Abstract
Biohybrid materials that integrate a biopolymer matrix with a nanoscale reinforcing network offer a promising strategy for developing synthetic fluids with tissue-mimetic mechanical functionality. Here, an in vitro model synovial fluid was engineered by incorporating ultralow concentrations of multi-walled carbon nanotubes (MWCNTs) into a high-molecular-weight hyaluronic acid (HA) matrix to reproduce the frequency- and temperature-dependent viscoelasticity of healthy synovial fluid. The optimized HA matrix reproduced key features of native fluid, including pronounced shear thinning and a viscous-to-elastic transition within the frequency range of human locomotion. MWCNT incorporation at concentrations below 0.05 vol% substantially broadened the linear viscoelastic region and introduced reversible thixotropic behavior. At physiological temperature, enhanced CNT network formation combined with thermal softening of the HA matrix increased the elastic contribution and shifted the G′–G″ crossover toward the frequency of normal walking. An optimal formulation emerged that combined broad strain tolerance, physiologically relevant viscous–elastic switching, non-monotonic intermediate-shear viscosity, and reversible structural recovery while maintaining low viscosity (η ≈ 20–50 mPa s) at high-shear rate ( ∼ 103 s–1). These findings establish ultralow CNT reinforcement as a rheological design principle for engineering temperature-responsive HA-based fluids that reproduce, in vitro, the adaptive rheological behavior of native synovial fluid prior to further tribological and biocompatibility evaluations.
1 Introduction
Diarthrodial joints represent highly sophisticated natural tribological systems, capable of sustaining exceptionally low friction coefficients (<0.01) and minimal wear over millions of loading cycles, despite repeated exposure to contact pressures exceeding 10 MPa (; Murakami et al., 2013). This remarkable tribological performance is mediated by synovial fluid (SF), a complex viscoelastic biolubricant that occupies the joint cavity and operates synergistically with the biphasic structure of articular cartilage to minimize friction, facilitate load transfer, and dissipate transient mechanical stresses (; Murakami et al., 2013; ). A defining feature of SF is its frequency-dependent viscoelastic duality, originally described by Ogston and Stanier, whereby the fluid exhibits predominantly viscous behavior under slow, quasi-static loading but develops an increasingly elastic response under rapid or impulsive loading, thereby contributing to load-bearing and mechanical protection of the articulating surfaces (Ogston and Stanier, 1953). In healthy human SF, the transition between these viscous- and elastic-dominated regimes occurs at frequencies of approximately 0.4–1 Hz, overlapping with the characteristic frequencies associated with walking and running (Thurston and Greiling, 1978; ). Reproducing this frequency-dependent viscoelastic transition, rather than simply matching the viscosity at a single shear rate, is therefore a fundamental design criterion for synthetic materials intended to replace or supplement native synovial fluid.
Hyaluronic acid (HA) is the principal macromolecular component underlying the distinctive viscoelasticity of synovial fluid. It is a linear, anionic polysaccharide composed of alternating D-glucuronic acid and N-acetyl-D-glucosamine residues. In healthy synovial fluid, HA is typically present at concentrations of approximately 2–4 mg mL–1 and with a weight-average molecular weight () in the range of 2–7 MDa, providing a major contribution to the fluid’s characteristic viscoelastic response (). At these concentrations, HA resides in the semidilute entangled regime, where its rheological behavior is dominated by intermolecular entanglements and reptation-mediated chain relaxation. Consequently, both the plateau modulus and zero-shear viscosity exhibit strong dependencies on HA concentration and molecular weight, consistent with established reptation-based descriptions of high-molecular-weight polyelectrolytes (Morris et al., 1978; Oelschlaeger et al., 2013; ; ). Moreover, the physiological electrolyte environment further modulates HA conformation and intermolecular interactions. Screening by monovalent ions reduces the electrostatic contribution to chain stiffness, whereas divalent cations, particularly Ca2+, can promote transient interchain associations that increase the effective network connectivity without necessarily introducing permanent crosslinks or fundamentally altering terminal flow behavior (). HA also plays a critical role in boundary lubrication, extending its function beyond bulk rheology. At the cartilage interface, surface-associated HA interacts synergistically with lubricin and phosphatidylcholine-rich lipid assemblies to promote highly hydrated interfacial layers capable of sustaining extremely low friction under physiological loads. Importantly, these interfacial interactions are sensitive to ionic composition, with Ca2+ reported to compromise the integrity and lubricating efficiency of the HA-mediated boundary layer (Seror et al., 2015; ; ). Thus, both the molecular characteristics of HA, particularly its molecular weight and concentration, and its interactions with the surrounding ionic and molecular environment are fundamental determinants of the rheological and tribological functionality of synovial fluid.
Osteoarthritis (OA) is the most prevalent degenerative joint disease and a leading global cause of disability. In OA, inflammatory and oxidative processes depolymerize HA, lowering both its molecular weight and its concentration, degrading the viscosity and elasticity of the fluid and impairing its protective function (More et al., 2020; ). The resulting loss of lubrication and shock absorption accelerates cartilage wear, driving a self-reinforcing degenerative cycle. Viscosupplementation is the intra-articular injection of exogenous HA, which is a widely adopted symptomatic therapy that aims to replenish the concentration, molecular weight, and rheological properties of the degraded fluid (; ). Recent systematic reviews and precision-medicine analyses converge on the conclusion that therapeutic efficacy depends strongly on molecular weight and rheological fidelity, with higher-, linear (non-crosslinked) formulations more consistently associated with durable restoration of SF viscoelasticity and improved clinical outcomes (Nicholls et al., 2018b; Sherman et al., 2025). Nonetheless, the clinical evidence base remains heterogeneous, and large meta-analyses continue to debate the magnitude of benefit, underscoring that rheological optimization of the injected fluid is an unresolved and clinically consequential problem (Pereira et al., 2022).
A consistent theme in the literature is that merely restoring HA concentration is insufficient to replicate the complex, frequency-dependent rheological behavior of healthy SF. It is essential to also recover the molecular and network architecture of the fluid (More et al., 2020; ). Consequently, replicating this frequency- and rate-dependent viscoelastic response in vitro is a prerequisite for the rational design of any SF analogue. This study is therefore focused on addressing this rheological challenge (Nicholls et al., 2018b; Nicholls et al., 2018a; Sherman et al., 2025). A fundamental materials-design tension constrains conventional products. Uncrosslinked HA solutions, though biocompatible, injectable, and characterized by the fully reversible, non-thixotropic flow of a physically entangled network, exhibit moduli below native SF and short intra-articular residence times (). Chemical crosslinking improves durability and strength but introduces permanent junctions that alter the natural, reversible flow response and can compromise injectability (; ). Reconciling mechanical reinforcement with preservation of the native, reversible viscoelasticity is therefore the crux of advanced viscosupplement design, and it has motivated a search for physically reinforced, biohybrid alternatives that strengthen the HA network without sacrificing its reversibility.
