Viscosity Measurements on Colloidal Dispersions ...€¦ · This article reports viscosity data on a series of colloidal dispersions collected as part of the International Nanoflu-

44582-1 Applied RheologyVolume 20 · Issue 4

Abstract:This article reports viscosity data on a series of colloidal dispersions collected as part of the International Nanoflu-id Property Benchmark Exercise (INPBE). Data are reported for seven different fluids that include dispersions ofmetal-oxide nanoparticles in water, and in synthetic oil. These fluids, which are also referred to as ‘nanofluids,’are currently being researched for their potential to function as heat transfer fluids. In a recently published paperfrom the INPBE study, thermal conductivity data from more than 30 laboratories around the world were report-ed and analyzed. Here, we examine the influence of particle shape and concentration on the viscosity of thesesame nanofluids and compare data to predictions from classical theories on suspension rheology.

Viscosity Measurements on Colloidal Dispersions (Nanofluids)for Heat Transfer Applications

David C. Venerus1*, Jacopo Buongiorno2, Rebecca Christianson3, JessicaTownsend3, In Cheol Bang4,5, Gang Chen2, Sung Jae Chung16, Minking Chyu16,Haisheng Chen6, Yulong Ding6, Frank Dubois7, Grzegorz Dzido8, Denis Funf-schilling9, Quentin Galand7, Jinwei Gao2, Haiping Hong10, Mark Horton10, Lin-wen Hu2, Carlo S. Iorio7, Andrzej B. Jarzebski8, Yiran Jiang1, Stephan Kabelac11,Mark A Kedzierski12, Chongyoup Kim13, Ji-Hyun Kim4, Sukwon Kim13, Thomas

McKrell2, Rui Ni9, John Philip14, Naveen Prabhat2, Pengxiang Song15, Stefan VanVaerenbergh7, Dongsheng Wen15, Sanjeeva Witharana6, Xiao-Zheng Zhao9,

Sheng-Qi Zhou9

1 Illinois Institute of Technology, 10 W. 33rd St., Chicago, IL 60616, USA2 Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue,

Cambridge, MA 02139, USA3 Olin College of Engineering, Olin Way, Needham, MA 02492, USA

4 Ulsan National Institute of Science and Technology, School of Energy Engineering,San 194 Banyeon-ri, Eonyang-eup, Ulju-gun, Ulsan Metropolitan City, Republic of Korea5 Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan

6 University of Leeds, Clarendon Road, Leeds LS2 9JT, UK7 Université Libre de Bruxelles, Chimie-Physique E.P. CP 165/62 Avenue P.Heger,

1050, Bruxelles, Belgium8 Silesian University of Technology, Department of Chemical and Processing Engineering,

ul. M. Strzody 7, 44-100 Gliwice, Poland9 Chinese University of Hong Kong, Department of Physics, G6, North Block,

Science Center, Shatin NT, Hong Kong, China10 South Dakota School of Mines and Technology, 501 E Saint Joseph Street,

Rapid City, SD 57702, USA11 Helmut-Schmidt University Hamburg, Institute for Thermodynamics,

22039, Hamburg, Germany12 National Institute of Standards and Technology (NIST), MS 863, Gaithersburg, MD 20899, USA

13 Korea University, Anam-dong, Sungbuk-ku, Seoul 136-713, Republic of Korea14 Indira Gandhi Centre for Atomic Research, SMARTS, NDED,Metallurgy and Materials Group, Kalpakkam-603102, India

15 Queen Mary University of London, School of Engineering and Materials Science,Mile End Road, London, E1 4NS, UK

16 University of Pittsburgh, Dept. Mechanical Engineering and Materials Science,648 Benedum Hall, 3700 O’Hara Street, Pittsburgh, PA 15261, USA

