Viscous forces and bulk viscoelasticity near jamming

Role of viscoelasticity in the appearance of low-Reynolds turbulence: considerations for modelling

Inertial effects caused by perturbations of dynamical equilibrium during the flow of soft matter constitute a hallmark of turbulence. Such perturbations are attributable to an imbalance between energy storage and energy dissipation. During the flow of Newtonian fluids, kinetic energy can be both stored and dissipated, while the flow of viscoelastic soft matter systems, such as polymer fluids, induces the accumulation of both kinetic and elastic energies. The accumulation of elastic energy causes local stiffening of stretched polymer chains, which can destabilise the flow. Migrating multicellular systems are hugely complex and are capable of self-regulating their viscoelasticity and mechanical stress generation, as well as controlling their energy storage and energy dissipation. Since the flow perturbation of viscoelastic systems is caused by the inhomogeneous accumulation of elastic energy, rather than of kinetic energy, turbulence can occur at low Reynolds numbers.This theoretical review is focused on clarifying the role of viscoelasticity in the appearance of low-Reynolds turbulence. Three types of system are considered and compared: (1) high-Reynolds turbulent flow of Newtonian fluids, (2) low and moderate-Reynolds flow of polymer solutions, and (3) migration of epithelial collectives, discussed in terms of two model systems. The models considered involve the fusion of two epithelial aggregates, and the free expansion of epithelial monolayers on a substrate matrix.

Cell jamming-to-unjamming transitions and vice versa in development: Physical aspects

Collective cell migration is essential for a wide range of biological processes such as: morphogenesis, wound healing, and cancer spreading. However, it is well known that migrating epithelial collectives frequently undergo jamming, stay trapped some period of time, and then start migration again. Consequently, only a part of epithelial cells actively contributes to the tissue development. In contrast to epithelial cells, migrating mesenchymal collectives successfully avoid the jamming. It has been confirmed that the epithelial unjamming cannot be treated as the epithelial-to-mesenchymal transition. Some other mechanism is responsible for the epithelial jamming/unjamming. Despite extensive research devoted to study the cell jamming/unjamming, we still do not understand the origin of this phenomenon. The origin is connected to physical factors such as: the cell compressive residual stress accumulation and surface characteristics of migrating (unjamming) and resting (jamming) epithelial clusters which depend primarily on the strength of cell-cell adhesion contacts and cell contractility. The main goal of this theoretical consideration is to clarify these cause-consequence relations.

Microrheology near jamming

The jamming transition is a nonequilibrium critical phenomenon, which governs characteristic mechanical properties of jammed soft materials, such as pastes, emulsions, and granular matters. Both experiments and theory of jammed soft materials have revealed that the complex modulus measured by conventional macrorheology exhibits a characteristic frequency dependence. Microrheology is a new type of method to obtain the complex modulus, which transforms the microscopic motion of probes to the complex modulus through the generalized Stokes relation (GSR). Although microrheology has been applied to jammed soft materials, its theoretical understanding is limited. In particular, the validity of the GSR near the jamming transition is far from obvious since there is a diverging length scale lc, which characterizes the heterogeneous response of jammed particles. Here, we study the microrheology of jammed particles by theory and numerical simulation. First, we develop a linear response formalism to calculate the response function of the probe particle, which is transformed to the complex modulus via the GSR. Then, we apply our formalism to a numerical model of jammed particles and find that the storage and loss modulus follow characteristic scaling laws near the jamming transition. Importantly, the observed scaling law coincides with that in macrorheology, which indicates that the GSR holds even near the jamming transition. We rationalize this equivalence by asymptotic analysis of the obtained formalism and numerical analysis on the displacement field of jammed particles under a local perturbation.

The role of viscoelasticity in long time cell rearrangement

Cell rearrangement caused by collective cell migration (CCM) during free expansion of epithelial monolayers has become a landmark in our current understanding of fundamental biological processes such as tissue development, regeneration, wound healing or cancer invasion. Cell spreading causes formation of mechanical waves which has a feedback effect on cell rearrangement and can lead to the cell jamming state. The mechanical waves describe oscillatory changes in cell velocity, as well as, the rheological parameters that affect them. The velocity oscillations, obtained at a time scale of hours, are in the form of forward and backward flows. Collision of forward and backward flows can induce an increase in the cell compressive stress accompanied with cell packing density which have a feedback impact on cell mobility, tissue viscoelasticity and alters the tissue stiffness. The tissue stiffness depends on the cell packing density and the active/passive (i.e. migrating/resting) state of single cells and can be used as an indicator of cell jamming state transition. Since cell stiffness can be measured it may directly show in which state the multicellular system is. In this work a review of existing modeling approaches is given along with assortment of published experimental findings, in order to invite experimentalists to test given theoretical considerations in multicellular systems.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

Moduli and modes in the Mikado model

We determine how low frequency vibrational modes control the elastic shear modulus of Mikado networks, a minimal mechanical model for semi-flexible fiber networks. From prior work it is known that when the fiber bending modulus is sufficiently small, (i) the shear modulus of 2D Mikado networks scales as a power law in the fiber line density, G ∼ ρα+1, and (ii) the networks also possess an anomalous abundance of soft (low-frequency) vibrational modes with a characteristic frequency ωκ ∼ ρβ/2. While it has been suggested that α and β are identical, the preponderance of evidence indicates that α is larger than theoretical predictions for β. We resolve this inconsistency by measuring the vibrational density of states in Mikado networks for the first time. Supported by these results, we then demonstrate analytically that α = β + 1. In so doing, we uncover new insights into the coupling between soft modes and shear, as well as the origin of the crossover from bending- to stretching-dominated response.

