-mixer is presented. Operatingaround the principles of a time dependent pressure disturbanceand the imposition of rotation address the unique requirementsfor successful CNT disentanglements, dispersion, distribution andfunctionalisation. The reactor, which is easily upscalable, relies ona controlled combination of flow micro-splitting–twisting–fold-ing–recombination in a time dependent chaotic regime and it isespecially suited for highly viscous fluids.

2. Materials

The NC7000 multi-wall CNTs (purity 90%) were supplied byNanocyl (Sambreville, Belgium) with average diameter 9.5 nm,average length 1.5 mm and bulk density�66 kg/m3. The CNTs arephysically entangled (entwined, interwoven, Fig. 1), chemicallyentangled (surface-to-surface attraction) and are forming agglom-erates of several hundreds of microns. The extremely high CNTaspect ratio (usually ranging from 100 to 1000) in combinationwith their high flexibility dramatically increase the formation ofloops between them, while the molecular attraction to each otherincreases further the dispersion difficulty. Small aggregates areoften connected by relatively weaker adhesion and electrostaticforces and deagglomeration starts usually from them.

In the present work polyphosphoric acid (PPA 117%) wasselected to disentangle–disperse CNTs at room temperature (highviscosity) and then to functionalise them at 130 1C (much lowerviscosity). PPA was supplied by Panreac (Barcelona, Spain) withtotal P2O5 84.4%, density (r) 2.06 g/cm3, kinematic viscosity (n) in

shear 13,400 cSt (therefore viscosity m¼rn¼26.8 Pa s) at roomtemperature and about 680 cSt (m¼rn¼1.36 Pa s) at 130 1C. PPAwas selected since it is a mild, less-destructive reaction mediumfor CNT functionalisation (Baek and Tan, 2003), its moderateacidic nature promotes CNTs deagglomeration and its viscouscharacter impedes reaggregation. The CNT agglomerates absorbextensively PPA and become flexible and permeable three-dimensional structures, flowing in a PPA fluid suspension. Theaddition of 1 wt% of CNTs in PPA at room temperature increasesthe PPA suspension viscosity before dispersion about 11%.

2.1. CNT disentanglement–deagglomeration and dispersion

considerations

The process of deagglomeration of CNTs depends on thebalance of hydrodynamic shearing-extensional forces applied onthe agglomerate to ‘‘break’’ it and on the cohesive forces actingwithin the agglomerate to resist separation. Since CNT breakageshould be avoided the de-agglomeration process should belimited to an erosion mechanism (a continuous CNTs detachmentfrom the outer surface of the agglomerate) and to a collision one,where agglomerates collide with each other and with the reactorwalls.

It has been known, for some time, that extensional flow ismore efficient than shear for both distributive and dispersivemixing in highly viscous fluids. Distributive mixing, whichinvolves distribution of a minor component throughout a majorfluid component, is greatly enhanced in shear flow by introduc-tion of obstacles that interrupt the flow and reorientate interfacialarea (Rauwendaal, 1991; Tadmor and Gogos, 2006). Dispersivemixing, which involves breakup of liquid drops or agglomerates,is easier in extensional flow than in shear. This was demonstratedby the design-construction of an extensional flow mixer (Lucianiand Ultracki, 1996), facilitating the hydrodynamic mixing in meltphase systems (polymer blends, filled systems) by flowingthrough a series of convergent/divergent regions. Also, the Kaoand Mason (1975) studies indicated that the extensional flow is

P. Michelis, J. Vlachopoulos / Chemical Engineering Science 90 (2013) 10–1612

more effective because the energy of fluid flow is consumed tobreak up aggregates, but not to rotate them. Higashitani andImura (1998) carried out a comparative analysis of shear andextensional flows based on the discrete element method (Cundalland Strack, 1979; Campbell and Brennen, 1985) and concludedthat ‘‘extensional flow is the preferable flow to use in dispersingcoagulated particles’’.

Instead of large undivided reaction volume, where the flowstrain and strain rates reach (to a great extent) intensities aboveand below the required level (like in stirring mixers, ultrasonica-tion mixing units) the micro-mixers contain a large number ofmicro- or millimetre-sized parallel channels, baffles etc., wherethe flow can be continuously splitted, oscillated and recombined,leading to increased mixing efficiency (Reis et al., 2005).

