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Viscoelastic Free Surface Flows: From Computational Models to Experiments and Physics-informed Neural Networks
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Flow-Driven Stretch Fluctuations Govern the Nonlinear Viscoelasticity of Elongating Associative Polymer Networks
We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating dynamics give rise to the rate-dependent extensional viscosity 𝜂 𝐸 measured in filament stretching experiments on H-bonding networks. Simulations model bivalent associative networks with a reactive bead-spring model for varying association strength and extensional strain rate. We observe that stretch fluctuations are driven by a new form of chain tumbling, where chains continually collapse and elongate as their associations break and reform within the advecting network. This produces a broad, nearly uniform distribution of chain stretch over a wide range of strain rates, manifesting as a rate-independent plateau in the extensional stress. Our results show that the nonlinear viscoelasticity of associative networks is dominated by large fluctuations in molecular response, which cannot be captured by current mean-field models.
Protorheology in practice: Avoiding misinterpretation
Protorheology is the paradigm that any observed flow or deformation is a chance to infer quantitative rheological properties. While this creates many opportunities for insight, there is significant risk of misunderstanding the physics involved, e.g. misinterpreting a liquid as a solid or mistaking viscous flow time as viscoelastic relaxation time. We describe these and other potential mistakes, use case studies to show how serious the problems can be, and contrast misinterpretations with correct approaches and interpretations. Some issues are especially important with materials involving colloidal particles and flows involving surface tension. Whether the reader is making inference from a tilted vial, time-lapse gravity-driven flow, a bounce test, die swell, or any other protorheology observation, the examples here serve as a guide for avoiding bad data in protorheology.
Rheology characterization of ionic liquids under high pressure and high temperature
Ionic liquids (ILs) are liquid salts that exist at or below ambient temperatures and are composed of ion pairs. They offer promising alternatives to toxic, hazardous, highly flammable, and volatile solvents in various applications such as solution preparation, dispersion, gel formation, composites, and polymer melts. ILs possess unique and interesting characteristics, including excellent chemical and thermal stability and low vapor pressures. Understanding the rheological properties of ILs is essential to optimizing IL performance. This paper presents a comparative analysis of the rheological properties of two ionic liquids, Nsingle bondHexylpyridinium tetrafluoroborate (HPyBF4) and Nsingle bondHexylpyridinium bromide (HPyBr), under different shear rates, temperatures, and pressures. Rheological measurements were performed under varying controlled pressure and temperature conditions. The experimental investigation covered a pressure range of 689–12,411 kPa [100–1800 psi] and a temperature range from room temperature up to 522 kelvin (K) [480°F]. The primary objective is to explore and compare the flow behavior and viscoelastic characteristics of HPyBF4 and HPyBr under high-pressure and high-temperature conditions. The experimental data showed that HPyBF4 and HPyBr exhibited shear-thinning behavior, and pressure had an insignificant effect on rheology compared to the temperature effect. Under the same testing conditions, HPyBr showed higher shear stress and viscosity than HPyBF4. This research significantly contributes to the improved understanding of the rheological behavior of these specific ionic liquids and their suitability for diverse industrial and scientific applications, particularly in high-pressure and high-temperature environments.
Egg yolk as a model for gelation: From rheometry to flow physics
Egg yolks are an excellent model for studying sol-gel transitions, particularly the power law viscoelasticity that defines the critical point of gelation. However, prior studies lack comprehensive datasets and fail to visualize flow behavior linked to temperature and time-dependent linear and nonlinear rheology. Here, we present a detailed dataset characterizing egg yolk viscoelasticity across temperature, time, and forcing amplitude using oscillatory shear, step strain, step stress, and constant high strain rate. Novel protorheology visualizations link rheological properties with observable flow behavior. Our findings highlight the nuanced determination of the critical gel point, emphasizing observation timescale dependencies. We compare methods to identify critical temperatures for gelation, including power law viscoelasticity, moduli crossover, diverging zero-shear viscosity, and emerging equilibrium elastic modulus, while visualizing flow consequences near these transitions. Egg yolk is an accessible, realistic, and nontoxic material relevant to the physicist and the chef alike, making it ideal for understanding the rheology of critical gels. By integrating protorheology photos and videos with rigorous rheometric data, we deepen the understanding of critical gels, with broader impacts for studying other materials with sol-gel transitions.
