flow-induced gelation of microfiber suspensions · flow-induced gelation of microfiber suspensions...

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Flow-induced gelation of microfiber suspensions Antonio Perazzo a,b,1 , Janine K. Nunes a,1 , Stefano Guido b,c , and Howard A. Stone a,2 a Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544; b Department of Chemical, Materials and Production Engineering, University of Napoli Federico II, 80125 Napoli, Italy; and c CEINGE Advanced Biotechnologies, 80145 Napoli, Italy Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved August 21, 2017 (received for review June 18, 2017) The flow behavior of fiber suspensions has been studied exten- sively, especially in the limit of dilute concentrations and rigid fibers; at the other extreme, however, where the suspensions are concen- trated and the fibers are highly flexible, much less is understood about the flow properties. We use a microfluidic method to produce uniform concentrated suspensions of high aspect ratio, flexible microfibers, and we demonstrate the shear thickening and gelling behavior of such microfiber suspensions, which, to the best of our knowledge, has not been reported previously. By rheological means, we show that flowing the suspension triggers the irrevers- ible formation of topological entanglements of the fibers resulting in an entangled water-filled network. This phenomenon suggests that flexible fiber suspensions can be exploited to produce a new family of flow-induced gelled materials, such as porous hydrogels. A significant consequence of these flow properties is that the micro- fiber suspension is injectable through a needle, from which it can be extruded directly as a hydrogel without any chemical reactions or further treatments. Additionally, we show that this fiber hydrogel is a soft, viscoelastic, yield-stress material. hydrogel | flow-induced gelation | flexible fiber suspension F iber suspensions usually behave like shear thinning fluids; that is, the suspension viscosity decreases upon the action of flow, even when changing fiber size, aspect ratio, flexibility, or in the presence of noticeable normal stress differences (13). Shear thickening, where the viscosity increases with increasing shear rate, is rarely observed in flowing fiber suspensions. However, shear thickening is commonly reported in dense suspensions of solid spherical particles (4, 5) where, depending on the shear rate, par- ticle size, and concentration (5), lubrication interactions (6) or frictional contacts (68) can trigger the change in viscosity. Shear thickening can also be indicative of a gelation process. For exam- ple, shear thickening is observed for some polymer-particle sus- pensions, where the mechanism of gelation involves the bridging of particles with polymer chains (9). Using flow to cause gelation has been reported for a few other systems including worm-like micelle solutions and nanoparticle suspensions (10, 11). Given the im- portance of hydrogels in several applications, including tissue en- gineering, drug delivery, surgical adhesives, and 3D bioprinting (1217), there are benefits to be achieved by exploring and de- veloping simple methods for producing hydrogels, beyond the synthetic and physical approaches that currently exist (16, 1821), since promising alternative strategies can be applied to new and emerging applications and may suggest new opportunities. In this work, we present a flow-induced gelation strategy that relies primarily on irreversible topological entanglements of very- high-aspect-ratio flexible fibers induced by flow, which is a simple yet general mechanical approach that to our knowledge has not been proposed or demonstrated previously. We note that sus- pensions of microfibrillated cellulose, which are polydisperse nanofibers of cellulose, have been reported to form gel-like states; however, little is known about how these hydrogels form (22). Similarly, small molecule gelators are known to produce gels composed of nanofibers, where the mechanism of gel formation is thought to be due to strong intermolecular interactions leading to fiber entanglements (23). In our experiments, fibers become entangled and separate from water, creating a single large bundle or cluster of fibers owing to the interplay of their high aspect ratio, flexibility, and the action of flow, thus allowing us to convert the suspension into a hydrogel. We provide evidence that the gelation of fibers in the suspensions, which may involve hydrodynamic interactions and frictional con- tacts, is based on the formation of topological entanglements and knots, which we refer to collectively as mechanical interlocking.This mechanism of gel formation, which does not involve chemical or intermolecular interactions, is different from that of typical physical gels formed from associative polymers, such as block copolymers, charged polymers, and polymers that exhibit strong intermolecular interactions (24, 25). A large body of literature, comprising experiments and simu- lations, has been devoted to suspensions of rigid rods (2638). Some of the simulations consider many kinds of fiberfiber in- teractions, such as hydrodynamic, lubrication, and friction, and reviews are available (28, 34). Most of the early research on flexible fiber suspensions was inspired by the flocculation of cel- lulose fibers during paper pulp processing (39). Among this lit- erature, Forgacs and Mason (40) reported the seminal result on the bending of a single fiber with the action of shear flow, a prerequisite for creating disconnected paper pulp flocs of fi- bers by flow-induced bending of adjacent flexible fibers, that is, the so-called mechanical interlocking mechanism described by Meyer and Wahren (41). Studies have followed trying to es- tablish a link between the elasticity of the single fiber and the hydrodynamic force induced by flow, considering the effects of friction and hydrodynamic interactions among fibers (4246). In addition, the ability of a single flexible fiber to self-entangle and create a knot when subjected to shear flow was simulated recently (47). Here we hypothesize that when concentrated suspensions of highly flexible microfibers are subjected to stresses generated by flow (45) the fibers will deform and bend, creating topological Significance Suspensions of flexible fibers usually behave as shear thinning fluids; that is, their effective viscosity, or resistance to flow, decreases as they are exposed to higher shear stresses. Here we demonstrate that for suspensions created with very-high- aspect-ratio fibers, which are highly flexible, shear thickening behavior of a fiber suspension is obtained. Such a property can be exploited to produce a biocompatible hydrogel by injecting the suspension from a standard needle and syringe without any chemical reactions (unlike a chemically cross-linked hydrogel) or chemical interactions (unlike a traditional physical hydrogel). Once extruded, the hydrogel is a yield-stress material with po- tentially useful mechanical properties for bioengineering and biomedical applications. Author contributions: J.K.N. and H.A.S. designed research; A.P., J.K.N., S.G., and H.A.S. performed research; A.P., J.K.N., S.G., and H.A.S. analyzed data; and A.P., J.K.N., S.G., and H.A.S. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. 1 A.P. and J.K.N. contributed equally to this work. 2 To whom correspondence should be addressed. Email: [email protected]. This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1710927114/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1710927114 PNAS | Published online September 18, 2017 | E8557E8564 APPLIED PHYSICAL SCIENCES PNAS PLUS Downloaded by guest on February 4, 2021

