Session Q35: Emerging Trends in Soft Microscale Mechanics III

in situ gelation of alginate in microchannel flows: gel properties determine deposition efficiency

Polymer flows through pores, nozzles and other small channels govern engineered and naturally occurring dynamics in many processes, from 3D printing to oil recovery in the earth's subsurface to a wide variety of biological flows. The crosslinking of polymers can change their material properties dramatically. In engineered flows, polymer crosslinking is often a situation to be avoided. For instance, in 3D printing it is greatly preferred for crosslinking to occur upon impact with a substrate rather than prior to exiting a nozzle. In blood flow, however, polymer crosslinking can either be advantageous, as in wound healing, or pathological, as in thromboembolism formation. In either of these situations, and others, it is advantageous to know a priori whether or not crosslinking polymers will lead to clogged channels or cessation of flow. In this study, we investigate the flow of a common biopolymer, alginate, while it undergoes crosslinking by the addition of a crosslinker, calcium, driven through a microfluidic channel at constant flow rate. While quantifying the limits on flowability and clogging in situ in this crosslinking polymer system, we observe a remarkable phenomenon in which the crosslinked polymer intermittently clogs the channel. We observe a pattern of deposition and removal of a crosslinked gel that is simultaneously highly reproducible, long-lasting and controllable by a variety of parameters. We map this behavior as a function of flow rate, polymer concentration, and crosslinker concentration, measuring the time-dependence of pressure that results from deposition and ablation. An analytical model of the diffusive boundary layer reasonably fits the pressure traces, suggesting that deposition is driven by a balance of diffusion and convection. Interestingly, the model suggests that deposition occurs more efficiently in regions of the phase diagram where gels are stiffer. Further, fractal analysis of the roughness of the pressure traces suggests that the route to failure, i.e. complete clogging of the channel, is signaled by a transition to non-linear dynamics, despite the fact that the flows are at low Reynolds number. This observation suggests intruguing possibilities for use of pressure traces to diagnose, and even predict, failure in crosslinking polymer flows.   

Shear-induced dynamical heterogeneities in soft particle glasses

Soft particle glasses (SPGs), which are jammed beyond the random close-packing fraction of equivalent hard spheres, show rich rheology under shear flow. These yield stress fluids show weak elastic solid response at low stresses and flow according to the Herschel-Bulkley behavior. In this work, we use our particle dynamics numerical method to unravel the interrelation between the softness, size distribution, volume fraction of the particles, and strength of the flow on the microscopic dynamics and rheology of SPGs using computational techniques. Results show that shear transformation zones in the form of domains with relatively high nonaffine displacement appear, grow, and then disappear at low shear rates close to the dynamic yield stress limit. This repeated cycle gives rise to the flow at low shear rates. On the other hand, the dynamics of the particles at high shear rates become localized, and small pockets of particles with high mobility appear and disappear periodically. We will demonstrate that there is a unique timescale set by the ratio of the solvent viscosity and shear modulus of the suspensions which controls the transition between these two limits and flow behavior in the yield stress fluids. Thus, a direct relationship between the microscopic dynamics and macroscopic rheology of SPGs will be established.   

Effect of Mechanical aging on the dynamics of soft particle glasses in start-up flow

Soft Particle Glasses (SPGs) are concentrated suspensions jammed above their close-packed volume fraction. Prior experiments show that the mechanical history of these pastes affects their rheology in start-up flow. In this study, particle dynamics simulations are used to determine the effect of the pre-shearing conditions on the dynamics of suspensions in start-up shear flow. Our results show that the SPGs with significant internal stress retain their memory with a perceptible decrease in the magnitude of their yield stress, while this behavior is less pronounced at stresses close to the dynamic yield point. Also, the microscopic dynamics of these particles are strongly influenced by the directionality of the pre-shear and the magnitude of the shear rate. Detailed analyses of mean squared displacement and intermediate scattering function of suspensions over a wide range of shear rates and volume fractions will be used to determine the microdynamics of SPGs. In summary, our results will provide a linkage between mechanical aging, in the form of the pre-shearing conditions, softness of particles, and flow strength with the macroscopic rheology of SPGs.    

