Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels.

Gels made of telechelic polymers connected by reversible cross-linkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low-valence cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials.

Soft Viscoelastic Magnetic Hydrogels from the In Situ Mineralization of Iron Oxide in Metal-Coordinate Polymer Networks.

The design of soft magnetic hydrogels with high concentrations of magnetic particles is complicated by weak retention of the iron oxide particles in the hydrogel scaffold. Here, we propose a design strategy that circumvents this problem through the in situ mineralization of iron oxide nanoparticles within polymer hydrogels functionalized with strongly iron-coordinating nitrocatechol groups. The mineralization process facilitates the synthesis of a high concentration of large iron oxide nanoparticles (up to 57 wt % dry mass per single cycle) in a simple one-step process under ambient conditions. The resulting hydrogels are soft (kPa range) and viscoelastic and exhibit strong magnetic actuation. This strategy offers a pathway for the energy-efficient design of soft, mechanically robust, and magneto-responsive hydrogels for biomedical applications.

Non-Maxwellian viscoelastic stress relaxations in soft matter.

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Anomalous crystalline ordering of particles in a viscoelastic fluid under high shear.

Addition of particles to a viscoelastic suspension dramatically alters the properties of the mixture, particularly when it is sheared or otherwise processed. Shear-induced stretching of the polymers results in elastic stress that causes a substantial increase in measured viscosity with increasing shear, and an attractive interaction between particles, leading to their chaining. At even higher shear rates, the flow becomes unstable, even in the absence of particles. This instability makes it very difficult to determine the properties of a particle suspension. Here, we use a fully immersed parallel plate geometry to measure the high-shear-rate behavior of a suspension of particles in a viscoelastic fluid. We find an unexpected separation of the particles within the suspension resulting in the formation of a layer of particles in the center of the cell. Remarkably, monodisperse particles form a crystalline layer which dramatically alters the shear instability. By combining measurements of the velocity field and torque fluctuations, we show that this solid layer disrupts the flow instability and introduces a single-frequency component to the torque fluctuations that reflects a dominant velocity pattern in the flow. These results highlight the interplay between particles and a suspending viscoelastic fluid at very high shear rates.

Elastoviscoplasticity, hyperaging, and time-age-time-temperature superposition in aqueous dispersions of bentonite clay.

Clay slurries are both ubiquitous and essential in the oil exploration industry, and are most commonly employed as drilling fluids. Due to its natural abundance, bentonite clay is often the de facto choice for these materials. Understanding and predicting the mechanical response of these fluids is critical for safe and efficient drilling operations. However, rheological modeling of bentonite clay suspensions is complicated by the fact that thermally-driven microscopic arrangements of particle aggregates lead to a continual evolution of the viscoelastic properties and the yield stress of the suspension with time. Ergodic relations fundamental to linear viscoelastic theory, such as the Boltzmann superposition principle, do not hold in this scenario of 'rheological aging'. We present an approach for modeling the linear viscoelastic response of aging bentonite suspensions across a range of temperatures that is based on the transformation from laboratory time to an effective 'material time' domain in which time-translation invariance holds, and the typical relations of non-aging linear viscoelastic theory apply. In particular, we model the constitutive relationship between stress and strain-rate in the bentonite suspensions as fractional Maxwell gels with constant relaxation dynamics in the material time domain, in parallel with a non-aging Newtonian viscous contribution to the total stress. This approach is supported by experimental measurements of the stress relaxation and rapid time-resolved measurements of the linear viscoelastic properties performed using optimized exponential chirps. This data is then reduced to master curves in the material domain using time-age-time superposition to obtain best fits of the model parameters over a range of operating temperatures.

Scientific machine learning for modeling and simulating complex fluids.

The formulation of rheological constitutive equations-models that relate internal stresses and deformations in complex fluids-is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these "digital fluid twins" to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation-a task that is not achievable using any previously developed data-driven rheological equation of state.

Rod-climbing rheometry revisited.