* Email: [email protected]: x1.312.567.8874

Received: 2.11.2009, Final version: 15.12.2009

© Appl. Rheol. 20 (2010) 44582 DOI: 10.3933/ApplRheol-20-44582

Applied_Rheology_Vol_20_4:Applied_Rheology_ 08.10.10 11:44 Seite 236

44582-2Applied RheologyVolume 20 · Issue 4

1 INTRODUCTIONSuspensions of nanometer-sized (1 – 100 nm), sol-id particles, also known as colloids or colloidal dis-persions, are of great technological importanceand can be found in applications ranging frominks to pharmaceuticals. For over a decade, col-loidal dispersions containing metallic, or metal-oxide, nanoparticles, sometimes referred to as‘nanofluids,’ have been the focus of intensiveresearch because of their potential as heat trans-fer fluids. This research has been driven by thepossibility of having fluids with enhanced ther-mal conductivity, relative to the suspending liq-uid (basefluid), while mitigating problems asso-ciated with erosion, sedimentation and cloggingthat plague suspensions of larger particles. Inter-est in nanofluids as heat transfer fluids has been

further intensified by early studies reportinganomalously large – relative to classical modelpredictions – enhancement of thermal conduc-tivity. Several review papers on nanofluid heattransfer have been published [1–4].

Transport properties (e.g. electrical or ther-mal conductivity) of heterogeneous systems areoften estimated using effective medium theory.For example, the effective thermal conductivityk of a suspension composed of solid particleswith thermal conductivity kp at volume fractionf (« 1) dispersed in a liquid of thermal conductiv-ity kf (« kp) can be written as

(1)

Zusammenfassung:In diesem Beitrag werden experimentelle Daten zur Viskosität verschiedener kolloidaler Dispersionen vorge-stellt, welche im Rahmen einer internationalen vergleichenden Ringmessung (International Nanofluid Proper-ty Benchmark Exercise INPBE) gewonnen wurden. Es werden hierbei sieben unterschiedliche Fluide betrachtet,unter anderem Wasser beziehungsweise synthetisches Oel mit suspendierten metalloxidischen Nanopartikeln.Diese auch Nanofluide genannten Dispersionen werden derzeit intensiv aufgrund ihres moeglichen Potenzialsals effizientes Wärmeträger-Fluid untersucht. Vor Kurzem wurden in einem weiteren Beitrag der INPBE-StudieDaten zur Wärmeleitfähigkeit von Nanofluiden veröffentlicht, wie sie in den über 30 teilnehmenden For-schungslabors weltweit gemessen wurden. In diesem Beitrag wird der Einfluss der Partikel-Gestalt und der Par-tikel-Konzentration auf die Viskosität der gleichen Nanofluide untersucht und mit Korrelationen aus der klassi-schen Rheologie von Suspensionen verglichen.

Résumé:Cet article présente des données de viscosité sur des séries de dispersions colloïdales qui font partie du «Inter-national Nanofluid Property Benchmark Exercise (INPBE)». Les données correspondent à sept fluides différentsincluant des dispersions de nano particules d’oxyde métalliques dans de l’eau et dans de l’huile synthétique. Cesfluides, également connus comme « nano fluides » font actuellement l’objet d’études pour leur potentiel com-me des fluides pour le transfert de chaleur. Dans un article récemment publié dans le cadre d’un étude INPBE,des données de conductivité thermique de plus de 30 laboratoires différents ont été présentées et analysées.Dans ce travail, on étudie l’influence de la forme et de la concentration des particules sur la viscosité des nanofluides qui en sont issus. Ces données sont comparées aux prédictions théoriques des modèles classiques sur larhéologie de suspensions.

Sommario:Questo articolo riporta dati sperimentali sulla viscosita’ di una serie di sistemi di nano-colloidi (nanofluidi) nelcontesto del programma internazionale INPBE (International Nanofluid Property Benchmark Exercise). I datiriguardano sette diversi sistemi, comprendenti particelle di ossidi metallici in acqua ed olio sintetico. Questi flui-di sono attualmente soggetti di interesse nella comunita’ scientifica per la loro possible applicazione come fluidtermici. I dati di conducibilita’ termica prodotti da piu’ di 30 laboratori internazionali sono stati riportati e discus-si in un articolo su INPBE di recente pubblicazione. Invece qui esaminiamo l’influenza della forma e concentra-zione delle nanoparticelle sulla viscosita’ degli stessi campioni, e confrontiamo i dati con i risultati delle classi-che teorie reologiche per sospensioni colloidali.

Key words: nanofluids, colloidal dispersion, viscosity, thermal conductivity


where [k] is defined as follows: [k] = limfÆ0{(k/kf- 1)/f}. Over 100 years ago, Maxwell [5] derivedan expression for the thermal (electrical) con-ductivity of a dilute system of spherical particlesthat yielded [k] = 3. Models for the effective ther-mal conductivity of heterogeneous systems havebeen formulated to account for the effects ofnon-spherical particle shape, particle-particleinteractions, and interfacial resistance betweenthe particle and continuous phases [1–4].