The above considerations regarding efficient mixing of CNTagglomerates were taken into account in designing the reactor.

2.2. Reactor design

The reactor consists of a stationary stainless-coated hollowcylinder, in which parallel grids and a perforated piston-rodassembly reciprocate (oscillates while it translates vertically),and simultaneously rotate thus causing extensional, shear andspiralling flow of the fluid contained in the cylinder as its volumeis repeatedly swept by the piston (Fig. 2).

The central micro-grid, usually with openings from 40 mm(corresponding to 1.7 million micro-openings in the present appli-cation) up to 600 mm is sandwiched between a stronger grid ofmany times larger openings (up to 10 times), which is supportedsymmetrically on the perforated piston (|3 mm hole diameter). Theaspect ratio of micro-grid openings (L/D, L¼thickness of the grid, D

opening diameter) ranges from 0.8 to 2.5 and the entrance/exitregions are responsible for a significant portion of the total pressuredrop (Phares et al., 2005; Hasegawa et al., 2009). The flow is ofextensional character (Hasegawa et al., 2009). The piston is rotatingand also it is moving axially (reaching the opposite cylinder ends) in

mixture

mixture

Fig. 2. Half of the cylinder, the piston with the grid. Axial (oscillating) and

rotational movement.

a reciprocating mode (for example 2 mm forwards and 1.5 mmbackwards) inside a cylindrical pressure vessel filled with liquid(Fig. 2). A seal is preventing CNT agglomerates to skip between thesliding piston and the internal wall of the reactor. This oscillatingprocess reduces effectively the clogging of the grid. Due to thereciprocating action, the fluid agglomerates cross the grid manytimes (Fig. 3). Since the effective (open) cross section of the grid ismuch smaller (20 times in the application) to the cross section ofthe piston, the fluid is accelerated as is approaching the entranceregion of each hole of the grid and then it is decelerated as it exitsthe holes of the grid and also when it exits the distributionchannels. It becomes clear that axial flow oscillation is super-imposed to the tangential rotation and therefore the fluid isinterwoven and folded. The streamline pattern flips up-side downafter each half period, yielding crossing pathlines. The flow direc-tion changes locally and the streamline is folded.

The generated loads in tension and compression are under-taken by a housing with proper shaft supporting arrangements toadditionally allow frictionless rotation even at high axial loads.High-precision, high temperature, extra heavy-duty taper rollerbearings were selected for this task, placed in a face-to-facearrangement under slight preload. A fatigue, tension-compres-sion–torsion machine for material testing (20 Ton) suitablyaccommodated the reactor (Fig. 4) for the application-control ofthe forces (overcoming the fluid resistance of the moving piston),for the control of the pressure vessel temperature and also forproviding a suitable operating software for real time evaluation ofthe measured parameters and finally unattended control of thereactor.

A stainless steel grid, corresponding to the initial size of theagglomerates (for example 600 mm), is used at the start of the de-agglomeration process and when the load (viscosity) is greatlyreduced (reaching 10% of the initial load) it is substituted by asmaller opening grid (40 mm). With the second grid the process isrepeated until the measured average load (corresponding toviscosity) per cycle begins to stabilise at a low value (less than10% of the initial), meaning that the process, associated with theselected grid size, has been completed. The process is completedwhen SEM photos of samples, obtained through the inspectionopening, show sufficient disentanglement of the CNTs. At the endof the process a thin layer of CNTs was covering the grids.The amount was very small (mainly due to the oscillating/reciprocating action of the piston-grid) and it was estimated less

Fig. 3. Fluid flow through the grids and the distribution channels (C is the piston

peripheral wall).

Fig. 4. The reactor.

P. Michelis, J. Vlachopoulos / Chemical Engineering Science 90 (2013) 10–16 13

than 3% of the initial CNT amount. When the process in thereactor is repeated for a new mixture of the same reactants, itscompletion may be determined by reaching the previous finalloadings (viscosity).

The reactor design can be easily scaled up and in addition itallows for easy assembly/disassembly for grid substitution, liquidremoval and cleaning.