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Page 1: Flow-induced gelation of microfiber suspensions · Flow-induced gelation of microfiber suspensions Antonio Perazzoa,b,1, Janine K. Nunesa,1, Stefano Guidob,c, and Howard A. Stonea,2

Flow-induced gelation of microfiber suspensionsAntonio Perazzoa,b,1, Janine K. Nunesa,1, Stefano Guidob,c, and Howard A. Stonea,2

aDepartment of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544; bDepartment of Chemical, Materials and ProductionEngineering, University of Napoli Federico II, 80125 Napoli, Italy; and cCEINGE Advanced Biotechnologies, 80145 Napoli, Italy

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved August 21, 2017 (received for review June 18, 2017)

The flow behavior of fiber suspensions has been studied exten-sively, especially in the limit of dilute concentrations and rigid fibers;at the other extreme, however, where the suspensions are concen-trated and the fibers are highly flexible, much less is understoodabout the flow properties. We use a microfluidic method to produceuniform concentrated suspensions of high aspect ratio, flexiblemicrofibers, and we demonstrate the shear thickening and gellingbehavior of such microfiber suspensions, which, to the best of ourknowledge, has not been reported previously. By rheologicalmeans, we show that flowing the suspension triggers the irrevers-ible formation of topological entanglements of the fibers resultingin an entangled water-filled network. This phenomenon suggeststhat flexible fiber suspensions can be exploited to produce a newfamily of flow-induced gelled materials, such as porous hydrogels. Asignificant consequence of these flow properties is that the micro-fiber suspension is injectable through a needle, fromwhich it can beextruded directly as a hydrogel without any chemical reactions orfurther treatments. Additionally, we show that this fiber hydrogel isa soft, viscoelastic, yield-stress material.

hydrogel | flow-induced gelation | flexible fiber suspension

Fiber suspensions usually behave like shear thinning fluids;that is, the suspension viscosity decreases upon the action of

flow, even when changing fiber size, aspect ratio, flexibility, or inthe presence of noticeable normal stress differences (1–3). Shearthickening, where the viscosity increases with increasing shear rate,is rarely observed in flowing fiber suspensions. However, shearthickening is commonly reported in dense suspensions of solidspherical particles (4, 5) where, depending on the shear rate, par-ticle size, and concentration (5), lubrication interactions (6) orfrictional contacts (6–8) can trigger the change in viscosity. Shearthickening can also be indicative of a gelation process. For exam-ple, shear thickening is observed for some polymer-particle sus-pensions, where the mechanism of gelation involves the bridging ofparticles with polymer chains (9). Using flow to cause gelation hasbeen reported for a few other systems including worm-like micellesolutions and nanoparticle suspensions (10, 11). Given the im-portance of hydrogels in several applications, including tissue en-gineering, drug delivery, surgical adhesives, and 3D bioprinting(12–17), there are benefits to be achieved by exploring and de-veloping simple methods for producing hydrogels, beyond thesynthetic and physical approaches that currently exist (16, 18–21),since promising alternative strategies can be applied to new andemerging applications and may suggest new opportunities.In this work, we present a flow-induced gelation strategy that