There have been numerous experimentalstudies reporting thermal conductivity data onnanofluids. Much of the reported data show bothquantitative and qualitative differences from theeffective medium theory prediction in Equation 1.For example, in many early studies, the measuredlevels of thermal conductivity enhancement fordilute nanofluids (f£0.01) were significantly larg-er than the classical prediction given in Equation1 with [k] = 3. Several investigators have reporteda dependence of thermal conductivity enhance-ment on particle size and on temperature, neitherof which is consistent with Equation 1. In additionto generating a great deal of optimism about thepotential of nanofluids for use as heat transfer flu-ids, early experimental results also sparked theo-retical interest to identify the mechanism(s)responsible for the ob served departures fromeffective medium theory predictions. Further dis-cussion of both ex per imental and theoreticalresearch on nanofluids can be found elsewhere[1–4]. At present, the study of nanofluids as heattransfer fluids remains both an active and contro-versial field of research.

It is well known that the addition of solidparticles to a liquid can significantly alter its rhe-ological behavior. In shear flows, the apparentviscosity of a fluid h is ratio of the shear stress tothe shear rate: h = s/g· . The zero-shear rate vis-cosity is defined as: h0= limg

·Æ0 {h}. The zero-shear

rate viscosity h0 of a dilute suspension with liq-uid phase viscosity hfcan be expressed as follows:

(2)

where the intrinsic viscosity [h] of the suspensionis defined as: [h] = limfÆ0 {(h0/hf - 1)/f}. The well-known prediction of Einstein [6] for a suspensionof spherical particles gives [h] = 2.5, while fordilute suspensions of particles with large aspect

ratio p, [h] ª p [7]. The linear dependence of h0 onparticle volume fraction in Equation 2 typicallyholds for f £ 0.03 [7].

In addition to thermal conductivity, it is alsoevident that viscosity has a significant impact onthe overall performance of a heat transfer fluid.Clearly, pumping a fluid with increased viscositythrough a heat exchanger requires an increase inpumping energy, thereby reducing the overall ben-efit of a higher thermal conductivity fluid. In lightof this, there have been a number of studies report-ing the viscosity of nanofluids [8-14]. These studiesconsidered nanofluids composed of metal-oxide(Al2O3, CuO, TiO2, Fe2O3) and metal (Cu), nanometer-sized, spherical particles in water, ethylene glycol,or hydrocarbon oil at concentrations f £ 0.05. Forall of these nanofluids, Newtonian behavior wasobserved, and the dependence of relative viscosityh/hf was approximately linear in particle concen-tration f. However, the reported intrinsic viscosity[h] for these nanofluids was in the range 4-16, whichis substantially larger than the theoretical value of2.5. Prasher et al., [9] and Garg et al., [12] proposedcriteria for the overall effectiveness of nanofluidsas heat transfer fluids suggesting that [h] should be4 – 5 times smaller than [k] appearing in Equation1. The effect of changes in specific heat due to thepresence of nanoparticles on the effectiveness ofnanofluids as heat transfer fluids has also beeninvestigated [15].

At the first scientific conference centered onnanofluids (Nanofluids: Fundamentals and Appli -cations, September 16-20, 2007, Copper Mountain,Colorado), it was decided to launch an Interna-tional Nanofluid Property Benchmark Exercise(INPBE), to resolve the inconsistencies in the data-base and help advance the debate on nanofluidproperties. Thermal conductivity data on eight dif-ferent nanofluids from this study, involving over30 laboratories around the world, are contained ina recently published paper [16]. A subset of INPBEparticipants also collected viscosity data on thesame set of nanofluids. These data are reported inthis paper. The methodology and samples used forthe INPBE are described in Section 2. The viscositydata are presented and discussed in Section 3. Thefindings of this study are summarized in Section 4.

2 INPBE METHODOLOGYEight different nanofluids were distributed in foursets to participating INPBE laboratories. To mini-



mize spurious effects due to nanofluid prepara-tion and handling, all organizations were givenidentical samples from these sets, and were askedto adhere to the same sample handling protocol.The exercise was ‘semi-blind,’ as only minimalinformation about the samples was given to theparticipants at the time of sample shipment. Thedata were then collected and posted, on the INPBEwebsite (http://mit.edu/nse/nanofluids/bench-mark/index.html). Additional details of the INPBEmethodology and list of participants can be foundin the paper containing the thermal conductivitydata [16] and at the INPBE website.