2.3. Reactor performance

The performance of the reactor is evaluated by its ability to fullydisentangle CNT agglomerates without attrition, at a comparativelyshort duration. Its suitability for CNT functionalisation is evaluatedin the next section. The reactor was filled with 12.7 l (26.16 kg) ofPPA/CNTs, CNT agglomerates represent 1.0 wt%. The grid micro-openings used at the start were 600 mm and the followings were200 mm and 40 mm. The piston oscillated axially, translating alongthe whole pressure vessel axis (�260 mm) up and down (a cycle)within 2.4 min and also simultaneously rotating at 1 Hz. Duringeach cycle the whole fluid volume passed many times (more than6) through the grid openings. For each selected grid more than 15cycles are performed and the mixture went through each gridopening more than 100 times. In the remaining period the mixturewas in an intense complex flow of horizontal rotation and verticalcirculation. The average axial flow velocity in the openings of the40 mm grid is 20 times greater than that of the piston. For the samegrid the average axial flow velocity in 1.7 million micro-openings isabout 1 m/s. This velocity was calculated from the average pistonvelocity and from the surface of the piston and the micro-openings.

For average velocity V¼1 m/s and a hydraulic diameter ofD¼40 mm the Reynolds number can be determined as

Re¼ rVD=m¼ 2006� 1� 40� 10�6=26:8C3� 10�3

at the start of the reactor operation and some ten times largertowards the end, due to the viscosity reduction with temperatureincrease. The flow is laminar in the small holes (Phares et al., 2005)

and a nominal shear rate _g at the wall can be determined as

_g ¼ 8V=D¼ 8� 1=40� 10�6¼ 2� 105 s�1

with the widely used assumption in fluid mechanics of no-slip at thewall. However, due to the high nominal shear rate, wall slip (which isencountered in polymer solutions and melts (Rao and Rajagopal,1999; Sunarso et al., 2007)), is possible also in the present solvent(PPA). As the fluid enters the smallest holes it is stretched and thisstretching results in an entry pressure loss and vortices (Kwag andVlachopoulos, 1991; Mitsoulis and Vlachopoulos, 1985). Assuming aconical entry, the area-averaged extensional strain rate _e at eachsection will increase towards the apex and its maximum value (atthe hole entrance) can be determined (Collyer and Clegg, 1988) from

_e ¼ 4Vtan a=D

where a is the half entry angleOf course, in the present case the flow field is very compli-

cated, but the above equation can give an approximate value ofthe maximum area-averaged extensional rate for equipmentdesign purposes, assuming a natural entrance angle 2a¼451. Thisgives for V¼1 m/s D¼40�10�6 m and _e¼4.1�104 s�1

From the above approximate calculations, it can be seen thatthe nominal wall shear rate and the maximum stretch rate arevery high for the current operating conditions of average velocitythrough the holes of V¼1 m/s. The solvent viscosity is high(26.8 Pa s at room temperature) and the drag forces exerted onthe CNT entangled aggregates will be large enough to causeerosion and splitting of parent aggregates into smaller fragments.The exact mechanism of breakup of aggregates is poorly under-stood, but in the present equipment the forces can easily beincreased or decreased to a level sufficient for disentanglementwithout causing any appreciable breakage of individual CNTs. Ateach position of the travelling grid and within the (million) micro-openings, similar complex flow patterns develop, which result inreproducible dispersions of disentangled CNTs.

Some results of a computer simulation using the OpenFOAMsoftware package for an assumed 451 flow inclination from thelarger grid to the smallest holes is shown in Fig. 5. For the presentoperating conditions of laminar viscous flow, the no-slip at wallassumption was used in the simulations. It can be seen that avortex forms at the corner and the extensional flow field gives riseto a very high stretch rate at the entry as expected from thesimple calculations above. Even if there was wall slip during thepassage through the smallest holes, the large extensional stressesat the entry would result in a breakup of the agglomerates. Ofcourse, due to the oscillations, the breakup process would occurduring each passage through the smallest holes.