relies primarily on irreversible topological entanglements of very-high-aspect-ratio flexible fibers induced by flow, which is a simpleyet general mechanical approach that to our knowledge has notbeen proposed or demonstrated previously. We note that sus-pensions of microfibrillated cellulose, which are polydispersenanofibers of cellulose, have been reported to form gel-like states;however, little is known about how these hydrogels form (22).Similarly, small molecule gelators are known to produce gelscomposed of nanofibers, where the mechanism of gel formation isthought to be due to strong intermolecular interactions leading tofiber entanglements (23).In our experiments, fibers become entangled and separate from

water, creating a single large bundle or cluster of fibers owing to

the interplay of their high aspect ratio, flexibility, and the action offlow, thus allowing us to convert the suspension into a hydrogel.We provide evidence that the gelation of fibers in the suspensions,which may involve hydrodynamic interactions and frictional con-tacts, is based on the formation of topological entanglements andknots, which we refer to collectively as “mechanical interlocking.”This mechanism of gel formation, which does not involve chemicalor intermolecular interactions, is different from that of typicalphysical gels formed from associative polymers, such as blockcopolymers, charged polymers, and polymers that exhibit strongintermolecular interactions (24, 25).A large body of literature, comprising experiments and simu-

lations, has been devoted to suspensions of rigid rods (26–38).Some of the simulations consider many kinds of fiber–fiber in-teractions, such as hydrodynamic, lubrication, and friction, andreviews are available (28, 34). Most of the early research onflexible fiber suspensions was inspired by the flocculation of cel-lulose fibers during paper pulp processing (39). Among this lit-erature, Forgacs and Mason (40) reported the seminal resulton the bending of a single fiber with the action of shear flow, aprerequisite for creating disconnected paper pulp flocs of fi-bers by flow-induced bending of adjacent flexible fibers, that is,the so-called mechanical interlocking mechanism described byMeyer and Wahren (41). Studies have followed trying to es-tablish a link between the elasticity of the single fiber and thehydrodynamic force induced by flow, considering the effects offriction and hydrodynamic interactions among fibers (42–46).In addition, the ability of a single flexible fiber to self-entangleand create a knot when subjected to shear flow was simulatedrecently (47).Here we hypothesize that when concentrated suspensions of

highly flexible microfibers are subjected to stresses generated byflow (45) the fibers will deform and bend, creating topological

Significance

Suspensions of flexible fibers usually behave as shear thinningfluids; that is, their effective viscosity, or resistance to flow,decreases as they are exposed to higher shear stresses. Here wedemonstrate that for suspensions created with very-high-aspect-ratio fibers, which are highly flexible, shear thickeningbehavior of a fiber suspension is obtained. Such a property canbe exploited to produce a biocompatible hydrogel by injectingthe suspension from a standard needle and syringe without anychemical reactions (unlike a chemically cross-linked hydrogel) orchemical interactions (unlike a traditional physical hydrogel).Once extruded, the hydrogel is a yield-stress material with po-tentially useful mechanical properties for bioengineering andbiomedical applications.

Author contributions: J.K.N. and H.A.S. designed research; A.P., J.K.N., S.G., and H.A.S.performed research; A.P., J.K.N., S.G., and H.A.S. analyzed data; and A.P., J.K.N., S.G., andH.A.S. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1A.P. and J.K.N. contributed equally to this work.2To whom correspondence should be addressed. Email: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1710927114/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1710927114 PNAS | Published online September 18, 2017 | E8557–E8564

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Page 2: Flow-induced gelation of microfiber suspensions · Flow-induced gelation of microfiber suspensions Antonio Perazzoa,b,1, Janine K. Nunesa,1, Stefano Guidob,c, and Howard A. Stonea,2

entanglements that lead to the irreversible formation of a porousentangled network of mechanically interlocked microfibers filledwith water, that is, a fiber hydrogel. We do not focus on eluci-dating the role of frictional contacts or lubrication interactions inthe shear thickening behavior and gelation in suspensions of longand highly flexible fibers; however, we show that shear thickeningis a clear signature of the bending of fibers to create topologicalentanglements, which may lead to gelation. Thus, we approachthis study from a rheological perspective to characterize the flowproperties of flexible microfiber suspensions and then show thata hydrogel is produced when the microfiber suspension is ex-truded from a needle and syringe.

