Rheology and Microstructure of Shear Thickening Fluid

1 INTRODUCTION

Suspension emulsions, or suspoemulsions, are mixturesof two fluids where the dispersed phase is a suspensionof solid particles in a suspending medium. Suspoemul-sions are industrially relevant as they are used by theagricultural, personal care, and pharmaceutical indus-tries [1, 2]. Many of these formulations use high concen-tration colloidal suspensions so it is important to under-stand how mixtures of Newtonian and non-Newtonianfluids behave under flow. The goal of this work is to ex -amine the rheological behavior of a novel suspoemul-sion comprised of a Newtonian poly(dimethyl siloxane)(PDMS) fluid melt blended with a non-Newtonian shearthickening fluid (STF). This is achieved by performingstress controlled rheological measurements simultane-ous with measurements of the blend microstructure dur-ing shear using a novel rheo-microscope. The use ofsimultaneous microstructure and rheology measure-ments is necessary as the properties of the STF suspo-emulsion depend strongly on the dispersion morpholo-

gy, which is in turn greatly affected by preparation andflow history. This study seeks to qualitatively and quan-titatively describe these relationships to develop a bet-ter understanding of the fundamental physics requiredto effectively formulate complex fluid suspoemulsionsfor targeted applications.

The shear thickening response of colloidal disper-sions has been a topic of considerable recent interest inboth industrial and academic research. The shear thick-ening behavior of concentrated particle suspensionsand the underlying microstructural mechanisms for theshear thickening have been studied extensively usingsimulations, [3 – 5] optical techniques, [6, 7] and neu-tron scattering techniques, [8 – 14] as well as rheo-microscopy [15]. The history of and underlying mecha-nisms for shear thickening in concentrated suspensionshas been recently reviewed [16, 17]. The viscosity ofshear thickening fluids (STFs) do not monotonicallyincrease with shear stress or shear rate, as the namewould superficially suggest. Rather, the viscosity of aSTF decreases throughout the low shear stress regime

© Appl. Rheol. 24 (2014) 43049 | DOI: 10.3933/ApplRheol-24-43049 | 1 |

Rheology and Microstructure of Shear Thickening FluidSuspoemulsions

Jeremy N. Fowler1, John Kirkwood2, Norman J. Wagner*

1 Current address: Syngenta Crop Protection, LLC. P.O. Box 18300 Greensboro, NC 27419-8300 USA2Current address: Valspar Corp., High Point NC, 27263 USA

Corresponding author: [email protected]: x1.302.831.1048

Received: 11.1.2014, Final version: 26.4.2014

Abstract:A novel shear thickening suspoemulsion is formulated and studied with a new rheo-microscope instrument. The experimen-tal fluid system is comprised of a immiscible blend of Newtonian, low molecular weight poly(dimethylsiloxane) and a shearthickening suspension of colloidal silica in poly(ethylene glycol). The blend is studied as a function of composition where phaseinversion is evident at low shear rates and is found to be shear rate dependent. A shear thickening viscosity curve is observedwhen blends comprised of shear thickening fluid dispersed as droplets are subjected to high shear rates. Dispersing a contin-uously shear thickening fluid, fsilica = 0.42, results in continuously shear thickening response from the blend. Dispersing a dis-continuously shear thickening fluid, fsilica = 0.51, results in bulk shear thickening that can also be discontinuous. Shear thick-ening in the final suspoemulsion is consistently first detected at fSTF = 0.2, with the magnitude of shear thickening beingdependent on the particle concentration in the STF phase. The onset of shear thickening also corresponds with the formationof extended droplet structures in the fluid. The complex properties of these suspoemulsions and the ability to formulate dis-persed droplet morphologies in this mixture are shown to result from the underlying shear thickening rheology of the dis-persed phase.

Key words:shear thickening, suspensions, emulsions, suspoemulsions, rheo-microscopy, thixotropy

| DOI: 10.3933/APPLRHEOL-24-43049 | WWW.APPLIEDRHEOLOGY.ORG

mailto:[email protected]

as the particles organize in the flow field to lower theirresistance to flow. At higher applied shear stresses theparticles form shear-induced hydroclusters and thehydrodynamic component of the viscosity increases.This is signaled by a viscosity minimum and this valueis typically taken as the critical shear stress, σcrit,between shear thinning and shear thickening respons-es. This general rheological pattern has been observedfor numerous colloidal dispersions [12, 18, 19].

