Flow-induced gelation of microfiber suspensions

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 potentially useful mechanical properties for bioengineering and biomedical applications.

Abstract

The flow behavior of fiber suspensions has been studied extensively, especially in the limit of dilute concentrations and rigid fibers; at the other extreme, however, where the suspensions are concentrated 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 irreversible 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 microfiber 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.

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 in the presence of noticeable normal stress differences (1–3). 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, particle size, and concentration (5), lubrication interactions (6) or frictional contacts (6–8) can trigger the change in viscosity. Shear thickening can also be indicative of a gelation process. For example, shear thickening is observed for some polymer-particle suspensions, 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 importance of hydrogels in several applications, including tissue engineering, drug delivery, surgical adhesives, and 3D bioprinting (12–17), there are benefits to be achieved by exploring and developing simple methods for producing hydrogels, beyond the synthetic and physical approaches that currently exist (16, 18–21), 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 suspensions 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 contacts, 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 simulations, has been devoted to suspensions of rigid rods (26–38). Some of the simulations consider many kinds of fiber–fiber interactions, 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 cellulose fibers during paper pulp processing (39). Among this literature, 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 fibers 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 establish 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 (42–46). 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 entanglements that lead to the irreversible formation of a porous entangled network of mechanically interlocked microfibers filled with water, that is, a fiber hydrogel. We do not focus on elucidating the role of frictional contacts or lubrication interactions in the shear thickening behavior and gelation in suspensions of long and highly flexible fibers; however, we show that shear thickening is a clear signature of the bending of fibers to create topological entanglements, which may lead to gelation. Thus, we approach this study from a rheological perspective to characterize the flow properties of flexible microfiber suspensions and then show that a hydrogel is produced when the microfiber suspension is extruded from a needle and syringe.

Results and Discussion

We and others have previously shown that using fabrication methods such as microfluidics, the properties of fibers, such as modulus, aspect ratio, morphology, composition, and encapsulated materials, can be tailored with a high degree of control (48–52). Some of the emerging applications of these fibers include tissue engineering and biomedical applications where the fibers are used in scaffolds, sutures, and meshes (13, 48). Here, we use a microfluidic method to produce microfibers with uniform dimensions, as this approach lets us precisely control the properties of the microfibers, which is necessary to prepare model suspensions of nearly monodisperse, high-aspect-ratio fibers. A schematic of the microfluidic process is illustrated in Fig. 1A. Unlike many other fiber-generating methods, we are able to control both the 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 glycol) diacrylate (PEG-DA) microfibers, 35 μm in diameter. Similar to other types of suspensions, our samples are prone to wall slip when sheared, so we use a measuring geometry with rough surfaces to minimize this effect (Rheology of Fiber Suspensions), and we use a parallel plate geometry to have the capability to change the distance between the two rotating plates (Fig. S1). For the results reported in the main text, the fiber length is ∼12 mm, to achieve an aspect ratio (length/diameter, L/D) ∼340; additional results for fiber lengths 4 mm and 8 mm, L/D = 114 and 228, respectively, are provided in Rheology of Fiber Suspensions, (Fig. S2). The microfibers are suspended in an aqueous solution and sheared using a rheometer.

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 of the 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 suspension with fiber volume fraction, ϕ = 0.1, at constant shear rates, $\dot{\gamma }$ = 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, $\dot{\gamma }$, is first increased from 0.1–12 s⁻¹ then decreased from 12–0.1 s⁻¹.

Fig. S1.

Viscosity behavior over time for fiber suspensions measured in different gap sizes: (A) ϕ = 0.07 and shear rate = 10 s⁻¹, (B) ϕ = 0.1 and shear rate = 10 s⁻¹, (C) ϕ = 0.2 and shear rate = 10 s⁻¹, and (D) ϕ = 0.07, 0.1, and 0.2 and shear rate = 15 s⁻¹.

Fig. S2.

Viscosity versus time for fiber suspensions with ϕ = 0.4. (A) L/D = 114, shear rate = 10 s⁻¹; (B) L/D = 114, shear rate = 500 s⁻¹; (C) L/D = 228, shear rate = 10 s⁻¹; and (D) L/D = 228, shear rate = 20 s⁻¹. (E) Shear rate reversal imposed on a ϕ = 0.4 fiber suspension with L/D = 228 initially sheared at 20 s⁻¹ for 90 s.