Extensional Rheology of Exopolysaccharide Solutions and Extensional Thinning Yield Stress Fluids

 Many commercial formulations that appear to flow only beyond a critical stress value are classified as yield stress fluids. Despite the wide availability and applications of such fluids, characterization of their response to extensional stresses and flows. We investigate the flow characteristics of extruded filaments and by analyzing the transition from solid to liquid in a neck and subsequent pinching dynamics, we characterize the extensional yield stress and response after yielding. The neck shapes, radius evolution as a function of time, and shape and size of dispensed drops are characterized and analyzed for prototypical yield stress fluids formulated by using densely packed microgels, particles, drops or macromolecules. We seek a deeper appreciation of the diversity in response as influenced by microstructure   

Microscopic theory of elasticity and yielding in ultra-dense attractive glass forming suspensions

The combined consequences of repulsive force caging and short-range attractions that induce physical bonds on the linear elastic, structural relaxation, and nonlinear rheological properties of ultra-dense colloidal suspensions and glasses remain an outstanding challenge to theoretically understand at a microscopic level. Questions of interest include glass melting and re-entrancy, non-monotonic evolution of the elastic modulus with attraction strength, and two-step versus one step yielding. We have analyzed these problems under quiescent conditions and in the presence of external forces (with and without deformation-induced structural changes) over a wide range of attraction strengths and spatial ranges with ideal Mode Coupling theory and the Elastically Collective Nonlinear Langevin Equation theory that includes coupled local activated hopping and longer range collective elasticity. The consequences of explicitly treating strong attractive forces, versus only indirectly via changes of pair structure, have also been determined. We find deformation-induced structural evolution, explicit treatment of attractive forces, and activated relaxation are of critical importance in ultra-dense attractive glass forming colloids. Comparisons are made with experimental and simulation studies.   

High-speed three-dimensional measurement of dynamics of colloidal membranes using dielectric tensor holographic tomography

A colloidal membrane is one rod-length thick fluid monolayer that spontaneously assembles in presence of non-adsorbing polymer [1]. Including the transformation from a flat 2D colloidal membrane to an edgeless 3D colloidal vesicle, colloidal membranes undergo a range of remarkable morphological and topological shape changes, yet quantitative insight into such dynamics is limited due to the limitations of the existing imaging techniques. Here, we present a study on non-equilibrium dynamics of colloidal membranes by employing dielectric tensor tomography (DTT) [2]. By recording diffracted light from colloidal membranes for various illumination angles, the principles of DTT enables the reconstructing of the 3D tomograms of directors and principal refractive indices with high temporal resolution without fluorescence labeling or the mechanical scanning for 3D imaging. Using the technique, we investigated the forming and closing dynamics of transient pores on colloidal vesicles in response to changing osmotic pressure, and the orientational change of constituent rod particles around the pore. [1] Sharma P, et al. "Hierarchical organization of chiral rafts in colloidal membranes." Nature 513.7516 (2014): 77-80 [2] Shin S, et al. "Tomographic measurement of dielectric tensors at optical frequency." Nature Materials 21 (2022): 317-324   

Colloidal network formation and evolution during gelation and coarsening

The gelation of attractive colloidal particles forms a space-spanning network, transforming a fluid-like suspension into a viscoelastic solid. The process begins with the formation of reversible particle-particle bond formation, characterized by interaction energy and percolation of the particulate structure, followed by long-term structure coarsening. Understanding these steps in this second-order phase transition is crucial for optimizing gel properties. However, pinpointing precise transition points remains a significant research gap. Using network science tools, we analyze the structural evolution during gelation. Findings indicate that the critical percolation point, marking the first transition phase, can be accurately estimated through network diameter analysis. This is in contrast with the modulus measurements that may or may not be able to pinpoint the percolation transition. Additionally, particle-level characteristics, like coordination number, exhibit distinct transitions before and after coarsening. This differentiation enables a clear identification of the initial sol-gel transition from the subsequent stage of maturation and coarsening. Additionally, we offer a comprehensive comparative analysis across varying attraction strength levels and volume fractions.   

