The popular interest in cornstarch and water mixturesknown as “oobleck” after the complex fluid in one of Dr.Seuss’s classic children’s books arises from their transitionfrom fluid-like to solid-like behavior when stressed. The vis-cous liquid that emerges from a roughly 2-to-1 (by volume)combination of starch to water can be poured into one’s hand.When squeezed, the liquid morphs into a doughy paste thatcan be formed into shapes, only to “melt” into a puddle whenthe applied stress is relieved. Internet videos show peoplerunning across a large pool of the stuff, only to sink once theystop in place, and “monsters” that grow out of the mixturewhen it’s acoustically vibrated (for an example, see the onlineversion of this article).

Shear-thickening fluids certainly entertain and spark ourcuriosity, but their effect can also vex industrial processes byfouling pipes and spraying equipment, for instance. And yet,when engineered into composite materials, STFs can be con-trolled and harnessed for such exotic applications as shock-absorptive skis and the soft body armor discussed in box 1.

Engineers and colloid scientists have wrestled with thescientific and practical problems of shear-thickening col-loidal dispersions—typically composed of condensed poly-

mers, metals, or oxides suspended in a liquid—for more thana century. More recently, the physics community has ex-plored the highly nonlinear materials in the context of jam-ming1 (see the article by Anita Mehta, Gary Barker, and Jean-Marc Luck in PHYSICS TODAY, May 2009, page 40) and themore general study of colloids as model systems for under-standing soft condensed matter.

Hard-sphere colloids are the “hydrogen atom” of col-loidal dispersions. Because of their greater size and interactiontimes compared with atomic and molecular systems, colloidaldispersions are often well suited for optical microscopy andscattering experiments using light, x rays, and neutrons. Thatmakes the dispersions, beyond their own intrinsic technolog-ical importance, ideal models for exploring equilibrium andnear-equilibrium phenomena of interest in atomic and molec-ular physics—for example, phase behavior and “dynamical ar-rest,” in which particles stop moving collectively at the glasstransition. The relevance of colloids to atomic and molecularsystems breaks down, though, for highly nonequilibrium phe-nomena. Indeed, shear thickening in strongly flowing colloidaldispersions may be among the most spectacular, and elucidat-ing, examples of the differences between the systems.

© 2009 American Institute of Physics, S-0031-9228-0910-010-8 October 2009 Physics Today 27

Shear thickening incolloidal dispersions Norman J. Wagner and John F. Brady

Shampoos, paints, cements, and soft body armor that stiffens under impactare just a few of the materials whose rheology is due to the change in viscosity that occurs when colloidal fluids experience shear stress.

Norm Wagner is the Alvin B. and Julia O. Stiles Professor and chairperson of the department of chemical engineering at the University ofDelaware in Newark. John Brady is the Chevron Professor of Chemical Engineering at the California Institute of Technology in Pasadena.

The unique material properties of increased energy dissipationcombined with increased elastic modulus make shear-thickening fluids (STFs) ideal for damping and shock-absorptionapplications. For example, so-called EFiRST fluids can beswitched between shear-thickened and flowing states using anapplied electric field, which controls the damping. Researchershave also explored the STF response in sporting equipment14

and automotive applications,15 such as skis and tennis racketsthat efficiently dissipate vibrations without losing stiffness orSTFs embedded in a passenger compartment liner designed toprotect passengers in a car accident.

One commercial application of STF composites is expectedto be protective clothing.16 The fabric imaged in these scanningelectron micrographs has STFs intercalatedinto its woven yarns. Initial applications areanticipated in flexible vests for correctionalofficers. Longer-term research is being performed in one of our laboratories (Wag-ner’s), in conjunction with the US ArmyResearch Laboratory, to use STF fabrics forballistic, puncture, and blast protection for

the military, police, and first responders. Tests of the materials demonstrate a marked enhancement in

performance. Consider this comparison between two STF-basedfabrics: The velocity at which a quarter-inch steel ball is likely topenetrate a single layer of Kevlar is measured at about 100 m/s.The velocity required to penetrate Kevlar formulated with poly-meric colloids (polymethyl-methacrylate) is about 150 m/s, andthat for Kevlar formulated with silica colloids is 250 m/s, 2.5 times that for the Kevlar alone. High-speed video dem -onstrations and further test details are available at http://www.ccm.udel.edu/STF. Many other composites are now underinvestigation for armor applications. (Images courtesy of EricWetzel, US Army Research Laboratory.)

