Mechanical rejuvenation and over-aging of glasses is investigated through stochastic simulations of the soft glassy rheology (SGR) model. Strain- and stress-controlled deformation cycles for a wide range of loading conditions are analyzed and compared to molecular dynamics simulations of a model polymer glass. Results indicate that deformation causes predominantly rejuvenation, whereas over-aging occurs only at very low temperature, small strains, and for high initial energy states. Although the creep compliance in the SGR model exhibits full aging independent of applied load, large stresses in the nonlinear creep regime cause configurational changes leading to rejuvenation of the relaxation time spectrum probed after a stress cycle. During recovery, however, the rejuvenated state rapidly returns to the original aging trajectory due to collective relaxations of the internal strain.
The aging dynamics after shear rejuvenation in a glassy, charged clay suspension have been investigated through dynamic light scattering (DLS). Two different aging regimes are observed: one is attained if the sample is rejuvenated before its gelation and one after the rejuvenation of the gelled sample. In the first regime, the application of shear fully rejuvenates the sample, as the system dynamics soon after shear cessation follow the same aging evolution characteristic of normal aging. In the second regime, aging proceeds very fast after shear rejuvenation, and classical DLS cannot be used.…
We provide a clear evidence that a two species mesoscopic Lattice Boltzmann (LB) model with competing short-range attractive and mid-range repulsive interactions supports emergent Herschel-Bulkley (HB) rheology, i.e. a power-law dependence of the shear-stress as a function of the strain rate, beyond a given yield-stress threshold. This kinetic formulation supports a seamless transition from flowing to non-flowing behaviour, through a smooth tuning of the parameters governing the mesoscopic interactions between the two species. The present model may become a valuable computational tool for the …
Glassy dynamics was investigated for thin films of atactic polystyrene by complex electric capacitance measurements using dielectric relaxation spectroscopy. During the isothermal aging process the real part of the electric capacitance increased with time, whereas the imaginary part decreased with time. It follows that the aging time dependences of real and imaginary parts of the electric capacitance were primarily associated with change in volume (film thickness) and dielectric permittivity, respectively. Further, dielectric permittivity showed memory and rejuvenation effects in a similar man…
The Soft Glassy Rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g. pastes, slurries, foams etc). In this paper, we cast SGR in a general, model independent framework for nonequilibrium thermodynamics called General Equation for the Nonequilibrium Reversible-Irreversible Coupling (GENERIC). This leads to a new formulation of SGR which clarifies how it can properly be coupled to hydrodynamic fields, resulting in a thermodynamically consistent, local, continuum version of SGR.…
We attribute similarities in the rheology of many soft materials (foams, emulsions, slurries, etc.) to the shared features of structural disorder and metastability. A generic model for the mesoscopic dynamics of ``soft glassy matter'' is introduced, with interactions represented by a mean-field noise temperature x. We find power law fluid behavior either with (x<1) or without (1<x<2) a yield stress. For 1<x<2, both storage and loss modulus vary with frequency as $ω^{x-1}$, becoming flat near a glass transition (x=1). Values of $x\approx 1$ may result from marginal dynamics as seen in some spin…
Molecular dynamics simulations are used to investigate the connection between thermal history and physical aging in polymer glasses, in particular the effects of a temperature square step. Measurements of two-time correlation functions show that a negative temperature step causes "rejuvenation" of the sample: the entire spectrum of relaxation times appears identical to a younger specimen that did not experience a temperature step. A positive temperature step, however, leads to significant changes in the relaxation times. At short times, the dynamics are accelerated (rejuvenation), whereas at l…
In this paper, we introduce a simple mode-coupling model for concentrated suspensions under flow . This model exhibits a jamming transition, and stress vs shear rate relations which are very similar to experimental results. Namely newtonian regime or yield stress are followed by a slow variation of the stress for higher shear rates, and by an apparent newtonian regime for very large shear rates. Another striking result is that under oscillating strain, even in the jammed state, the system exhibits a relaxation time which depends on the strain amplitude.