Nanomaterial reinforcement provides a compelling strategy for overcoming the inherent limitations of conventional HA formulations while preserving their reversible network dynamics. Among carbon-based nanomaterials, graphene, graphene oxide, and carbon nanotubes (CNTs) have attracted considerable attention as reinforcing elements in biohybrid nanocomposite hydrogels, where they can substantially enhance mechanical strength, network connectivity, and functional performance in applications ranging from tissue engineering and drug delivery to wound healing and load-bearing biomaterials (; Shar et al., 2023; ). CNTs are particularly attractive because their exceptionally high aspect ratio and intrinsic mechanical stiffness enable the formation of mechanically effective networks at remarkably low volume fractions. Indeed, rigidity-percolation thresholds as low as φc ≈ 0.0026 vol% have been reported for aqueous nanotube suspensions, with the emergent elasticity arising predominantly from inter-tube interactions rather than from the intrinsic stiffness of individual nanotubes (; ; ).
Within polymeric and polysaccharide matrices, CNTs can form reversible non-covalent bonds with host chains. These interactions include van der Waals forces, hydrophobic associations (Scott and Heatley, 1999), and CH–π interactions between sugar C–H groups and the graphitic surface of the nanotubes. Additionally, the chains physically wrap around and become sterically entangled with the nanotubes, creating extra load-bearing physical crosslinks in the polymer network. Such interactions can enhance network connectivity, broaden the linear viscoelastic region, and substantially increase resistance to deformation (; ). Importantly, the high reinforcing efficiency of CNTs permits their use at ultralow concentrations, an attractive characteristic for biomedical formulations in which minimizing nanomaterial loading is desirable. An additional advantage is the temperature dependence of CNT network formation. Increasing temperature can promote nanotube–nanotube association and facilitate network connectivity, effectively lowering the concentration required for mechanical percolation (). Consequently, a CNT network that contributes only weakly to the mechanical response at ambient temperature may become significantly more influential under physiological conditions. This temperature-responsive reinforcement provides an attractive design principle for injectable model synovial fluids, which must remain readily processable and injectable during preparation and storage while developing the requisite viscoelastic functionality after reaching the physiological temperature of 37 °C.
Previous research on HA–CNT nanocomposites has not fully utilized the contrasting temperature-dependent properties of their components as a design principle. The HA matrix undergoes thermal relaxation, becoming softer with heat, while the CNT network exhibits increased stiffness at higher temperatures. This interaction, particularly under conditions close to physiological environments, remains unexplored. Understanding this interaction is crucial as it provides a means to achieve both low-viscosity injectability at room temperature and improved elastic strength at body temperature, without the need for additional polymer content or irreversible chemical crosslinks. The primary aim of this study is to establish this thermally responsive, percolation-driven reinforcement as a rheological design strategy, rather than focusing solely on the HA–CNT combination itself. Initially, we focus on refining the neat HA matrix within the semi-dilute entangled regime to determine the concentration that most accurately reflects the linear, nonlinear (large-amplitude oscillatory), and steady-shear characteristics of healthy SF. Subsequently, biocompatible CNTs are introduced at ultra-low volume fractions (0.0015–0.044 vol%). The modified fluids are then subjected to dynamic frequency sweeps, amplitude sweeps at both ambient (25 °C) and physiological (37 °C) temperatures, steady-shear flow curves, and thixotropic hysteresis measurements. Our primary goals are to (i) ascertain the CNT loading that optimally adjusts the frequency- and temperature-dependent viscoelasticity of the HA matrix to align with the biomechanical response of native SF, and (ii) investigate the rheological mechanisms, such as entanglement, temperature-enhanced percolation, and reversible network reorganization, that dictate this behavior. Through this study, we aim to establish differential-temperature, crosslink-free reinforcement as a rheological design principle for biomimetic model fluids that replicate the characteristic viscoelastic and flow behavior of synovial fluid.
2 Experimental section
2.1 Materials
Hyaluronic acid (HA), with an average molecular weight, = 2 MDa, and lecithin were purchased from Henan Tianfu, Chemical Co., Ltd., China. The multi–walled carbon nanotubes (CNTs; US Research Nanomaterials, Inc., Stock#: US4303, CAS#: 308068-56-6) have a manufacturer-specified purity of >95 wt%, outer diameter 5–15 nm (nominal 10 nm), length ∼50 μm, as revealed from the transmission electron micrographs in Supplementary Figure S1. Energy Dispersive X-ray Spectroscopy (EDXS) results revealed that the composition consisted of 98.86% carbon, with the remaining 1.14% made up of residual catalysts (Fe, Ni, Cl, and S) as a consequence of CVD synthesis method. Sodium chloride (NaCl, ≥99%) and calcium chloride (CaCl2, ≥97%) were purchased from Sigma-Aldrich, United States.
2.2 Sample preparation
All samples were prepared in a medium that mimics the physiological medium, containing 155 mM NaCl, 4 mM CaCl2, and pH 7.4, the so–called physiological saline (PS). Therefore, stock solutions of NaCl(aq) and CaCl2(aq), in deionized water (DIW), were initially prepared at higher concentrations to obtain the target ionic (physiological) concentration after dilution/addition. The pH was adjusted. A stock concentrated solution of HA was prepared by simple dissolution of a weighed amount of HA powder in the physiological medium using mild stirring (to avoid HA chain scission) for 24 h at ambient temperature. The stock HA solution was stored in the refrigerator at 2 °C–5 °C to avoid microbial growth.
Stock dispersion of CNTs was prepared in PS by dispersing a weighed amount of CNTs using a bath sonicator (Elma, Germany) continuously operating at 37 kHz and ca. 50 °C and for 2 h. After sonication, coarse aggregates and undispersed bundles were removed from the cold dispersion by vacuum filtration through a filter membrane (Whatman®, 0.2 μm pore size from Sigma-Aldrich, USA). The retained mass was dried and weighed, and the CNT content of the filtrate was calculated. The CNT stock solution was left at ambient temperature to equilibrate for 2 days. Several HA–CNT formulations were prepared by mixing weighted amounts of CNT and HA stock solutions using mechanical stirring at ambient temperature for 1–2 days in sealed glass vials. The dispersions were left to equilibrate for 1 day before measurements. The volume fraction of CNT (φCNT) in the HA–CNT dispersions, at a fixed amount of HA (7 mg mL–1), was calculated based on Supplementary Equation S1, and shown in Table 1.
TABLE 1
| Sample name | Mass of CNT stock (mg) | Volume fraction of CNT (φCNT) | Vol% |
|---|---|---|---|
| HAC1 | 5.4 | 1.51 × 10−5 | 0.0015 |
| HAC2 | 12.4 | 3.47 × 10−5 | 0.0035 |
| HAC3 | 23.4 | 6.55 × 10−5 | 0.0066 |
| HAC4 | 51.8 | 1.45 × 10−4 | 0.015 |
| HAC5 | 80 | 2.23 × 10−4 | 0.022 |
| HAC6 | 156 | 4.37 × 10−4 | 0.044 |
Composition of HA-CNT dispersions.
The examined solutions (either pure HA or a mixture with CNTs) were prepared by mixing weighed amounts of the stock solutions and diluting with PS to achieve the target concentration. The mixtures were gently stirred at ambient temperature for 6 h, then left to equilibrate overnight before further examination.