Results and DiscussionWe and others have previously shown that using fabricationmethods such as microfluidics, the properties of fibers, such asmodulus, aspect ratio, morphology, composition, and encapsu-lated materials, can be tailored with a high degree of control (48–52). Some of the emerging applications of these fibers includetissue engineering and biomedical applications where the fibersare used in scaffolds, sutures, and meshes (13, 48). Here, we use amicrofluidic method to produce microfibers with uniform di-

mensions, as this approach lets us precisely control the propertiesof the microfibers, which is necessary to prepare model suspen-sions of nearly monodisperse, high-aspect-ratio fibers. A sche-matic of the microfluidic process is illustrated in Fig. 1A. Unlikemany other fiber-generating methods, we are able to control boththe diameter and length of the fiber in situ during fabrication,using pulsed UV light and a photoreactive fiber solution (50)(Materials and Methods). We produce flexible poly(ethylene gly-col) diacrylate (PEG-DA) microfibers, 35 μm in diameter. Similarto other types of suspensions, our samples are prone to wall slipwhen sheared, so we use a measuring geometry with rough sur-faces to minimize this effect (Rheology of Fiber Suspensions), andwe use a parallel plate geometry to have the capability to changethe distance between the two rotating plates (Fig. S1). For theresults reported in the main text, the fiber length is ∼12 mm, toachieve an aspect ratio (length/diameter, L/D) ∼340; additionalresults for fiber lengths 4 mm and 8 mm, L/D = 114 and 228, re-spectively, are provided in Rheology of Fiber Suspensions, (Fig. S2).The microfibers are suspended in an aqueous solution and shearedusing a rheometer.Initially the fibers are well-dispersed and unentangled in the

suspension (Fig. 1B). After shearing, the suspension separates into

Fig. 1. Effect of shear rate on flexible high-aspect-ratio fiber suspensions. (A) Schematic representation of the microfluidic fiber fabrication setup with (Inset)bright-field image of flowing solutions in the flow-focusing device (scale bar, 500 μm.) (B) Nonsheared fiber suspension, ϕ = 0.1, and (C and D) different regions ofthe fiber-rich zone of the fiber suspension after shearing at 10 s−1 until phase separation. (Scale bars, 500 μm.) (E) Time-dependent viscosity of a fiber suspensionwith fiber volume fraction, ϕ = 0.1, at constant shear rates, _γ = 0.1, 1, 10, and 15 s−1. The gap size is 0.7 mm. (F) Demonstration of irreversibility: flow curve of a ϕ =0.2 fiber suspension, showing viscosity as shear rate, _γ, is first increased from 0.1–12 s−1 then decreased from 12–0.1 s−1.

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a fiber-rich region (Fig. 1 C and D) and a region composed mostlyof water with very few fibers. In the fiber-rich regions, the fiberscan have any random orientation, and we have observed alignedand nonaligned fibers, as well as fibers bent in random orienta-tions (Fig. 1 C and D). To gain some understanding of this pro-cess, we measure the viscosity, η, of the suspensions as a functionof time for different shear rates, _γ, and volume fractions of fibers,ϕ. We find that the fiber suspensions exhibit shear thickeningbehavior (Fig. 1E), which, at this point, we suggest is due to theirreversible mechanical interlocking of fibers.To understand the variations of viscosity with shear rate, we

report, in Fig. 1E, the behavior of a suspension, ϕ = 0.1, whereshear thickening occurs for _γ ≥ 1 s−1. Before shear thickening, theinitial (time→ 0) viscosity of the suspension decreases as the shearrate increases, which is evidence of shear thinning before thick-ening. In Fig. 1F, we demonstrate irreversibility of the flow-induced microstructural change of a suspension, ϕ = 0.2, by firststeadily increasing the shear rate to 12 s−1, followed by decreasingthe shear rate. During the decreasing phase, the viscosity of thesuspension continues to increase higher than the viscosity at thehighest shear rate. This behavior highlights not only the irrevers-ibility of the transformation of the fiber network but also that thestructure is being stretched and aligned along the flow direction asit forms when a shear stress is applied, that is, during the in-creasing shear rate ramp. When the applied stress decreases, that

is, during the decreasing shear rate ramp, the structure relaxes,and as a consequence of the mechanical entanglements the vis-cosity is increased.The viscosity as a function of time for fiber suspensions sheared

at four different shear rates is reported in Fig. 2, where each plotgives results for different fiber volume fractions. The zero-shearviscosity increases as the fiber concentration increases. One sig-nificant rheological feature of these fiber suspensions is thepresence of shear thickening in the microfiber suspensions. Whenapplying lower shear rates, that is, 0.1 and 1 s−1, we do not observeshear thickening for the smallest volume fraction of fibers in-vestigated, ϕ = 0.07, whereas for the highest volume fraction offibers investigated, ϕ = 0.4, the suspension is quickly expelled fromthe parallel-plate gap in the rheometer and climbed along therotating plate when sheared at 15 s−1, which is characteristic ofthe Weissenberg effect (53). This behavior is a consequence of thesignificant viscoelasticity of the suspensions (Figs. S3 and S4),which increased with fiber concentration. Note that we reportmeasurements until the time at which fluid is expelled from therheometer. As we commented above for Fig. 1E, we observe shearthinning when reporting the initial value of the viscosity (time →0) as a function of the different shear rates, that is, for any volumefraction, the viscosity starts from a lower value for higher shearrates. This effect is more noticeable when comparing the dataobtained for the smallest shear rate, 0.1 s−1, to the data measured