A systematic study for a single-specie lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions is presented. The equilibrium analysis is performed along the guidelines proposed by [X. Shan, Phys. Rev. E 77, 066702 (2008)] and allows us to determine the surface tension density and the resulting disjoining pressure developing in a thin film when two interfaces overlap. Numerical simulations of confined flows are then performed with a multicomponent model and are successfully tested against the recent suggestion by Bocquet and coworkers on the exis…
We explore the origins of slow dynamics, aging and glassy rheology in soft and living matter. Non-diffusive slow dynamics and aging in materials characterised by crowding of the constituents can be explained in terms of structural rearrangement or remodelling events that occur within the jammed state. In this context, we introduce the jamming phase diagram proposed by Liu and Nagel to understand the ergodic-nonergodic transition in these systems, and discuss recent theoretical attempts to explain the unusual, faster-than-exponential dynamical structure factors observed in jammed soft materials…
Soft Glassy Materials, Non Linear Rheology, Lattice Kinetic models, frustrated phase separation} We present numerical simulations based on a Boltzmann kinetic model with competing interactions, aimed at characterizating the rheological properties of soft-glassy materials. The lattice kinetic model is shown to reproduce typical signatures of driven soft-glassy flows in confined geometries, such as Herschel-Bulkley rheology, shear-banding and histeresys. This lends further credit to the present lattice kinetic model as a valuable tool for the theoretical/computational investigation of the rheolo…
We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully-thermal and nearly-athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.
We report studies of the frequency dependent shear modulus, $G^*(ω)=G'(ω)+iG''(ω)$, of the liquid crystal octylcyanobiphenyl (8CB) confined in a colloidal aerosil gel. With the onset of smectic order, $G'$ grows approximately linearly with decreasing temperature, reaching values that exceed by more than three orders of magnitude the values for pure 8CB. The modulus at low temperatures possesses a power-law component, $G^*(ω) \sim ω^α$, with exponent $α$ that approaches zero with increasing gel density. The amplitude of $G'$ and its variation with temperature and gel density indicate that the l…
We use linear rheology and multispeckle dynamic light scattering (MDLS) to investigate the aging of a gel composed of multilamellar vesicles. Light scattering data indicate rearrangement of the gel through an unusual ultraslow ballistic motion. A dramatic slowdown of the dynamics with sample age $t_{w}$ is observed for both rheology and MDLS, the characteristic relaxation time scaling as $t_{w}^μ$. We find the same aging exponent $μ=0.78$ for both techniques, suggesting that they probe similar physical processes, that is the relaxation of applied or internal stresses for rheology or MDLS, resp…
Chocolate is known to undergo solid-liquid transition upon an increase in temperature as well as under application of deformation field. Upon sudden reduction in temperature from a molten state (or thermal rejuvenation), rheological properties of chocolate undergo evolution as a function of time under isothermal conditions, a behavior reminiscent of physical aging in polymeric glasses. Then again, subsequent to cessation of shear flow (or mechanical rejuvenation), chocolate shows temporal evolution of the rheological properties, a behavior similar to physical aging in soft glassy materials. In…
We introduce a new model for the dynamics of a wormlike chain in an environment that gives rise to a rough free energy landscape, which we baptise the glassy wormlike chain. It is obtained from the common wormlike chain by an exponential stretching of the relaxation spectrum of its long-wavelength eigenmodes, controlled by a single stretching parameter. Predictions for pertinent observables such as the dynamic structure factor and the microrheological susceptibility exhibit the characteristics of soft glassy rheology and compare favourably with experimental data for reconstituted cytoskeletal …
Yield stress fluids display a rich rheological phenomenology. Beyond the defining existence of a yield stress in the steady state flow curve, this includes in many materials rather flat viscoelastic spectra over many decades of frequency in small amplitude oscillatory shear; slow stress relaxation following the sudden imposition of a small shear strain; stress overshoot in shear startup; logarithmic or sublinear power law creep following the imposition of a shear stress below the yield stress; creep followed by yielding after the imposition of a shear stress above the yield stress; richly feat…