The resistance to translate the piston is greatly reduced duringthe first cycle and after about 12 cycles it becomes less than 1/10of the initial. In the following cycles the resistance remains almostthe same, indicating that the agglomerate size is not essentiallydecreasing. Then the grid is substituted by the selected finer oneand the procedure is completed with the 40 mm openings grid.Fig. 6 shows the uniform reduction of CNT agglomerates duringthe disentanglement–dispersion process. A large number of SEMphotos revealed that in an optically homogeneous and finesuspension almost all CNTs were disentangled (Fig. 7).

Regarding the duration for CNTs disentanglement–dispersion–distribution in PPA, the reactor operated about 2 h for preparing262 g of CNTs.

Optical observations and electrical impedance measurementsfrom samples from different locations of the vessel indicated thatCNT distribution was uniform throughout the fluid mixture.

The CNT attrition was examined at a later production phase bymeasuring the AC and DC conductivity of thin CNT/PEEK tapes ofCNTs content ranging from 0.15 to 1.5 wt%. The percolation

30 µm30 µm

Fig. 6. Optical photos of the CNT agglomerates (darker regions) in PPA in the reactor at the middle of the process (left) and before the end of the disentanglement–

dispersion phase (right).

Fig. 5. Streamline pattern as the fluid enter the micro-openings and stretch rate along a streamline passing through the axis of the micro-hole.

Fig. 7. Disentangled CNTs.

P. Michelis, J. Vlachopoulos / Chemical Engineering Science 90 (2013) 10–1614

threshold was estimated at 0.17 wt%, very low for semicrystallinethermoplastics, indicating efficient CNT disentanglement anddispersion. Also, the length of the disentangled CNTs predicted

by measuring AC conductivity according to the Li et al. (2007)model was L¼1.2 mm against the initial L¼1.5 mm reported fromthe CNT manufacturer. In addition, functionalized CNTs weremixed (0.5 wt%) with PEEK grains and after melting, melt draw-ing, a tape was produced. Tensile experiments revealed thatstrength and moduli of the tape were more than three timesgreater than the corresponding ones of the neat PEEK tape(strength �110 MPa, E¼2.6 GPa). Fig. 8 shows the tensilestress–strain relation for PEEK reinforced with 0.5% functionalizedCNTs. This great enhancement of the composite material is clearlyrelated with the CNT reinforcement, which is more effective asCNT attrition is kept minimum (Fu et al., 2009).

Regarding the PPA disposal after the dispersion process, it isdiluted in water and may be safely used in other applications (i.e.farming).

2.4. CNT functionalisation

In the reactor the PPA slurry of disentangled, dispersed anddistributed CNTs is heated to 130 1C, resulting in a viscosity reduc-tion more than 17 times, and then P2O5 and 4-phenoxybenzoic acid(4-PBA) are added. The functionalisation follows a Friedel–Craftsalkylation (Baek and Tan, 2003; Oh et al., 2006). In the reaction PPAand P2O5 are used as drying reagents. At the first, functionalisation of4-PBA onto CNTs proceeds and then followed by in-situ polymerisa-tion (Oh et al., 2006).

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10

σ (M

Pa)

ε (%)

E=8,1GPa

Fig. 8. Tensile stress–strain curve for functionalized CNT-reinforced PEEK.

Fig. 9. FT-IR spectrum of functionalized CNTs.

P. Michelis, J. Vlachopoulos / Chemical Engineering Science 90 (2013) 10–16 15

The addition of P2O5 and 4-PBA in PPA develops new agglom-erates of large size (several hundred microns) and their dispersion–distribution is again attained by the subsequent use of grids in aprocess similar to the one described earlier. However, since theCNTs are already disentangled and dispersed, the whole mixturebecomes again dispersed after a few cycles for each grid, while theCNT functionalisation and 4-PBA polymerisation have initiated.

Since the defect sites for each extremely long CNT are limitedand the number of CNTs is extraordinary high (in the PPAsuspension43� �109 mm�3), a high degree of functionalisationis a very demanding procedure. Again, the flow in the entry regionof the grid micro-openings seems suitable, since it is characterisedby intense change of the local flow field (high _g) and particularly byhigh local rotational and extensional velocities, developing chaoticadvection. A grid of 40 mm size openings was selected for the mainfunctionalisation process and 50 cycles were assessed as sufficient.