Stress Distributions in Soft Particle Glasses: Insights from a Thermodynamic Model

Jammed suspensions of soft particle glasses (SPGs) exhibit intriguing rheological response under different shear flows, such as stress overshoot in start-up shear and Herschel-Bulkley behavior in steady shear. However, the fundamental link between microscopic processes and macroscopic (bulk) behavior remains elusive. To address this, we employ large-scale 3d simulations of model SPGs to study the impact of shear-induced microstructural rearrangements on particle stress distributions. These rearrangements cause significant changes in stress distribution, consequently influencing the overall stress and bulk rheology of the system. The characteristics of stress distribution, including its width and peak, are found to be influenced by factors such as particle volume fraction, applied shear rate, and system history. Building upon previous works, we introduce a thermodynamic model that offers insights into the particle stress distribution in SPGs, providing a microscopic basis for understanding bulk rheology. Furthermore, we present a self-consistent model based on the advection-diffusion equation, which describes the evolution of particle stress distribution in SPGs under steady shear. Our findings emphasize the importance of stress distributions in elucidating bulk rheology and highlight the utility of thermodynamics as a valuable tool for modelling these complex materials.   

Universal Scaling of Shear Thickening Suspensions Under Acoustic Perturbation

Nearly all dense suspensions undergo dramatic and abrupt thickening transitions in their flow behavior when sheared at high stresses. Such transitions occur when suspended particles come into frictional contact with each other to form structures that resist the flow. These frictional contacts can be disrupted with acoustic perturbations, thereby lowering the suspension's viscosity. Acoustic perturbations offer a convenient way to control the suspension's shear thickening behavior in real time, as the suspension responds to the perturbation nearly instantaneously. Here, we fold these acoustic perturbations into a universal scaling framework for shear thickening, in which the viscosity is described by a crossover scaling function from the frictionless jamming point to a frictional shear jamming critical point. We test this theory on sheared suspensions with acoustic perturbations and find experimentally that the data for all shear stresses, volume fractions, and acoustic powers can be collapsed onto a single universal curve. Within this framework, a scaling parameter that is a function of stress, volume fraction and acoustic power determines the proximity of the system to the frictional shear jamming critical point and ultimately the viscosity. Our results demonstrate the broad applicability of the scaling framework, its utility for experimentally manipulating the system, and open the door to importing the vast theoretical machinery developed to understand equilibrium critical phenomena to elucidate fundamental physical aspects of the non-equilibrium shear thickening transition.   

Damage propagation in Architected-Interfaces

This study tackles the intricate task of modeling heterogeneous and architected materials, necessitating advanced homogenization techniques. In simplifying this challenge, we leverage micropolar elasticity. Simultaneously, elastic foundation theory is widely applied in fracture mechanics and delamination analysis of composite materials. The objective is to seamlessly integrate these frameworks, refining elastic foundation theory to accommodate materials exhibiting micropolar behavior. Our elastic foundation theory for micropolar materials employs a stress potentials formulation, leading to closed-form solutions for stress and couple stress reactions, including the associated restoring stiffness. Additionally, we delve into the mechanical properties of conceptual structural adhesive joints, where the adhesive function is assumed by an architected interface. Diverging from isotropic interfaces, architected interfaces exert control over properties through tailored microstructures. To augment existing theoretical frameworks, we introduce our elastic foundation theory, encompassing emerging micromechanical effects. Illustrating how characteristic lengths govern the Mode I fracture behavior of architected interfaces, we assert control over the fracture process zone size. Our findings, validated through numerical simulations, underscore the effectiveness of the proposed method.   

Position Control and Detection of Domain Wall in Multi-stable Metamaterial

In this presentation, we consider the dynamics of a domain wall (i.e., transition wavefront) in a multi-stable metamaterial on an elastic substrate. Under strain, the position of a transition wavefront can be precisely controlled, and then remotely determined. As an application, we propose a mechanical multi-level (i.e., high-density) memory device. Position control is achieved by a (strain-)tunable potential energy landscape that conveys the wavefront from one stabilizing defect site to another. Position determination is achieved by leveraging the distinct linear dynamics of the domains on either side of the wavefront: a harmonic wave injected with a frequency transparent in one domain will not pass into the opposing opaque domain, instead returning the with a time delay consistent with the wavefront position. In general, we anticipate that the concepts presented here toward a command of the transition wave position will enhance the development and applicability of transition waves in multi-stable metamaterials.   