1 mm 50 µm 5 µm

Box 1. Soft armor and other applications

Figure 1 illustrates the effect. The addition of colloidalparticles to a liquid such as water results in an increase in theliquid’s viscosity and, with further addition, the onset of non-Newtonian behavior—the dependence of its viscosity on anapplied shear stress or shear rate. At high particle concentra-tions, the fluid behaves as if it has an apparent yield stress.That is, it must be squeezed, like ketchup, before it can actu-ally flow. At such concentrations, the colloidal dispersions fitinto the general paradigm for jamming in soft matter:2 Athigh particle densities and low stresses (and low tempera-tures, usually), the system dynamically arrests, just as atomic,molecular, polymeric, and granular systems do. But once theyield stress is exceeded, the fluid’s viscosity drops, a responseknown as shear thinning. That rheology is engineered into arange of consumer products, from shampoos and paints toliquid detergents, to make them gel-like at rest but still ableto flow easily under a weak stress. Again, the colloid modelfits the general paradigm for how matter behaves: It flowswhen sheared strongly enough.

At higher stresses, shear thickening occurs: Viscosityrises abruptly, sometimes discontinuously, once a criticalshear stress is reached. The rise is counterintuitive and incon-sistent with our usual experience. Experiments and simula-tions on atomic and small-molecule liquids predict onlyshear thinning, at least until the eventual onset of turbulenceat flow rates that vastly exceed those of interest here.

The ubiquity of the phenomenon in the flow of sus-pended solids is a serious limitation for materials processing,especially when it involves high shear-rate operations. In a1989 review, Howard Barnes writes,

Concentrated suspensions of nonaggregatingsolid particles, if measured in the appropriateshear rate range, will always show (reversible)shear thickening. The actual nature of the shearthickening will depend on the parameters of thesuspended phase: phase volume, particle size(distribution), particle shape, as well as those of

the suspending phase (viscosity and the details ofthe deformation, i.e., shear or extensional flow,steady or transient, time and rate of deformation).3

Inks, polymeric binders for paints, pastes, alumina castingslurries, blood, and clays are all known to shear thicken. Butthe earliest searches for the root cause came from industriallaboratories that coated paper at high speeds (shear rates typ-ically up to 106 Hz), a process in which the coating’s increasingviscosity would either tear the paper or ruin the equipment.Industrial labs remain intensely interested in the science. Hun-dreds of millions of metric tons of cement are used globallyeach year, for example, and production engineers are carefulto formulate modern high-strength cements and concretes thatdon’t suffer from the effect—at least in a range of shear ratesimportant for processing and construction.4

In pioneering work in the 1970s, Monsanto’s RichardHoffman developed novel light-scattering experiments toprobe the underlying microstructural transitions that accom-panied shear thickening in concentrated latex dispersions.5

The transition was observed to correlate with a loss of Braggpeaks in the scattering measurement. On that basis, Hoffmandeveloped a micromechanical model of shear thickening asa flow- induced order–disorder transition.

In the 1980s and early 1990s BASF’s Martin Laun andothers interested in products such as paper coatings andemulsion-polymerized materials used then emerging small-angle neutron-scattering techniques to demonstrate that anorder–disorder transition was neither necessary nor alonesufficient to induce significant shear thickening.6 Becauseshear thickening is a highly nonequilibrium, dissipative state,though, a full understanding had to await the developmentof new theoretical and experimental tools.

