Unbiased construction of constitutive relations for soft materials from experiments via rheology-informed neural networks.

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.

Network physics of attractive colloidal gels: Resilience, rigidity, and phase diagram.

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.

Digital rheometer twins: Learning the hidden rheology of complex fluids through rheology-informed graph neural networks.

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.

Role of interaction range on the microstructure and dynamics of attractive colloidal systems.

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.

Small variations in particle-level interactions lead to large structural heterogeneities in colloidal gels.

Colloidal gels typically exhibit mechanical properties akin to a viscoelastic solid, influenced by their underlying particulate network. Hence, the structural and morphological characteristics of the colloidal network have a significant effect on the rigidity of the gel. In this study, we show how seemingly small variations in the particle-level interactions throughout the system result in larger scale structural heterogeneities. While the microscale particle level descriptors of the colloidal network remain largely unaffected by heterogeneous interactions, larger scale properties of a colloidal gel change appreciably. The overall cluster-level mesostructure of a colloidal gel is found to be sensitive to the small variations in the interaction potential at the particle level.

Topological origins of yielding in short-ranged weakly attractive colloidal gels.

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.

Circulating cell clusters aggravate the hemorheological abnormalities in COVID-19.

Microthrombi and circulating cell clusters are common microscopic findings in patients with coronavirus disease 2019 (COVID-19) at different stages in the disease course, implying that they may function as the primary drivers in disease progression. Inspired by a recent flow imaging cytometry study of the blood samples from patients with COVID-19, we perform computational simulations to investigate the dynamics of different types of circulating cell clusters, namely white blood cell (WBC) clusters, platelet clusters, and red blood cell clusters, over a range of shear flows and quantify their impact on the viscosity of the blood. Our simulation results indicate that the increased level of fibrinogen in patients with COVID-19 can promote the formation of red blood cell clusters at relatively low shear rates, thereby elevating the blood viscosity, a mechanism that also leads to an increase in viscosity in other blood diseases, such as sickle cell disease and type 2 diabetes mellitus. We further discover that the presence of WBC clusters could also aggravate the abnormalities of local blood rheology. In particular, the extent of elevation of the local blood viscosity is enlarged as the size of the WBC clusters grows. On the other hand, the impact of platelet clusters on the local rheology is found to be negligible, which is likely due to the smaller size of the platelets. The difference in the impact of WBC and platelet clusters on local hemorheology provides a compelling explanation for the clinical finding that the number of WBC clusters is significantly correlated with thrombotic events in COVID-19 whereas platelet clusters are not. Overall, our study demonstrates that our computational models based on dissipative particle dynamics can serve as a powerful tool to conduct quantitative investigation of the mechanism causing the pathological alterations of hemorheology and explore their connections to the clinical manifestations in COVID-19.

Structure and Dynamics of Force Clusters and Networks in Shear Thickening Suspensions.

Dense suspensions can exhibit shear thickening in response to large deformation. A consensus has emerged over the past few years on the formation of force networks, that span the entire system size, that lead to increased resistance to motion. Nonetheless, the characteristics of these networks are to a large extent poorly understood. Here, force networks formed in continuous and discontinuous shear thickening dense suspensions (CST and DST, respectively) are studied. We first show the evolution of the network formation and its topological heterogeneities as the applied stress increases. Subsequently, we identify force communities and coarse grain the suspension into a cluster network, and show that cluster-level dynamics are responsible for stark differences between the CST and DST behavior. Our results suggest that the force clusters formed in the DST regime are considerably more constrained in their motion, while CST clusters are loosely connected to their surrounding clusters.

Thixotropy and rheological hysteresis in blood flow.

Hemorheology is known to be a major diagnostic tool for many blood-altering diseases. While hemorheological measures of blood, such as the general flow curve, shear-thinning behavior, and its yield stress, are much more studied in detail, thixotropic behavior and thermokinematic memory formation in blood are less understood. Here, we study the thermokinematic memory formation in blood, resulting in a clear sensitivity to the flow history, i.e., thixotropic behavior. We also measure the thixotropic timescale for blood flow using a well-defined flow protocol. Employing a series of in silico flow loops in which the blood is subject to a sweep down/up flow, we measure and discuss the dependence of the thixotropic timescale to the concentration of fibrinogen in the plasma as the main driver of structural evolution under flow.

In silico biophysics and hemorheology of blood hyperviscosity syndrome.