2.3 Rheological characterization
The rheological measurements were performed on an Anton Paar MCR 102 rotational rheometer equipped with a concentric cylinder geometry (CC27; bob radius 13.33 mm, cup radius 14.46 mm, bob length 40 mm, and gap 5.0 mm) and a Peltier temperature-control unit. Approximately 10 mL of sample was loaded and equilibrated at 25 °C for 5 min before starting the measurements. To ensure measurement reliability, all samples were subjected to an identical pre-shear (at 100 s–1 for 5 min) and equilibration (for 10–15 min) protocol on a calibrated rheometer.
3 Results and discussions
3.1 Viscoelastic behaviour of HA solutions
Because HA is the main constituent of the SFs, it is worth investigating the rheological behaviour of pure HA solutions to precisely determine the optimal concentration of HA (for this molecular weight (MW)). First, the dynamic frequency sweep test was performed in the linear viscoelastic region (LVR), over which a minimal disturbance to the microstructure of HA solutions is applied, thereby conserving the structure. Figure 1 demonstrates the dynamic frequency sweep results for selected HA solutions. At low HA concentrations (CHA = 3 and 5 mg mL–1), the solutions exhibit a liquid-like response over the accessible frequency range, with G″ > G′ throughout. However, the steep rise of G′ at high ω, particularly evident for the 5 mg mL–1 sample approaching the upper frequency limit, indicates that these solutions are in the entangled semi-dilute regime, with terminal relaxation times placing the G′–G″ crossover near or beyond the experimental window. The concentrated solution at CHA = 7 mg mL–1 exhibits a clear crossover at an intermediate frequency, above which elastic behavior dominates (G′ > G″). This behavior is consistent with a well-developed entangled network with a relaxation time accessible within the measurement range. Increasing CHA from 3 to 7 mg mL–1 obviously results in (i) a progressive shift of the crossover to lower frequencies reflecting longer terminal relaxation times, and (ii) doubling the magnitudes of G′ (over an intermediate ω range), which exhibit a scaling relation with CHA, analogous to that reported for HA in semi-dilute entangled regimes. This dependency may arise from a higher entanglement density, consistent with reptation dynamics in high–MW polyelectrolytes (Morris et al., 1978; Xu et al., 2012). The presence of Ca2+ cations, in particular, is likely to additionally enhance the apparent crosslink density and raise G′ without fundamentally altering the terminal flow behavior through the plausible formation of a mediated transient network ().
FIGURE 1
Healthy human synovial fluid contains HA at concentrations of ca. 2–4 mg mL–1 with ranging from 2 to 7 MDa (). The native fluid exhibits G′∼10–100 Pa and G″∼5–40 Pa at ω = 1–10 rad s–1, with a crossover at approximately 1 rad s–1. The present 7 mg mL–1 sample at 2 MDa shows dynamic moduli that are approximately one order of magnitude below those of the native synovial fluid at equivalent frequencies. This behavior is likely consistent with the combined effect of lower MW and absence of other SF’s constituents, such as proteins (e.g., lubricin, PRG4) that contribute to the overall viscoelasticity of the biological fluid (Seror et al., 2011; ). The 3 mg mL–1 dataset approaches the concentration range of the native HA in SF but shows much weaker viscoelasticity, further confirming the dominant role of MW in the biological context. Therefore, the concentrated HA solution at 7 mg mL–1 has been selected for further investigation.
To probe the viscoelastic response under deformation conditions relevant to human joint biomechanics, amplitude (strain) sweep measurements were performed at different oscillatory frequencies (f) corresponding to human activity states (e.g., rest, walking, and running) (Ogston and Stanier, 1953; Thurston and Greiling, 1978), as shown in Figure 2 for the HA solution at CHA = 7 mg mL–1. At all frequencies, both G′ and G″ remain constant within a well-defined linear viscoelastic region (LVR) over strain amplitudes (γ) < 100%, confirming that the entangled HA network is probed without structural perturbation. Within the LVR, a progressive frequency-dependent increase in both the plateau moduli and is observed, reflecting the inability of entangled chains to reptate within increasingly short oscillatory timescales. This behavior is well–documented for high–MW HA in the semi-dilute entangled regime (Oelschlaeger et al., 2013; ).
FIGURE 2
A critical, biomechanically significant observation from Figure 2 is the systematic evolution of the relationship between plateau moduli within the LVR as f increases. At f = 0.5 Hz (corresponding to near–resting or slow-walking state), the HA solution exhibits a decisively viscous-dominant response ( > ), with plateau values of ≈10–6 Pa and ≈3–4 Pa. As f increases to 0.8–1 Hz (corresponding to normal to brisk walking state), the two moduli converge, approaching near-crossover conditions ( ≈ ≈ 40–7 Pa). At f = 3 and 5 Hz (corresponding to running and dynamic impact loading), the response transitions to an elastic–dominant regime ( > ), with plateau values rising to approximately 8–15 Pa for and 9–12 Pa for at 5 Hz. This frequency-driven inversion from viscous to elastic dominance is the rheological signature of viscoelastic synovial fluid function. Ogston and Stanier were the first to delineate this dual function, demonstrating that at low strain rates HA acts as a viscous lubricant reducing interfacial friction, while at high rates the elastic component dominates to absorb and redistribute impulsive articular loads (Ogston and Stanier, 1953). Subsequent studies have confirmed that for native SF, the G′–G″ crossover falls at approximately 0.4–1 Hz (Thurston and Greiling, 1978; Rwei et al., 2008), which is precisely the walking–to–running transition frequency reproduced by the present HA solution.
Beyond the LVR and above a critical strain γᴄ, G′ declines monotonically with strain as entanglement junctions are disrupted by elastic yielding, and γᴄ decreases inversely with the frequency (from γᴄ ≈ 10–20% at f = 0.5 Hz to γᴄ ≈ 1–3% at f = 5 Hz). This trend indicates that the stiffer high–frequency network is more susceptible to structural breakdown at smaller deformations, consistent with the nonlinear rheological behavior reported for entangled HA and analogous biopolymer networks (; Storm et al., 2005; Wang et al., 2025). From a biomechanical viewpoint, this behavior implies that under the rapid loading rates associated with running or impact activities (f = 3–5 Hz), the HA network is more readily yielded by the applied articular deformation, transitioning into a shear–thinning flow regime (as will be described in Section 3.2) that reduces the viscosity and facilitates joint movement. At the same time, the elastic energy stored within the LVR provides impulsive load support. Such self–regulating viscoelastic transition is a key functional attribute of SFs repeatedly emphasized in the tribological literature (Ogston and Stanier, 1953; Thurston and Greiling, 1978; ).
Indeed, the absolute moduli of the present formulation are one to two orders of magnitude lower than native synovial fluid (G′ = 10–400 Pa at f = 1–10 Hz), owing to the lower MW and absence of synergistic lubricin (PRG4) aggregates that reinforce the HA phase in vivo (). However, the physiologically essential frequency–dependent crossover is faithfully reproduced, corroborating that 7 mg mL–1 at 2 MDa represents the most biomechanically adequate concentration examined in this study.
