Designing Complex Fluids
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Ewoldt, Randy H.↗
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nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling
Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. Here, in this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.
42 ENGINEERING↗
Conjugated Polyelectrolyte-Based Complex Fluids as Aqueous Exciton Transport Networks
The ability to assemble artificial systems that mimic aspects of natural light-harvesting functions is fascinating and attractive for materials design. Given the complexity of such a system, a simple design pathway is desirable. Here, we argue that associative phase separation of oppositely charged conjugated polyelectrolytes (CPEs) can provide such a path in an environmentally benign medium: water. We find that complexation between an exciton–donor and acceptor CPE leads to formation of a complex fluid. We interrogate exciton transfer from the donor to the acceptor CPE within the complex fluid and find that transfer is highly efficient. We also find that excess molecular ions can tune the modulus of the inter-CPE complex fluid. Even at high ion concentrations, CPEs remain complexed with significantly delocalized electronic wavefunctions. In conclusion, our work lays the rational foundation for complex, tunable aqueous light-harvesting systems via the intrinsic thermodynamics of associative phase separation.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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.
Science & Technology - Other Topics↗
Optical tweezer measurements of asymptotic nonlinearities in complex fluids
This article presents micro-medium-amplitude oscillatory shear (μMAOS), a method to measure the frequency-dependent micromechanical properties of soft materials in the asymptotically nonlinear regime using optical tweezers. For this work, we have developed a theoretical framework to extract these nonlinear mechanical properties of the material from experimental measurements and also proposed a physical interpretation of the third-order nonlinearities measured in single-tone oscillatory tests. We validate the method using a well-characterized surfactant solution of wormlike micelles, and subsequently employ this technique to demonstrate that the cytoplasm of a living cell undergoes strain softening and shear thinning when locally subjected to weakly nonlinear oscillatory deformations.
59 BASIC BIOLOGICAL SCIENCES↗
Complex Fluid‐Driven Fractures Caused by Crack‐Parallel Stress
Abstract Managing fluid‐driven fracture networks is crucial for subsurface resource utilization, yet the current understanding of the key controlling factors remains insufficient. While geologic discontinuities have been shown to significantly influence fracture network complexity, this study identifies another major contributor. We conducted a new set of experiments using a transparent true triaxial cell, which enabled video recording of the temporal evolution of fluid‐driven fracture paths. Using pseudo‐2D samples without macroscale structural discontinuities, we observed multiple occurrences of hydraulic fracture curving and branching under anisotropic boundary stresses. We proposed a theoretical model demonstrating that the stress parallel to the crack line in the solid matrix near the crack tip (i.e., the T ‐stress) accounts for the observed fracture curving behavior. This finding suggests that T ‐stress is an additional mechanism contributing to the complexity of fluid‐driven fracture networks in the subsurface, besides the geologic discontinuities.
58 GEOSCIENCES↗
Lie–Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries
An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie–Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie–Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie–Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.
Data-based modeling↗
Anticipating gelation and vitrification with medium amplitude parallel superposition (MAPS) rheology and artificial neural networks
Abstract Anticipating qualitative changes in the rheological response of complex fluids (e.g., a gelation or vitrification transition) is an important capability for processing operations that utilize such materials in real-world environments. One class of complex fluids that exhibits distinct rheological states are soft glassy materials such as colloidal gels and clay dispersions, which can be well characterized by the soft glassy rheology (SGR) model. We first solve the model equations for the time-dependent, weakly nonlinear response of the SGR model. With this analytical solution, we show that the weak nonlinearities measured via medium amplitude parallel superposition (MAPS) rheology can be used to anticipate the rheological aging transitions in the linear response of soft glassy materials. This is a rheological version of a technique called structural health monitoring used widely in civil and aerospace engineering. We design and train artificial neural networks (ANNs) that are capable of quickly inferring the parameters of the SGR model from the results of sequential MAPS experiments. The combination of these data-rich experiments and machine learning tools to provide a surrogate for computationally expensive viscoelastic constitutive equations allows for rapid experimental characterization of the rheological state of soft glassy materials. We apply this technique to an aging dispersion of Laponite ® clay particles approaching the gel point and demonstrate that a trained ANN can provide real-time detection of transitions in the nonlinear response well in advance of incipient changes in the linear viscoelastic response of the system.
Lennon, Kyle R. (ORCID:0000000212515461)↗
Robotic pendant drop: containerless liquid for μs-resolved, AI-executable XPCS
Abstract The dynamics and structure of mixed phases in a complex fluid can significantly impact its material properties, such as viscoelasticity. Small-angle X-ray Photon Correlation Spectroscopy (SA-XPCS) can probe the spontaneous spatial fluctuations of the mixed phases under various in situ environments over wide spatiotemporal ranges (10 −6 –10 3 s /10 −10 –10 −6 m). Tailored material design, however, requires searching through a massive number of sample compositions and experimental parameters, which is beyond the bandwidth of the current coherent X-ray beamline. Using 3.7-μs-resolved XPCS synchronized with the clock frequency at the Advanced Photon Source, we demonstrated the consistency between the Brownian dynamics of ~100 nm diameter colloidal silica nanoparticles measured from an enclosed pendant drop and a sealed capillary. The electronic pipette can also be mounted on a robotic arm to access different stock solutions and create complex fluids with highly-repeatable and precisely controlled composition profiles. This closed-loop, AI-executable protocol is applicable to light scattering techniques regardless of the light wavelength and optical coherence, and is a first step towards high-throughput, autonomous material discovery.