Initially the fibers are well-dispersed and unentangled in the suspension (Fig. 1B). After shearing, the suspension separates into a fiber-rich region (Fig. 1 C and D) and a region composed mostly of water with very few fibers. In the fiber-rich regions, the fibers can have any random orientation, and we have observed aligned and nonaligned fibers, as well as fibers bent in random orientations (Fig. 1 C and D). To gain some understanding of this process, we measure the viscosity, η, of the suspensions as a function of time for different shear rates, $\dot{\gamma }$, and volume fractions of fibers, ϕ. We find that the fiber suspensions exhibit shear thickening behavior (Fig. 1E), which, at this point, we suggest is due to the irreversible 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, where shear thickening occurs for $\dot{\gamma }$ ≥ 1 s⁻¹. Before shear thickening, the initial (time → 0) viscosity of the suspension decreases as the shear rate increases, which is evidence of shear thinning before thickening. In Fig. 1F, we demonstrate irreversibility of the flow-induced microstructural change of a suspension, ϕ = 0.2, by first steadily increasing the shear rate to 12 s⁻¹, followed by decreasing the shear rate. During the decreasing phase, the viscosity of the suspension continues to increase higher than the viscosity at the highest shear rate. This behavior highlights not only the irreversibility of the transformation of the fiber network but also that the structure is being stretched and aligned along the flow direction as it forms when a shear stress is applied, that is, during the increasing 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 viscosity 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 plot gives results for different fiber volume fractions. The zero-shear viscosity increases as the fiber concentration increases. One significant rheological feature of these fiber suspensions is the presence of shear thickening in the microfiber suspensions. When applying lower shear rates, that is, 0.1 and 1 s⁻¹, we do not observe shear thickening for the smallest volume fraction of fibers investigated, ϕ = 0.07, whereas for the highest volume fraction of fibers investigated, ϕ = 0.4, the suspension is quickly expelled from the parallel-plate gap in the rheometer and climbed along the rotating plate when sheared at 15 s⁻¹, which is characteristic of the Weissenberg effect (53). This behavior is a consequence of the significant viscoelasticity of the suspensions (Figs. S3 and S4), which increased with fiber concentration. Note that we report measurements until the time at which fluid is expelled from the rheometer. As we commented above for Fig. 1E, we observe shear thinning when reporting the initial value of the viscosity (time → 0) as a function of the different shear rates, that is, for any volume fraction, the viscosity starts from a lower value for higher shear rates. This effect is more noticeable when comparing the data obtained for the smallest shear rate, 0.1 s⁻¹, to the data measured at the highest shear rate, 15 s⁻¹ (see also η versus $\dot{\gamma }$ flow curves in Fig. S3).

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 (■), and 0.4 (X) at constant shear rates: (A) 0.1, (B) 1, (C) 10, and (D) 15 s⁻¹. The gap size is 0.7 mm.

Fig. S3.

(A–C) Typical flow curves, where viscosity, η, and first normal stress difference, N₁, are plotted as a function of shear rate for microfiber suspensions at volume fractions, ϕ, equal to (A) 0.07, (B) 0.1, and (C) 0.2. We report measurements until the shear rate at which the fluid was expelled from the rheometer. Lines in A–C are guides to the eye.

Fig. S4.

Viscoelasticity of fiber suspensions. (A) Linear viscoelasticity of a ϕ = 0.4 suspension as a function of frequency for a given oscillatory stress of 0.7 Pa. (B) Viscoelasticity of a ϕ = 0.2 suspension as a function of oscillatory shear stress for a given frequency of 1 Hz. The elastic modulus, G′, is shown by filled symbols and the viscous modulus, G″, is shown by open symbols.

The fibers used in this study are non-Brownian (Rheology of Fiber Suspensions) and in the flexible regime. Fiber flexibility can be characterized by the effective stiffness, S^eff:

$$s^{eff}=\frac{E_Y\pi D^4}{64{\eta }_m\dot{\gamma }{L}^4},$$

where E_Y is the Young’s modulus, L and D are fiber length and diameter, respectively, ${\eta }_m$ the viscosity of the continuous phase, and $\dot{\gamma }$ the shear rate (54). S^eff compares fiber stiffness and hydrodynamic forces. Specifically, the flexibility of the elastic fiber is compared with the hydrodynamic torque induced by shear flow (44); some authors (40) include an additional ln(L/D) factor, but this term changes the value of S_eff only slightly. For S^eff << 1, fibers are flexible, whereas for large values of S^eff fibers are classified as rigid. Given that E_Y is ∼10⁵ Pa for the PEG-DA fibers and $\dot{\gamma }$ ranges from 0.1–15 s⁻¹, our effective stiffness ranges between 2.4 × 10⁻⁵ < S_eff < 3.6 × 10⁻³, and hence the fibers investigated in this study can be considered flexible, which is consistent with their highly bent conformations when suspended in water (Fig. 1B). Within this flexible regime, we investigated the effect of fiber aspect ratio (L/D) for a fixed E_Y (Rheology of Fiber Suspensions). For concentrated suspensions of relatively low aspect ratio fibers, L/D = 114 and ϕ = 0.4, we observed only shear thinning. We start to observe shear thickening for intermediate length fibers, L/D = 228 and ϕ = 0.4, at higher shear rates, 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 effect of a higher shear rate or of a higher fiber concentration is to accelerate the separation from the continuous water phase. As mentioned above, the gelation of fibers is possible through the creation of entanglements, and a prerequisite for the creation of entanglements is that fibers are bent by the stresses produced by flow. Theories of single flexible fibers have been developed to predict the onset of fiber deformation in suspensions, and to relate those predictions to bulk flow properties of fiber suspensions (55). These theories, however, cannot be directly applied to our high volume fraction and extremely flexible (entangling) fibers. Others have taken a different approach to predict the flow behavior of dense non-Brownian fiber suspensions, establishing criteria that consider the number of contacts among fibers in a given volume (39), and while these criteria can be used to estimate whether flocs, that is, disconnected fiber bundles, will form, they are unable to predict gel modulus or the dynamics of gel formation (Rheology of Fiber Suspensions).

To support our hypothesis that the fibers are entangling and separating from water during flow, we perform in situ visualization of the microstructure while measuring the viscosity under shear of the ϕ = 0.4 fiber suspension. For this experiment, we use counterrotating smooth glass parallel plates while visualizing the sample from the bottom of the plates (Materials and Methods for details). Transparent smooth glass plates are necessary to visualize the sample under flow; however they induce significant fiber wall slip. This effect translates to a shift in the onset of shear thickening to higher shear rates compared with the data measured with rough plates (compare Fig. 3 A and B to Fig. 2 A and C). The transition from shear thinning to shear thickening behavior allows us to observe the different morphological behaviors associated with the two flow regimes as obtained with two different shear rates. Fibers get close together already in the shear thinning regime; however, they are 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 observed some fibers buckle, create loops, and become partially oriented in the direction orthogonal to flow (Fig. 3D and Movie S2).

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 shear rate 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 fiber suspension 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 a constant shear rate of 10 s⁻¹ at 77 s (time point indicated on B). (Scale bar, 200 µm.)

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 (Movie S3). We observe that when we inject a concentrated suspension of the microfibers from a needle with an inner diameter of 0.21 mm a hydrogel is immediately extruded, where excess water is squeezed out of the network (Fig. 4A and Movie S4). We can consistently produce hydrogels by extrusion when the suspension of fibers has a volume fraction, ϕ ≥ 0.2. The fiber hydrogels also swell in water (Fig. S7), which is another common property of hydrogels. We confirm that we have in fact formed a hydrogel by measuring the shear moduli with a rheometer by applying a small oscillatory stress at different frequencies. Our extruded material exhibited typical viscoelastic properties of a hydrogel, with the shear elastic modulus, G′, greater than the viscous modulus, G″ (Fig. 4B and Rheology of Fiber Hydrogels, Fig. S5).

Fig. 4.

Flow-induced gelation of a ϕ = 0.4 fiber suspension: rheological properties of the fiber hydrogel. (A) Extrusion of the hydrogel from a needle and syringe containing a concentrated suspension of microfibers. (Inset ) A tilted vial containing a concentrated suspension of microfibers. (B) Linear viscoelasticity as a function of frequency of the extruded hydrogel for an oscillatory stress of 0.7 Pa. The elastic modulus, G′, is represented by filled symbols 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.

Fig. S7.

Swelling properties of extruded hydrogel. (A) Image of the fiber hydrogel as extruded and (B) the swollen hydrogel a minute after a few drops of water were added. (Scale bars, 2 mm.) (C) Microscopic detail of the fiber hydrogel as extruded and (D) microscopic detail of the swollen hydrogel a minute after a few drops of water were added. (Scale bars, 200 μm.)

Fig. S5.

Mechanical properties of fiber hydrogels. (A) Measurements showing viscoelasticity as a function of oscillatory shear stress for a given frequency of 1 Hz for the hydrogel obtained by extrusion through syringe and needle of a suspension, ϕ = 0.4. (B) Measurements showing linear viscoelasticity as a function of frequency for the same hydrogel sample in A for a given oscillatory stress of 0.7 Pa. The elastic modulus, G′, is shown by filled symbols and the viscous modulus, G″, is shown by open symbols.