Fig. 2. Effect of shear rate and concentration. Time-dependent viscosity of suspensions of fibers with fiber volume fractions ϕ = 0.07 (●), 0.1 (▲), 0.2 (■), and0.4 (X) at constant shear rates: (A) 0.1, (B) 1, (C) 10, and (D) 15 s−1. The gap size is 0.7 mm.

Perazzo et al. PNAS | Published online September 18, 2017 | E8559

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Page 4: Flow-induced gelation of microfiber suspensions · Flow-induced gelation of microfiber suspensions Antonio Perazzoa,b,1, Janine K. Nunesa,1, Stefano Guidob,c, and Howard A. Stonea,2

at the highest shear rate, 15 s−1 (see also η versus _γ flow curves inFig. S3).The fibers used in this study are non-Brownian (Rheology of

Fiber Suspensions) and in the flexible regime. Fiber flexibility canbe characterized by the effective stiffness, Seff:

seff =EYπD4

64ηm _γL4,

where EY is the Young’s modulus, L and D are fiber length anddiameter, respectively, ηm the viscosity of the continuous phase,and _γ the shear rate (54). Seff compares fiber stiffness and hydro-dynamic forces. Specifically, the flexibility of the elastic fiber iscompared with the hydrodynamic torque induced by shear flow(44); some authors (40) include an additional ln(L/D) factor, butthis term changes the value of Seff only slightly. For Seff << 1,fibers are flexible, whereas for large values of Seff fibers areclassified as rigid. Given that EY is ∼105 Pa for the PEG-DAfibers and _γ ranges from 0.1–15 s−1, our effective stiffness rangesbetween 2.4 × 10−5 < Seff < 3.6 × 10−3, and hence the fibersinvestigated in this study can be considered flexible, which isconsistent with their highly bent conformations when suspended

in water (Fig. 1B). Within this flexible regime, we investigatedthe effect of fiber aspect ratio (L/D) for a fixed EY (Rheology ofFiber Suspensions). For concentrated suspensions of relativelylow aspect ratio fibers, L/D = 114 and ϕ = 0.4, we observed onlyshear thinning. We start to observe shear thickening for inter-mediate length fibers, L/D = 228 and ϕ = 0.4, at higher shearrates, that is, ≥20 s−1 (Fig. S2).A possible explanation for the observed rheological behavior is

the flow-driven formation of entanglements of fibers. The effectof a higher shear rate or of a higher fiber concentration is toaccelerate the separation from the continuous water phase. Asmentioned above, the gelation of fibers is possible through thecreation of entanglements, and a prerequisite for the creation ofentanglements is that fibers are bent by the stresses produced byflow. Theories of single flexible fibers have been developed topredict the onset of fiber deformation in suspensions, and torelate those predictions to bulk flow properties of fiber suspen-sions (55). These theories, however, cannot be directly applied toour high volume fraction and extremely flexible (entangling) fi-bers. Others have taken a different approach to predict the flowbehavior of dense non-Brownian fiber suspensions, establishingcriteria that consider the number of contacts among fibers in a

Fig. 3. In situ visualization of sheared fiber suspensions. Time-dependent viscosity of a fiber suspension with fiber volume fraction ϕ = 0.4 at a constant shearrate of (A) 1 s−1 (shear thinning observed) and (B) 10 s−1 (shear thickening observed) using smooth glass parallel plates. In situ images of sheared fibersuspension of a fiber suspension with fiber volume fraction ϕ = 0.4 (C) at a constant shear rate of 1 s−1 at 262 s (time point indicated on A) and (D) at aconstant shear rate of 10 s−1 at 77 s (time point indicated on B). (Scale bar, 200 μm.)

E8560 | www.pnas.org/cgi/doi/10.1073/pnas.1710927114 Perazzo et al.

