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Predicting the response of complex fluids to different flow conditions has been the focal point of rheology and is generally done via constitutive relations. There are, nonetheless, scenarios in which not much is known from the material mathematically, while data collection from samples is elusive, resource-intensive, or both. In such cases, meta-modeling of observables using a parametric surrogate model called multi-fidelity neural networks (MFNNs) may obviate the constitutive equation development step by leveraging only a handful of high-fidelity (Hi-Fi) data collected from experiments (or high-resolution simulations) and an abundance of low-fidelity (Lo-Fi) data generated synthetically to compensate for Hi-Fi data scarcity. To this end, MFNNs are employed to meta-model the material responses of a thermo-viscoelastic (TVE) fluid, consumer product Johnson’s® Baby Shampoo, under four flow protocols: steady shear, step growth, oscillatory, and small/large amplitude oscillatory shear (S/LAOS). In addition, the time–temperature superposition (TTS) of the material response and MFNN predictions are explored. By applying simple linear regression (without induction of any constitutive equation) on log-spaced Hi-Fi data, a series of Lo-Fi data were generated and found sufficient to obtain accurate material response recovery in terms of either interpolation or extrapolation for all flow protocols except for S/LAOS. This insufficiency is resolved by informing the MFNN platform with a linear constitutive model (Maxwell viscoelastic) resulting in simultaneous interpolation and extrapolation capabilities in S/LAOS material response recovery. The roles of data volume, flow type, and deformation range are discussed in detail, providing a practical pathway to multifidelity meta-modeling of different complex fluids.

 

Colloidal gelation phase diagram has been traditionally characterized using three key factors: particle volume fraction, strength of attraction, and range of attraction. While there's a rich body of literature on the role of attraction strength and particle volume fraction, majority of studies have been limited to short range interactions. Using Brownian dynamics simulations, we explored the effect that the range of attractions has on the microstructure and dynamics of both weakly and strongly attractive colloidal systems. Although gelation occurs significantly faster at high attraction strength, by an order of magnitude compared to low strength, we did not observe any clear trend in gelation-rate with respect to a change in the range of interaction. However, as the attraction range increases in both systems, the final structure undergoes a transition from a single connected network to a fluid of dense clusters. This results in a new gelation phase boundary for long range attractive colloids.

 

 

The ability to concisely describe the dynamical behavior of soft materials through closed-form constitutive relations holds the key to accelerated and informed design of materials and processes. The conventional approach is to construct constitutive relations through simplifying assumptions and approximating the time- and rate-dependent stress response of a complex fluid to an imposed deformation. While traditional frameworks have been foundational to our current understanding of soft materials, they often face a twofold existential limitation: i) Constructed on ideal and generalized assumptions, precise recovery of material-specific details is usually serendipitous, if possible, and ii) inherent biases that are involved by making those assumptions commonly come at the cost of new physical insight. This work introduces an approach by leveraging recent advances in scientific machine learning methodologies to discover the governing constitutive equation from experimental data for complex fluids. Our rheology-informed neural network framework is found capable of learning the hidden rheology of a complex fluid through a limited number of experiments. This is followed by construction of an unbiased material-specific constitutive relation that accurately describes a wide range of bulk dynamical behavior of the material. While extremely efficient in closed-form model discovery for a real-world complex system, the model also provides insight into the underpinning physics of the material.

 

Colloidal gels exhibit solid-like behavior at vanishingly small fractions of solids, owing to ramified space-spanning networks that form due to particle–particle interactions. These networks give the gel its rigidity, and with stronger attractions the elasticity grows as well. The emergence of rigidity can be described through a mean field approach; nonetheless, fundamental understanding of how rigidity varies in gels of different attractions is lacking. Moreover, recovering an accurate gelation phase diagram based on the system’s variables has been an extremely challenging task. Understanding the nature of colloidal clusters, and how rigidity emerges from their connections is key to controlling and designing gels with desirable properties. Here, we employ network analysis tools to interrogate and characterize the colloidal structures. We construct a particle-level network, having all the spatial coordinates of colloids with different attraction levels, and also identify polydisperse rigid fractal clusters using a Gaussian mixture model, to form a coarse-grained cluster network that distinctly shows main physical features of the colloidal gels. A simple mass-spring model then is used to recover quantitatively the elasticity of colloidal gels from these cluster networks. Interrogating the resilience of these gel networks shows that the elasticity of a gel (a dynamic property) is directly correlated to its cluster network’s resilience (a static measure). Finally, we use the resilience investigations to devise [and experimentally validate] a fully resolved phase diagram for colloidal gelation, with a clear solid–liquid phase boundary using a single volume fraction of particles well beyond this phase boundary. 

Rheology-informed neural networks (RhINNs) have recently been popularized as data-driven platforms for solving rheologically relevant differential equations. While RhINNs can be employed to solve different constitutive equations of interest in a forward or inverse manner, their ability to do so strictly depends on the type of data and the choice of models embedded within their structure. Here, the applicability of RhINNs in general, and the interplay between the choice of models, parameters of the neural network itself, and the type of data at hand are studied. To do so, a RhINN is informed by a series of thixotropic elasto-visco-plastic (TEVP) constitutive models, and its ability to accurately recover model parameters from stress growth and oscillatory shear flow protocols is investigated. We observed that by simplifying the constitutive model, RhINN convergence is improved in terms of parameter recovery accuracy and computation speed while over-simplifying the model is detrimental to accuracy. Moreover, several hyperparameters, e.g., the learning rate, activation function, initial conditions for the fitting parameters, and error heuristics, should be at the top of the checklist when aiming to improve parameter recovery using RhINNs. Finally, the given data form plays a pivotal role, and no convergence is observed when one set of experiments is used as the given data for either of the flow protocols. The range of parameters is also a limiting factor when employing RhINNs for parameter recovery, and ad hoc modifications to the constitutive model can be trivial remedies to guarantee convergence when recovering fitting parameters with large values.

 

Developing constitutive models that can describe a complex fluid’s response to an applied stimulus has been one of the critical pursuits of rheologists. The complexity of the models typically goes hand-in-hand with that of the observed behaviors and can quickly become prohibitive depending on the choice of materials and/or flow protocols. Therefore, reducing the number of fitting parameters by seeking compact representations of those constitutive models can obviate extra experimentation to confine the parameter space. To this end, fractional derivatives in which the differential response of matter accepts non-integer orders have shown promise. Here, we develop neural networks that are informed by a series of different fractional constitutive models. These fractional rheology-informed neural networks (RhINNs) are then used to recover the relevant parameters (fractional derivative orders) of three fractional viscoelastic constitutive models, i.e., fractional Maxwell, Kelvin-Voigt, and Zener models. We find that for all three studied models, RhINNs recover the observed behavior accurately, although in some cases, the fractional derivative order is recovered with significant deviations from what is known as ground truth. This suggests that extra fractional elements are redundant when the material response is relatively simple. Therefore, choosing a fractional constitutive model for a given material response is contingent upon the response complexity, as fractional elements embody a wide range of transient material behaviors.

 

Yielding of the particulate network in colloidal gels under applied deformation is accompanied by various microstructural changes, including rearrangement, bond rupture, anisotropy, and reformation of secondary structures. While much work has been done to understand the physical underpinnings of yielding in colloidal gels, its topological origins remain poorly understood. Here, employing a series of tools from network science, we characterize the bonds using their orientation and network centrality. We find that bonds with higher centralities in the network are ruptured the most at all applied deformation rates. This suggests that a network analysis of the particulate structure can be used to predict the failure points in colloidal gels a priori.