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 are chemically cross-linked, while in our case the contact points are free to slide. Other theories predict the shear modulus of a bundle of dry fibers where the modulus is a function of the fiber volume fraction and the elasticity of a single fiber (57, 58). This prediction overestimates the modulus of our hydrogel by two orders of magnitude, likely because the contact points are lubricated by water, free to slide, and fibers are more flexible than the ones typically 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 has the potential to be further developed as a new type of injectable hydrogel, which is attractive for many in vivo applications where hydrogels need to be delivered in a minimally invasive manner (18–20). A desirable property of such injectable hydrogels is yielding upon the application of flow, where we define yielding as a transition where the material starts to flow or spread following the imposition of a critical shear stress. Our fiber hydrogels, which are obtained from extrusion from a needle and syringe, exhibit such a property. Similarly, other soft materials have been engineered to exhibit shear thinning and yielding properties (60). In Fig. 4C we show that the hydrogel produced from a suspension at ϕ = 0.4 is a material that has a yield stress, whose value depends on the confinement of the fiber network (Fig. S6). It should be noted, moreover, that the material shows a full recovery of its initial viscosity once the shear rate is decreased back to the lowest value. This feature permits the extruded hydrogel material to be easily spread over the site of application, and once the stress is removed its increased viscosity locks the hydrogel onto the site, avoiding any possible sliding/leakage.

Fig. S6.

Determination of yield stress of fiber hydrogels produced by extrusion from a syringe and needle of a ϕ = 0.4 suspension. (A) Continuous shear stress ramp (shown by filled circles) and stress reversal (shown by filled triangles), gap size = 1.42 mm. (B) Oscillatory shear stress variation at a given frequency of 1 Hz, gap size = 1.42 mm. (C) Continuous shear stress ramp and stress reversal, gap size = 0.7 mm. (D) Oscillatory shear stress variation at a given frequency of 1 Hz, gap size = 0.7 mm. (E) Continuous shear stress ramp and stress reversal, gap size = 0.5 mm. (F) Oscillatory shear stress variation at a given frequency of 1 Hz, gap size = 0.5 mm. (G) Oscillatory shear stress variation at a given frequency of 1 Hz, gap size = 0.3 mm. The elastic modulus, G′, is shown by filled symbols and the viscous modulus, G″, is shown by open symbols.

We use confocal and electron microscopy to investigate the microstructure of the hydrogel, which we found to be a dense network of microfibers with a random microporous network (Fig. 5). In particular, Fig. 5 A and B shows the 3D reconstruction of an extruded hydrogel produced from a fiber suspension, ϕ = 0.2 (see also Movie S5). The fiber volume fraction of the hydrogel increased significantly from that of the suspension. We roughly estimated a percent pore volume (or percent water-filled volume between fibers) for the suspensions and the hydrogels from confocal image analysis and found that for the ϕ = 0.2 suspension percent pore volume ≈ 76 ± 4%, and for the resulting extruded hydrogel percent pore volume ≈ 24 ± 4%. For the ϕ = 0.4 suspension, the percent pore volume ≈ 56 ± 4%, and for the hydrogel ≈ 10 ± 5%. Both confocal and SEM images confirm the presence 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 each other and mechanically interlock.

Fig. 5.

Porosity and microstructure of fiber suspensions and fiber hydrogels. (A and B) Three-dimensional confocal reconstructions of a fiber hydrogel prepared 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, such as (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, with magnified (Inset) images showing different regions of the hydrogel. (Scale bars, 200 μm in the low-magnification image and 100 μm in higher-magnification images.)

During the extrusion of the hydrogel from the needle and syringe, fiber entanglements are created. Fibers need a stress to become entangled and such a stress can be provided by the action of flow. Pressure-driven flow in a syringe is made of two components: Poiseuille flow in the region of the syringe with a constant cross-sectional area and extensional flow brought about by the abrupt change of cross-sectional area when the suspension flows from the main body of the syringe into the needle. Extensional flow, along with Poiseuille flow within the needle, plays a key role in hydrogel formation. The former can cause rapid local elongation and induce a stress proportional to the abrupt fluid velocity change due to the passage from a larger section into a smaller one, whereas the latter, given the small diameter of the needle, can keep the fibers confined as well as provide a stress proportional to the velocity gradient along the needle cross-sectional area, thus promoting fiber entanglements. The characterization of fiber entanglements identified in this work has been realized with shear flow rheometry (e.g., Figs. 1–3). Although shear stress could represent part of the total stress involved during extrusion, shear rheology, as described in Figs. 2 and 3, represents a method to investigate the process of entanglement formation and to demonstrate that our fiber suspensions can be converted into a hydrogel using flow.

Conclusions

In this work we explored the rheological behavior of highly flexible microfiber suspensions to gain understanding of our observations of the gelation process that occurs when concentrated suspensions of non-Brownian microfibers experience various flow conditions. The microfibers must be very flexible, so that they can bend under flow without breaking to form topological entanglements. The results indicate that the suspensions undergo irreversible gel formation, which depends on the stress imposed by flow. Our study contributes rheological insight into the flow behavior of concentrated flexible, high aspect ratio fiber suspensions and highlights the need for improved theoretical models to better predict characteristics of these entangled microstructures. Furthermore, we believe that the entanglements that form lead to the macroscopic gelation of the suspension when subjected to strong shear and extensional flows, such as those produced during extrusion from a needle and syringe.