Further evidence for the impact of f on the viscoelasticity of the polymer solution can be seen from the variation of the loss tangent (tan δ = G″/G′) with γ as depicted in Figure 3. Such a dimensionless ratio of energy dissipated to energy stored per oscillatory cycle is uniquely sensitive to the viscoelastic nature of the polymer network, elucidating the onset and rate of structural breakdown, to be compared simultaneously across all f values in a single curve (Rwei et al., 2008). In the LVR, tan δ exhibits well–defined plateau values which decrease monotonically with increasing f (Figure 3). Importantly, the plateau sequence confirms that the G′–G″ crossover (corresponds to tan δ = 1) occurs between f = 1 and 3 Hz, in direct agreement with the crossover frequency identified in Figure 1 at ω ≈ 10 rad s–1 for the solution at 7 mg mL–1. This crossover frequency corresponds to the transition from walking to running, and falls within the 0.4–3 Hz range reported for native healthy SF (Thurston and Greiling, 1978; ) and for commercial biomimetic fluids of comparable MW (Nicholls et al., 2018b), validating the physiological relevance of this formulation. Structurally, the decreasing tan δ with f in the LVR reflects the progressive shift in the measurement timescales (t) in comparison to the terminal reptation relaxation time (λ). At f = 0.5–0.8 Hz, t is longer than λ, which implies that the HA chains relax within each cycle and the energy is predominantly dissipated. At f = 3–5 Hz, t is shorter than λ, where incomplete chain relaxation occurs, and the elastic energy storage dominates, with λ ≈ 0.1 s for this system, as can be deduced from Figure 1 (Oelschlaeger et al., 2013).
FIGURE 3
Beyond the LVR, tan δ commonly rises above its respective plateau at γᴄ, which decreases systematically with increasing f: from γᴄ ≈ 10–15% at f = 0.5 Hz to γᴄ ≈ 2–3% at f = 5 Hz. This deviation implies the onset of network yielding when the applied deformation disrupts the chain entanglements faster than they can reform. Accordingly, G′ falls more steeply than G″, and the ratio G″/G′ increases. The inverse relationship between the LVR stiffness (captured in Figure 1 as rising with f) and the critical strain γᴄ is a key diagnostic marker of an entangled physical network, in which the yield strain scales as γᴄ ∼ (/ )½. This implies that the network becomes stiffer but proportionally more fragile to strain–induced disentanglement (Storm et al., 2005; ). The γᴄ values are in good agreement with the published ones for entangled HA of comparable MW and concentration (Oelschlaeger et al., 2013; Wang et al., 2025). Biomechanically, the narrow LVR at running and impact frequencies (f = 3–5 Hz, γᴄ ≈ 2–5%) means that physiological articular deformations at these frequencies routinely trigger yielding, driving a shear–thinning response that reduces the viscosity and activates squeeze–film lubrication across the joint surfaces (Ogston and Stanier, 1953; Zhang and Christopher, 2015). Further deformation at very large strains (γ > 200%) converges to tan δ > 3–4 regardless of the frequency, which marks a fully disentangled, frequency-insensitive viscous flow limit. This convergence defines the upper boundary of the frequency-selective viscoelastic behavior where the rich elastic–viscous transition that characterizes the intact entangled network is entirely confined to the LVR (γ < γᴄ) and the intermediate yielding transition, and is lost once the network is fully disrupted by large-amplitude deformation.
3.2 Flow behavior of HA solutions
The impact of shear flow on the viscosity of HA solutions at varied concentrations is depicted in Figure 4. First, the PS medium exhibits typical Newtonian behavior over the extended shear–rate () range, with zero–shear viscosity (η0) ≈ 1.3 mPa s. The HA solutions generally exhibit a common behavior: a transition from Newtonian to non–Newtonian behavior as increases. Initially, the viscosity of solutions is nearly independent of the applied before it decreases above a critical rate (). As the HA concentration increases, η0 increases monotonically, following the scaling law: , with an exponent (3.7) characteristic of the reptation regime (; ; Oelschlaeger et al., 2013). Particularly, the concentrated HA solution at 7 mg mL–1 exhibits η0 (≈4 Pa s) similar to that reported for HA solutions under physiological conditions (; ) and lower than that for healthy human SF, validating the physiological relevance of this concentration when formulated with other additives such as lubricin, albumin, and phospholipids (). The power–law fitting yields flow behavior index n ≈ 0.48 (for 7 mg mL–1), consistent with the reported values for entangled high–MW HA (; ), and a shear–thinning ratio ≈ 76 falls within the range reported for healthy human SF (70–250) (Schurz and Ribitsch, 1987; Nicholls et al., 2018a; Rebenda et al., 2020), indicating that the formulation reproduces the characteristic non-Newtonian flow behavior of native SF despite its lower η0.
FIGURE 4
The shear–thinning behavior arises from the same microstructural mechanism deduced from the dynamic rheology (Figures 2, 3). Under shear flow, the applied chain deformation progressively overcomes the topological constraints imposed by chain entanglements, forcing chains to orient and elongate in the flow direction and to reptate out of their equilibrium tube configurations at a rate faster than they can re–entangle. This reduces the effective number of inter–chain constraints per chain segment, and consequently lowers the macroscopic viscosity. The onset of shear thinning occurs at ≈ 5 s–1 for the HA solution at 7 mg mL–1, which corresponds to the inverse of the terminal relaxation time λ ≈ 0.2 s in agreement with the time estimated from the frequency sweep crossover (ωᴄ ≈ 10 rad s–1): at shear rates below λ−1, the network can relax within each unit of applied strain and responds with its full η0; above λ−1, chains cannot relax fast enough, progressively disentangle, and viscosity falls (; Rwei et al., 2008; ). This chain–disentanglement mechanism has been confirmed in multiple recent studies on high–MW HA solutions using a combination of steady–shear, oscillatory, and microrheological measurements (; ; Sayko et al., 2023).
The upscan and downscan viscosity profiles overlap closely throughout the measured range, with no significant hysteresis loop (Figure 4). This coincidence implies that the shear–induced structural changes, namely, chain disentanglement, alignment, and extension under flow, are fully and rapidly reversible on the timescale of the measurement. Moreover, the HA solutions examined here exhibit non–thixotropic or minimally thixotropic behavior (Rwei et al., 2008; ). This behavior may be linked to a physically transient structure of the entangled HA network in which the HA chains reversibly disentangle and re–entangle through reptation. No permanent, kinetically trapped, or chemically crosslinked structures that would prevent full structural recovery upon shear scission. This conclusion is reinforced by the amplitude sweep data (Figure 2), which showed near–identical tan δ rise and fall profiles across the measured strain range, consistent with a network that does not age or permanently restructure under large–amplitude deformation. The absence of thixotropy in the present HA solutions is consistent with published literature on non-crosslinked high–MW HA solutions in physiological saline (Rwei et al., 2008). Recently, Kim et al. investigated polynucleotide/HA viscosupplement blends and distinguished between HA solutions (rapid structural recovery, minimal hysteresis) and crosslinked HA networks (prolonged recovery, measurable hysteresis). The authors attributed the difference to the presence or absence of permanent network junctions that resist instantaneous re–entanglement. From a biomechanical perspective, the rapid, complete reversibility of the viscosity response is functionally critical (Ogston and Stanier, 1953; ; ). During the alternating loading and unloading cycles of walking and running, the synovial HA network must be able to switch repeatedly between its elastic–dominant (high–ω) and viscous-dominant (low–ω) states without cumulative structural degradation, a requirement that is directly satisfied by the non–thixotropic, fully reversible behavior demonstrated in Figure 4.