Table 1 gives the main characteristics of thenanofluids used in the INPBE study; the samplenames in the first column of the table indicateSet#Sample# as designated in the previouspaper [16]. Samples S1S1-S1S7 were provided bySasol. Sample S1S2 is simply de-ionized H2O andis the base fluid for S1S1; sample S1S7 is a mixtureof poly-alpha olefin (PAO) oil (SpectraSyn-10 byExxon Oil) and 5%wt. dispersant (Solsperse21000 by Lubrizol Chemical) and is the base flu-id for samples S1S3-S1S6. The nanofluids desig-nated as S1S1 and S1S3-S1S6 contain alumina(Al2O3) nanoparticles with the shapes and sizesindicated in Table 1. Sample S3S1 was supplied byW. R. Grace & Co. and is a colloidal dispersion ofsilica (SiO2) nanoparticles dispersed in de-ionizedH2O stabilized by the addition of small amountsof Na2SO4 (pH = 9). Finally, samples in Set 4 weresupplied by Dr. Jorge Gustavo Gutierrez of theUniversity of Puerto Rico – Mayaguez (UPRM).Sample S4S2 is a solution of de-ionized H2O (75%wt) and tetramethylammonium hydroxide[(CH3)4NOH] stabilizer (25% wt). Sample S4S1 con-tains Mn-Zn ferrite (Mn1/2-Zn1/2-Fe2O4) nanoparti-cles dispersed in a based fluid S4S2. To summa-rize, this study involves seven nanofluids andthree base fluids. Note that one of the eightnanofluids that were part of the INPBE study, adilute colloidal gold dispersion, is excluded fromthis paper because its rheology was indistin-guishable from that of water. Additional detailsconcerning these samples and their characteri-zation can be found elsewhere [16].

Viscosity data on each of the fluids listed inTable 1 were reported by approximately 8-10 dif-ferent laboratories. All reported data wereobtained using well-established methods withcommercial viscometers that can be broadly sep-arated into two categories according to the type

of deformation applied to the sample. In one cat-egory, that includes gravity driven capillary, con-centric cylinder and immersion viscometers,sample deformation is non-homogeneous andthe (average) rate of deformation is usually notknown. In the other category are viscometersthat apply a controlled and (approximately) uni-form deformation to the sample such as cone-plate viscometers. Only two of the 10 samplesconsidered in this study showed non-Newtonianbehavior (i.e., viscosity hwas dependent on shearrate g· ), so that data from both types of viscome-ters are included for the eight Newtonian fluids.For the two samples displaying non-Newtonianbehavior, only data from cone-plate viscometerswill be presented. Finally, all data reported herewere collected at room temperature, which wasin the range 20-26 ºC. We recognize that changesin viscosity of roughly 10% are possible over thisrange of temperatures.

3 RESULTS AND DISCUSSIONFirst we examine the viscosity versus shear ratebehavior of several fluids listed in Table 1. Datafor samples S1S3 and S1S4 from four different lab-oratories are shown in Figure 1. The dashed linein Figure 1 represents the average viscosity of thebase fluid, sample S1S7. From this figure, it is clearthat these nanofluids are Newtonian over therange of shear rates considered. This is expectedgiven that these fluids contain spherical particlesat relatively modest volume fractions (f = 0.01,0.03); this is consistent with previous results on


Figure 1:Viscosity versus shear ratefor spherical Al2O3 nanopar-ticles in oil: filled symbolsf = 0.01 (S1S3); open sym-bols f� = 0.03 for (S1S4).Different symbols indicatedata from different labora-tories. Dashed line is aver-age for oil base fluid (S1S7).

Table 1:Characteristics of nanofluidand base fluid samples.


similar systems [8 - 14]. It is also evident from Fig-ure 1 that there is good agreement between thedata reported by the different laboratories withvariations of approximately 10%. Results similarto those shown in Figure 1 were obtained for sam-ples S1S1, S1S7, S4S1 and S4S2; therefore only theaverage viscosity of these Newtonian fluids willbe presented later in this section.