Since the action of injecting the fiber suspension triggers its gelation, we believe this system can be used to develop a new class of injectable hydrogel materials, where a wholly mechanical approach is used to physically and irreversibly cross-link a free-flowing suspension. The cross-linking mechanism is independent of chemical reactions or restructuring of individual components in the gelling solution but depends primarily on the microfiber aspect ratio, flexibility, concentration, and stress induced by flow. These materials offer a promising approach for the in situ fabrication of scaffolds, possibly incorporating chemicals and/or cells encapsulated in the microfibers, in various applications spanning industry and medicine.

Materials and Methods

Microfluidic Synthesis of Fibers.

Microfluidic channels were prepared using standard methods of soft lithography (61). Polydimethylsiloxane (PDMS) (Dow Corning Sylgard 184; Ellsworth Adhesives) channels were plasma-bonded to PDMS-coated glass slides using a Corona Surface Treater (Electro-Technic Products, Inc.). The microfluidic device had two inlets, one for the oil continuous phase and the other for the oligomer solution. The individual liquid phases met at a hydrodynamic focusing region where a cylindrical oligomer jet formed. The jet, sheathed by the continuous phase, flowed through a main channel of width 200 μm and height 120 μm. The oil continuous phase was composed of 62 vol % heavy mineral oil (Fisher Scientific), 27 vol % hexadecane, 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, and 4 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). Unless 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 of light supplied from the lamp, and thus the light incident on the PEG-DA jet was not monochromatic. We measured the UV light intensity at the bottom surface of the device to be in the range 20–24 mW/cm² for all presented results. The length of the fibers was controlled optically by pulsing the UV light incident on the monomer jet. The shutter was programmed to open for 370 ms and close for 630 ms for a specified number of cycles, depending on the 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 % Tween 80 solution. For rheology measurements, the fibers were resuspended in an aqueous solution containing 0.1 wt % Tween 80 and 12 wt % CsCl to avoid interfiber sticking and fiber settling.

Characterization of the Physical Properties of the Fibers.

For length measurements, we captured images of fibers flowing through long serpentine microchannels and measured the length of the fibers (Fig. S8). Fiber diameter was measured from images of random dilute fiber suspensions. The fiber length and diameter were taken as the average length and diameter of ∼100 different 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 modulus, E_Y, was estimated to be ∼10⁵ Pa, based on previously reported small-amplitude oscillatory measurements of the shear moduli, G′ and G″, of bulk cross-linked PEG-DA hydrogels (of the same molecular weight used here) using the Anton Paar MCR 501 Rheometer (49), given that G* = G′ + iG″ and E_Y = 2G*(1 + ν) (62), where ν is the Poisson ratio and can range from ∼0.25–0.4 for hydrogels depending on the degree of cross-linking (63).

Fig. S8.

Bright-field images of fibers flowing in serpentine channels with constrictions. Fiber aspect ratios (L/D) are (A) 114, (B) 228, and (C) 340. The fibers were collected in serpentine channels and the fiber length was measured using ImageJ. (Scale bar, 1 mm.)

Laser scanning confocal microscopy was performed on a Leica TCS SP5, and images were analyzed with ImageJ software. Scanning electron microscopy images 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 suspensions 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 obtain a homogeneous velocity gradient throughout the sample. Nevertheless, in the cone and plate geometry the gap size at the (truncated) cone tip is fixed around 50 μm, thus confining the fibers, that is, the fiber diameter is comparable with the gap. In the latter case, undesired wall effects act to induce faster fiber orientation compared with the unconfined case. Hence, the parallel-plate geometry, where the gap can be varied, is commonly adopted for non-Brownian suspension rheometry, and so we used a parallel-plate geometry to reduce wall effects. To minimize the effect of wall slip, a parallel plate geometry with a roughness, Ra = 6–7 μm, and a plate diameter of 50 mm was used. For imaging the suspension in flow, we conducted measurements 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 two plates (5×, long-work-distance objective; Mitutoyo). The gap was fixed at 0.70 mm in the smooth geometry and 0.70 mm in the rough apparatus as it was more difficult to contain a water-based suspension between the plates for higher gap size (see also Rheology of Fiber Suspensions).

Rheology of Fiber Suspensions

Non-Brownian Fibers.