We study the low-velocity (0.1--100 $μ$m.s$^{-1}$) frictional properties of interfaces between a rough glassy polymers and smooth silanized glass, a configuration which gives direct access to the rheology of the adhesive joints in which shear localizes. We show that these joints exhibit the full phenomenology expected for confined quasi 2D soft glasses: they strengthen logarithmically when aging at rest, and weaken (rejuvenate) when sliding. Rejuvenation is found to saturate at large velocities. Moreover, aging at rest is shown to be strongly accelerated when waiting under finite stress below …
We investigate the nonlinear rheological behavior of colloidal suspensions of Laponite, a synthetic clay, driven by a steady and homogeneous shear strain. We show that the external drive leads to a drastic slowing down of the aging dynamics or even, in some cases, in the rejuvenation of the system. Under shear, after a surprisingly long time, the spontaneous aging process observed at rest is suppressed. The system then reaches a non-equilibrium stationary state, characterised by a complex viscosity depending on the applied shear rate. In addition, the glass exhibits a non-Newtonian shear-thinn…
Mechanically driven glassy systems and complex fluids exhibit a wealth of rheological behaviors that call for theoretical understanding and predictive modeling. A distinct feature of these nonequilibrium systems is their dynamically evolving state of structural disorder, which determines their rheological responses. Here we highlight a recently developed nonequilibrium thermodynamic framework in which the structural state is characterized by an evolving effective disorder temperature that may differ from the ordinary thermal temperature. The specific properties of each physical system of inter…
We present an integrated experimental and quantitative theoretical study of the mechanics of self-crosslinked, neutral, repulsive pNIPAM microgel suspensions over concentration (c) range spanning the fluid, glassy and putative "soft jammed" regimes. In the glassy regime we measure a linear elastic dynamic shear modulus over 3 decades which follows an apparent power law concentration dependence G'~$c^{5.64}$, followed by a sharp crossover to a nearly linear growth at high concentrations. We formulate a theoretical approach to address all three regimes within a single conceptual Brownian dynamic…
Glassy polymers show strain hardening: at constant extensional load, their flow first accelerates, then arrests. Recent experiments have found this to be accompanied by a striking and unexplained dip in the segmental relaxation time. Here we explain such behavior by combining a minimal model of flow-induced liquefaction of a glass, with a description of the stress carried by strained polymers, creating a non-factorable interplay between aging and strain-induced rejuvenation. Under constant load, liquefaction of segmental motion permits strong flow that creates polymer-borne stress. This slows …
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；College of Physics, Chengdu University of Technology（成都理工大学物理学院）；Med-X Research Institute and School of Biomedical Engineering, Shanghai Jiao Tong University（上海交通大学Med-X研究院与生物医学工程学院）；School of Physics, East China Normal University（华东师范大学物理系）；Jiangsu First-Imaging Medical Equipment Co., Ltd.（江苏首影医疗设备有限公司）；State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology（成都大学地质灾害防治与地质环境国家重点实验室）
Mesoscopic models play an important role in our understanding of the deformation and flow of amorphous materials. One such description, based on the Shear Transformation Zone (STZ) theory, has recently been re-formulated within a non-equilibrium thermodynamics framework, and found to be consistent with it. We show here that a similar interpretation can be made for the Soft Glassy Rheology (SGR) model. Conceptually this means that the "noise temperature" x, proposed phenomenologically in the SGR model to control the dynamics of a set of slow mesoscopic degrees of freedom, can consistently be in…
Based on numerical simulations of a lattice kinetic model for soft-glassy materials, we characterize the global rheology of a dense emulsion-like system, under three representative load conditions: Couette flow, time-oscillating Strain and Kolmogorov flow. It is found that in all cases the rheology is described by a Herschel-Bulkley (HB) relation, $σ= σ_{Y} + A S^β$, with the yield stress $σ_{Y}$ largely independent of the loading scenario. A proper rescaling of the HB parameters permits to describe heterogeneous flows with space-dependent stresses, based on the notion of cooperativity, as rec…