Hyperviscosity syndrome (HVS) is characterized by an increase of the blood viscosity by up to seven times the normal blood viscosity, resulting in disturbances to the circulation in the vasculature system. HVS is commonly associated with an increase of large plasma proteins and abnormalities in the properties of red blood cells, such as cell interactions, cell stiffness, and increased hematocrit. Here, we perform a systematic study of the effect of each biophysical factor on the viscosity of blood by employing the dissipative particle dynamic method. Our in silico platform enables manipulation of each parameter in isolation, providing a unique scheme to quantify and accurately investigate the role of each factor in increasing the blood viscosity. To study the effect of these four factors independently, each factor was elevated more than its values for a healthy blood while the other factors remained constant, and viscosity measurement was performed for different hematocrits and flow rates. Although all four factors were found to increase the overall blood viscosity, these increases were highly dependent on the hematocrit and the flow rates imposed. The effect of cell aggregation and cell concentration on blood viscosity were predominantly observed at low shear rates, in contrast to the more magnified role of cell rigidity and plasma viscosity at high shear rates. Additionally, cell-related factors increase the whole blood viscosity at high hematocrits compared with the relative role of plasma-related factors at lower hematocrits. Our results, mapped onto the flow rates and hematocrits along the circulatory system, provide a correlation to underpinning mechanisms for HVS findings in different blood vessels.

Jamming Distance Dictates Colloidal Shear Thickening.

We report experimental and computational observations of dynamic contact networks for colloidal suspensions undergoing shear thickening. The dense suspensions are comprised of sterically stabilized poly(methyl methacrylate) colloids that are spherically symmetric and have varied surface roughness. Confocal rheometry and dissipative particle dynamics simulations show that the shear thickening strength ß scales exponentially with the scaled deficit contact number and the scaled jamming distance. Rough colloids, which experience additional rotational constraints, require an average of 1.5-2 fewer particle contacts as compared to smooth colloids, in order to generate the same ß. This is because the surface roughness enhances geometric friction in such a way that the rough colloids do not experience a large change in the free volume near the jamming point. The available free volume for colloids of different roughness is related to the deficiency from the maximum number of nearest neighbors at jamming under shear. Our results further suggest that the force per contact is different for particles with different morphologies.

Correction: Hemorheology: the critical role of flow type in blood viscosity measurements.

Correction for 'Hemorheology: the critical role of flow type in blood viscosity measurements' by Elahe Javadi et al., Soft Matter, 2021, 17, 8446-8458, DOI: 10.1039/D1SM00856K.

Hemorheology: the critical role of flow type in blood viscosity measurements.

The crucial role of the hemorheological characteristics of blood in a range of diagnoses, treatments and drug delivery mechanisms is widely accepted. Nonetheless, the literature on blood rheology remains inconclusive and sometimes even contradictory. This is in part due to natural variance of blood samples from one study to another, but also stems from fundamental differences in the consequences of the choice of rheometric flow employed. Here, and using a detailed and accurate computational scheme, we thoroughly study the role of flow type in measurement of blood viscosity. Performing these in silico measurements, we isolate the role of flow type and geometry at different hematocrit levels. We show that flow curves obtained in pressure-driven flows relevant to laminar circulatory flows deviate greatly from ones obtained in drag flow at the same hematocrit level. Our numerical platform also allows for the yield stress to be measured under quiescent conditions and without imposing any flow for different hematocrits. We discuss the scaling of the yield stress with the hematocrit level, and show that the differences in pressure vs. drag flows stem from the Red Blood Cell (RBC) orientation at different flow rates as well as the existence of a cell free layer close to the walls.

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. 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.

Alternative Frictional Model for Discontinuous Shear Thickening of Dense Suspensions: Hydrodynamics.

A consensus has emerged that a constraint to rotational or sliding motion of particles in dense suspensions under flow is the genesis of the discontinuous shear thickening (DST) phenomenon. We show that tangential fluid lubrication interactions due to finite-sized asperities on particle surfaces effectively provide these constraints, changing the dynamics of particle motion. By explicitly resolving for the surface roughness of particles, we show that, while smooth particles exhibit continuous shear thickening, purely hydrodynamic interactions in rough particles result in DST. In contrast to the frictional contact model, the hydrodynamic model predicts negative first and second normal stress differences for dense suspensions in the shear thickened state.

Multiscale Nature of Thixotropy and Rheological Hysteresis in Attractive Colloidal Suspensions under Shear.