The rod-climbing or "Weissenberg" effect in which the free surface of a complex fluid climbs a thin rotating rod is a popular and convincing experiment demonstrating the existence of elasticity in polymeric fluids. The interface shape and steady-state climbing height depend on the rotation rate, fluid elasticity (through the presence of normal stresses), surface tension, and inertia. By solving the equations of motion in the low rotation rate limit for a second-order fluid, a mathematical relationship between the interface deflection and the fluid material functions, specifically the first and second normal stress differences, emerges. This relationship has been used in the past to measure the climbing constant, a combination of the first (Ψ1,0) and second (Ψ2,0) normal stress difference coefficients from experimental observations of rod-climbing in the low shear rate limit. However, a quantitative reconciliation of such observations with the capabilities of modern-day torsional rheometers is lacking. To this end, we combine rod-climbing experiments with both small amplitude oscillatory shear (SAOS) flow measurements and steady shear measurements of the first normal stress difference from commercial rheometers to quantify the values of both Ψ1,0 and Ψ2,0 for a series of polymer solutions. Furthermore, by retaining the oft-neglected inertial terms, we show that the "climbing constant"  = 0.5Ψ1,0 + 2Ψ2,0 can be measured even when the fluids, in fact, experience rod descending. A climbing condition derived by considering the competition between elasticity and inertial effects accurately predicts whether a fluid will undergo rod-climbing or rod-descending. Our results suggest a more general description, "rotating rod rheometry" instead of "rod-climbing rheometry", to be more apt and less restrictive. The analysis and observations presented in this study establish rotating rod rheometry combined with SAOS measurements as a prime candidate for measuring normal stress differences in complex fluids at low shear rates that are often below commercial rheometers' sensitivity limits.

3D Printability of Silk/Hydroxyapatite Composites for Microprosthetic Applications.

Micro-prosthetics requires the fabrication of mechanically robust and personalized components with sub-millimetric feature accuracy. Three-dimensional (3D) printing technologies have had a major impact on manufacturing such miniaturized devices for biomedical applications; however, biocompatibility requirements greatly constrain the choice of usable materials. Hydroxyapatite (HA) and its composites have been widely employed to fabricate bone-like structures, especially at the macroscale. In this work, we investigate the rheology, printability, and prosthetic mechanical properties of HA and HA-silk protein composites, focusing on the roles of composition and water content. We correlate key linear and nonlinear shear rheological parameters to geometric outcomes of printing and explain how silk compensates for the inherent brittleness of printed HA components. By increasing ink ductility, the inclusion of silk improves the quality of printed items through two mechanisms: (1) reducing underextrusion by lowering the required elastic modulus and, (2) reducing slumping by increasing the ink yield stress proportional to the modulus. We demonstrate that the elastic modulus and compressive strength of parts fabricated from silk-HA inks are higher than those for rheologically comparable pure-HA inks. We construct a printing map to guide the manufacturing of HA-based inks with excellent final properties, especially for use in biomedical applications for which sub-millimetric features are required.

Microscopic dynamics underlying the stress relaxation of arrested soft materials.

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Versatile acid solvents for pristine carbon nanotube assembly.

Chlorosulfonic acid and oleum are ideal solvents for enabling the transformation of disordered carbon nanotubes (CNTs) into precise and highly functional morphologies. Currently, processing these solvents using extrusion techniques presents complications due to chemical compatibility, which constrain equipment and substrate material options. Here, we present a novel acid solvent system based on methanesulfonic or p-toluenesulfonic acids with low corrosivity, which form true solutions of CNTs at concentrations as high as 10 g/liter (≈0.7 volume %). The versatility of this solvent system is demonstrated by drop-in application to conventional manufacturing processes such as slot die coating, solution spinning continuous fibers, and 3D printing aerogels. Through continuous slot coating, we achieve state-of-the-art optoelectronic performance (83.6 %T and 14 ohm/sq) at industrially relevant production speeds. This work establishes practical and efficient means for scalable processing of CNT into advanced materials with properties suitable for a wide range of applications.

Crack morphologies in drying suspension drops.

A drop of an aqueous suspension of nanoparticles placed on a substrate forms a solid deposit as it dries. For dilute suspensions, particles accumulate within a narrow ring at the drop edge, whereas a uniform coating covering the entire wetted area forms for concentrated suspensions. In between these extremes, we report two additional regimes characterized by non-uniform deposit thicknesses and by distinct crack morphologies. We show that both the deposit shape and the number of cracks are controlled exclusively by the initial particle volume fraction. The different regimes share a common avalanche-like crack propagation dynamics, as a result of the delamination of the deposit from the substrate.

Spectral Universality of Elastoinertial Turbulence.

Dissolving small amounts of polymer into a Newtonian fluid can dramatically change the dynamics of transitional and turbulent flows. We investigate the spatiotemporal dynamics of a submerged jet of dilute polymer solution entering a quiescent bath of Newtonian fluid. High-speed digital Schlieren imaging is used to quantify the evolution of Lagrangian features in the jet revealing a rich sequence of transitional and turbulent states. At high levels of viscoelasticity, we identify a new distinct transitional pathway to elastoinertial turbulence (EIT) that does not feature the conventional turbulent bursts and instead proceeds via a shear-layer instability that produces elongated filaments of polymer due to the nonlinear effects of viscoelasticity. Even though the pathways to the EIT state can be different, and within EIT the spatial details of the turbulent structures vary systematically with polymer microstructure and concentration, there is a universality in the power-law spectral decay of EIT with frequency, f^{-3}, independent of fluid rheology and flow parameters.