The functionalisation was checked by FT-IR measurements (Fig. 9):

i.

No peak at 2922 cm�1 (C–H stretching band), denoting thatfree defect sites on the CNTs or open ends were not detected.

ii.

Peak at 1650 cm�1 (ketone CQO stretching band) denotingthat functionalisation was detected.

The extent (the degree) of functionalisation was checked byexamining the C–H stretching band in a mixture, which followedthe presented functionalisation process, and in mixtures wherevery small quantities (0.1% and 0.5%) of disentangled and dis-persed CNTs in PPA (but not functionalized) were added. The FT-IR measurements did not detect any peak corresponding to C–Hstretching band in the case of the functionalized mixture but theydetected this stretching band peaks in all mixtures, where disen-tangled CNTs in PPA were added. Therefore these measurementsconfirm that CNT functionalisation was successful to a very highdegree.

Regarding the duration of functionalisation (totally about 2 h)this is 24 times less than the one reported earlier (Oh et al., 2006).

3. Concluding remarks

A novel micro-structured reactor was designed and builthaving a perforated disk which supports a grid of micro-openings. The disk is oscillating and rotating, as it moves down-wards and upwards in a cylindrical vessel filled with a mixture ofa highly viscous solvent (PPA) and entangled MWCNTs. Thedisentanglement is accomplished mainly through extensionalflow at the entrance of the smallest holes, which are of 40 mmdiameter. The oscillations help in de-clogging of the holes and therotation and translation help in evening out the distribution of thede-agglomerating particles throughout the entire fluid mass. Thedisentangled CNTs are functionalized at a temperature of 1301through a Friedel–Crafts alkylation followed by in-situ polymer-isation. SEM, FT-IR observations and AC–DC conductivity mea-surements show that sufficient disentanglement of MWCNTs wasachieved without any appreciable attrition. The reactor oscilla-tion, translation and rotation speeds are controlled and can easilybe optimised for achieving disentanglement and functionalizationwithout attrition.

Acknowledgements

The work was partially supported by the FP7 Programme ofthe European Commission (Contract NMP3-LA-2010-246067).The authors thank V. Spitas, S. Nychas and C. Pandis for con-structive discussions.

References

Baek, J.B., Tan, L.S., 2003. Improved synthesis of poly (oxy-1, 3-phenylenecarbonyl-1, 4-phenylene) and related poly (ether-ketone) using polyphosphoric acid/P2O5 as polymerization medium. Polymer 44, 4135–4147.

Campbell, C.S., Brennen, C.E., 1985. Computer simulation of granular shear flows. J.Fluid Mech. 151, 167–188.

Collyer, A.A., Clegg, D.W., 1988. Rheological Measurements. Elsevier AppliedScience, London. (chapter 3).

Cundall, P.A., Strack, O.D.L., 1979. Discrete numerical model for granular assem-blies. Geotechnique 29, 47–65.

Delsman, E.R., Croon, M., Elzinga, G., Cobden, P., Kramer, G., Schouten, J., 2005. Theinfluence of differences between microchannels on microreactors perfor-mance. Chem. Eng. Technol. 28, 367–375.

Frankland, S.J.V., Caglar, A., Brenner, D.W., Griebel, M., 2002. Molecular simulationof the influence of chemical cross-links on the shear strength of carbonnanotubes–polymer interfaces. J. Phys. Chem. B106, 3046–3048.

Fu, S.Y., Chen, Z.k., Hong, S., Han, C.C., 2009. The reduction of carbon nanotubelength during the manufacture of CNT/polymer composites and a method tosimultaneously determine the resulting CNT and interfacial strengths. Carbon47, 3192.

Hasegawa, T., Ushida, A., Narumi, T., 2009. Huge reduction in pressure drop ofwater, glycerol/water mixture and aqueous solution of polyethylene oxide inhigh speed flows through micro-orifices. Phy. Fluids 21, 052002-1–052002-9.

Higashitani, K., Imura, K., 1998. Two-dimensional simulation of the breakupprocess of aggregates in shear and elongational flows. J. .Colloid InterfaceSci. 204, 320–327.