3.3 Linear viscoelastic properties of CNT–HA dispersions
The thermal stability of HA-CNT dispersions is investigated using a temperature sweep test, as shown in Supplementary Figure S2. In general, the dispersions exhibit liquid-like viscoelastic behavior over the temperature range 10 °C–70 °C. The dispersions become more flowable as the temperature rises, as evident from the increased difference between G′ and G″ and the decrease in the magnitude of both moduli. Moreover, the dispersions at higher CNT content are more structured at T < 20 °C. The viscosity of formulations does not differ significantly from that of physiological SF at 25 °C and is, interestingly, lower at 37 °C (data not shown).
Figure 5 demonstrates the dynamic frequency sweep results for selected formulations at various CNT contents and different temperatures (25 °C and 37 °C). These temperatures were chosen to bracket the intended service life of the dispersion: 25 °C represents the ambient, reference condition under which the model SF is stored, whereas 37 °C corresponds to the physiological temperature the fluid experiences once injected into the joint. It can be seen from Figure 5 that the loss modulus exceeds the storage modulus (G″ > G′) for every formulation, including neat HA solution, across the entire accessible window (ω ≈ 10−1–102 rad s–1) and at both temperatures. This implies that all formulations are viscoelastic liquids (sol state) in which dissipative character dominates even at high CNT content (0.044 vol%) and both temperatures. This is the correct baseline for a model SF where the native SF is designed to be viscous–dominated when the joint is near rest (low ω, energy is dissipated) and to become elastic–dominated only under rapid motion (high ω). The two regimes meet at a characteristic crossover frequency (ωc) (; ). The present fluids reproduce the rest–state signature (G″ > G′ at low ω); any elastic crossover, if it exists, lies at or beyond the upper end of the window, a point to which we return below.
FIGURE 5
As can be seen from Figure 5a, the neat HA solution, at 25 °C, exhibits the largest dynamic moduli with a terminal spectrum (G′ ∼ ω2, G″ ∼ ω1, G″ > G′) that is characteristic of entangled polymer chains under physiological conditions (). The HA solution retains the same terminal form at 37 °C (Figure 5b). Still, it turns uniformly softer due to plausible thermal disruption of HA hydrogen bonding and the Arrhenius temperature dependence reported for SF across the room–to–body–temperature range ().
Although the dependence of the dispersions’ viscoelasticity on φCNT is not monotonic at 25 °C, the observed behavior can be divided into three distinct regimes (Figure 5a). At low φCNT (HAC1, 0.0015 vol%; HAC3, 0.0066 vol%), both dynamic moduli are markedly reduced relative to the neat HA solution, with HAC3 exhibiting the lowest moduli among all investigated formulations. This reduction in viscoelasticity may arise from the disruption of the HA entangled network by dispersed, non-percolated nanotubes, which could decrease the density of effective interchain junctions and thereby weaken the network connectivity. Similar behavior has been reported in polysaccharide–CNT systems (). However, a contribution from sonication–induced HA chain scission cannot be ruled out and should be evaluated using an appropriate HA matrix–only control. At φCNT ≈ 0.015 vol% (HAC4), the dynamic moduli began to recover, suggesting the onset of a weak, space–spanning CNT network. While the current measurements do not directly visualize the network, the recovery is most plausibly explained by the gradual formation of CNT–CNT contacts and CNT-mediated bridging of the HA chains, collectively establishing a fragile percolated scaffold.
Such behavior is consistent with the exceptionally low rigidity–percolation thresholds reported for high–aspect–ratio nanotube networks, where percolation can occur at very low φCNT (e.g., φc ≈ 0.0026 vol% for aqueous single–walled carbon nanotube suspensions), with the emergent elasticity governed primarily by inter–tube interactions rather than the intrinsic stiffness of the individual nanotubes (). At the highest CNT loading (HAC5, 0.022 vol%), the viscoelastic response shows no further enhancement and instead approaches a slight saturation. This behavior may indicate the onset of nanotube re–aggregation into bundles, which effectively reduces the nanotubes’ aspect ratio and, consequently, the number of load–bearing junctions within the network (; ). It should be noted that this interpretation is derived from the rheological response and has not been confirmed through direct structural imaging in the current study. Notably, all G′ curves at 25 °C exhibit terminal behavior, with no discernible low–frequency plateau (Figure 5a). This absence suggests that the sparse CNT network remained mechanically subordinate to the relatively stiff HA matrix at room temperature and therefore did not produce a distinct rheological signature. Consequently, the observed ranking of the samples at 25 °C appears to be governed primarily by the extent to which the dispersed nanotubes may perturb the structure and connectivity of the HA entangled network.
At the physiological temperature (37 °C), a qualitative change in the viscoelastic response of the dispersions, rather than a simple shift in magnitude, can be noticed (Figure 5b). This behavior can be attributed to two concurrent effects. First, thermal softening of the HA matrix reduces both dynamic moduli and accelerates the terminal relaxation (). Second, the CNT network is likely to percolate more readily at elevated temperatures, as enhanced inter-tube interactions promote network formation and lower the rheological percolation threshold (). These effects are most clearly manifested in HAC4, which at 37 °C developed a sustained low–frequency G′ plateau of approximately 0.03 Pa over ω ≈ 0.15–0.4 rad s–1, replacing the terminal decay observed at 25 °C. The emergence of this low–frequency plateau is characteristic of a percolated CNT network capable of sustaining elasticity over long relaxation times (; ; ). The comparison with the neat HA solution provides a direct basis for attributing this response to the plausible CNT network. Under identical conditions, HAC0 retained a terminal G′ decay, reaching approximately 0.013 Pa at ω ≈ 0.2 rad s–1, with no evidence of a low–frequency plateau. Thus, the increased and frequency-independent G′ observed in HAC4 cannot be solely ascribed to the HA matrix. Given that HAC0 and HAC4 differ exclusively in the inclusion of nanotubes and were assessed under identical conditions, the distinct low-frequency plateau observed only in HAC4 suggests, albeit indirectly, the presence of a mechanically effective CNT-associated network. However, direct microstructural evidence is necessary to substantiate this hypothesis. Notably, within this low–frequency regime, HAC4 exhibits a G′ approximately two–to three–fold higher than that of neat HA, while the corresponding G″ values remained essentially comparable. Hence, incorporation of only 0.015 vol% CNTs enhanced the low–frequency elasticity of the high–MW HA solution without substantially altering its viscous response. This behavior may indicate genuine network reinforcement rather than simply recovery of the matrix viscoelasticity. By contrast, HAC1 remains below the neat HA response, indicating persistent sub–percolation suppression even at physiological temperature, whereas HAC5 shows no further enhancement relative to HAC4, consistent with the persistence of nanotube bundling. Accordingly, the low–frequency elastic response follows the approximate order HAC4 > HAC0 ≈ HAC3 > HAC1, with HAC5 exhibiting an intermediate response. Accordingly, HAC4 (0.015 vol%) can be identified as the most favorable formulation, as its temperature–enhanced CNT network provides the enhanced low–frequency elasticity required to reproduce the resting–state viscoelastic characteristics of a model SF under physiological conditions.