Composites containing shear thickening fluids havebeen demonstrated to provide improved ballistic, stab,and impact protection [20– 24]. However, containmentof STFs has proven to be challenging and new approach-es must be considered if they are to be realistically usedin protective devices. Here we explore a new compositecomprised of an immiscible blend of a shear thickeningfluid and a model polymer melt, termed a shear thick-ening fluid suspoemulsion. For example, the energy dis-sipating properties of STFs suggest their value for use inpersonal protective devices, but the kinetic energy of abullet is significantly different from that of a knife or ablunt weapon such that the fluid’s response may needto be engineered differently for these different applica-tions [20– 22]. Furthermore, the coupling of the shearthickening response to the rest of the composite archi-tecture is also critical for meeting a specific applicationrequirement [20, 22]. It is important to understand boththe blend morphology and the complex rheology ofshear thickening fluids to engineer STF suspoemulsionsfor specific applications.

The bulk properties of immiscible polymer blendsdepend strongly on the size and arrangement of dis-persed droplets within the matrix phase, or the topolo-gy of any co-continuous microstructures, as well as therheological properties of the individual components [25].For blends of two immiscible homopolymers subjectedto steady shear, the time-independent droplet size gen-erally decreases with shear rate [26]. Often, this steadydispersion is the result of the balance between shearbreak up of droplets and shear-induced coalescence [27].The capillary number, Ca= Rhmg

· /a, is commonly used todescribe the conditions related to coalescence andbreakup as it represents the balance of shearing forces,given by the medium viscosity hmmultiplied by the shearrate g· , which acts to pull the droplets of size R apart rel-ative to the interfacial tension a, that acts as a restoringforce to pull the droplet back into a spherical shape. Asthe value of Ca becomes significantly greater than 1,droplets in concentrated emulsions deform, transition-ing to ellipsoidal and so called string shapes in responseto steady shear flow [28, 29]. However, this parameterdoes not include the potential non-Newtonian nature ofthe droplet and often must be considered in conjunctionwith the viscosity ratio, l = hd/hm, for this reason (where

hd is the viscosity of the dispersed phase and hm is the vis-cosity of the matrix phase). Migler and co-workers havestudied the formation and stability of fluid strings inimmiscible polymer blends [30, 31]. According to theseobservations, the strings persist until their diameter isless than half of the thickness of the flow device gap. Atthis point the walls no longer have a stabilizing effect onthe strings and capillary instabilities cause the string tobreak up in flow. The authors also observed that for moreconcentrated systems (fPDMS = 0.28 dispersed phase inPIB matrix) there was a stabilizing effect, possibly fromdroplet strings closing on themselves to form completerings. These experiments are particularly relevant be -cause the confinement described in the studies of Miglerand co-workers is similar to the parallel plate geometryused for the rheo-microscopy experiments describedbelow. While mixtures of immiscible Newtonian andshear thinning polymers show bulk shear thinning, shearthickening fluids of the type described here have not yetbeen widely investigated [32]. Previous studies haveshown bulk shear thickening due to polymer-inducedbridging flocculation, or the use of non-colloidal, dilatantcorn starch granules, but to the best of our knowledgeno bulk shear thickening in suspoemulsions comprisedof concentrated colloidal suspensions has been demon-strated [1, 33, 34].

Viscosity models for polymers have been employedsuccessfully for modeling mixtures of homopolymersand thus, are candidates for making first order predic-tions for more complex systems, such as the suspo-emulsions discussed here. The fluidity-additivity equa-tion was first developed as an empirical method fordescribing the bulk viscosity for mixtures of polymer flu-ids [35, 36].The fluidity-additivity model is given as:

(1)

In the above, h is the bulk viscosity of the mixture, fi isthe volume fraction of each component, and hi is theviscosity of each component, which are considered tobe Newtonian. The morphology of the phases is notspecified in this empirical approach so it can be appliedto cocontinuous morphologies. Utracki and co-workersnote that the relationship arises from the continuity ofshear stress across a multi-layered structure. The rela-tionship was rederived in 1979 by Lin and continues tobe used as a first approximation for a mixing rule inmore contemporary research regarding polymer blends[37 – 39].