HydrodynamicsThe dynamics of colloidal dispersions is inherently a many-body, multiphase fluid-mechanics problem. But first considerthe case of a single particle. Fluid drag on the particle leadsto the Stokes- Einstein- Sutherland fluctuation–dissipation relationship:

(1)

The diffusivity D0 scales with the thermal energy kT dividedby the suspending medium’s viscosity μ and the particle’s hy-drodynamic radius a. That diffusivity sets the characteristictime scale for the particles’ Brownian motion; it takes the par-ticle a2/D0 seconds to diffuse a distance equal to its radius. Thetime scale defines high and low shear rates γ..

A dimensionless number known as the Péclet number,Pe, relates the shear rate of a flow to the particle’s diffusionrate; alternatively, the Péclet number can be defined in termsof the applied shear stress τ:

(2)

The number is useful because dispersion rheology is oftenmeasured by applied shear rates or shear stresses. Low Pe isclose enough to equilibrium that Brownian motion canlargely restore the equilibrium microstructure on the timescale of slow shear flow. At sufficiently high shear rates orstresses, though, deformation of the colloidal microstructureby the flow occurs faster than Brownian motion can restoreit. Shear thinning is already evident around Pe ≈ 1. Andhigher shear rates or stresses (higher Pe) trigger the onset ofshear thickening.

D0 = .kT

6πμa

D0 kTPe = .=

γa2 τa3.

28 October 2009 Physics Today www.physicstoday.org

ϕ = 0.47

ϕ = 0.43

ϕ = 0.34ϕ = 0.28

ϕ = 0

ϕ = 0.18ϕ = 0.09

ϕ = 0.50

SHEAR STRESS (Pa)

VIS

CO

SIT

Y (P

a·s)

10−3

10−3

10−2

10−2

10−1

10−1

100

100

101

101

102

102

103 104 105

Figure 1. The viscosity of colloidal latex dispersions, as afunction of applied shear stress. The volume fraction ϕ oflatex particles in each dispersion distinguishes the curves. Acritical yield stress must be applied to induce flow in a dis-persion with high particle concentration. Beyond that criti-cal stress, the fluid’s viscosity decreases (shear thinning). Atyet higher stress, its viscosity increases (shear thickening), atleast for latex dispersions above some concentration thresh-old. (Adapted from ref. 12.)

The presence of two or more particles in the suspensionfundamentally alters the Brownian motion due to the inher-ent coupling, or hydrodynamic interaction, between the mo-tion of the particles and the displacement of the suspendingfluid. In a series of seminal articles in the 1970s, CambridgeUniversity’s George Batchelor laid a firm foundation for un-derstanding the colloidal dynamics.7 In essence, because anyparticle motion must displace incompressible fluid, a long-ranged—and inherently many-body—force is transmittedfrom one particle through the intervening fluid to neighbor-ing particles; the result is that all particles collectively disturbthe local flow field through hydrodynamic interactions. Suchinteractions are absent in atomic and molecular fluids, wherethe intervening medium is vacuum.

Batchelor’s calculation of the trajectories of non- Brownian particles under shear flow identified the critical im-portance of what’s known as lubrication hydrodynamics,which describes the behavior of particles interacting via thesuspending medium at very close range. Those hydrodynam-ics were already well known in the fluid mechanics of journalbearings, which Osborne Reynolds investigated in the late1800s and which remain of great importance to the workingsof modern machines. As box 2 explains, the force required topush two particles together in a fluid diverges inversely withtheir separation distance. Of particular significance is that atclose range, the trajectories that describe their relative motionbecome correlated. That is, the particles effectively orbit eachother—indefinitely if they are undisturbed.

Batchelor’s work also led to a formal understanding of how hydrodynamic coupling alters the fluctuation–dissipation relationship, which, in turn, enabled him to cal-culate the diffusion coefficient and viscosity of dilute disper-sions of Brownian colloids at equilibrium.7 Although it wasnot fully appreciated at the time, the effect of hydrodynamic

interactions on particle trajectories is the basis for under-standing the shear-thickening effect.