These hypothesized structural mechanisms are inferred from rheological responses, rather than direct observation. Three independent rheological indicators, the temperature-induced low-frequency G′ plateau, frequency-independent LVR broadening, and non-monotonic intermediate-shear viscosity with reversible hysteresis, together with the neat-HA control (HAC0) measured under the same conditions, support a CNT-associated network. Direct structural confirmation was beyond this study; including cryogenic transmission electron microscopy, electrical-conductivity percolation (impedance spectroscopy) measurements, and small-angle X-ray scattering are needed to ascertain the microstructure of the dispersions.
3.4 Strain-dependent viscoelasticity of HA–CNT dispersions
Now, it is worth investigating the impact of frequency on the LVR of the dispersions, represented by the oscillatory strain sweep tests at 25 °C (Figure 6), analogous to the results of neat HA solutions (Figure 2). The selected frequencies (f = 0.5, 0.8, 1, 3, and 5) correspond to rest, walking, brisk walking, running, and high–impact loading, respectively (Rwei et al., 2008; ). These measurements enable probing whether the strain–dependent mechanical response at physiological frequencies and independently corroborate the conclusion from Figure 5a that HAC4 represents the most favorable HA–CNT formulation. Figure 6 demonstrates a pronounced broadening of the LVR upon incorporation of CNTs. For the neat HA solution (7 mg mL–1; Figure 2), the critical strain, γc, at which G′ deviates from its plateau decreases from approximately 10%–15% at f = 0.5 Hz to 1%–3% at f = 5 Hz, reflecting the limited strain tolerance of the entanglement–dominated HA network under faster deformation. In contrast, all HAC formulations sustain linear viscoelastic behavior up to γc ≈ 100–200% across the investigated frequency range, corresponding to an increase of approximately one to two orders of magnitude that is largely independent of CNT concentration. This substantial extension of the LVR confirms that the γ ≈ 1% strain used for the frequency sweeps in Figure 5a remains well within the linear regime for all formulations, ensuring that the measured moduli represent intrinsic, deformation–independent viscoelastic properties. The enhanced strain tolerance is ascribed to the establishment of supplementary load-bearing junctions via non-covalent interactions between the high-aspect-ratio CNTs and HA chains. These interactions primarily involve van der Waals forces, hydrophobic associations with the amphiphilic HA backbone (Scott and Heatley, 1999), and CH–π contacts at the graphitic surface, along with the steric wrapping of the chains around the tubes. Collectively, these factors is likely to strengthen the entangled network and inhibit strain-induced network disruption (; ). Within the LVR, both and increase with frequency, consistent with the frequency–dependent relaxation behavior observed for neat HA. This, incorporating CNT is anticipated to substantially improve the mechanical stability and strain tolerance of the HA network, while still preserving its fundamental frequency-dependent viscoelastic properties.
FIGURE 6
Despite these common features, Figure 6 reveals a pronounced formulation-dependent difference in the balance between elastic and viscous responses within the LVR. For HAC1 (0.0015 vol%), remains higher than over the entire frequency range (0.5–5 Hz), except for a brief G′ overshoot at 5 Hz and γ < 0.3%. This transient increase in elasticity may reflect a kinetic response of the sparse CNT–HA network, in which the oscillation period (∼0.2 s) becomes comparable to the relaxation time of CNT–HA junctions. This allows a temporary elastic loading before structural relaxation restores the viscous–dominant response (Storm et al., 2005; ). Importantly, this transient feature does not imply a sustained transition to an elastic–dominated regime. At the higher CNT concentration of HAC3 (0.0066 vol%), consistently exceeds at all investigated frequencies, with no detectable overshoot. This behavior suggests a more stable network response while retaining predominantly viscous behavior. HAC5 (0.022 vol%) exhibits a similar > relationship throughout the LVR at all frequencies. Thus, despite exhibiting the highest absolute moduli among the examined dispersions, HAC5 does not develop elastic dominance within the investigated frequency range. This behavior suggests that excessive CNT loading may introduce local aggregation or steric constraints that interfere with the cooperative HA entanglement network, thereby limiting the fraction of the mechanical response arising from elastically effective network connectivity (; ). HAC4 (0.015 vol% CNT) exhibits a distinct frequency-dependent viscoelastic response that differentiates it from the other formulations. At 0.5–0.8 Hz, corresponding to rest and walking, G″ remains higher than G′, indicating predominantly viscous behavior favorable for hydrodynamic lubrication. At 1 Hz, the two moduli approach crossover, whereas at 3 and 5 Hz, G′ becomes comparable to or slightly exceeds G″, indicating a transition toward elastic–dominated behavior at running and high–impact frequencies. This reversible frequency–dependent inversion of the G′/G″ hierarchy closely resembles the characteristic dual viscoelastic response of healthy SF, which combines viscous lubrication at low loading frequencies with enhanced elasticity at higher frequencies (Thurston and Greiling, 1978; ; ; Nicholls et al., 2018b). The agreement between the LVR moduli in Figure 6 and the corresponding values from the frequency sweep in Figure 5a further confirms that the observed crossover is an intrinsic, strain–independent property of HAC4 dispersion rather than an artifact of the selected strain amplitude. Moreover, the exceptionally broad LVR (γc ≈ 100–200%) demonstrates that this frequency–dependent functionality is maintained over a deformation range far exceeding physiological joint strains, in marked contrast to neat HA, whose LVR contracts to only 1%–3% at 5 Hz.
Beyond the LVR, all HAC formulations exhibit the characteristic nonlinear response observed for neat HA solution, with a progressive decrease in G′ accompanied by a transient G″ overshoot before both moduli decline at large strains. The persistence of higher moduli in the dispersions indicates that the CNT network retains partial structural integrity after yielding of the HA entanglement network. At very large strains (γ > 500–800%), the responses converge toward a common viscous limit, consistent with extensive disruption of both networks and the onset of chain–dominated flow. Collectively, these amplitude–sweep results independently identify HAC4 dispersion as the most favorable formulation, combining a substantially broadened LVR with viscous–dominant behavior at low (rest and walking) frequencies and enhanced elasticity at higher (running and loading) frequencies. This combination provides the key rheological characteristics required for a model SF capable of simultaneously supporting lubrication during low–frequency motion and elastic energy dissipation during rapid or high–impact loading (Ogston and Stanier, 1953; Nicholls et al., 2018b; Vassallo et al., 2025; Rivarola et al., 2026).