Figure 2 shows the viscosity versus shearrate behavior of the concentrated colloidal silicadispersion sample S3S1. At low shear rates, thesedata appear to approach a constant viscosity h0with a value of approximately 0.4 Pa-s, and a con-stant viscosity at shear rates greater than 10 s-1.At intermediate shear rates, between 0.1 - 10 s-1,pronounced shear thinning is observed. The scat-ter among the data from different laboratories islarger in Figure 2 than Figure 1, and is probablythe result of the higher sensitivity to shear his-tory of the more concentrated system, asexplained next. Shear thinning behavior, whichis typical for concentrated suspensions of spher-ical particles, can be explained by the flow-induced perturbation of particle positions [7].The rate of particle displacement by flow is giv-en roughly by the shear rate g· , and the rate ofparticle movement by Brownian motion isroughly kBT/hd3. Hence, when flow perturbs par-ticle positions at a rate faster than they are recov-ered by thermal fluctuations, the viscosity of thesuspension becomes shear-rate dependent. The

inset to Figure 2 shows a commonly used meansof rescaling viscosity and shear rate to demon-strate the competition between convection(flow) and diffusion (Brownian motion) in sus-pensions [7].

Viscosity versus shear rate data from fourdifferent laboratories for the nanofluids com-prised of rod-shaped Al2O3 particles in oil (S1S5and S1S6) are shown in Figure 3. The dashed linein Figure 3 represents the average viscosity of thebase fluid (S1S7). From this figure, we see that thelower concentration (f = 0.01) fluid is Newton-ian, while the higher concentration (f= 0.03) flu-id is non-Newtonian. Again, agreement betweenthe different laboratories is good. Comparison ofthe data in Figures 1 and 3 for f = 0.03 shows, asexpected, that the viscosity of the fluid with non-spherical particles is more sensitive to shear com-pared to the fluid with spherical particles. Fornon-spherical particles, non-Newtonian effectsare the result of flow-induced perturbation ofparticle orientations from the random state thatexists at equilibrium [7]. In this case, it is a com-petition between the tendency for flow to orientparticles and thermally driven rotation of parti-cles.

Viscosity data for the nanofluid comprisedof spherical Al2O3 particles with f = 0.03 (S1S4)and its oil base fluid (S1S7) as reported by differ-ent INPBE participants are shown in Figure 4. Fora given laboratory, the reported uncertainty wastypically around ± 5%, which is roughly the sizeof the symbols in Figure 4. The data in this figuregive an idea of consistency of viscosity datareported by different laboratories using differenttechniques, which is within approximately ±20%. Similar results were found for the othernanofluids used in this study.

The relative viscosity versus particle con-centration for nanofluids with spherical particlesand rod-shaped particles are shown in Figures 5and 6 respectively. As expected, the data in bothfigures indicate a linear dependence of h/hf on f.The measured dependence [h], however, isroughly ten times larger than predicted, with


Figure 2 (left above):Viscosity versus shear ratefor spherical SiO2 nanoparti-cles in water:f = 0.32 (S3S1). Differentsymbols indicate data fromdifferent laboratories. Insetshows relative viscosity ver-sus dimensionless shear ratefor one set of data.

Figure 3 (right above):Viscosity versus shear ratefor rod-shaped Al2O3nanoparticles in oil: filledsymbols f = 0.01 (S1S5);open symbols f = 0.03 for(S1S6). Different symbolsindicate data from differentlaboratories. Dashed line isaverage for oil base fluid(S1S7).

Figure 4 (below):Viscosity of spherical Al2O3nanoparticles in oil as mea-sured by different laborato-ries: filled symbols are forf = 0.03 (S1S4); open sym-bols are for base fluid (S1S7).Solid and dashed lines indi-cate average values.


[h] = 23.4 for the spherical particles and [h] = 70.8for the rod-shaped particles. The shear thinningbehavior observed in alumina nanorod suspen-sions can also be due to shear induced reorgani-zation of nanorods under confined geometrywhere the packing can become more efficient. Asimilar result has been reported in recently pub-lished data for nanofluids with spherical particles[8–13], although somewhat lower values of [h] =4–16 were found. A possible explanation forthese pronounced differences between theoryand experiment is particle agglomeration, whichwould increase the effective volume fraction ofthe particles [10–14]. Indeed, light scatteringresults on these fluids reported elsewhere [16]are consistent with the occurrence of particleagglomeration.