Levitation of fizzy drops.

As first described by Leidenfrost, liquid droplets levitate over their own vapor when placed on a sufficiently hot substrate. The Leidenfrost effect not only confers remarkable properties such as mechanical and thermal insulation, zero adhesion, and extreme mobility but also requires a high energetic thermal cost. We describe here a previously unexplored approach using active liquids able to sustain levitation in the absence of any external forcing at ambient temperature. We focus on the particular case of carbonated water placed on a superhydrophobic solid and demonstrate how millimetric fizzy drops self-generate a gas cushion that provides levitation on time scales on the order of a minute. Last, we generalize this new regime to different kinds of chemically reactive droplets able to jump from the Cassie-Baxter state to a levitating regime, paving the way to the levitation of nonvolatile liquids.

Characterizing viscoelastic properties of synthetic and natural fibers and their coatings with a torsional pendulum.

Characterizing and understanding the viscoelastic mechanical properties of natural and synthetic fibers is of great importance in many biological and industrial applications. Microscopic techniques such as micro/nano indentation have been successfully employed in such efforts, yet these tests are often challenging to perform on fibers and come with certain limitations in the interpretation of the obtained results within the context of the macroscopic viscoelasticity in the fiber. Here we instead explore the properties of a series of natural and synthetic fibers, using a freely-oscillating torsional pendulum. The torsional oscillation of the damped mass-fiber system is precisely recorded with a simple HD video-camera and an image processing algorithm is used to analyze the resulting videos. Analysis of the processed images show a viscoelastic damped oscillatory response and a simple mechanical model describes the amplitude decay of the oscillation data very well. The natural frequency of the oscillation and the corresponding damping ratio can be extracted using a logarithmic decrement method and directly connected to the bulk viscoelastic properties of the fiber. We further study the sensitivity of these measurements to changes in the chemo-mechanical properties of the outer coating layers on one of the synthetic fibers. To quantify the accuracy of our measurements with the torsional pendulum, a complementary series of tests are also performed on a strain-controlled rheometer in both torsional and tensile deformation modes.

Time-connectivity superposition and the gel/glass duality of weak colloidal gels.

Colloidal gels result from the aggregation of Brownian particles suspended in a solvent. Gelation is induced by attractive interactions between individual particles that drive the formation of clusters, which in turn aggregate to form a space-spanning structure. We study this process in aluminosilicate colloidal gels through time-resolved structural and mechanical spectroscopy. Using the time-connectivity superposition principle a series of rapidly acquired linear viscoelastic spectra, measured throughout the gelation process by applying an exponential chirp protocol, are rescaled onto a universal master curve that spans over eight orders of magnitude in reduced frequency. This analysis reveals that the underlying relaxation time spectrum of the colloidal gel is symmetric in time with power-law tails characterized by a single exponent that is set at the gel point. The microstructural mechanical network has a dual character; at short length scales and fast times it appears glassy, whereas at longer times and larger scales it is gel-like. These results can be captured by a simple three-parameter constitutive model and demonstrate that the microstructure of a mature colloidal gel bears the residual skeleton of the original sample-spanning network that is created at the gel point. Our conclusions are confirmed by applying the same technique to another well-known colloidal gel system composed of attractive silica nanoparticles. The results illustrate the power of the time-connectivity superposition principle for this class of soft glassy materials and provide a compact description for the dichotomous viscoelastic nature of weak colloidal gels.

In situ mechanical reinforcement of polymer hydrogels via metal-coordinated crosslink mineralization.

Biological organic-inorganic materials remain a popular source of inspiration for bioinspired materials design and engineering. Inspired by the self-assembling metal-reinforced mussel holdfast threads, we tested if metal-coordinate polymer networks can be utilized as simple composite scaffolds for direct in situ crosslink mineralization. Starting with aqueous solutions of polymers end-functionalized with metal-coordinating ligands of catechol or histidine, here we show that inter-molecular metal-ion coordination complexes can serve as mineral nucleation sites, whereby significant mechanical reinforcement is achieved upon nanoscale particle growth directly at the metal-coordinate network crosslink sites.

Programmable Anisotropy and Percolation in Supramolecular Patchy Particle Gels.