A second model based on a cell model for a dispersedphase within a matrix is the Choi-Schowalter model [40],which gives the blend viscosity as:


(2)

In the above the variables have the same meaning as inEquation 1 with f the volume fraction of the dispersedphase, and l the viscosity ratio [40]. This model has thepotential to describe the behavior of suspoemulsionswithout cocontinuity because it was derived assumingnon-dilute volume fractions of deformable fluid drop -lets. However, as Newtonian emulsion behavior is as -sumed, there will be limitations on its applicability to theresults presented here. This model has yielded goodagreement with experimental results for blends of New-tonian homopolymers such as PET/Nylon-6,6,poly(buty-lene succinate) (PBS)/polylactide (PLA), and poly(propy-lene) (PP)/ethylene octane copolymers [41 – 43]. Simula-tion level details for complex mixtures of fluids can becomputationally very difficult to obtain so, as we willshow, the modeling described above is useful as a cor-relative and semi-empirical predictive tool for the com-plex suspoemulsions considered herein.

2 MATERIALS AND METHODS

2.1 SUSPOEMULSION PREPARATION

The emulsions discussed in this article were made byemulsifying a shear thickening fluid (STF) dispersion intoan industrially produced PDMS matrix. The STFs wereprepared by combining nearly monodisperse ShokubaiSeahostar KE-P50 silica particles (450 ± 5 nm diameter)and Clariant poly(ethylene glycol) (PEG) with molecularweight 200 g/mol. The silica nanoparticles were slowlyadded to the desired quantity of PEG in a Nalgene stor-age bottle. The mixture was then roll-mixed for 2 days toallow the particles to fully disperse. The final volume frac-

tion of silica particles in the STFs are fsilica = 0.42 andfPDMS = 0.51 for the two systems under investigation,where the latter exhibits more extreme shear thicken-ing [16, 21].

The homopolymer used to make the suspensionemulsions is poly (dimethyl siloxane) (PDMS) obtainedfrom Gelest and designated by the manufacturer as hav-ing kinematic viscosity of 30 Pas. The PDMS and PEG usedfor the STF are immiscible and the particles do not dis-perse in the PDMS. Desired volumes of STF and PDMSwere mixed using a Silverson Mixer with the high shearsquare hole screen and impeller in a glass sample jar. Themixing protocol was to blend for a total of 10 minutes at6000 RPM, stopping every 2 – 3 minutes to scrape theSTF/PDMS mixture from the sides of the jar. The samplewas degassed using a vacuum oven operated at 25°C and- 30 in. Hg until bubbles were no longer observed in themixture.

The PDMS used to formulate all of the emulsionshas a measured average viscosity of 31.8 Pas, as seen inFigure 1. The viscosity and shear stress dependence onshear rate reflect a nearly Newtonian flow response overthe range of shear stresses investigated. A simple New-tonian homopolymer was chosen to highlight the impactof immiscible blending with a fluid with shear thicken-ing rheology. Two shear thickening fluids are used todemonstrate the impact of STF silica volume fraction onthe bulk properties of a suspoemulsion. The first STF,characterized in Figure 1, has fsilica = 0.42 in PEG 200 andhas a critical shear stress of 17 Pa, corresponding to ashear rate of 39.8 1/s. This suspension has a very smalland gradual thickening response and it is referred to asa continuously shear thickening fluid. The second shearthickening fluid, shown in Figure 1, has fsilica = 0.51 andhas a critical shear stress of 25 Pa, corresponding to ashear rate of 13 1/s. This suspension displays the behav-ior that has been well established for discontinuously


Figure 1: Viscosity versus shear rate for the pure PDMShomopolymer (O), and neat STF suspensions withfsilica = 0.42 (p) and fsilica = 0.51 ().

Figure 2: Viscosity versus shear stress for repeated stresssweeps of the fSTF = 0.3 suspoemulsion. Filled symbols corre-spond to the forward stress sweeps, from 0.01 to 1000 Pa.The open symbols correspond to the backward stress sweeps,from 1000 to 0.01 Pa.

shear thickening fluids. For both STFs the low shearregime exhibits shear thinning until the critical stress,where shear thickening begins.

2.2 HANDLING AND LOADING

The suspoemulsions samples were blended and thendegassed for approximately 15 minutes immediately pri-or to loading in the rheo-microscope or rheometer. Nosignificant phase separation occurred during thisprocess and the sample was well dispersed by the timeit was loaded onto the Peltier plate. For the rheo-micro-scope experiments the STF phase was dyed blue usingone drop of blue food coloring per 30 mL of STF. The bluedye was only soluble in PEG and did not transfer to thePDMS during mixing. The geometry was first lowered toa trim gap following TA Instruments guidelines whereexcess sample was gently removed. The experimentstarted promptly after reaching the geometry gap. Dur-ing the loading process, the STF and PDMS componentsin the gap were observed to remain mixed and no seg-regation due to sample loading was observed. The sus-poemulsion material that was squeezed out of the gapduring loading was observed to be similar in appearanceand texture to the bulk suspoemulsion sample.