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given volume (39), and while these criteria can be used to esti-mate whether flocs, that is, disconnected fiber bundles, will form,they are unable to predict gel modulus or the dynamics of gelformation (Rheology of Fiber Suspensions).To support our hypothesis that the fibers are entangling and

separating from water during flow, we perform in situ visualizationof the microstructure while measuring the viscosity under shear ofthe ϕ = 0.4 fiber suspension. For this experiment, we use coun-terrotating smooth glass parallel plates while visualizing the samplefrom the bottom of the plates (see Materials and Methods for de-tails). Transparent smooth glass plates are necessary to visualize thesample under flow; however they induce significant fiber wall slip.This effect translates to a shift in the onset of shear thickening tohigher shear rates compared with the data measured with roughplates (compare Fig. 3 A and B to Fig. 2 A and C). The transitionfrom shear thinning to shear thickening behavior allows us to ob-serve the different morphological behaviors associated with the twoflow regimes as obtained with two different shear rates. Fibers getclose together already in the shear thinning regime; however, theyare mostly aligned and stretched along the main flow direction (Fig.3C and Movie S1). Conversely, in the shear thickening regime,although bundles of fibers aligned with the flow are still observedsome fibers buckle, create loops, and become partially oriented inthe direction orthogonal to flow (Fig. 3D and Movie S2).Even for concentrated suspensions of these microfibers, that is,

ϕ = 0.4, we observe that the suspensions can flow, as shown in Fig.4A, and as such can be poured and transferred as desired (MovieS3). We observe that when we inject a concentrated suspension ofthe microfibers from a needle with an inner diameter of 0.21 mm ahydrogel is immediately extruded, where excess water is squeezedout of the network (Fig. 4A and Movie S4). We can consistentlyproduce hydrogels by extrusion when the suspension of fibers hasa volume fraction, ϕ ≥ 0.2. The fiber hydrogels also swell in water(Fig. S7), which is another common property of hydrogels. Weconfirm that we have in fact formed a hydrogel by measuring theshear moduli with a rheometer by applying a small oscillatorystress at different frequencies. Our extruded material exhibitedtypical viscoelastic properties of a hydrogel, with the shear elasticmodulus, G′, greater than the viscous modulus, G″ (Fig. 4B andRheology of Fiber Hydrogels, Fig. S5).There are theories to estimate the shear modulus (G* = G′ +

iG″) of a hydrogel made of a filamentous network (56, 57).However, they typically assume that contacts among fibers arechemically cross-linked, while in our case the contact points arefree to slide. Other theories predict the shear modulus of a bundleof dry fibers where the modulus is a function of the fiber volumefraction and the elasticity of a single fiber (57, 58). This predictionoverestimates the modulus of our hydrogel by two orders ofmagnitude, likely because the contact points are lubricated bywater, free to slide, and fibers are more flexible than the onestypically considered (59) (Rheology of Fiber Suspensions).We have shown that the injection of a fluid-like suspension of

fibers triggers hydrogel formation, suggesting that this system hasthe potential to be further developed as a new type of injectablehydrogel, which is attractive for many in vivo applications wherehydrogels need to be delivered in a minimally invasive manner(18–20). A desirable property of such injectable hydrogels isyielding upon the application of flow, where we define yielding asa transition where the material starts to flow or spread followingthe imposition of a critical shear stress. Our fiber hydrogels, whichare obtained from extrusion from a needle and syringe, exhibitsuch a property. Similarly, other soft materials have been engi-neered to exhibit shear thinning and yielding properties (60). InFig. 4C we show that the hydrogel produced from a suspension atϕ = 0.4 is a material that has a yield stress, whose value dependson the confinement of the fiber network (Fig. S6). It should benoted, moreover, that the material shows a full recovery of itsinitial viscosity once the shear rate is decreased back to the lowest

value. This feature permits the extruded hydrogel material to beeasily spread over the site of application, and once the stress isremoved its increased viscosity locks the hydrogel onto the site,avoiding any possible sliding/leakage.

Fig. 4. Flow-induced gelation of a ϕ = 0.4 fiber suspension: rheologicalproperties of the fiber hydrogel. (A) Extrusion of the hydrogel from a needleand syringe containing a concentrated suspension of microfibers. (Inset ) Atilted vial containing a concentrated suspension of microfibers. (B) Linearviscoelasticity as a function of frequency of the extruded hydrogel for anoscillatory stress of 0.7 Pa. The elastic modulus, G′, is represented by filledsymbols and the viscous modulus, G″, is represented by open symbols.(C) Demonstration of yielding behavior of the fiber hydrogel with increasing,up to 250 Pa, and decreasing stress ramps plotted against shear rate.