For comparison, we show the relative ther-mal conductivity versus particle concentrationdata from the INPBE study [16] in Figures 7 and 8.As with the viscosity data, nanofluids with bothspherical and rod-shaped particles show a lineardependence of k/kf on f. The data for the fluidswith spherical particles in Figure 7 show a slightlystronger dependence on particle concentrationthan predicted: measured [k] = 4.0, and predicted[k] = 3. This observation is consistent with the pres-ence of particle agglomeration in these systems,and suggests that particle clustering has a largereffect on viscosity than thermal conductivity innanofluids with spherical particles. The situation

is different for the nanofluids with rod-shapedparticles as shown in Figure 8. Here, the observeddependence on particle concentration is weakerthan predicted: measured [k] = 5.6, and predicted[k] = 13.1. Apparently, particle agglomeration cansignificantly reduce the effective thermal conduc-tivity of nanofluids with rod-shaped particles. Asecond explanation for the reduction in effectivethermal conductivity in these nanofluids is inter-facial thermal resistance [16].

4 CONCLUSIONSViscosity data have been collected as part of anInternational Nanofluid Property BenchmarkExercise (INPBE). These data are from approxi-mately 10 different laboratories around theworld on a series of 10 different nanofluids andtheir base fluids. In general, the agreementbetween different laboratories was good withvariations of approximately ± 20%, which, inpart, could be explained by lab-to-lab tempera-ture variations. Two of seven nanofluids showedshear-thinning behavior; the remaining fiveshowed Newtonian behavior. For nanofluidswith both spherical and rod-shaped nanoparti-cles, the dependence of viscosity (relative to thebase fluid viscosity) on particle concentration(volume fraction) was significantly stronger thanpredicted by dilute suspension theory. This dis-crepancy was attributed to particle agglomera-


Figure 5 (left above):Relative viscosity h/hf versusparticle concentration f fornanofluids with sphericalparticles: filled circles forAl2O3 particles in oil (S1S3and S1S4) and open trianglefor Mn1/2Zn1/2Fe2O3 in water(S4S1). Lines indicate h/hf = 1+ [h]f with prediction [h] =5/2 (dashed) and fit [h] =23.4 (solid).

Figure 6 (right above):Relative viscosity h/hf versusparticle concentration f fornanofluids with rod-shapedparticles: filled circles forAl2O3 particles in oil (S1S5and S1S6) and open circle forAl2O3 in water (S1S1). Linesindicate h/hf = 1 + [h]f withprediction [h] = 8 (dashed)and fit [h] = 70.8 (solid).

Figure 7 (left below):Relative thermal conductivi-ty k/kf versus particle con-centration f for nanofluidswith spherical particles:filled circles for Al2O3 parti-cles in oil (S1S3 and S1S4) andopen triangle forMn1/2Zn1/2Fe2O3 in water(S4S1). Data taken fromINPBE study [16]. Lines indi-cate k/kf = 1 + [k]f with pre-diction [k] = 3 (dashed) andfit [k] = 4.0 (solid).

Figure 8 (right below):Relative thermal conductivi-ty k/kf versus particle con-centration f for nanofluidswith rod-shaped particles:filled circles for Al2O3 parti-cles in oil (S1S5 and S1S6)and open circle for Al2O3 inwater (S1S1). Data takenfrom INPBE study [16]. Linesindicate k/kf = 1 + [k]f withprediction [k] = 13.1 (dashed)and fit [k] = 5.6 (solid).


tion. In contrast, the observed enhancement inthermal conductivity was slightly larger for thespherical particle fluids, and significantly lowerfor the rod-shaped particle fluids, than predictedby effective medium theory. As noted in theintroduction, criteria for the overall effectivenessof nanofluids as heat transfer fluids have beenproposed [9, 12], which suggest [h] should be 4 -5 times smaller than [k]. Clearly, the nanofluidsconsidered in this study would fail; this suggeststhat the overall effect of adding nanoparticles tothe base fluid is negative in terms of heat trans-fer performance.

ACKNOWLEDGEMENTSThis work was made possible by the support ofthe National Science Foundation under grantCBET-0812804. The authors are also grateful toSasol and W. R. Grace & Co. for donating some ofthe samples used in INPBE.

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Map:Map showing locations oflaboratories participating inthe International NanofluidProperties Benchmark Exer-cise (INPBE).


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Viscosity Measurements on Colloidal Dispersions ...€¦ · This article reports viscosity data on a series of colloidal dispersions collected as part of the International Nanoflu-