2.3 RHEOLOGICAL PROTOCOLS

All rheological measurements for the suspoemulsionsdescribed here were performed on a TA Instruments AR-G2 stress controlled rheometer. The STF suspoemulsionswere initially characterized by multiple consecutivesteady state stress sweeps, from 0.01 Pa to 1000 Pa andback, where the first stress sweep acts as a preshear stepwhich establishes a uniform flow history for all samples.The steady state criteria were less than 3% change in thesignal for three consecutive sampling periods of ten sec-onds each, for a total observation time of 30 seconds. Thechosen geometry for the bulk viscosity measurementswas a 40 mm 1° cone which was used with a Peltier plateset to 25°C. The hysteresis in the viscosity vs. shear stresscurve diminishes after the completion of the first for-ward and backward stress sweeps which shows that theconfined flow in the rheometer may aid in further dis-persing the minority phase. Subsequent forward and

backward sweeps all match within experimental uncer-tainty and the second backward sweep is compared forall STFs made from the same particle type. Figure 2demonstrates how the viscosity curves change withrepeated stress sweeps for the fSTF = 0.3 suspoemulsion.The first forward and backward sweeps are very differ-ent from each other and distinguishable from the stresssweeps that follow them. The second and third backwardsweeps show reasonable agreement, as do the secondand third forward sweeps, which support the assertionthat the morphology in the suspoemulsion samplesundergo further refinement during the first forward andbackward stress sweeps. Following this protocol result-ed in reproducible data.

2.4 RHEO-MICROSCOPY

A new rheo-microscope attachment for the TA Instru-ments AR-G2 stress controlled rheometer was developedto take high-speed micrographs and video of the suspo-emulsion droplets in situ while performing rheology onthe sample. Figure 5 shows a schematic of the construc-tion of the rheo-microscope and a photograph of the ful-ly functional prototype that was used in this study. Thewhite LED light source is located within a modified low-er peltier plate and illuminates the sample through a sap-phire window (available from TA Instruments). A customquartz 50 mm upper parallel disk (2 mm thick) allows forreal time observation during rheology experiments. Theobservation point is located at a radial distance of 0.76times the quartz plate diameter, i.e., 19 mm from the axisof rotation of the disk, which corresponds to the single-point correction for the viscosity for a parallel plategeometry. [44] The use of a Peltier plate allows for excel-lent temperature control during rheo-microscopy, whichis essential for accurate rheological measurements. Therheo-microscope has magnification of 15X (as deter-mined using a stage micrometer) and was designed tobe used with a 200 micron gap height where the focalplane is located in the middle of the sample, 100 micronsabove the surface of the Peltier plate. The upper opticsare a modification of the TA Instruments Rheo-SALSdevice, where a convex lens and pin hole replace the stan-dard lens and beamstop arrangement [45].

The rheo-microscopy experiments were performedwith a preshear step of 1200 Pa flow for 5 minutes toestablish a uniform flow history for all of the samples.The forward (0.1 to 1000 Pa) and backward (1000 to0.1 Pa) steady state stress sweeps were performed to cap-ture changes in microstructure in response to changingshear stress. The steady state criteria were identical tothat used for the cone and plate stress sweeps. Thedroplet morphology of each suspoemulsion was quanti-fied by recording the entire experiment as a series of


Figure 3: Schematic and photograph of the rheo-microscopeapparatus.

QuickTime™ videos, using the time signature of thevideos to synchronize with the measured shear stress.The micrographs shown in the figures of the followingsections are single frames pulled from these videos.