Figure 7 presents the amplitude–sweep responses of the four HA–CNT dispersions at 37 °C under otherwise identical conditions to those used in Figure 6, thereby isolating the effect of physiological temperature on their nonlinear viscoelastic behavior. Two features are common to all formulations. First, the LVR remains broad, with γc ≈ 100–200%, indicating that the enhanced strain tolerance imparted by the CNT network is largely preserved at body temperature and confirming that the strain amplitude (γ ≈ 1%) used for the frequency sweeps at 37 °C lies safely within the LVR. Second, both and decrease relative to 25 °C, consistent with thermally accelerated HA chain relaxation and the resulting reduction in viscoelastic moduli at a given frequency (Rwei et al., 2008; ). The reduction is more pronounced for G″ than for G′, reflecting the greater sensitivity of the viscous response to HA chain mobility, whereas G′ retains additional support from the CNT network. Consequently, heating generally increases the G′/G″ ratio and shifts the dispersions toward a more elastic response at physiological temperature. The extent and direction of this shift depend strongly on CNT concentration. HAC1 (0.0015 vol% CNT) exhibits the largest increase in elastic dominance, with substantially exceeding across the entire frequency (0.5–5 Hz) range. Although this behavior indicates the persistence of an elastic CNT–associated contribution at 37 °C, the strongly elastic response at low frequency is inconsistent with the predominantly viscous character expected for effective lubrication under quasi–static loading. The HAC3 formulations (0.0066 vol% CNT) provides a more balanced response, retaining > at f = 0.5–0.8 Hz and approaching crossover at higher frequencies. However, the relatively small separation between G′ and G″ at running frequencies limits the extent of elastic reinforcement. The HAC5 dispersion (0.022 vol% CNT) remains predominantly viscous, with exceeding throughout the investigated frequency range, indicating that increasing the CNT content beyond HAC4 does not produce a significant enhancement in the elastic response. Interestingly, the HAC4 dispersion (0.015 vol% CNT) exhibits the most favorable temperature–dependent behavior. At 25 °C, this formulation showed ≥ at f = 3–5 Hz while remaining viscous–dominant at low frequencies (Figure 6). At 37 °C, preferential reduction of G″ shifts the G′–G″ crossover toward lower frequency, approaching approximately 1 Hz. Thus, the HAC4 formulation exhibits > at f = 0.5 Hz, near equality of the two moduli around f = 1 Hz, and a progressively more balanced response at f = 3–5 Hz. This frequency–dependent modulation provides a favorable combination of viscous dissipation at low loading frequencies and increasing elastic contribution during faster motion, consistent with the functional requirements of synovial–fluid–like lubrication (Thurston and Greiling, 1978; ; ; Nicholls et al., 2018b). Importantly, the shift of the crossover toward approximately 1 Hz at 37 °C represents a closer correspondence with physiological joint-motion frequencies than observed at 25 °C.
FIGURE 7
Beyond the LVR, all formulations exhibit the same qualitative yielding behavior observed at 25 °C, characterized by a progressive decrease in G′, a transient G″ overshoot, and eventual convergence of the moduli at large strains. Thus, temperature primarily alters the modulus magnitude and the frequency at which the elastic–viscous balance occurs, while leaving the underlying mechanism of network disruption essentially unchanged (; ). Overall, the combined amplitude–sweep results at 25 °C and 37 °C identify HAC4 as the most balanced formulation, providing broad strain tolerance together with a temperature–dependent viscoelastic response that is particularly well suited to the contrasting mechanical demands encountered during low–and high–frequency joint motion.
3.5 Shear-induced structural changes and reversibility in HA–CNT dispersions
Figure 8 presents the steady-state flow behavior of the neat HA solution (HAC0) and the four HA–CNT composites over a shear-rate range of 10−3–103 s–1 at 25 °C (Figure 8a) and 37 °C (Figure 8b). All formulations demonstrate significant pseudoplasticity, which is evidenced by a gradual reduction in shear viscosity as the shear rate increases. This behavior is likely due to the deformation-induced disentanglement and alignment of the HA chains. In the composites, this is further accompanied by the progressive disruption and reorganization of the CNT–HA network (Rwei et al., 2008; ). At 25 °C, HAC0 is the only formulation displaying a discernible low-shear Newtonian plateau below ≈ 10−2 s–1, corresponding to the terminal relaxation regime of the entangled HA network. At higher shear rates, the solution undergoes conventional shear thinning as approaches and exceeds the inverse terminal relaxation time. Interestingly, HAC0 exhibits the greatest resistance to viscosity reduction at high shear rates, surpassing the composite formulations above ≈ 102 s–1 and retaining the highest viscosity at 103 s–1 (η ≈ 0.03–0.05 Pa s). This crossover likely reflects the distinct structural responses of the systems to strong deformation: disruption of the CNT-associated network removes load-bearing CNT–CNT and CNT–HA junctions, whose recovery is kinetically limited, whereas the entangled HA matrix can progressively re-establish chain connectivity (; ).
FIGURE 8
At low shear rates, the apparent viscosities of the dispersions at 25 °C follow the order HAC5 > HAC1 > HAC4 ≈ HAC3, with η ≈ 8–10, 5–7, 3–4, and 2.5 Pa s, respectively, at = 10−3 s–1. This variation reflects differences in the effective density and strength of CNT–HA interactions and is broadly consistent with the viscoelastic trends obtained from the frequency–and amplitude–sweep measurements (Figures 5a, 6). A particularly notable feature is the emergence of a non-monotonic intermediate-shear viscosity in HAC3 and HAC4. In these formulations, the initial viscosity decreases at ≈ 10−2 s–1 is followed by a weak viscosity recovery or secondary plateau over approximately 10−2–1−1 s–1, before viscosity decreases again at higher shear rates. This non–monotonic response is consistent with sequential structural rearrangements within the composite network: initial yielding of the HA entanglement structure is followed by progressive alignment and load redistribution within the CNT–HA network, which temporarily sustains the viscosity before undergoing further breakdown at higher deformation rates (). We emphasize that this sequence is proposed on the basis of the flow response and is not directly observed.
The absence of this feature in HAC1 and HAC5 suggests that both insufficient CNT connectivity and excessive CNT loading can suppress the cooperative restructuring responsible for the intermediate-shear response. At high shear rates ( ≫ 10 s-1), the viscosities of all formulations approach a narrow range of approximately 20–50 mPa s, indicating substantial disruption of the load-bearing microstructure and convergence toward a common flow regime. From a rheological standpoint, the retention of relatively low viscosities at the high shear rates representative of needle flow is a necessary condition for injectability; we note, however, that injectability was not assessed directly and would require dedicated injection-force measurements (; Nicholls et al., 2018b).
Increasing the temperature to 37 °C produces two notable changes. First, the low–shear Newtonian plateau of HAC0 is no longer resolved within the experimental window, and the viscosity decreases continuously from the lowest measured shear rate. This behavior is consistent with thermally accelerated HA relaxation, which shifts the terminal regime toward shear rates below the accessible range; consequently, the apparent low–shear viscosity measured at 10−3 s–1 should not be interpreted as the true zero–shear viscosity. This interpretation is consistent with the temperature-dependent reduction in the viscoelastic moduli observed in Figures 5b, 7 (Rwei et al., 2008; ; Smith et al., 2014). Second, the temperature dependence becomes strongly formulation-specific. HAC4 retains a pronounced intermediate-shear viscosity enhancement, whereas HAC1 and HAC3 exhibit a more substantial reduction in viscosity. The persistence of the HAC4 response suggests that, at the critical CNT concentration of 0.015 vol% CNT, the CNT–HA network possesses sufficient connectivity to maintain an effective contribution to flow resistance at physiological temperature, despite thermally accelerated relaxation of the HA matrix. In contrast, the less–developed networks in HAC1 and HAC3 appear more susceptible to thermally induced weakening or rearrangement of the non-covalent CNT–HA interactions (; ).