Mesomeric Effects of Azobenzene Bearing Natural Product-Based Molecules for Liquid Crystal Materials: An Overview

Latest progress in the liquid crystal (LC) field related to azo molecules incorporated into natural product- based moieties for the improvement of LC texture and mesomeric phases has received great interest among researchers. A LC containing natural product-based moieties i.e. menthol, kojic acid, cholesterol and chalcone with stable azo and azobenzene scaffolds with specific optical tunability, has been widely used in photo-active materials such as Liquid Crystal Display (LCD), LC films, smart windows and other devices. This review discusses the influence of azobenzene, a renowned photo-responsive and stable LC scaffold, in mesogenic phases due to photo-isomerization and optical switching. The incorporation of mesomeric phases of natural product moieties to azo molecules has improved the properties of LC, i.e, from the nematic phase to the smectic phase with proper magnetic field alignment. Natural product-based LC can be useful in numerous applications, especially practical electronic or optic devices such as optical image storage, display devices, solar cells, optical switching.

Permanent and reversibly programmable shapes in liquid crystal elastomer microparticles capable of shape switching

Reversibly programmable liquid crystal elastomer microparticles (LCEMPs), formed as a covalent adaptable network (CAN), with an average diameter of 7 μm ± 2 μm, were synthesized via a thiol-Michael dispersion polymerization. The particles were programmed to a prolate shape via a photoinitiated addition-fragmentation chain-transfer (AFT) exchange reaction by activating the AFT after undergoing compression. Due to the thermotropic nature of the AFT-LCEMPs, shape switching was driven by heating the particles above their nematic-isotropic phase transition temperature (T_NI). The programmed particles subsequently displayed cyclable two-way shape switching from prolate to spherical when at low or high temperatures, respectively. Furthermore, the shape programming is reversible, and a second programming step was done to erase the prolate shape by initiating AFT at high temperature while the particles were in their spherical shape. Upon cooling, the particles remained spherical until additional programming steps were taken. Particles were also programmed to maintain a permanent oblate shape. Additionally, the particle surface was programmed with a diffraction grating, demonstrating programmable complex surface topography via AFT activation.

Computational study of transient shear banding in soft jammed solids

We have designed three-dimensional numerical simulations of a soft spheres model, with size polidispersity and in athermal conditions, to study the transient shear banding that occurs during yielding of jammed soft solids. We analyze the effects of different types of drag coefficients used in the simulations and compare the results obtained using Lees-Edwards periodic boundary conditions with the case in which the same model solid is confined between two walls. The specific damping mechanism and the different boundary conditions indeed modify the load curves and the velocity profiles in the transient regime. Nevertheless, we find that the presence of a stress overshoot and of a related transient banding phenomenon, for large enough samples, is a robust feature for overdamped systems, where their presence do not depend on the specific drag used and on the different boundary conditions.

Glass Stability Changes the Nature of Yielding under Oscillatory Shear

We perform molecular dynamics simulations to investigate the effect of a glass preparation on its yielding transition under oscillatory shear. We use swap Monte Carlo to investigate a broad range of glass stabilities from poorly annealed to highly stable systems. We observe a qualitative change in the nature of yielding, which evolves from ductile to brittle as glass stability increases. Our results disentangle the relative role of mechanical and thermal annealing on the mechanical properties of amorphous solids, which is relevant for various experimental situations from the rheology of soft materials to fatigue failure in metallic glasses.

Scaling laws for frictional granular materials confined by constant pressure under oscillatory shear

Herein we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have been found. The scaling laws in plastic regime for large strain amplitude can be understood by the angular distributions of the contact force. The scaling exponents are estimated by considering the physical mechanism.

Stress Relaxation above and below the Jamming Transition

We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states, which is a key ingredient of linear viscoelastic theory. The vibrational density of states exhibits an extra slow mode that emerges below jamming, which we utilize to demonstrate the anomalous exponent below jamming.

Jamming state transition and collective cell migration

Jamming state transition has been used in literature to describe migrating-to-resting cell state transition during collective cell migration without proper rheological confirmation. Yield stress often has been used as an indicator of a jamming state. Yield stress points to the liquid-to-solid state transition, but not a priori to jamming state transition. Various solid states such as elastic solid and viscoelastic solids can be considered in the context of their ability to relax. The relaxation time for (1) an elastic solid tends to zero, (2) Kelvin-Voigt viscoelastic solid is finite, and (3) jamming state tends to infinity.