3 RESULTS AND DISCUSSION

3.1 BULK RHEOLOGY

The focus of this paper is on the role of a discontinuouslyshear thickening fluid in a suspoemulsion, but it is veryuseful to consider two additional reference cases as coun-terpoints: a blend where the dispersed phase is the 200g/mol PEG without any particles present and a suspo-emulsion made from a continuously (more gently) shearthickening fluid. Mixtures of immiscible fluids with a largeviscosity mismatch are often difficult to blend into a dis-persed morphology. It is common for the lower viscositycomponent to flow preferentially to the high shear ratezones while the higher viscosity component remainsintact. This was observed when attempting a steady stateflow experiment with a mixture that has fPEG = 0.3 andfPDMS = 0.7 with 32 Pas PDMS. The lower viscosity PEG sim-ply flowed over the PDMS and out of the gap during sam-ple loading. The PEG that remained in the gap comprisedsignificantly less than fPEG = 0.3, inhibiting the ability todo quality rheological measurements on this type of mix-ture. The following sections will demonstrate that it is eas-ier to blend a high concentration colloidal suspension intoa high viscosity material be cause the dispersed phase vis-cosity increases at the high shear rates commonly associ-ated with mixing pro cesses, thus reducing the viscositymismatch. We are un aware of any prior observation of theuse of shear thickening fluids to enhance blend dispersion.The suspo emulsions made from fsilica= 0.42 and fsilica= 0.51STFs were readily blended and remaining dispersed for aminimum of 1 to 2 hours.

As shown in Figure 4, blends made with the contin-uously shear thickening fsilica = 0.42 STF show very mod-erate bulk shear thinning and thickening responses dur-ing shear flow. Note that the viscosity of the STF phase islower than that of the PDMS for all shear stresses inves-tigated. The fSTF= 0.1 blend shows a viscosity plateau closeto that of the pure PDMS viscosity in the low shear stressregime. A shear thinning response is detectable in thebulk rheology at shear stresses comparable to whereshear thinning is observed in the bulk suspension. A bulkshear thickening response is significant and observablefor blends where fSTF = 0.1 –0.3 of the fsilica = 0.42 STF. Themagnitude of the bulk shear thickening response for thefSTF = 0.5 – 0.7 blends is less significant, appearing to bemore similar to the bulk shear thickening of the purefsilica= 0.42 STF. Overall the addition of a moderately shearthickening colloidal suspension, such as the fsilica = 0.42STF, to a higher viscosity Newtonian homopolymerdecreases the viscosity of the blend. Note that the non-Newtonian response of the dispersed phase is manifestin the bulk rheology for volume fractions as low as fSTF =0.1 – 0.3.

The emulsions made by dispersing the discontin-uously shear thickening fsilica= 0.51 STF into PDMS showmore dramatic bulk shear thickening as compared toblends made with fsilica = 0.42 STF. The steady shear vis-cosities of each emulsion are shown in Figure 5 as afunction of shear stress. The fSTF = 0 curve shows thepure PDMS viscosity data from Figure 1 to facilitate com-parison. Emulsions with fSTF = 0.3 or less exhibit a vis-cosity plateau in the low stress regime, prior to shearthinning. This shows that the rheology of these emul-sions is dominated by the response of the PDMShomopolymer until stresses of 10 Pa for fSTF = 0.1, 3 Pafor fSTF = 0.2, and 0.2 Pa for fSTF = 0.3. Note that the lowshear rate viscosity of blends with fSTF = 0.1 – 0.3 is ele-vated due to the presence of viscous STF droplets, which


Figure 4: Viscosity versus shear stress for fSTF = 0.42 STF vol-ume fraction 0.1 – 0.7. Pure PDMS appears as a solid line at31.8 Pas and pure STF appears as a dashed line. A mild shearthickening effect is observed for all blends.

Figure 5: Viscosity versus shear stress for fsilica = 0.51 STF at vol-ume fractions from 0.1 – 0.7. Pure PDMS appears as a solid lineat 31.8 Pas and pure STF appears as a dashed line. The onset ofa bulk shear thickening response can be observed for volumefractions of STF present in the blend of 0.2 and greater.

is the opposite trend as compared to the fsilica= 0.42 STFblends. The shear stress required for the onset of bulkshear thinning decreases as the volume fraction of STFincreases. Emulsions with fSTF = 0.4 – 0.7 are qualita-tively different and are dominated by the response ofthe shear thickening fluid in the low shear stress region.These blends show no evidence of a low shear plateauover the range of shear rates tested.

The viscosity minimum, where the shear thinningregime transitions to shear thickening, moves to lowervalues as the volume fraction of STF increases. The shearstress where the viscosity reaches a minimum value isdesignated as the critical shear stress, σcrit. Starting withfSTF = 0.3 the bulk shear thickening response is signifi-cant, with the viscosity increasing by a factor 2 – 3 overthe range probed depending on STF volume fraction. Thisobservation is important because it clearly demonstratesthat blends containing as little as 30% of a dispersedphase comprised of a shear thickening colloidal suspen-sion can exhibit significant bulk shear thickening, aneffect that has not been demonstrated previously in thesuspoemulsion literature.