Coarse-Grained Simulations of Polyrotaxane Hydrogels under Quiescent and Shear Conditions
Cyclodextrin-based polyrotaxanes (PR) form hydrogels in water through cyclodextrin (CD) aggregation and crystallization. These networks can break under shear flows, making them versatile platforms for extrusion-based 3D printing. To optimize the material properties of 3D-printed PR gels, a microscopic understanding of the structural evolution during 3D printing is necessary. Here, we employ coarse-grained (CG) simulations to reveal the PR assembly process at the molecular level. Our simulations reproduce the experimental crystal morphologies of PR at varying concentrations and chain lengths under quiescent conditions. Using nonequilibrium simulations, we show shear flow ruptures crystalline domain connectivity in PR gels and stacks the lamellae in the gradient direction, allowing the materials to flow during 3D printing. After the cessation of flow, the anisotropic crystal alignment and absence of available dangling PR diminish the intercrystal connectivity. The printed materials are therefore mechanically weaker than the pristine hydrogels, in agreement with experimental results. Nonetheless, by relating the microscopic structural evolution with viscoelastic properties of PR gels and solutions, we elucidate how flow conditions and sample composition affect the 3D printing performance of PR hydrogels.
Recovery of postconsumer mechanically recycled polymers
Mechanical recycling plays a key role in reducing landfill bound plastics that pollute our environment. This process converts plastic waste into marketable pellets by sorting, cleaning, grinding into flakes, compounding in the molten state, and ultimately pelletizing. A primary restriction for the widescale usage of mechanical recycling is the highly variable quality and mechanical properties of the plastic waste feedstock. Degradation can occur during the plastic life cycle with the consumer, during the mechanical processing itself, or during the complex sorting process required to produce the feedstock. This study explores how rheological characterization can mitigate the batch-to-batch variability and identify a potential application for each batch. Shear and extensional rheology of “application-specific” virgin high-density polyethylene (HDPE) and virgin polypropylene (PP) was used as the control for this categorization process. Recycled HDPE and PP from three different streams were then measured and compared to the results from the control study. Rheological measurements proved to be very effective at providing sufficient differentiation to categorize the recycled polymer as suitable for different applications such as injection molding, blow molding, or thermoforming. Finally, the usage of an additional step to sort the recycled polymers by their initial use application was found to achieve a remarkably consistent recovery of application-specific material properties. Furthermore, this secondary sorting could provide significant added value for mechanically recycled polymers.
A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition
Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.
Insights into mixing of non-isothermal multi-polymer melts for complex plastics recycling
Catalytic recycling or upcycling of plastics is often limited not by catalyst performance, but by transport, arising from highly viscous, non-Newtonian polymer melts. In this work, we develop a reactor-scale framework that integrates rheological measurements, constitutive modeling, computational fluid dynamics (CFD), and experiments to quantify mixing, heat transfer, and dispersion in surrogate hydrocarbon melts representing mixed plastics systems. Temperature- and shear rate-dependent viscosity of low-density polyethylene (LDPE) and high-density polyethylene (HDPE) is measured to create two surrogate polymers (PLD and PHD) that capture the dominant shear-thinning flow behavior while neglecting strong elastic effects, enabling tractable simulation of non-isothermal, polymer-melt mixing using a Carreau-Arrhenius generalized Newtonian framework. Three-dimensional CFD simulations are employed to evaluate impeller performance in PLD using mixing time, cavern volume, thermal uniformity, and interfacial area for regimes in which viscoelastic effects are not dominant. We show that magnetic stir bars commonly used in lab-scale studies produce large thermal gradients (~60 °C) and poor mixing, even under idealized power delivery and polymer flow conditions. In contrast, close-clearance anchor impellers achieve near-isothermal operation, reduce mixing times by up to 5×, and provide >90% active circulation volume. We further demonstrate that, at low pseudo-Deborah number (De*), motor power requirements can be predicted directly from shear rate-dependent rheology using the Carreau-Arrhenius framework, enabling rational selection of operating conditions. Extension to surrogate immiscible multi-polymer systems based on PLD and PHD shows that interfacial area is highly sensitive to operating conditions and impeller design, with coaxial anchor-turbine configurations enhancing dispersion by up to 4 × .