We study shear banding in soft glassy materials subject to a large amplitude oscillatory shear flow (LAOS). By numerical simulations of the widely used soft glassy rheology model, supplemented by more general physical arguments, we demonstrate strong banding over an extensive range of amplitudes and frequencies of the imposed shear rate $\dotγ(t)=\dotγ_0\cos(ωt)$, even in materials that do not permit banding as their steady state response to a steady imposed shear flow $\dotγ=\dotγ_0=$const. Highly counterintuitively, banding persists in LAOS even in the limit of zero frequency $ω\to 0$, where…
Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural ($α$) relaxation rate and the shear-induced relaxation rate. A dif…
Many soft materials, including foams, dense emulsions, micro gel bead suspensions, star polymers, dense packing of surfactant onion micelles, and textured morphologies of liquid crystals, share the basic "glassy" features of structural disorder and metastability. These in turn give rise to several notable features in the low frequency shear rheology (deformation and flow properties) of these materials: in particular, the existence of a yield stress below which the material behaves like a solid, and above which it flows like a liquid. In the last decade, intense experimental activity has also r…
We study theoretically the dynamics of soft glassy materials during the process of stress relaxation following the rapid imposition of a shear strain. By detailed numerical simulations of a mesoscopic soft glassy rheology model and three different simplified continuum fluidity models, we show that a dramatic shear localisation instability arises, in which the strain field suddenly becomes heterogeneous within the sample, accompanied by a precipitous drop in the stress. Remarkably, this instability can arise at extremely long delay times after the strain was applied, due to the long-term memory…
The coupling of active, self-motile particles to topological constraints can give rise to novel non-equilibrium dynamical patterns that lack any passive counterpart. Here we study the behavior of self-propelled rods confined to a compact spherical manifold by means of Brownian dynamics simulations. We establish the state diagram and find that short active rods at sufficiently high density exhibit a glass transition toward a disordered state characterized by persistent self-spinning motion. By periodically melting and revitrifying the spherical spinning glass, we observe clear signatures of tim…
Motivated by recent experimental studies of rheological hysteresis in soft glassy materials, we study numerically strain rate sweeps in simple yield stress fluids and viscosity bifurcating yield stress fluids. Our simulations of downward followed by upward strain rate sweeps, performed within fluidity models and the soft glassy rheology model, successfully capture the experimentally observed monotonic decrease of the area of the rheological hysteresis loop with sweep time in simple yield stress fluids, and the bell shaped dependence of hysteresis loop area on sweep time in viscosity bifurcatin…
The nonlinear rheology of a soft glassy material is captured by its constitutive relation, shear stress vs shear rate, which is most generally obtained by sweeping up or down the shear rate over a finite temporal window. For a huge amount of complex fluids, the up and down sweeps do not superimpose and define a rheological hysteresis loop. By means of extensive rheometry coupled to time-resolved velocimetry, we unravel the local scenario involved in rheological hysteresis for various types of well-studied soft materials. We introduce two observables that quantify the hysteresis in macroscopic …
We study the instability to necking of an initially cylindrical filament of soft glassy material subject to extensional stretching. By numerical simulation of the soft glassy rheology model and a simplified fluidity model, and by analytical predictions within a highly generic toy description, we show that the mode of instability is set by the age of the sample relative to the inverse of the applied extensional strain rate. Young samples neck gradually via a liquid-like mode, the onset of which is determined by both the elastic loading and plastic relaxation terms in the stress constitutive equ…
The rheological behavior of soft glassy materials basically results from the interplay between shearing forces and an intrinsic slow dynamics. This competition can be described by a microscopic theory, which can be viewed as a nonequilibrium schematic mode-coupling theory. This statistical mechanics approach to rheology results in a series of detailed theoretical predictions, some of which still awaiting for their experimental verification. We present new, preliminary, results about the description of yield stress, flow heterogeneities and activated processes within this theoretical framework.