The location of the critical shear stress depends onthe formulation of the STF suspoemulsion. Figure 6shows that there are two general trends for σcrit as vol-ume fraction as STF increases. From fSTF = 0– 0.4 the crit-ical shear stress decreases with increasing STF loading,such that is approaches that for the bulk STF. There is alocal minimum at fSTF = 0.4 and a local maximum atfSTF = 0.5, indicating a transition in the way stress prop-agates throughout the system. At fSTF = 0.5 and abovethe samples exhibit a shear viscosity more similar to thatof the bulk STF. Interestingly, much higher stresses arerequired to yield bulk shear thickening, but this criticalstress reduces with increasing STF loading. More com-plex phase structure forms, as seen in the micrographsin the following section. As will be shown, this abrupttransition in behavior and in particular, the value of the

critical shear stress, is a direct indication of whether theSTF component is a continuous phase in the blend.

3.2 RHEO-MICROSCOPY: fsilica = 0.51 STF SUSPO -EMULSIONS

Quiescent microscopy was first done to understand thetime scale related to droplet sedimentation under grav-ity due to the density difference between the STF and thePDMS matrix. The goal is to complete any rheology ex -periments before droplet sedimentation changes thedistribution of droplets throughout the sample volume.In the absence of flow, the STF droplets do not sponta-neously coalesce. Instead, the larger and thus heavierdroplets fall out of suspension. Larger droplets driftedout of the focal plane after approximately 30 minutes,with smaller droplets following after 90 minutes. Attimes longer than this the changes in microstructure andrheological signal can no longer be attributed to the flowalone.

The fSTF= 0.3 suspoemulsion exhibited three distinctflow regimes during rheo-microscopy experiments asshown in Figure 5. At low shear stresses the sample isonly very slightly shear thinning, which can be attributedto two factors. First, the volume fraction of STF is too lowat fSTF = 0.3 for the shear thinning of the droplet phaseto dominate the bulk response of the fluid. Secondly, theviscosity ratio for the system is greater than 1 untilapproximately 0.3 Pa where the viscosities match andthe ratio is 1. In the low shear stress regime where vis-cosity ratio is very close to 1, the lack of contrast in vis-cosity results in the apparent viscosity plateau. Addi-tionally, the droplet size was not observed to be changingdue to coalescence because the droplets are spaced toofar apart to collide frequently at small deformations; thiscan be seen directly in Figure 7a.

As the STF droplet phase shear thins to viscositiessignificantly lower than the PDMS component (between1 and 100 Pa, where the viscosity ratio reaches a mini-mum of 0.06) the bulk suspoemulsion rheology showsmore pronounced shear thinning. The micrographs forthis regime, as seen in Figure 7b, show that coalescencebecomes more prevalent. The presence of fewer and larg-


Figure 6: Critical shear stress versus volume fraction of STF,taken from the minimum viscosity measurements in Figure 5.There is an apparent transition in σcrit between fSTF = 0.4 andfSTF = 0.6

Figure 7: Micrographs for the fSTF = 0.3 suspoemulsion ata) 0.1 Pa, b) 2.5 Pa, c) 79 Pa, and d) 316 Pa. Scale bars are 250 mm.

er droplets supports this physical explanation. Shearthinning is observed in Figure 5 up to the critical shearstress of 79 Pa, where shear thinning transitions to shearthickening. It is useful to note that the viscosity mea-sured during rheo-microscopy rheology will differ slight-ly from that shown in the previous section because of thedifference in geometry between parallel plate and coneand plate.

Beyond the critical shear stress for shear thickeningthe droplets begin to elongate in response to the shearflow. The elongated droplets merge when they collideand the well-dispersed microstructure evolves into smallnumber of threadlike droplets as seen in Figure 7c. As thestress increases, it is expected that the STF droplet phaseshear thickens and the threadlike droplets begin to resistthe flow as a result of the thickening. The increasingdeformation rate coupled with increasing viscosityresults in the threadlike droplets breaking apart, restor-ing the well dispersed microstructure between 100 and1000 Pa. The viscosity ratio increases during this regimeback to a value close to 1 just below 1000 Pa. The micro-graph in Figure 7d shows that the droplets decrease insize above the critical shear stress. The work of Miglerand co-workers described in the introduction shows thatthe breakup of droplet strings with increasing shearstress is not unique to STF suspoemulsions and thatshear thinning is broadly observed; thus the rich, non-linear rheological behavior observed here can be solelyattributed to the non-Newtonian properties of the STFphase and not the coalescence or breakup of the dropletsthemselves.