Filament extension atomizers: A study of integration potential into spray dryers for high-viscosity and non-Newtonian fluids
Filament extension atomizers (FEAs) are an emerging class of spray nozzles designed to atomize high-viscosity and non-Newtonian fluids that are challenging for conventional pressure or two-fluid nozzles. In this study, we investigate the influence of roller geometry, surface velocity, roller material, and fluid rheology on the atomization performance of FEA systems using concentrated whey protein suspensions (50–70 wt. %). Extensional and shear rheology experiments, along with high-speed imaging and particle image velocimetry, reveal that filament breakup dynamics are governed by competition between inertial, capillary, and viscoelastic stresses. High roller rotational velocity leads to narrower spray cones, contradicting rheology experiments and suggests a significant inertial contribution to filament breakup. Smaller rollers operating at the same rotational velocity led to broader spray cones consistent with expectations. An FEA nozzle was integrated into a conventional dryer producing particles in the 100 μm range. Results suggest that FEA technology enables atomization of highly viscous fluids at industrially relevant spray cone angles similar to those generated by pressure nozzles, offering a pathway to improve energy efficiency in spray drying by enabling higher solids loading feedstocks. Furthermore, these insights provide critical guidance for optimizing FEA nozzle designs and process parameters across a range of applications.
An attention-based neural ordinary differential equation framework for modeling inelastic processes
To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain while leaving the inferred state unconstrained, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars, while maintaining fundamental principles by design.
Should I stay or should I flow? An exploration of phase‐separated metallosupramolecular liquid crystal polymers
Abstract Dynamic liquid crystalline polymers (dLCPs) incorporate both liquid crystalline mesogens and dynamic bonds into a single polymeric material. These dual functionalities impart order‐dependent thermo‐responsive mechano‐optical properties and enhanced reprocessability/programmability enabling their use as soft actuators, adaptive adhesives, and damping materials. While many previous works studying dynamic LCPs utilize dynamic covalent bonds, metallosupramolecular bonds provide a modular platform where a series of materials can be accessed from a single polymeric feedstock through the variation of the metal ion used. A series of dLCPs were prepared by the addition of metal salts to a telechelic 2,6‐bisbenzimidazolylpyridine (Bip) ligand endcapped LCP to form metallosupramolecular liquid crystal polymers (MSLCPs). The resulting MSLCPs were found to phase separate into hard and soft phases which aids in their mechanical robustness. Variations of the metal salts used to access these materials allowed for control of the thermomechanical, viscoelastic, and adhesive properties with relaxations that can be tailored independently of the mesogenic transition. This work demonstrates that by accessing phase separation through the incorporation of metallosupramolecular moieties, highly processable yet robust MSLCP materials can be realized. This class of materials opens the door to LCPs with bulk flow behavior that can also be utilized as multi‐level adhesives.