At > 102 s–1, the dispersions again converge toward similarly low viscosities, with the 37 °C values being slightly lower than those measured at 25 °C, confirming that the CNT–induced structural differences become largely irrelevant once the networks are extensively disrupted. Overall, Figure 8 provides independent steady–flow evidence that HAC4 offers the most favorable balance among the investigated formulations, combining a persistent intermediate–shear viscosity contribution, a distinct two–stage yielding response, and low high–shear viscosity at both 25 °C and 37 °C. These characteristics complement the dynamic viscoelastic behavior established in Figures 5–7 and further support HAC4 (0.015 vol% CNT) as the most promising formulation for a synovial–fluid–mimicking system.
To account for the reversibility of shear-induced structural changes, the thixotropic response for two selected dispersions (namely, HAC1 and HAC4) is depicted in Supplementary Figure S3. Unlike the neat HA solution (Figure 4), both dispersions exhibit pronounced hysteresis over an intermediate shear-rate range ( ≈ 10−2–10 s–1), with ηdown > ηup at equivalent shear rates. This hysteresis is consistent with a plausible shear-induced disruption of the CNT–HA network occurs faster than its structural recovery, resulting in a temporarily reduced network connectivity during the downscan (; Mewis and Wagner, 2009). The convergence of the two branches at both very low ( ≈ 10−3 s–1) and high shear rates ( > 10 s–1) indicates that the hysteresis is reversible rather than associated with permanent structural damage. In other words, the CNT–HA network is likely to recover when sufficient time is available, whereas at high shear rates the network is extensively disrupted and its contribution to the flow response becomes negligible.
The two formulations nevertheless exhibit distinct structural responses. HAC1 shows a pronounced viscosity minimum around ≈ 0.01–0.02 s–1, followed by a weak plateau before further shear thinning, suggesting relatively abrupt yielding of its sparse CNT–HA crosslinked network. In contrast, HAC4 undergoes a more gradual viscosity decrease over the intermediate shear-rate regime, suggesting a denser and more interconnected CNT–HA network that undergoes progressive structural rearrangement rather than abrupt failure. The substantially larger hysteresis loop observed for HAC4, with ηdown > ηup by nearly 1 decade around ≈ 10−1 s–1, compared with approximately 0.3–0.5 decades for HAC1. This behavior further demonstrates the greater extent of reversible structural reorganization in HAC4. This enhanced hysteresis is consistent with the higher density and cooperativity of its CNT–HA crosslinked network, which requires longer times for complete re-establishment following shear-induced disruption (Mewis and Wagner, 2009; ).
From a rheological standpoint, the reversible hysteresis observed in formulations containing CNTs presents a potentially advantageous characteristic for a synovial-fluid-mimicking material. Under high shear, the structural breakdown leads to a reduction in viscosity. Conversely, when the shear rate decreases, there is a progressive recovery of the network and a partial restoration of viscosity. However, determining whether this result in enhanced lubrication cannot be ascertained solely through bulk rheology; direct tribological testing is necessary.
4 Conclusion
This study introduces a rheological design concept that leverages the contrasting temperature reactions of hyaluronic acid (HA) and carbon nanotubes (CNTs) to create a biomimetic model of synovial fluid (SF). The refined HA matrix, with a concentration of 7 mg mL-1 and a molecular weight of 2 MDa, successfully replicated the key rheological characteristics of healthy SF. These include a transition from viscous to elastic behavior dependent on frequency and a shear-thinning index of approximately n ≈ 0.48, all while maintaining full reversibility and non-thixotropic properties, characteristic of a purely entangled reptating network.
Ultra-low nanotube reinforcement altered this response via two interconnected mechanisms. Firstly, non-covalent junctions expanded the linear-viscoelastic window by one to two orders of magnitude and introduced a reversible structural recovery thixotropy. Secondly, a temperature-enhanced percolation, driven by the preferential thermal softening of the viscous HA modulus compared to the nanotube-supported elastic modulus, revealed a mechanically effective scaffold at 37 °C, which was less prominent at 25 °C. The reinforcement was thus non-monotonic in terms of nanotube content and was governed by network connectivity rather than mass loading, with a single favorable composition occupying a narrow connectivity window. This composition alone developed a temperature-enhanced low-frequency elastic plateau, relocated its viscoelastic crossover to the normal-walking frequency at body temperature, retained a persistent intermediate-shear viscosity, and exhibited the most pronounced yet fully reversible structural recovery, all while preserving injectable high-shear viscosity.
More broadly, these findings articulate a design principle in which the mechanical response of a biohybrid material is rendered latent during ambient storage and enhanced upon delivery by the differential temperature sensitivity of its polymeric and nanostructured components—a thermally gated, percolation-controlled reinforcement strategy for injectable functional materials that are dormant in the syringe yet optimally expressed in the joint. Future research should build upon this rheological foundation by quantifying the tribological performance of these model fluids under conditions that accurately replicate the friction environment of articulating joints. This involves simulating physiological contact pressures, sliding velocities, and cyclic loading frequencies typical of human activities such as walking and running. Such an approach will directly establish the lubrication and wear-protection efficacy of the fluids under conditions relevant to their intended service.
Statements
Data availability statement
All original contributions from the study are contained within the article or Supplementary Material. For further questions, please contact the corresponding author.
Author contributions
MY: Conceptualization, Formal Analysis, Funding acquisition, Project administration, Supervision, Writing – original draft, Writing – review and editing. YM: Data curation, Methodology, Validation, Visualization, Writing – review and editing. ZA-A: Data curation, Methodology, Validation, Visualization, Writing – review and editing. MF: Data curation, Methodology, Validation, Visualization, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. The authors wish to acknowledge the financial support from the Qatar National Research Fund, UREP award (UREP31-132-1-030).
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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The author(s) declared that generative AI was not used in the creation of this manuscript.
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Supplementary material
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmats.2026.1974075/full#supplementary-material
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Summary
Keywords
biohybrid materials, biomimetic fluids, carbon nanotube, hyaluronic acid, rheological percolation, synovial fluid
Citation
Youssry M, Mashhour Y, Al-Abdulla ZF and Fazili M (2026) Carbon nanotube–reinforced hyaluronic acid dispersions as a rheological model for synovial fluids. Front. Mater. 13:1974075. doi: 10.3389/fmats.2026.1974075
Received
21 August 2026
Revised
03 September 2026
Accepted
10 September 2026
Published
07 October 2026
Volume
13 - 2026
Edited by
Leo Zeyang Liu, Peking University, China
Reviewed by
Elsa Gabriela Ordoñez Casanova, Universidad Autónoma de Ciudad Juárez, Mexico
Muyuan Chai, South China University of Technology, China
Updates
Copyright
© 2026 Youssry, Mashhour, Al-Abdulla and Fazili.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Mohamed Youssry, myoussry@qu.edu.qa
Disclaimer
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