The fSTF = 0.4 blend has different rheology from thefSTF = 0.3 blend at low shear stresses, showing that theSTF dominates the bulk rheology across the full shearstress range starting at fSTF = 0.4. The micrographs forthe fSTF = 0.4 blend shows that the increased number ofdroplets results in the formation of a droplet networkwhere most droplets are in physical contact with at leastone neighbor. Video taken during the stress sweep alsoshows that the fSTF = 0.4 blend experiences a significantamount of coalescence even at the lowest stress tested,

which was 0.1 Pa. The fSTF = 0.3 blend had no significantcoalescence at the same shear stress due to the lowervolume fraction. The lack of a viscosity plateau for thefSTF = 0.4 sample is therefore the result of having a larg-er volume of non-Newtonian component and having thesize and number of droplets changing via coalescence.

The fSTF = 0.6 blend shows a transition from a STFdroplet surrounded by PDMS morphology to more of aco-continuous 2 liquid phase system. During the shear-thinning regime the microscope images show disperseddroplet morphology, as seen in Figure 8a. The well-dis-persed regions appear to have STF volume fraction low-er than fSTF = 0.6, which suggests that larger pure STFregions exist within the total sample volume. This can beobserved visually through the glass tooling and so thesample is co-continuous and very heterogeneous inmicrostructure. At 25 Pa, which is near the viscosity min-imum shown in Figure 5, the boundary between a pureSTF region and the dispersed region comes into view andcan be seen in Figure 8b. Coalescence during the shearthinning part of the curve causes more of the STF volumeto be contained in these large STF regions. At 199.5 Pa theshear thickening response causes the large STF phasesto start to break apart as seen in Figure 8c, but thebreakup is subtle at first, but becoming more significantas the shear stress approaches 1000 Pa. Figure 8d showsthat at 1000 Pa the large STF phases have been signifi-cantly re-dispersed due to flow break up.

3.3 VISCOSITY MODELING

The bulk viscosity of STF suspoemulsions is observed tobe highly reflective of the STF’s nontrivial rheology. Toaccount for this, we adapt both the fluidity-additivityand the Choi-Schowalter models by computing the vis-cosity of each phase corresponding to the shear stressset in the experiment, i.e., the bulk shear stress on thesample. Figures 9 and 10 demonstrate that the modifiedfluidity-additivity model is a good first order prediction


Figure 8: Micrographs of the fSTF = 0.6 blend, where the STF isfsilica = 0.51 in PEG 200 at a) 15.85 Pa, b) 25 Pa, c) 199.5 Pa, andd) 1000 Pa. Figure 9: Viscosity versus shear stress for experimental data

for fSTF = 0.1 – 0.4 with corresponding fluidity-additivity mod-el predictions.

of the qualitative features of the viscosity curve for STFsuspoemulsions. The model correctly predicts the shapeof the curve and the location of the viscosity minima forthe fSTF= 0.3 suspoemulsion, though the model over pre-dicts the magnitude of shear thinning compared to theexperimental measurement. The model shows the vis-cosity plateau in the limit of low shear stress, shear thin-ning and bulk shear thickening that were observed in theexperimental data for the fSTF = 0.3 blend. However, thefluidity-additivity model incorrectly predicts a similarviscosity plateau for the fSTF = 0.4 to 0.7 blends. This is tobe expected because the model adds fluidity in series,whereas the co-continuous microstructures would beexpected to act in parallel. When the STF viscositybecomes much greater than the PDMS viscosity, the flu-idity of the STF becomes very small and has less influenceon the predicted bulk viscosity. This is one of the majorlimitations of using this model to predict the bulk vis-cosity of STF suspoemulsions. However, above fSTF = 0.4,the fluidity-additivity model correctly predicts the orderof magnitude for the viscosity between applied shearstresses in the range of 0.1 Pa and 1000 Pa. The modelsystematically over predicts the viscosity minimum,showing that the experimental data has less shear thin-ning than predicted. The major advantage of the modelis that it is computationally very simple, making it fastand easy to use to get an order of magnitude viscosityprediction that also shows correct relative effect of vary-ing volume fraction of non-Newtonian component. Thisalso shows that above fSTF= 0.3, a suspoemulsion is func-tionally very similar to a 2 phase fluid system, showinggood agreement with the rheo-microscopic observa-tions.