The Peclet number compares hydrodynamic forces to Brownian forces, and we used it to discriminate between Brownian and non-Brownian suspensions, where Pe can be estimated from

$$\text{Pe}=\frac{{\eta }_m\dot{\gamma }\pi L^3}{3k_{B}T\hspace{0.17em}\ln \left(\frac{L}{D}\right)},$$ [S1]

where L and D are fiber length and diameter, respectively, η_m is the medium viscosity, $\dot{\gamma }$ is the shear rate, $k_B$ is the Boltzmann constant, and T is the absolute temperature. The Pe number calculated at the lowest shear rate of 0.1 s⁻¹ is ∼10¹⁰; hence, the suspension can be considered non-Brownian (64).

Theoretical Considerations.

Using the Euler–Bernoulli equation for the shape of a rod subjected to small deformations under compressive forces from a shear flow, Forgacs and Mason (40) provided a criterion to estimate the threshold shear stress, τ, at which a single elastic fiber is bent by flow, which is given by

$$\tau =\frac{E_b\left(\ln \frac{2L}{D}-1.75\right)}{2{\left(\frac{L}{D}\right)}^4},$$ [S2]

where τ $={\eta }_m\dot{\gamma }$ and E_b is the bending modulus, defined as E_b = E_YI, where E_Y is the Young’s modulus of the fiber and I is the second moment of the fiber cross-sectional area, which for a circular fiber of radius R = D/2 is defined as $I=\frac{\pi }{4}{R}^4$. Alternatively, a fiber bends when the dimensionless parameter, bending ratio, B_R, is less than one (44):

$$B_R=\frac{E_Y\left[\ln \left(2r_e\right)-1.50\right]}{{\eta }_m\dot{\gamma }2{\left(\frac{L}{D}\right)}^4},$$ [S3]

where $r_e=1.24\frac{\frac{L}{D}}{\sqrt{\ln \frac{L}{D}}}$. As reported in the main text, this formulation is similar to the effective stiffness, S_eff, used by Klingenberg and coworkers (44), where the difference is an additional factor including ln(L/D) that changes the magnitude of the dimensionless parameter only slightly. The two dimensionless parameters are related by

$$S_{eff}=\frac{\pi B_R}{32\left[\ln \left(2r_e\right)-1.5\right]}.$$ [S4]

Tornberg and Shelley (46) also make use of a definition similar to B_R and S_eff, referred to as the effective viscosity, $\stackrel{\sim }{\mu }$:

$$\stackrel{\sim }{\mu }=\frac{8\pi {\eta }_m\dot{\gamma }{L}^4}{E_b}$$ [S5]

or the elastoviscous number (65), $\stackrel{\sim }{\eta }$, which includes a factor proportional to ln(L²/D²):

$$\stackrel{\sim }{\eta }=\frac{8\pi {\eta }_m\dot{\gamma }{L}^4}{E_b\ln \frac{4L^2}{e{D}^2}}.$$ [S6]

One limitation of the threshold stress criterion for fiber bending in shear flow provided by Forgacs and Mason (40) is the assumption of small deformations. Becker and Shelley (54) considered high-aspect-ratio flexible fiber buckling in the nonlinear regime, that is, large deformation, finding that the threshold stress for fiber bending is 2.4 times higher than the prediction based on linear theory (40, 46). Nonetheless, in our system, where the Young’s modulus is ∼10⁵ Pa and aspect ratio is ∼340, we found that both criteria are unable to predict the onset stress of shear thickening for our suspensions.

Paper pulp rheology often displays fiber flocculation (39). Many hypotheses have been proposed regarding this phenomenology, for example chemical effects due to fiber–fiber attraction and mechanical effects such as fiber–fiber friction and flocculation (1, 39, 66). A possible method to predict whether fiber flocculation occurs in a given system/flow is given by evaluating the crowding factor N (67), which is defined as the number of fibers in a spherical volume of diameter equal to the length of a fiber (39). Usually, it is considered more convenient to adopt a mass-based definition of N for pulp fiber suspensions so the unit of measurement is in kilograms per cubic meter (39, 67, 68). This description is based on the concept that the flocculation is related to a large number of contacts among fibers occurring when fibers are highly concentrated. Because the aspect ratio of our fibers is large, N predicts flocculation even at very low suspension concentrations, but this phenomenological characterization, however, cannot be exploited to establish if a hydrogel will eventually form from a fiber suspension.

There are theories to estimate the complex shear modulus, G*, of a bundle of fibers (57–59, 69), where G* is found to be a linear function of the single fiber elastic modulus, G_f, and the cubic volumetric fraction, ϕ, of fibers according to

$$G^{\ast }\sim G_f{\varphi }^3.$$ [S7]

Given our G_f ∼ E_Y = 10⁵ Pa and the volume fraction of fibers in the gel extruded from the needle and syringe ϕ ∼ 0.8–0.9, the estimated complex shear modulus of the gel overestimates our measured value (∼1,000 Pa) by about two orders of magnitude. These theories have been derived for and applied to more rigid fibers and often also dry fibers, that is, without lubricated contact points, which may explain the discrepancy between our experimental data and the estimated value of the elastic modulus.