Beyond two particlesHydrodynamic interactions in real colloidal suspensions re-quire numerical methods to solve. The method of Stokesiandynamics outlined in box 3 calculates the properties of ensem-bles of colloidal and noncolloidal spheres under flow. A greatadvantage of the simulations is their ability to resolve whichforces contribute to the viscosity. Moreover, they demonstratethat the ubiquitous shear thinning in hard-sphere colloidaldispersions is a direct consequence of particle rearrangementdue to the applied shear.

The equilibrium microstructure is set by the balance ofstochastic and interparticle forces at play—including electro-static and van der Waals forces—but is not affected by hydro-dynamic interactions. The low-shear (Pe ≪ 1) viscosity hastwo components, one due to direct interparticle forces, whichdominate, and one due to hydrodynamic interactions.7

Under weak but increasing shear flow (Pe ~ 1), the fluidstructure becomes anisotropic as particles rearrange to re-duce their interactions so as to flow with less resistance. Fig-ure 2 illustrates the evolution schematically. Near equilib-rium, the resistance to flow is naturally high because shearingthe random distribution of particles causes them to fre-quently collide, like cars would if careening haphazardlyalong a road. With increasing shear rates, though, particlesbehave as if merging into highway traffic: The flow becomesstreamlined and the increasingly efficient transport of col-loidal particles reduces the system’s viscosity.

Simulations that ignore hydrodynamic coupling be-tween particles show that the ordered, low-viscosity statepersists even as the Péclet number approaches infinity. Thinkof particles sliding by in layers orthogonal to the shear-

www.physicstoday.org October 2009 Physics Today 29

When two colloidal particles approacheach other, rising hydrodynamic pressurebetween them squeezes fluid from thegap. At close range, the hydrodynamicforce increases inversely with the distancebetween the particles’ surfaces anddiverges to a singularity. The graph at rightplots the normalized force required todrive two particles together (along a linethrough their centers) at constant velocity.The Navier–Stokes equations that governthe flow behavior between particles aretime reversible, so the force is the sameone required to separate two particles.

In simple shear flow, particle trajecto-ries are strongly coupled by the hydro -dynamic interactions if the particles areclose together. The inset of the plot showsa test particle’s trajectories, sketched aspaths as it moves in a shear flow relative to a reference particle(gray sphere). The trajectories are reversible and can be dividedinto two classes: those that come and go to infinity and thosethat lead to correlated orbits—so-called closed trajectories—around the reference particle.

Simulations and theory of concentrated dispersions thataccount for those short-range hydrodynamics show that athigh shear rates, particles that are driven into close proximity

remain strongly correlated and are reminiscent of the closedtrajectories observed in dilute suspensions. The flow-induceddensity fluctuations are known as hydroclusters. Because theparticle concentration is higher in the clusters, the fluid is undergreater stress, which leads to an increase in energy dissipationand thus a higher viscosity. The illustration at right during astage of the Stokesian dynamics simulation shows colloidal par-ticles in hydro clusters.8

Box 2. Lubrication hydrodynamics and hydroclusters

NO

RM

AL

IZE

D L

UB

RIC

AT

ION

FO

RC

E

DISTANCE BETWEEN PARTICLE SURFACES

1000

100

10

10 0.1 0.2 0.3 0.4 0.5

FLOW DIRECTION

SHE

AR

GR

AD

IEN

T

−4 −3 −2 −1 0 1 2 3 4−2

−1

0

1

2

Closed

SHE

AR

DIR

EC

TIO

N

gradient direction. Stokesian dynamics simulations, however,demonstrate that hydrodynamic forces become larger at highshear rates (Pe ≫ 1) than do interparticle forces that driveBrownian motion. So when the particles are driven close to-gether by applied shear stresses, lubrication hydrodynamicsstrongly couple the particles’ relative motion. The result is acolloidal dispersion that has a microstructure significantly

different from the one near equilibrium, and hence, the energydissipation increases. In hindsight, that should not be surpris-ing given Batchelor’s calculation of closed trajectories.