Colloids with short range attractions self-assemble into sample-spanning structures, whose dynamic nature results in a thermokinematic memory of the deformation history, also referred to as "thixotropy." Here, we study the origins of the thixotropic effect in these time- and rate-dependent materials by investigating hysteresis across different length scales: from particle-level local measurements of coordination number (microscale), to the appearance of density and velocity fluctuations (mesoscale), and up to the shear stress response to an imposed deformation (macroscale). The characteristic time constants at each scale become progressively shorter, and hysteretic effects become more significant as we increase the strength of the interparticle attraction. There are also strong correlations between the thixotropic effects we observe at each scale.

Microstructural Rearrangements and their Rheological Implications in a Model Thixotropic Elastoviscoplastic Fluid.

We identify the sequence of microstructural changes that characterize the evolution of an attractive particulate gel under flow and discuss their implications on macroscopic rheology. Dissipative particle dynamics is used to monitor shear-driven evolution of a fabric tensor constructed from the ensemble spatial configuration of individual attractive constituents within the gel. By decomposing this tensor into isotropic and nonisotropic components we show that the average coordination number correlates directly with the flow curve of the shear stress versus shear rate, consistent with theoretical predictions for attractive systems. We show that the evolution in nonisotropic local particle rearrangements are primarily responsible for stress overshoots (strain-hardening) at the inception of steady shear flow and also lead, at larger times and longer scales, to microstructural localization phenomena such as shear banding flow-induced structure formation in the vorticity direction.

Rheological State Diagrams for Rough Colloids in Shear Flow.

To assess the role of particle roughness in the rheological phenomena of concentrated colloidal suspensions, we develop model colloids with varying surface roughness length scales up to 10% of the particle radius. Increasing surface roughness shifts the onset of both shear thickening and dilatancy towards lower volume fractions and critical stresses. Experimental data are supported by computer simulations of spherical colloids with adjustable friction coefficients, demonstrating that a reduction in the onset stress of thickening and a sign change in the first normal stresses occur when friction competes with lubrication. In the quasi-Newtonian flow regime, roughness increases the effective packing fraction of colloids. As the shear stress increases and suspensions of rough colloids approach jamming, the first normal stresses switch signs and the critical force required to generate contacts is drastically reduced. This is likely a signature of the lubrication films giving way to roughness-induced tangential interactions that bring about load-bearing contacts in the compression axis of flow.

Structural fingerprints of yielding mechanisms in attractive colloidal gels.

Core-Modified Dissipative Particle Dynamics (CM-DPD) with a modified depletion potential and full hydrodynamics description is used to study non-equilibrium properties of colloidal gels with short range attraction potentials at an intermediate volume fraction (ϕ = 0.2) under start-up shear deformation. Full structural and rheological analysis using the stress fabric tensor complemented by bond number and bond distribution evolution under flow reveals that similarly to dilute colloidal gels, flow-induced anisotropy and strain-induced stretching of bonds are present during the first yielding transition. Unlike in low volume fraction depletion gels however, a small fraction of bond dissociation is required to facilitate bond rotation at intermediate volume fractions. The strain at which structural stretching and anisotropy in bond distribution emerge coincides with the first maximum in the shear stress (first yielding transition). At higher strains, depending on flow strength, a second peak in stress signal appears which is attributed to the compaction and melting of clusters. In this work, for the first time we provide evidence that multibody hydrodynamic interactions are essential to predict the correct dynamics of depletion gels under flow, namely two-step yielding process.

Polymer-mediated nanorod self-assembly predicted by dissipative particle dynamics simulations.

Self-assembly of nanoparticles in polymer matrices is an interesting and growing subject in the field of nanoscience and technology. We report herein on modelling studies of the self-assembly and phase behavior of nanorods in a homopolymer matrix, with the specific goal of evaluating the role of deterministic entropic and enthalpic factors that control the aggregation/dispersion in such systems. Grafting polymer brushes from the nanorods is one approach to control/impact their self-assembly capabilities within a polymer matrix. From an energetic point of view, miscible interactions between the brush and the matrix are required for achieving a better dispersibility; however, grafting density and brush length are the two important parameters in dictating the morphology. Unlike in previous computational studies, the present Dissipative Particle Dynamics (DPD) simulation framework is able to both predict dispersion or aggregation of nanorods and determine the self-assembled structure, allowing for the determination of a phase diagram, which takes all of these factors into account. Three types of morphologies are predicted: dispersion, aggregation and partial aggregation. Moreover, favorable enthalpic interactions between the brush and the matrix are found to be essential for expanding the window for achieving a well-dispersed morphology. A three-dimensional phase diagram is mapped on which all the afore-mentioned parameters are taken into account. Additionally, in the case of immiscibility between brushes and the matrix, simulations predict the formation of some new and tunable structures.