Other theories, known as filamentous network theories (55, 56, 59), have been applied successfully to athermal fibrous macromolecular systems. The main prediction of these models is that the elastic modulus of the network is either proportional to G_fA in the affine regime of deformation, where A is the single fiber cross-sectional area, or to G_fI in the nonaffine regime, where I is the moment of inertia (70). Given our fiber diameter = 35 μm and the single fiber elastic modulus ∼10⁵ Pa, both of these predictions greatly underestimate the measured value of the elastic modulus of our hydrogel. These models typically assume nonsliding contact points among fibers, that is, chemically cross-linked, making them unsuitable for our case.

Rheometer Limitations.

A quantitative prediction of fiber mechanical flocculation based on rheometric measurements is difficult and is an open question in rheology. Many phenomena affect the rheological behavior. It is impossible to avoid some fiber entanglements when preloading the suspension of flexible fibers, thus affecting the onset of mechanical flocculation, as well as the initial value of viscosity before starting the shearing. Moreover, to minimize fiber confinement we were forced to use larger gaps compared with the cone and plate geometry. A parallel-plate geometry allowed us to set a gap much larger than the fiber diameter. Nevertheless, with this geometry the stress is not imposed uniformly over the sample. Eventually, wall slip, a phenomenon by which fiber concentration is lower at the wall and higher in the core of the geometry, is always present within such suspensions. We partially overcome such an effect by using a “rough” parallel-plate geometry; that is, the parallel plates have a roughness Ra = 6–7 μm on their surfaces.

We are also aware that Yoshimura and Prud’homme (71) developed an elegant method to calculate slip velocity and to remove the effect of wall slip from rheometrical data by shearing at different gap sizes. However, in our case the gap size cannot be increased above 0.70 mm because some of the suspension leaks out of the measuring geometry. Using a smaller gap size confines the fibers, thus the opposing effects of confinement and wall slip on viscosity cannot be separated, making it impossible to apply the wall slip correction proposed by Yoshimura and Prud’homme (71). For completeness, we report the measurements performed at different gap sizes both for the suspensions (Fig. S1) and the fiber hydrogels (Fig. S5). We stop the measurements of the suspension viscosity when the Weissenberg effect is observed, and we report measurements for ϕ = 0.07, 0.1, and 0.2 and for shear rates of 10 s⁻¹ (Fig. S1 A–C) and 15 s⁻¹ (Fig. S1D). Because of the fiber network confinement, the tendency is to obtain higher viscosities for smaller gap size. Note that at a shear rate of either 10 s⁻¹ or 15 s⁻¹ the initial viscosity of the fiber suspension at ϕ = 0.07 is higher than the suspension viscosity at ϕ = 0.1. This trend can be attributed to shear thinning of the suspension that is more pronounced in the ϕ = 0.1 suspension. For higher fiber concentration (ϕ = 0.2) this shear thinning effect is overwhelmed by the higher crowding of fibers, thus making the initial viscosity of the ϕ = 0.2 suspension higher than that for both ϕ = 0.07 and 0.1 suspensions.

The Threshold Aspect Ratio for Mechanical Interlocking.

We measured viscosity as a function of shear rate and time for suspensions containing ϕ = 0.4 fibers having always a Young’s modulus of ∼10⁵ Pa, but an aspect ratio (L/D) of 114 and 228. The aspect ratio was changed by reducing fiber length while maintaining the fiber diameter at 35 µm. Changing aspect ratio means changing S_eff of the fibers. Similar to the suspensions of fibers having aspect ratio of 340, shear thickening over time is exhibited for fibers with aspect ratio of 228, but not for the aspect ratio of 114, regardless of the shear rate applied (for L/D = 114, we tested shear rates up to 500 s⁻¹). This result is evidence that for a given Young’s modulus there is a critical length beyond which fibers are irreversibly entangled and thus able to create an irreversible network. We show irreversibility of the formed network by applying a shear reversal (from 20 s⁻¹ to almost 0) to a fiber suspension ϕ = 0.4 and L/D = 228 that has been kept for 90 s at constant shear rate of 20 s⁻¹ (Fig. S2E). As reported in the main text for higher-aspect-ratio fiber suspensions, when the applied stress is decreased, that is, during the decreasing shear rate ramp, the structure relaxes, and hence the viscosity increases due to the entanglements created during the first stage of shearing. This behavior also suggests that the structure is undergoing yielding during the increasing shear rate ramp.

