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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

SignificanceScience-based data-driven methods that can describe the rheological behavior of complex fluids can be transformative across many disciplines. Digital rheometer twins, which are developed here, can significantly reduce the cost, time, and energy required to characterize complex fluids and predict their future behavior. This is made possible by combining two different methods of informing neural networks with the rheological underpinnings of a system, resulting in quantitative recovery of a gel's response to different flow protocols. The platform developed here is general enough that it can be extended to areas well beyond complex fluids modeling.