Recently introduced constitutive equations for the rheology of dense, disordered materials are investigated in the context of stick-slip experiments in boundary lubrication. The model is based on a generalization of the shear transformation zone (STZ) theory, in which plastic deformation is represented by a population of mesoscopic regions which may undergo non affine deformations in response to stress. The generalization we study phenomenologically incorporates the effects of aging and glassy relaxation. Under experimental conditions associated with typical transitions from stick-slip to stea…
Molecular dynamics simulations are performed for a polymer melt composed of short chains in quiescent and sheared conditions. The stress relaxation function $G(t)$ exhibits a stretched exponential form in a relatively early stage and ultimately follows the Rouse function in quiescent supercooled state. Transient stress evolution after application of shear obeys the linear growth $\int_0^t dt'G(t')$ for strain less than 0.1 and then saturates into a non-Newtonian viscosity. In steady states, strong shear-thinning and elongation of chains into ellipsoidal shapes are found at extremely small shea…
We study shear yielding and steady state flow of glassy materials with molecular dynamics simulations of two standard models: amorphous polymers and bidisperse Lennard-Jones glasses. For a fixed strain rate, the maximum shear yield stress and the steady state flow stress in simple shear both drop linearly with increasing temperature. The dependence on strain rate can be described by a either a logarithm or a power-law added to a constant. In marked contrast to predictions of traditional thermal activation models, the rate dependence is nearly independent of temperature. The relation to more re…
We study the emergence of critical dynamics in the steady shear rheology of fluidized soft glassy materials. Within a mesoscale elasto-plastic model accounting for a shear band instability, we show how an additional noise can induce a transition from phase separated to homogeneous flow, accompanied by critical-like fluctuations of the macroscopic shear rate. Both macroscopic quantities and fluctuations exhibit power law behaviors in the vicinity of this transition, consistent with previous experimental findings on vibrated granular media. Altogether, our results suggest a generic scenario for …
We study theoretically shear banding in soft glassy materials subject to large amplitude time-periodic shear flows, considering separately the protocols of large amplitude oscillatory shear strain, large amplitude square or triangular or sawtooth strain rate, and large amplitude oscillatory shear stress. In each case, we find shear banding to be an important part of the material's flow response for a broad range of values of the frequency $ω$ and amplitude of the imposed oscillation. Crucially, and highly counterintuitively, in the glass phase this persists even to the lowest frequencies acces…
Universal Dynamic Scaling for Sub-Yield Aging and Over-Yield Rejuvenation in A Cyclically Driven Metallic Glass
School of Materials Science and Engineering, Anhui University of Technology（安徽工业大学材料科学与工程学院）；Advanced Interdisciplinary Science Research Center (AiRCenter), Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences（中国科学院宁波材料技术与工程研究所先进交叉科学研究院）；State Key Laboratory of High Performance Roll Materials and Composite Forming, School of Material Science and Engineering, Hebei University of Technology（河北工业大学材料科学与工程学院高性能轧辊材料及复合成形省部共建国家重点实验室培育基地）
The memory and rejuvenation aspects of intermittent heat transport are explored theoretically and by numerical simulation for Ising spin glasses with short-ranged interactions. The theoretical part develops a picture of non-equilibrium glassy dynamics recently introduced by the authors. Invoking the concept of marginal stability, this theory links irreversible `intermittent' events, or `quakes' to thermal fluctuations of record magnitude. The pivotal idea is that the largest energy barrier $b(t_w,T)$ surmounted prior to $t_w$ by thermal fluctuations at temperature $T$ determines the rate $r_q …
We study the viscoelastic response of amorphous polymers using theory and simulations. By accounting for internal stresses and considering instantaneous normal modes (INMs) within athermal non-affine theory, we make parameter-free predictions of the dynamic viscoelastic moduli obtained in coarse-grained simulations of polymer glasses at non-zero temperatures. The theoretical results show very good correspondence with rheology data collected from molecular dynamics simulations over five orders of magnitude in frequency, with some instabilities that accumulate in the low-frequency part on approa…
In this work, we study ageing behavior of aqueous laponite suspension, a model soft glassy material, in creep. We observe that viscoelastic behavior is time dependent and is strongly influenced by the deformation field; the effect is known to arise due to ageing and rejuvenation. We show that irrespective of strength of deformation field (shear stress) and age, when imposed time-scale is normalized with dominating relaxation mode of the system, universal ageing behavior is obtained demonstrating time-stress superposition; the phenomena that may be generic in variety of soft materials.