Normal Stresses and Viscoelasticity of Fiber Suspensions.

To check the effect of a shear rate ramp on our suspensions, we impose a linear increase in the shear rate every 40 s during continuous shear flow in a rough parallel-plate measuring geometry (diameter of the plate = 75 mm and gap size = 0.70 mm) until the fluid is expelled from the rheometer. As soon the suspension is in the shear thickening regime, the first normal stress difference starts to increase with increasing shear rate, similar to the viscosity (Fig. S3 A and B). As a consequence of the significant viscoelasticity of the suspensions (Fig. S4), due to the suspension’s becoming a progressively more elastic network with increasing shear rate and time, the suspension was expelled from the parallel-plate gap in the rheometer and climbed along the rotating plate, which is characteristic of the Weissenberg effect (53). Note that we report measurements until the shear rate at which fluid is expelled from the rheometer. This phenomenon is a signature of the onset of largely positive first normal stress differences in flows of flexible fiber suspensions, which has been reported previously in the literature (2, 72). However, before the present work no shear thickening or gelling of fiber suspensions has been associated with the onset of positive normal stress difference.

The fiber suspensions are viscoelastic with a significant shear elastic modulus, G′. However, the elastic modulus of the suspension is always lower than that of the hydrogel obtained by extrusion of the same suspension (Fig. S5). Again, we point out that the higher elasticity of the hydrogel derives from the irreversible creation of a mechanically locked network and the fact that a large amount of water has been separated from the fibers when squeezing the suspension through the syringe and needle. Also, the higher the fiber concentration the higher is the viscoelasticity of the suspension. For the fiber suspension at ϕ = 0.2 we report moduli as a function of oscillatory shear stress because it is more difficult to first identify the linear viscoelastic regime to then perform frequency sweeps (Fig. S4B).

Rheology of Fiber Hydrogels

Measuring the Mechanical Properties of Fiber Hydrogels.

Although fiber hydrogels can be produced from fiber suspensions with ϕ ≥ 0.2, we focused on hydrogels produced from extruding suspension with ϕ = 0.4 (Fig. S5). We observed variability in the value of G′ among the different samples analyzed, with G′ ranging from ∼200 Pa to 1,000 Pa. Also, some samples exhibited frequency-dependent G′ behavior. Such sample-to-sample variability is due to the prestress that is applied to the material when it is loaded into the instrument. Moreover, a certain amount of water is always present in the extruded hydrogel, contributing to the variability in the elastic modulus of the samples. Nonetheless, we always observe rheological behavior that is typical of a hydrogel.

Investigating the Flow Behavior of Fiber Hydrogels.

We use fiber hydrogels obtained by extrusion of a ϕ = 0.4 suspension from a syringe and needle to study the flow behavior. We infer yield stress from two different tests, the classical ramp in continuous shear stress (Fig. S6 A, C, and E) and a ramp of large oscillatory shear stresses (which may be considered as a large amplitude oscillatory shear), where, in the latter, yield stress is typically assumed to be at the cross-over between G′ and G″ (Fig. S6 B, D, F, and G). The value of yield stress as inferred from the two tests rarely matches; however, one can understand from the first that the material is yielding under an applied stress and from the second that the gel still preserves its gel structure for gap sizes of 0.5 mm (Fig. S6F) and 0.3 mm (Fig. S6G). The observed yield stress and elasticity is enhanced by decreasing the gap size, an effect that can be attributed to the compression of the network at the scale of the single fiber. Actually, the elastic modulus of the gel for a gap size of 0.3 mm approaches the Young’s modulus of the single fiber (Fig. S6G). For gap sizes greater than 0.70 mm, G′ and G″ have a cross-over in the large amplitude oscillatory stress shear test. This means that the structure is more prone to lose its elastic/solid behavior when sheared but fully recovers it when the applied stress is released. When the applied stress is released, the material recovers from its deformation. For the hydrogel at a gap size of 0.3 mm, it is difficult to perform a continuous ramp in the stress given the high strength of the material, and hence we reported only the oscillatory stress measurements (Fig. S6G).

Swelling Behavior of Fiber Hydrogels

Another common feature of hydrogels is that they can be swollen with water. We observed that when a few drops of water are added to the hydrogel it swells because of the porous nature of the network and the hydrophilic nature of the microfibers (Fig. S7). The fiber hydrogel exhibits a fast and large uptake of water that we have estimated, by weighing a small amount of hydrogel before and after complete immersion in water, to be an increase of 70 ± 20% of the hydrogel weight within about 1 s. For times longer than a second it is impossible to collect and weigh the hydrogel accurately because it already spreads all over the water.