P. Michelis, J. Vlachopoulos / Chemical Engineering Science 90 (2013) 10–1616

Hilding, J., Grulke, E., Zhang, Z., Lockwood, F., 2003. Dispersion of carbonnanotubes in liquids. J. Dispersion Sci. Technol. 24, 1–41.

Kao, S.V., Mason, S.G., 1975. Dispersion of Particles by Shear, 253. Nature, London,

pp. 619–621.Kasaliwal, G.R., Pegel, S., Goldel, A., Potschke, P., Heinrich, G., 2010. Analysis of

agglomerate dispersion mechanisms of multiwalled carbon nanotubes duringmelt mixing in polycarbonate. Polymer 51, 2708–2720.

Krause, B., Boldt, R., Potschke, P., 2011. A method for determination of lengthdistributions of multiwalled carbon nanotubes before and after melt proces-sing. Carbon 49, 1243.

Kumar, V., Paraschinoiu, M., Nigan, K.D.P., 2011. Single-phase fluid flow andmixing in microchannels. Chem. Eng. Sci. 66, 1329–1373.

Kwag, C., Vlachopoulos, J., 1991. An assessment of Cogswell method for measure-ment of extensional viscosity. Polym. Eng. Sci. 31, 1015–1021.

Li, J., Ma, P.C., Chow, W.S., To, C., Tang, B.Z., Kim, J.-K., 2007. Correlations betweenpercolation threshold, dispersion state and aspect ratio of carbon nanotubes.

Adv. Funct. Mater. 17, 3207–3215.Logakis, E., Pandis, C., Peoglos, V., Pissis, P., Pionteck, J., Potschke, P., Micusik, M.,

Omastova, M., 2009. Electrical/dielectric properties and conduction mechan-ism in melt processed polyamide/multiwalled carbon nanotubes composites.Polymer 50, 5103–5111.

Lu, K.L., Lago, R.M., Chen, Y.K., Green, M.L.H., Harris, P.J.F., Tsang, S.C., 1996.Mechanical damage of carbon tubes by ultrasound. Carbon 34, 814–816.

Luciani, A., Ultracki, L.A., 1996. The extensional flow mixer EFM. Int. Polym.Process. 11, 299–309.

Luo, P.C., Cheng, Y., Wang, W., Jin, Y., Yang, W., 2006. Fast liquid mixing by cross-flow impingement in millimeter channels. Ind. Eng. Chem. Res. 45, 863.

Mitsoulis, E., Vlachopoulos, J., 1985. Effect of Reynolds number in laminar flowthrough a sudden planar contraction. AIChE J. 31, 1736–1739.

Oh, S.J., Lee, H.-J., Keum, D.-K., Lee, S.-W., Wang, D.H., Park, S.Y., Tan, L.-S., Baek, J.–B., 2006. Multiwalled carbon nanotubes and nanofibers grafted with poly-etherketones in mild and viscous polym’1qeric acid. Polymer 47, 1132–1140.

Phares, D.J., Smedley, G.T., Zhou, J., 2005. Laminar flow resistance in shortmicrotubes. Int. J. Heat Fluid Flow 26, 506–512.

Rao, I.J., Rajagopal, K.R., 1999. The effect of the slip boundary condition on the flowof fluids in a channel. Acta Mech. 135, 113–126.

Rauwendaal, C., 1991. Mixing in Polymer Processing. Marcel Dekker, New York.Reis, N., Harvey, A.P., Mackley, M.R., Vicente, A.A., Teixeira, J.A., 2005. Fluid

mechanics and design aspects of a novel oscillatory flow screening mesor-eactor. Chem. Eng. Res. Des. 83, 357–371.

Sunarso, A., Yamamoto, T., Mori, N., 2007. Numerical analysis of wall slip effects onflow of Newtonian and non-Newtonian fluids in macro and micro contractionchannels. J. Fluids Eng. 129, 23–30.

Suslick, K.S., 1990. Sonochemistry. Science 247, 1439–1445. (Part I).Sutherland, D.N., Tan, C.T., 1970. Sedimentation of a porous sphere. Chem. Eng. Sci.

25, 1948–1950.Tadmor, Z., Gogos., C., 2006. Principles in Polymer Processing. Wiley, Hoboken, N.J..