The `soft glassy rheology' (SGR) model gives an appealing account of the flow of nonergodic soft materials in terms of the local yield dynamics of mesoscopic elements. Newtonian, power-law, and yield-stress fluid regimes arise on varying a `noise temperature', x. Here we extend the model, to capture the idea that the noise is largely caused by yield itself. The extended model can account for the viscosity-bifurcation and shear-banding effects reported recently in a wide range of soft materials. A variant model may shed light on shear banding and strain-rate hysteresis seen in glassy star polym…
We study the Couette flow of a quasi-2d soft-glassy material in a Hele-Shaw geometry. The material is chosen to be above the jamming point, where a yield stress $σ_Y$ emerges, below which the material deforms elastically and above which it flows like a complex fluid according to a Herschel-Bulkley (HB) rheology. Simultaneously, the effect of the confining plates is modelled as an effective linear friction law, while the walls aside the Hele-Shaw cell are sufficiently close to each other to allow visible cooperativity effects in the velocity profiles (Goyon et al., Nature 454, 84-87 (2008)). Th…
We study the transient start-up dynamics of a fluidity model which captures the rheological behavior of aging soft glassy materials, in a rectilinear shear flow upon application of step shear rate. We observe that when the steady state flow curve is non-monotonic the system shows transient and/or apparent steady state shear banding in close qualitative agreement with experimental observations. Due to a competetion between aging and rejuvenation during the start up, we show that there is an apparent steady state banding at large times even for shear rates such that the steady state flow curve a…
A model is proposed that considers aging and rejuvenation in a soft glassy material as respectively a decrease and an increase in free energy. The aging term is weighted by inverse of characteristic relaxation time suggesting greater mobility of the constituents induce faster aging in a material. A dependence of relaxation time on free energy is proposed, which under quiescent conditions, leads to power law dependence of relaxation time on waiting time as observed experimentally. The model considers two cases namely, a constant modulus when aging is entropy controlled and a time dependent modu…
The population growth of a Staphylococcus aureus culture was followed by rheological measurements, under steady-state and dynamic shear flows. We observed a rich viscoelastic behaviour as a consequence of the bacteria activity. First, the viscosity increased ~10 times due to cell multiplication and aggregation. This viscosity increase presented several drops and full recoveries, which are reproducible, allowing us to evoke the existence of a percolation phenomenon. Eventually, as the bacteria population reached a final stage of development, fulfilling the sample volume, the viscosity returned …
Emergent odd viscoelasticity in chiral soft glassy materials
University of Göttingen（哥廷根大学）；Ecole Polytechnique de l’Université de Nantes, LTeN, U6607, Nantes Université（南特大学理工学院，LTeN，U6607）；King’s College London（伦敦国王学院）
We present a framework for analyzing the rheology of dense driven granular materials, based on a recent proposal of a stress-based ensemble. In this ensemble fluctuations in a granular system near jamming are controlled by a temperature-like parameter, the angoricity, which is conjugate to the stress of the system. In this paper, we develop a model for slowly driven granular materials based on the stress ensemble and the idea of a landscape in stress space. The idea of an activated process driven by the angoricity has been shown by Behringer et al (2008) to describe the logarithmic strengtheni…
Mechanical response of a simple DNA nanostar hydrogel: symptoms of disorder and glassy emergence of solidity
Institut Néel-CNRS/UGA-Grenoble INP（内尔研究所）；LIMMS-CNRS/Institute of Industrial Science-The University of Tokyo（理化学研究所-东京大学工业科学研究所）；LIP-CNRS/ENS Lyon（里昂高等师范学校）；Universite Claude Bernard Lyon 1, CNRS, Institut Lumière Matière（里昂第一大学）
By using fluid-kinetic simulations of confined and concentrated emulsion droplets, we investigate the nature of space non-homogeneity in soft-glassy dynamics and provide quantitative measurements of the statistical features of plastic events in the proximity of the yield-stress threshold. Above the yield stress, our results show the existence of a finite stress correlation scale, which can be mapped directly onto the {\it cooperativity scale}, recently introduced in the literature to capture non-local effects in the soft-glassy dynamics. In this regime, the emergence of a separate boundary (wa…