As shown, the fluidity additivity model does not ade-quately describe the viscosity of more dilute STF suspo-emulsions where an STF dispersed phase is evident. Thisis the physical situation considered in the Choi-Schowal-ter polymer emulsion model. As shown in Figure 11, whenthe viscosities of the matrix and dispersed phases are

evaluated at the applied stress levels, the model correctlypredicts the qualitative trends in the viscosity, but gen-erally overestimates the bulk viscosity. The modifiedemulsion model predicts shear thinning at much lowerstresses as compared to the experimental measure-ments. However, it does provide an estimate for thestress at which shear thickening is observed in the bulksuspoemulsion. This further supports the concept thatthe shear thickening observed in the bulk suspoemulsionis a direct consequence of shear thickening in the dis-persed STF phase for blends with fSTF< 0.4. The qualita-tive discrepancy is expected in part because the rheo-microscope observations show the formation of elon -gated structures in the flow, which are not considered bythe model.

The overall physical picture described by the appli-cation of the two models discussed here is that at lowfSTF, the suspoemulsion acts qualitatively like a polymeremulsion. As the STF volume fraction increases, a co-con-tinuous fluid phase composed of STF forms and the mix-ture is described by the physics of the fluidity additivitymodel at medium and high stresses. Both models arecomputationally simple, have no fitting parameters, andyet as shown here, can be useful for describing some gen-eral rheological features for STF suspoemulsions. Theseresults provide an early indication of the types of math-ematical expressions that can be developed further tocompletely describe the behavior shown here.

4 CONCLUSIONS

We have demonstrated a novel shear thickening sus-poemulsion formed by immiscible blending of a con-centrated shear thickening fluid with a low molecularweight polymer melt. It is noteworthy that the shearthickening rheology of the STF is in part necessary forthe ability to form blends. Suspoemulsions made froma discontinuously shear thickening fluid and a New-


Figure 10: Viscosity versus shear stress for experimental datafor fSTF = 0.5 – 0.7 with corresponding fluidity-additivity mod-el predictions.

Figure 11: Viscosity versus shear stress for experimental databetween 10 and 30% STF with corresponding Choi-Schowalteremulsion model predictions.

tonian homopolymer can exhibit significant bulk shearthickening at volume fractions as low as fSTF = 0.3,whereas suspoemulsions made from the weakly con-tinuous shear thickening fluid do not show significantshear thickening. Thus, the presence of a strong shearthickening response in the STF is necessary for observeda shear thickening response in the suspoemulsion.

For the suspoemulsion blended with the discontin-uously shear thickening fluid, below fSTF = 0.3 threeregimes are observed in the rheology: a viscosity plateauin the limit of low shear stress, a shear thinning regime,and a shear thickening regime at stresses above the crit-ical shear stress of the pure STF. The rheo-microscopyshows that for all STF suspoemulsions tested, coales-cence is significant system wide during the shear-thin-ning regime. At low to moderate STF content, a thread-like phase was observed under flow near the viscosityminimum. These threads break-up in to droplets in thethickening regime with increasing applied shear stressincreases. The implication of this is that a well disperseddroplet morphology can be restored for these suspo-emulsions by imposing a shear stress sufficiently high soas to be in the shear thickening regime of the STF dis-persed phase (on the order of 1000 Pa for the suspo-emulsions discussed here). For blends with fSTF > 0.4behavior closer to that of the pure STF is observed at allshear rates.

The limited modeling analysis shows that simple,phenomenological viscosity models can qualitativelydescribe the behavior of the shear thickening suspo-emulsion. The modified polymer emulsions model cap-tures the qualitative behavior for the dilute suspoemul-sions, providing a reasonable prediction of the stress nec-essary to achieve shear thickening in the suspoemulsion.For STF loadings above fSTF= 0.3 volume fraction, the flu-idity-addivity model describes the qualitative features ofthe viscosity vs. shear stress curve between 0.1 and 1000Pa. However, this model incorrectly predicts a viscosityplateau below 0.1 Pa for suspoemulsions with fSTF = 0.4to 0.7 STF as it does not account for the co-continuousmicrostructure observed in the rheo-microscope. Theseapproaches are useful for guiding formulations of novelSTF suspoemulsions for specific applications.

ACKNOWLEDGEMENTS

Financial and technical support from TA Instruments forprototyping the rheo-microscope is gratefully acknowl-edged.

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Rheology and Microstructure of Shear Thickening Fluid