Associative polymers with controlled sticker placement: How reversible bond distribution and density govern polymer dynamics
Associative polymers with precisely arranged stickers offer opportunities to program material properties with molecular precision. Yet, it remains unclear how the placement and fraction of stickers dictate structure, dynamics, and macroscopic properties. By developing a model unentangled polymer system with hydrogen-bonding stickers, we show that randomly distributed stickers neither form clusters nor change flow properties, whereas stickers placed at chain ends drive nanocluster formation even at low concentrations. Adding more end stickers produces a rubbery plateau spanning eight decades in frequency with two distinct relaxation timescales, in contrast to the single plateau predicted by the classic sticky Rouse model. These results demonstrate that sticker distribution dictates whether associative polymers undergo nanocluster formation or microphase separation, while substantial alterations in dynamics and viscoelasticity require both sticker aggregation and thermomechanical stability of associated domains. Our findings resolve a longstanding debate on associative polymer dynamics and provide molecular design rules for programmable soft materials.
Rheological and Structural Properties of k‐Carrageenan/Xanthan Gum Gummies Architected With a New Natural Additive
ABSTRACT Biohybrids (BHs)based on bentonite and anthocyanins can be produced as alternatives to synthetic colorants. However, no information is available on the interaction of biohybrid with food system. This research studies the rheological properties of gummies containing k‐carrageenan and xanthan gum incorporated with a BH. The incorporation of BH (≤ 2% w/w) increased the flow consistency index and shear thinning effect in melted gummies at 85°C. During cooling from 90°C to 25°C, the presence of BH altered the sol–gel transition temperature typical in carrageenan systems, probably by the formation of carrageenan complexes. At 25°C, all gummies had a solid‐like response with elastic modulus ( G ') higher than viscous modulus ( G "). G ' values increased linearly with BH concentration, and the linear viscoelastic region and breaking strain decreased with BH concentration, indicating that this natural additive acted as a reinforcing material.
Dynamic Binary Complexes (DBC) as Super-Adjustable Viscosity Modifiers for Hydraulic Fracturing Fluids
In the preceding project year two, we refined three DBC formulations from a selection of over 50 different chemistries. The optimization study primarily encompassed testing for (i) reversibility extent, (ii) performance in the presence of chemical additives, (iii) adhesion and friction behavior during displacement in wellbores and pipelines, (iv) corrosion protection performance, and (v) injection performance with model fracture systems at the laboratory scale. Highly promising results obtained from all these tests signify the significant potential of DBCs in enhancing hydrocarbon recovery from unconventional reservoirs. The primary activities in the third project year included publishing experimental findings across multiple articles and conducting outreach initiatives. Throughout the year, we undertook tasks such as replicating experimental results, further optimizing various formulations and their associated experimental sets, and conducting additional tests to address missing components based on reviewer feedback and suggestions. We also explored the surfactant and friction-reduction aspects of selected formulations through drag reduction tests. In addition, we constructed an improved fracturing performance setup and performed flow injection tests. The specific DBC formulations focused on during this project period were A8/B1, A12/B5, and A10/B12. We also obtained results for additional DBC formulations and a select few commercial fracturing fluids for the purpose of comparison. Within the project's scope, we aim to enhance the experimental findings with the development of various models. The first two years focused on two key aspects: (i) the creation of a high-fidelity hydraulic fracturing model for non-Newtonian fluids to gain insights into the implementation of DBC fluids in fracking environments, and (ii) the development of a multiphase flow simulator for estimating total production, fluid saturation in the reservoir, and the creation of a fracture propagation model and kinetic Monte Carlo (kMC) models for diverse applications. In the third year, we delved into the fundamental nanostructural properties of DBCs, exploring aspects such as material chemistry, pH tunability, and control of DBC formation and stability. Subsequently, in the extension year, we conducted a systematic investigation of various building blocks containing primary, secondary, and tertiary amine functional groups to understand their impact on rheological and viscoelastic properties. Furthermore, we explored a Dissipative Particle Dynamics (DPD) model to simulate self-assembly processes with precision, creating a high-fidelity representation of relevant nanostructures. The tasks performed this year with the significant results obtained have been discussed in Section 2.