In both semidilute and concentrated dispersions, thestrong hydrodynamic coupling between particles leads to theformation of hydroclusters—transient concentration fluctua-tions that are driven and sustained by the applied shear field.Here again, the analogy to traffic collisions disrupting or-ganized, low-dissipation flow may be helpful. Unlike theseemingly random microstructure observed close to equilib-rium, however, this microstructure is highly organized and

30 October 2009 Physics Today www.physicstoday.org

The flow of particles suspended in an incompressible Newtonianfluid is a challenging fluid-mechanics problem that can be han-dled analytically for a single sphere and semianalytically for twospheres. For three or more particles, though, it requires a numer-ical solution to the Stokes equation—the Navier–Stokes equa-tion without inertia. Solution strategies range from brute-forcefinite-element calculations, to more elegant boundary integralmethods, to coarse-grained methods, such as smoothed-particle hydrodynamics or lattice Boltzmann techniques, for rep-resenting the fluid. The method of Stokesian dynamics17 startswith the Langevin equation for N-particle dynamics,

in which the tensor M is a generalized mass, a 6N × 6N mass andmoment-of-inertia matrix; U is the 6N-dimensional particle trans-lational and rotational velocity vector; and the 6N-dimensionalforce and torque vectors represent the interparticle and externalforces FP (such as gravity), hydrodynamic forces FH acting on theparticles due to their motion relative to the fluid, and stochasticforces FB that give rise to Brownian motion. The stochastic forcesare related to the hydrodynamic interactions through the fluctuation–dissipation theorem.

In Stokes flow the hydrodynamic forcesand torques are linearly related to the par-ticle translational and rotational velocitiesas FH = −R · U, where R is the configura-tion-dependent hydrodynamic resistancematrix. In the Stokesian dynamics method,the necessary matrices are computed bytaking advantage of the linearity of theStokes equations and their integral solu-tions. Long-range many-body hydro -dynamic effects are accurately computed

by a force-multipole expansion and combined with the exact,analytic lubrication hydrodynamics to calculate the forces.

Armed with that method, one can predict the colloidalmicrostructure associated with a particular shear viscosity. Take,for instance, a concentrated colloidal dispersion whose particlesoccupy nearly half the volume. If the positions of those particlesare represented as dots, the figure illustrates how the hydro -dynamic forces affect their probable locations around somearbitrary test particle (black). The three panels differ only in theshear rate, represented by the Péclet number Pe, the ratio of theshear and diffusion rates.

At low Péclet number (0.1), the distribution of neighboringparticles is isotropic, which is typical of a concentrated liquid.Red indicates the most probable particle positions as nearestneighbors and green the least probable. At Pe = 1, significantshear distortion appears in neighbor distributions, such thatparticles are convected together along the compression axes(135° and −45°) relative to the shear flow. At high Péclet num-bers, the shear-thickening regime, particles aggregate intoclosely connected clusters, which is manifest as yet greateranisotropy in the microstructure. Particles are more closelypacked and thus occupy a narrower region (red) around the testparticle than at lower Péclet numbers, indicative of beingtrapped by the lubrication forces.18

Box 3. Stokesian dynamics

Pe = 0.1 Pe = 1 Pe = 1000

M • ,= F + F + FP H BdU

dt

SHEAR STRESS OR SHEAR RATE

VIS

CO

SIT

Y

Equilibrium Shear thinning Shear thickening

Figure 2. The change in microstructure of a colloidal disper-sion explains the transitions to shear thinning and shear thick-ening. In equilibrium, random collisions among particles makethem naturally resistant to flow. But as the shear stress (or,equivalently, the shear rate) increases, particles become organ-ized in the flow, which lowers their viscosity. At yet highershear rates, hydrodynamic interactions between particles dom-inate over stochastic ones, a change that spawns hydroclusters(red)—transient fluctuations in particle concentration. The dif-ficulty of particles flowing around each other in a strong flowleads to a higher rate of energy dissipation and an abrupt in-crease in viscosity.

anisotropic. The transient hydroclusters are the defining fea-ture of the shear-thickening state.