Perazzo et al. PNAS | Published online September 18, 2017 | E8561

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We use confocal and electron microscopy to investigate themicrostructure of the hydrogel, which we found to be a densenetwork of microfibers with a random microporous network (Fig.5). In particular, Fig. 5 A and B shows the 3D reconstruction ofan extruded hydrogel produced from a fiber suspension, ϕ = 0.2(see also Movie S5). The fiber volume fraction of the hydrogelincreased significantly from that of the suspension. We roughlyestimated a percent pore volume (or percent water-filled volumebetween fibers) for the suspensions and the hydrogels fromconfocal image analysis and found that for the ϕ = 0.2 suspen-sion percent pore volume ≈ 76 ± 4%, and for the resulting ex-truded hydrogel percent pore volume ≈ 24 ± 4%. For the ϕ =0.4 suspension, the percent pore volume ≈ 56 ± 4%, and for thehydrogel ≈ 10 ± 5%. Both confocal and SEM images confirm thepresence of both aligned and bent fiber regions in the hydrogel(Fig. 5 C–E). Topological entanglements occur where fibers that

are strongly bent into loops, coils, and twists overlap with eachother and mechanically interlock.During the extrusion of the hydrogel from the needle and

syringe, fiber entanglements are created. Fibers need a stress tobecome entangled and such a stress can be provided by the ac-tion of flow. Pressure-driven flow in a syringe is made of twocomponents: Poiseuille flow in the region of the syringe with aconstant cross-sectional area and extensional flow brought aboutby the abrupt change of cross-sectional area when the suspensionflows from the main body of the syringe into the needle. Ex-tensional flow, along with Poiseuille flow within the needle, playsa key role in hydrogel formation. The former can cause rapidlocal elongation and induce a stress proportional to the abruptfluid velocity change due to the passage from a larger sectioninto a smaller one, whereas the latter, given the small diameterof the needle, can keep the fibers confined as well as provide a

Fig. 5. Porosity and microstructure of fiber suspensions and fiber hydrogels. (A and B) Three-dimensional confocal reconstructions of a fiber hydrogelprepared from a suspension with ϕ = 0.2 (see also Movies S1–S5). (C and D) Individual confocal z-slices showing typical fiber deformations in the hydrogel, suchas (C) twisted loop or coiled and (D) aligned and looped fibers, as indicated by the dashed lines. (Scale bars, 200 μm.) (E) SEM image of a dried hydrogel, withmagnified (Inset) images showing different regions of the hydrogel. (Scale bars, 200 μm in the low-magnification image and 100 μm in higher-magnificationimages.)

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stress proportional to the velocity gradient along the needlecross-sectional area, thus promoting fiber entanglements. Thecharacterization of fiber entanglements identified in this workhas been realized with shear flow rheometry (e.g., Figs. 1–3).Although shear stress could represent part of the total stressinvolved during extrusion, shear rheology, as described in Figs. 2and 3, represents a method to investigate the process of entan-glement formation and to demonstrate that our fiber suspensionscan be converted into a hydrogel using flow.

ConclusionsIn this work we explored the rheological behavior of highly flexiblemicrofiber suspensions to gain understanding of our observationsof the gelation process that occurs when concentrated suspensionsof non-Brownian microfibers experience various flow conditions.The microfibers must be very flexible, so that they can bend underflow without breaking to form topological entanglements. Theresults indicate that the suspensions undergo irreversible gel for-mation, which depends on the stress imposed by flow. Our studycontributes rheological insight into the flow behavior of concen-trated flexible, high aspect ratio fiber suspensions and highlightsthe need for improved theoretical models to better predict char-acteristics of these entangled microstructures. Furthermore, webelieve that the entanglements that form lead to the macroscopicgelation of the suspension when subjected to strong shear andextensional flows, such as those produced during extrusion from aneedle and syringe.Since the action of injecting the fiber suspension triggers its

gelation, we believe this system can be used to develop a new classof injectable hydrogel materials, where a wholly mechanical ap-proach is used to physically and irreversibly cross-link a free-flowing suspension. The cross-linking mechanism is independentof chemical reactions or restructuring of individual components inthe gelling solution but depends primarily on the microfiber aspectratio, flexibility, concentration, and stress induced by flow. Thesematerials offer a promising approach for the in situ fabrication ofscaffolds, possibly incorporating chemicals and/or cells encapsu-lated in the microfibers, in various applications spanning industryand medicine.

Materials and MethodsMicrofluidic Synthesis of Fibers. Microfluidic channels were prepared usingstandard methods of soft lithography (61). Polydimethylsiloxane (PDMS) (DowCorning Sylgard 184; Ellsworth Adhesives) channels were plasma-bonded toPDMS-coated glass slides using a Corona Surface Treater (Electro-TechnicProducts, Inc.). The microfluidic device had two inlets, one for the oil contin-uous phase and the other for the oligomer solution. The individual liquidphases met at a hydrodynamic focusing region where a cylindrical oligomer jetformed. The jet, sheathed by the continuous phase, flowed through a mainchannel of width 200 μm and height 120 μm. The oil continuous phase wascomposed of 62 vol % heavy mineral oil (Fisher Scientific), 27 vol % hex-adecane, and 11 vol% Span 80. The oligomer solution was composed of 54 vol%PEG-DA (molecular weight = 575 g/mol), 42 vol % deionized (DI) water, and4 vol % 2-hydroxy-2-methylpropiophenone (photoinitiator). The oil and PEG-DA phases were pumped at constant flow rates of 1.2 mL/h and 0.16 mL/h,respectively, using syringe pumps (KD Scientific and Harvard Apparatus). Un-less otherwise stated, all chemicals were purchased from Sigma-Aldrich.