36 MATERIALS SCIENCE↗
Analytical EOS Formulation Progress on developing a complete EOS formulation for approximating complex reacting fluids
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Mace, Jonathan Lee↗
Supercritical fluids behave as complex networks
Abstract Supercritical fluids play a key role in environmental, geological, and celestial processes, and are of great importance to many scientific and engineering applications. They exhibit strong variations in thermodynamic response functions, which has been hypothesized to stem from the microstructural behavior. However, a direct connection between thermodynamic conditions and the microstructural behavior, as described by molecular clusters, remains an outstanding issue. By utilizing a first-principles-based criterion and self-similarity analysis, we identify energetically localized molecular clusters whose size distribution and connectivity exhibit self-similarity in the extended supercritical phase space. We show that the structural response of these clusters follows a complex network behavior whose dynamics arises from the energetics of isotropic molecular interactions. Furthermore, we demonstrate that a hidden variable network model can accurately describe the structural and dynamical response of supercritical fluids. These results highlight the need for constitutive models and provide a basis to relate the fluid microstructure to thermodynamic response functions.
42 ENGINEERING↗
Transforming Energy Through Computational Excellence: NREL Computational Fluid Dynamics Modeling Complex, Dynamic Systems
Computational fluid dynamics (CFD) enables modeling, analysis, and visualization of phenomena that would usually be impossible or extremely expensive to measure experimentally.
97 MATHEMATICS AND COMPUTING↗
Bayesian estimations of orientation distribution functions from small-angle scattering enable direct prediction of mechanical stress in anisotropic materials
Properties of soft materials are influenced by their anisotropic structuring under nonequilibrium fields. Although anisotropic structure-property relationships have been extensively explored theoretically, comparison to experiments requires determination of the microstructural orientation probability distribution function (OPDF) of microstructural elements. Small angle scattering (SAS) measurements encode information about the OPDF, but tools to navigate this connection are incomplete. Here, we develop and validate an explicit framework to link arbitrary OPDFs to SAS measurements. Specifically, we propose, validate, and apply a method, maximum a posteriori scattering inference (MAPSI), whereby the OPDF may be obtained from SAS measurements using a Bayesian estimation method. Using this method, we obtain estimates of the full 3D OPDF for two model semidilute fd-virus (rodlike) dispersions at concentrations that are approximately equal to and twice the overlap concentration. From the OPDF, we calculate its second and fourth moments and compare these to predictions for a dilute suspension of rigid rods and to a recent theory for semidilute suspensions. Finally, we use both the theoretical and measured moments to calculate the stress, both for dilute and semidilute suspensions. These predictions are not only compared to each other, but also to measured values of the shear stress, and point to new insights into the behavior of suspensions of highly elongated particles in the transition between dilute and semidilute behavior. We also use this new framework to provide perspective on the connection between scalar parameterizations of scattering and the OPDF that have frequently been used in the past. Here, the new tools developed in this work provide an unprecedented path toward experimental validation of dynamical theories of rodlike colloids and polymers, and for measurement of nonequilibrium structures and stresses of other complex fluids and soft materials with SAS.
36 MATERIALS SCIENCE↗
Heterogeneous Dynamics in Shear Thickening Colloids Revealed by Intrinsic Heterodyne Correlation Spectroscopy
Shear induced frictional networks have been proposed to be responsible for the emergence of discontinuous shear thickening (DST) in complex fluids. However, little experimental evidence exists to support this model directly. Here, in this study, using x-ray photon correlation spectroscopy (XPCS), we show the existence of an intrinsic heterodyne feature during shear cessation, which originates from the relative motion of mobile particles against an aggregated or jammed network induced by shear thickening. Upon removing the shear, the shear stress dissipates rather quickly in a two-step fashion, whereas the heterogeneous particle dynamics persist much longer with the relative velocity decaying slowly with time as 𝑡 −1 . More importantly, both continuous shear thickening (CST) and DST show similar heterodyne features, indicating the intrinsic mechanisms causing shear thickening are similar in nature
Complex fluid↗
Evaluating Chemical Kinetics Predictions for Propane Using 3-D and 0-D Models in a Boosted Spark-Ignited Engine
Propane has been shown to be a promising alternative fuel to reduce emissions while simultaneously achieving high efficiencies in medium- and heavy-duty engines. These high-power density applications require boosted engines which, combined with high compression ratio, can lead to auto-ignition and knock. While three-dimensional (3-D) computational fluid dynamics (CFD) models are often used for resolving the complex fluid flow in engines, these models can become computationally expensive when simulating detailed chemical kinetics. Likewise, zero-dimensional (0-D) models are computationally concise enough for kinetics development, but lack any flow-field information which governs the flame propagation processes in spark ignition (SI) engines. This work presents a comprehensive comparison between 3-D and 0-D closed cycle simulations at knocking conditions in a high compression ratio high stroke-to-bore ratio propane engine. In order to initialize the flow-field for the 3-D closed cycle (intake valve closing, (IVC) to exhaust valve opening, (EVO)) simulation, a motored multi-cycle 3-D model was run using Converge to create a map at IVC, reducing the computational time. The map allowed a non-homogeneous 3-D closed cycle simulation to be satisfactorily validated against experiments, while a homogeneous case using only the turbulence field mapping was also simulated, mimicking 0-D modeling. The 3-D simulations were used to prescribe the initial conditions (e.g., IVC thermodynamics, speciation, burn-rate profile) for a 2-zone 0-D SI engine model in Chemkin Pro for both cases. It was found that 2-zone 0-D modeling underpredicted the knock onset timing, likely due to the lack of thermal stratification in the unburned gas region. Future work will carry multi-zone 0-D modeling to capture the fuel auto-ignition in the unburned region.
Douvry-Rabjeau, Julien [Oakland University, Roches↗