Referring back to figure 1, one can see that a colloidalvolume fraction ϕ = 0.50 produces a latex dispersion whoseviscosity is 1 Pa·s at a low shear stress and again at one morethan four orders of magnitude higher. The same viscosityemerges for very different reasons, though. Changes in theparticles’ size, shape, surface chemistry, and ionic strengthand in properties of the suspending medium all affect the in-terparticle forces, which dominate the viscosity at low shearstress. Hydrodynamic forces, in contrast, dominate at highshear stress. Understanding the difference is critical to for-mulating a dispersion that behaves as needed for specificprocesses or applications.

As shown in figure 3, rheo-optical measurements onmodel dispersions experimentally confirm the predictions of

simulations that the shear-thickened state is driven by dissi-pative hydrodynamic interactions. The flow generates stronganisotropy in the nearest-neighbor distributions (see box 3).The anisotropies give rise to clusters of particles and con-comitant large stress fluctuations8 that, in turn, lead to highdissipation rates and thus a high shear viscosity. The forma-tion of hydroclusters is generally reversible, though, so re-ducing the shear rate returns the suspension to a stable, flow-ing suspension with lower viscosity. Moreover, even verydilute dispersions will shear thicken, although the effect ishard to observe.9

Controlling shear thickening requires different strate-gies from those typically employed to control the low-shearviscosity. The addition, for example, of a polymer “brush”grafted or adsorbed onto the particles’ surface can preventparticles from getting close together. With the right selectionof graft density, molecular weight, and solvent, the onset ofshear thickening moves out of the desired processingregime.10 The strategy is often used to reduce the viscosity athigh processing rates but could increase the suspension’slow-shear viscosity.

Indeed, because the separation between hydroclusteredparticles is predicted to be on the order of nanometers for typ-ical colloidal dispersions, shear-thickening behavior directlyreflects the particles’ surface structure and any short-rangeinterparticle forces at play. Fluid slip, adsorbed ions, surfac-tants, polymers, and surface roughness all significantly influ-ence the onset of shear thickening. Simple models based onthe hydrocluster mechanism have proven valuable in pre-dicting the onset of shear thickening and its dependence onthose stabilizing forces.11

Figure 4 shows a toy-model calculation in which shearthickening is suppressed by imposing a purely repulsiveforce field—akin to the effect of a polymer brush—aroundeach particle that prevents the particles from getting too closeto each other.9 When the range of the repulsive force ap-proaches 10% of the particle radius, the shear thickening iseffectively eliminated and the suspension flows with low vis-cosity. Manipulating those nanoscale forces, the particles’composition and shape, and properties of the suspendingfluid so as to control the sheer thickening, however, remainsa challenge for the suspension formulator.

Beyond hard spheresAlthough the basic micromechanics of shear behavior in col-loidal suspensions are understood, many aspects of the fas-cinating and complex fluids remain active research problems.

At very high particle densities, dispersions can un-dergo discontinuous shear thickening whereby thesuspension will not shear at any higher rate. Rather,increasing the power to a rheometer, for example,leads to such dramatic increases in viscosity and

www.physicstoday.org October 2009 Physics Today 31

VIS

CO

SIT

Y (P

a·s)

SHEAR STRESS (Pa)

101

100

100 101 102 103

10−1

10−2

10−1

Figure 3. The measured viscosity of a concentrated col-loidal suspension (squares) can be resolved into two com-ponents—a thermodynamic component (circles) associatedwith the stochastic motion of particles and a hydrodynamiccomponent (triangles) associated with forces acting be-tween particles due to motion through the suspendingfluid. Light-scattering experiments combined with numeri-cal simulations determine which forces dominate in differ-ent stress regimes. (Adapted from ref. 13.)