UV light was used to initiate the cross-linking reaction in the monomer jet.The UV light was supplied by a fluorescence light source (120-W mercury

short-arc lamp) on a Leica DMI4000B inverted microscope via the 20×magnification objective lens. No filters were used to modify the spectrum oflight supplied from the lamp, and thus the light incident on the PEG-DA jetwas not monochromatic. We measured the UV light intensity at the bottomsurface of the device to be in the range 20–24 mW/cm2 for all presentedresults. The length of the fibers was controlled optically by pulsing the UVlight incident on the monomer jet. The shutter was programmed to open for370 ms and close for 630 ms for a specified number of cycles, depending onthe desired suspension concentration.

The fibers were collected in DI water and washed three times in 1 wt %Tween 80 solution, followed by at least two washes in 0.1 wt % Tween80 solution. For rheology measurements, the fibers were resuspended in anaqueous solution containing 0.1 wt % Tween 80 and 12 wt % CsCl to avoidinterfiber sticking and fiber settling.

Characterization of the Physical Properties of the Fibers. For length measure-ments, we captured images of fibers flowing through long serpentine micro-channels and measured the length of the fibers (Fig. S8). Fiber diameter wasmeasured from images of random dilute fiber suspensions. The fiber lengthand diameter were taken as the average length and diameter of ∼100 differ-ent fibers as measured using ImageJ software (ImageJ version 1.44p; NIH):length = 11.76 ± 0.52 mm and diameter = 35.3 ± 3.4 μm. The Young’s mod-ulus, EY, was estimated to be ∼105 Pa, based on previously reported small-amplitude oscillatory measurements of the shear moduli, G′ and G″, of bulkcross-linked PEG-DA hydrogels (of the samemolecular weight used here) usingthe Anton Paar MCR 501 Rheometer (49), given that G* = G′ + iG″ and EY =2G*(1 + ν) (62), where ν is the Poisson ratio and can range from ∼0.25–0.4 forhydrogels depending on the degree of cross-linking (63).

Laser scanning confocal microscopy was performed on a Leica TCS SP5, andimages were analyzed with ImageJ software. Scanning electron microscopyimages of the fibers in the dried hydrogel were captured on a Quanta 200 FE-ESEM, in low vacuum mode.

Rheological Measurements. The rheological properties of the fiber suspen-sions were measured using a stress-controlled rheometer (Physica MCR 301;Anton Paar). All of the rheometry experiments were carried out at 23 °C.Usually, in rotational rheometry, a cone-plate geometry is exploited to ob-tain a homogeneous velocity gradient throughout the sample. Nevertheless,in the cone and plate geometry the gap size at the (truncated) cone tip isfixed around 50 μm, thus confining the fibers, that is, the fiber diameter iscomparable with the gap. In the latter case, undesired wall effects act toinduce faster fiber orientation compared with the unconfined case. Hence,the parallel-plate geometry, where the gap can be varied, is commonlyadopted for non-Brownian suspension rheometry, and so we used a parallel-plate geometry to reduce wall effects. To minimize the effect of wall slip, aparallel plate geometry with a roughness, Ra = 6–7 μm, and a plate diameterof 50 mm was used. For imaging the suspension in flow, we conductedmeasurements with a rheometer (MCR 702 Twin-Drive Rheo-Microscope;Anton Paar) equipped with counterrotating smooth glass parallel plates(diameter of 43 mm) and imaged the sample from the bottom of the twoplates (5×, long-work-distance objective; Mitutoyo). The gap was fixed at0.70 mm in the smooth geometry and 0.70 mm in the rough apparatus as itwas more difficult to contain a water-based suspension between the platesfor higher gap size (see also Rheology of Fiber Suspensions).

ACKNOWLEDGMENTS. We thank Dr. Gary Laevsky (Confocal MicroscopyCore Facility) for assistance with confocal microscopy; Luca Sicignano forassistance with 3D reconstruction; Bruce Perrulli, James Eickhoff (AntonPaar), Nan Yao [Princeton University Imaging & Analysis Center (IAC)] fortheir support in setting up the rheomicroscope; and Prof. Giuseppe Marruccifor useful discussions. This work was supported by Princeton University, NSFGrant CMMI-1661672, and IAC funding in part from the Princeton Center forComplex Materials, a Materials Research Science and Engineering Centersupported by NSF Grant DMR 1420541.

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