Reflexes turn active metamaterials into robots

Materials composed of energy-generating constituents such as active matter and distributed robots are promising platforms to create autonomous functional materials. However, the control of such materials is typically achieved using feed-forward schemes, which do not work well in unpredictable environments and in under-actuation scenarios. Here, we introduce active metamaterials with a minimal feedback control that both exhibit unusual non-reciprocal responses and display adaptable and autonomous robotic locomotion. Inspired by reflex actions in animals and robots, we create metamaterials with translation-invariant reflex control, in which the active forces exerted are dependent on strains at neighboring sites. We demonstrate experimentally that these odd elastic materials are able to roll or crawl uphill and in complex terrains. Integrating reflexes in metamaterials opens avenues towards animate matter with autonomous, adaptable and interactive functionalities.   

Representation Theory for Wave Propagation through Buckled Phononic Crystals

Elastic Phononic Crystals (EPC) are soft deformable metamaterials that have periodic modulations in material properties such as shear modulus, bulk modulus, and density, whose microstructure is characterized by a repeatable region called the unit cell. The dispersion relation, described by band diagrams, of waves propagating through phononic crystals is affected not only by material properties but also by symmetry properties of the crystal. It has been shown that buckling of compressed phononic crystals could tune wave propagation properties – for example, by decreasing the number of intersections (degeneracies) in the band diagram, potentially leading to the opening of band gaps. In our previous work, we used a group representation theory (GRT)-based framework to explain the effect of primitive unit cell symmetries on degeneracies in the band diagram for undeformed EPCs. In this work, we extend our GRT framework to include the effect of deformation- and buckling-induced symmetry-breaking on wave propagation. We find that degeneracies in the post-buckling band diagrams can be explained by the symmetries of the stress distribution that characterize the post-buckling crystal and the effect of compression on non-primitive unstressed unit cells that are used to capture post-buckling behavior. We then have the potential to predict how different loading paths affect symmetry and hence wave propagation properties, which would be helpful for the rational design of deformation tunable EPCs.   

Predicting stress propagation in two-dimensional mechanical metamaterials using graph theory

In materials with extensive percolation networks, the mechanical properties are dependent on both connectivity patterns and material properties. Interplay of local and global mechanics of the network as well as the correlation between topology, dynamic stress transmission and failure behavior make it difficult to predict mechanical responses. For the case of impact, global descriptors such as elastic modulus and density define the acoustic wave speed but are not sufficient to describe how stresses propagate locally within a discretized material. In addition, current predictive numerical approaches can be inefficient. Therefore, new tools that can accurately and efficiently predict the location and the magnitude of stresses in ordered and disordered systems are needed.  Here, we use graph theory (GT) as a general methodology to describe mechanical metamaterials as sets of nodes (n) and edges (e) to predict the propagation and magnitude of stresses. Our experimental platform is based on macroscale 2D samples tested in quasistatic and dynamic conditions. High-speed polarized videography is used to characterize stress propagation and the data is compared against GT predictions and Finite Element models (FEM). We show that predictions of deformations closely matching experiments are achieved when classical GT parameters are modified to include geometric information that is usually ignored. We use these insights to propose stress wave management strategies in architected strut-based materials.   

3D phase space geometry of wave-defect interaction in bistable mechanical lattices in the presence of radiation damping

The fate of a solitary wave propagating in a bistable mechanical lattice can be tailored using a local inhomogeneity (`defect'). The defect gives rise to a localized oscillatory mode (`breather'). The resulting wave-breather dynamics were studied in our prior work, where we derived a 2 degrees-of-freedom reduced-order Hamiltonian model, and analyzed the system using the methods of lobe dynamics. The lobe dynamics analysis showed that depending upon its initial speed, an incoming solitary wave can get transmitted, reflected, or temporarily captured upon interaction with the defect. In the current work, we modify the reduced-order model to include the loss of energy in the two localized degrees-of-freedom to the dispersive modes (`phonons'), a phenomenon known as `radiation damping'. We employ the framework of (partial) Lagrangian Coherent Structures (LCS) in the resulting 3D non-Hamiltonian system to compute 2D transport barriers in the phase space. We demonstrate that these 2D LCS can be used to perform lobe dynamics computations. These computations give a more accurate delineation of initial conditions that lead to the different fates for the incoming wave, and provide an insight into wave control strategies. This research represents a step forward in establishing a systematic approach to defect engineering for manipulating nonlinear waves in mechanical metamaterials.