NO

RM

AL

IZE

DV

ISC

OSI

TY

PÉCLET NUMBER10−2 10−1 100 101 102 103 104

0.4

0.6

0.8

1.0

2.0

Figure 4. Shear thickening can be suppressed byreducing the interactions between particles, asshown here based on numerical calculations. The ex-tent of the reduction affects whether an increasingPéclet number (a measure of shear rate) leads to ashear-thickening state or a shear-thinning one. Theeffect is evident experimentally when a polymerlayer, or brush, is grated onto the particles: The dis-persion becomes progressively less viscous as thebrush thickness on each particle increases. (Adaptedfrom ref. 9.)

large fluctuations in stress that the suspension either refusesto flow any faster or solidifies. Samples that exhibit strongshear thickening are particularly interesting as candidates forsoft body armor (see box 1), and that application hasprompted investigations of transient shear thickening at mi-crosecond time scales and at stresses that approach the idealstrength of the particles.

Another active research topic concerns jamming transi-tions under flow. As figure 1 suggests, concentrated suspen-sions could be jammed at low and high shear stresses butflow in between. Evidence also exists, as the figure more sub-tly suggests, that dispersions may exhibit a second regime ofshear thinning at the highest stresses rather than continuingto resist the increasing shear rate. The effect can be under-stood as a manifestation of the finite elasticity of the parti-cles—relatively soft plastic in this case. At very high stresses,particles stop behaving like billiard balls and elastically de-form, which alters their rheology. The same forces that drivethe hydrocluster formation, which is reversible as the flow isreduced, can also lead to irreversible aggregation. That is,particles forced into contact remain in contact even as theflow weakens. Such shear-sensitive dispersions irreversiblythicken and are often undesirable in practice.

Conversely, in dispersions composed of particle aggre-gates or fillers such as fumed silica or carbon black, the ex-treme forces can lead to particle breakage and thixotropy(time-dependent viscosity). Indeed, propagating those forcesinto the colloids may be key to splitting the colloids intonanoparticles. It’s thought, for instance, that the extreme me-chanical stress required to grind up and pulverize particlesis more effectively transferred to the particles when they arein a shear-thickened state in the slurry of a mill.

Interesting questions arise in the role of shear thickeningin chemical mechanical planarization, a critical step in semi-conductor processing. Concentrated dispersions are usefulfor other polishing operations as well, and the control of theirshear thickening can be critical to performance.

Although it’s impossible to completely survey the sci-ence surrounding shear thickening in colloidal dispersionsand its applications, we hope the highly counterintuitive rhe-ology has piqued your interest. A wealth of fascinating chal-lenges and applications awaits.

References1. C. B. Holmes et al., J. Rheol. 49, 237 (2005).2. A. J. Liu, S. R. Nagel, Nature 396, 21 (1998).3. H. A. Barnes, J. Rheol. 33, 329 (1989).4. F. Toussaint, C. Roy, P.-H. Jézéquel, Rheol. Acta, doi:10.1007/

s00397-009-0362-z (2009).5. R. L. Hoffman, J. Rheol. 42, 111 (1998).6. H. M. Laun et al., J. Rheol. 36, 743 (1992).7. W. B. Russel, D. A. Saville, W. R. Schowalter, Colloidal Disper-

sions, Cambridge U. Press, New York (1989).8. J. R. Melrose, R. C. Ball, J. Rheol. 48, 961 (2004).9. J. Bergenholtz, J. F. Brady, M. Vicic, J. Fluid Mech. 456, 239 (2002).

10. L.-N. Krishnamurthy, N. J. Wagner, J. Mewis, J. Rheol. 49, 1347(2005).

11. B. J. Maranzano, N. J. Wagner, J. Chem. Phys. 114, 10514 (2001).12. H. M. Laun, Angew. Makromol. Chem. 123, 335 (1984).13. J. Bender, N. J. Wagner, J. Rheol. 40, 899 (1996).14. C. Fischer et al., Smart Mater. Struct. 15, 1467 (2006).15. H. M. Laun, R. Bung, F. Schmidt, J. Rheol. 35, 999 (1991).16. Y. S. Lee, E. D. Wetzel, N. J. Wagner, J. Mater. Sci. 38, 2825 (2003).17. For a review, see J. F. Brady, G. Bossis, Annu. Rev. Fluid Mech. 20,

111 (1988).18. D. R. Foss, J. F. Brady, J. Fluid Mech. 407, 167 (2000). ■

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