Patchy particle interactions are predicted to facilitate the controlled self-assembly and arrest of particles into phase-stable and morphologically tunable "equilibrium" gels, which avoids the arrested phase separation and subsequent aging that is typically observed in traditional particle gels with isotropic interactions. Despite these promising traits of patchy particle interactions, such tunable equilibrium gels have yet to be realized in the laboratory due to experimental limitations associated with synthesizing patchy particles in high yield. Here, we introduce a supramolecular metal-coordination platform consisting of metallic nanoparticles linked by telechelic polymer chains, which validates the predictions associated with patchy particle interactions and facilitates the design of equilibrium particle hydrogels through limited valency interactions. We demonstrate that the interaction valency and self-assembly of the particles can be effectively controlled by adjusting the relative concentration of polymeric linkers to nanoparticles, which enables the gelation of patchy particle hydrogels with programmable local anisotropy, morphology, and low mechanical percolation thresholds. Moreover, by crowding the local environment around the patchy particles with competing interactions, we introduce an independent method to control the self-assembly of the nanoparticles, thereby enabling the design of highly anisotropic particle hydrogels with substantially reduced percolation thresholds. We thus establish a canonical platform that facilitates multifaceted control of the self-assembly of the patchy nanoparticles en route to the design of patchy particle gels with tunable valencies, morphologies, and percolation thresholds. These advances lay important foundations for further fundamental studies of patchy particle systems and for designing tunable gel materials that address a wide range of engineering applications.

Lubricant-Impregnated Surfaces for Mitigating Asphaltene Deposition.

Asphaltenes are heavy aromatic components of crude oil. Their complex chemical makeup-an aromatic core surrounded by aliphatic side chains-enables them to adhere to most surfaces. Their buildup in pipes can result in clogging and lead to interruption of production operations and expensive mechanical cleaning. We demonstrate the use of liquid-impregnated surfaces (LIS) to prevent asphaltene deposition and buildup on substrates. Indeed, these surfaces expose a liquid interface to the working fluid, which combines the benefits of a dynamic defect-free surface and tunable interfacial properties. In contrast to bulk additives that are typically mixed into the oil phase, the impregnating liquid also provides the great benefit of protecting the underlying solid surface with a stable and minimal layer of lubricant, thereby reducing costs and eliminating the need for subsequent downstream removal. We first select and confirm the thermodynamic stability of a suitable lubricant and its lack of interaction with asphaltenes. By using a carefully selected system composed of a textured and functionalized solid substrate in conjunction with a fluorinated lubricant, we show that asphaltene adsorption is prevented over long time scales. We further demonstrate the possibility of building such a system with representative industrial materials such as aluminum and expose the resulting substrate to an external shear flow to simulate pipe flow conditions.

Asphaltene Adsorption on Functionalized Solids.

Asphaltenes, heavy aromatic components of crude oil, are known to adsorb on surfaces and can lead to pipe clogging or hinder oil recovery. Because of their multicomponent structure, the details of their interactions with surfaces are complex. We investigate the effect of the physicochemical properties of the substrate on the extent and mechanism of this adsorption. Using wetting measurements, we relate the initial kinetics of deposition to the interfacial energy of the surface. We then quantify the long-term adsorption dynamics using a quartz crystal microbalance and ellipsometry. Finally, we investigate the mechanism and morphology of adsorption with force spectroscopy measurements as a function of surface chemistry. We determine different adsorption regimes differing in orientation, packing density, and initial kinetics on different substrate functionalizations. Specifically, we find that alkane substrates delay the initial monolayer formation, fluorinated surfaces exhibit fast adsorption but low bonding strength, and hydroxyl substrates lead to a different adsorption orientation and a high packing density of the asphaltene layer.

Epidermal biopolysaccharides from plant seeds enable biodegradable turbulent drag reduction.

The high cost of synthetic polymers has been a key impediment limiting the widespread adoption of polymer drag reduction techniques in large-scale engineering applications, such as marine drag reduction. To address consumable cost constraints, we investigate the use of high molar mass biopolysaccharides, present in the mucilaginous epidermis of plant seeds, as inexpensive drag reducers in large Reynolds number turbulent flows. Specifically, we study the aqueous mucilage extracted from flax seeds (Linum usitatissimum) and compare its drag reduction efficacy to that of poly(ethylene oxide) or PEO, a common synthetic polymer widely used as a drag reducing agent in aqueous flows. Macromolecular and rheological characterisation confirm the presence of high molar mass (≥2 MDa) polysaccharides in the extracted mucilage, with an acidic fraction comprising negatively charged chains. Frictional drag measurements, performed inside a bespoke Taylor-Couette apparatus, show that the as-extracted mucilage has comparable drag reduction performance under turbulent flow conditions as aqueous PEO solutions, while concurrently offering advantages in terms of raw material cost, availability, and bio-compatibility. Our results indicate that plant-sourced mucilage can potentially serve as a cost-effective and eco-friendly substitute for synthetic drag reducing polymers in large scale turbulent flow applications.