In order to clarify the meaning of jamming state from the rheological standpoint we formulated the constitutive model of this state based on following conditions (1) migration of the system constituents is much damped such that the diffusion coefficient tends to zero, (2) relaxation time tends to infinity, (3) storage and loss moduli satisfy the condition G^′(ω)/G^"(ω) = const > 1. Jamming state represents the non-linear viscoelastic solid state. The main characteristic of this state is that the system cannot relax.

Jamming state transition of multicellular systems caused by collective cell migration is discussed on a model system such as cell aggregate rounding after uni-axial compression between parallel plates based on the data from the literature. Cell aggregate rounding occurs via successive relaxation cycles. Every cycle corresponds to a different scenario of cell migration. Three scenarios were established depending on the magnitude of mechanical and biochemical perturbations (1) ordered scenario with reduced perturbations corresponds to the case that most of the cells migrate, (2) disordered scenario corresponds to the case that some cell groups migrate while the others (at the same time) stay in resting state (corresponds to medium perturbations), and (3) highly suppressed cell migration under large perturbations corresponds to the viscoelastic solid under jamming state. If cells reach the jamming state in one cycle, they are able to overcome this undesirable state and start migrating again in the next cycle by achieving the first or second scenarios again.

Nonlocal Effects in Inhomogeneous Flows of Soft Athermal Disks

We numerically investigate nonlocal effects on inhomogeneous flows of soft athermal disks close to but below their jamming transition. We employ molecular dynamics to simulate Kolmogorov flows, in which a sinusoidal flow profile with fixed wave number is externally imposed, resulting in a spatially inhomogeneous shear rate. We find that the resulting rheology is strongly wave-number-dependent, and that particle migration, while present, is not sufficient to describe the resulting stress profiles within a conventional local model. We show that, instead, stress profiles can be captured with nonlocal constitutive relations that account for gradients to fourth order. Unlike nonlocal flow in yield stress fluids, we find no evidence of a diverging length scale.

Sticky Matters: Jamming and Rigid Cluster Statistics with Attractive Particle Interactions

While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a first-order transition, with no growing cluster size. We further show that the weakly attractive scenario is a finite size effect, so that for any nonzero attraction strength, a sufficiently large system will fall in the strongly attractive universality class. We therefore expect attractive jamming to be generic in the laboratory and in nature.

Coarsening and mechanics in the bubble model for wet foams

Aqueous foams are an important model system that displays coarsening dynamics. Coarsening in dispersions and foams is well understood in the dilute and dry limits, where the gas fraction tends to zero and one, respectively. However, foams are known to undergo a jamming transition from a fluidlike to a solidlike state at an intermediate gas fraction ϕ_{c}. Much less is known about coarsening dynamics in wet foams near jamming, and the link to mechanical response, if any, remains poorly understood. Here we probe coarsening and mechanical response using numerical simulations of a variant of the Durian bubble model for wet foams. As in other coarsening systems we find a steady state scaling regime with an associated particle size distribution. We relate the time rate of evolution of the coarsening process to the wetness of the foam and identify a characteristic coarsening time that diverges approaching jamming. We further probe mechanical response of the system to strain while undergoing coarsening. There are two competing timescales, namely the coarsening time and the mechanical relaxation time. We relate these to the evolution of the elastic response and the mechanical structure.

Normal Stresses, Contraction, and Stiffening in Sheared Elastic Networks

When elastic solids are sheared, a nonlinear effect named after Poynting gives rise to normal stresses or changes in volume. We provide a novel relation between the Poynting effect and the microscopic Grüneisen parameter, which quantifies how stretching shifts vibrational modes. By applying this relation to random spring networks, a minimal model for, e.g., biopolymer gels and solid foams, we find that networks contract or develop tension because they vibrate faster when stretched. The amplitude of the Poynting effect is sensitive to the network's linear elastic moduli, which can be tuned via its preparation protocol and connectivity. Finally, we show that the Poynting effect can be used to predict the finite strain scale where the material stiffens under shear.

Softening and yielding of soft glassy materials

Solids deform and fluids flow, but soft glassy materials, such as emulsions, foams, suspensions, and pastes, exhibit an intricate mix of solid- and liquid-like behavior. While much progress has been made to understand their elastic (small strain) and flow (infinite strain) properties, such understanding is lacking for the softening and yielding phenomena that connect these asymptotic regimes. Here we present a comprehensive framework for softening and yielding of soft glassy materials, based on extensive numerical simulations of oscillatory rheological tests, and show that two distinct scenarios unfold depending on the material's packing density. For dense systems, there is a single, pressure-independent strain where the elastic modulus drops and the particle motion becomes diffusive. In contrast, for weakly jammed systems, a two-step process arises: at an intermediate softening strain, the elastic and loss moduli both drop down and then reach a new plateau value, whereas the particle motion becomes diffusive at the distinctly larger yield strain. We show that softening is associated with an extensive number of microscopic contact changes leading to a non-analytic rheological signature. Moreover, the scaling of the softening strain with pressure suggest the existence of a novel pressure scale above which softening and yielding coincide, and we verify the existence of this crossover scale numerically. Our findings thus evidence the existence of two distinct classes of soft glassy materials - jamming dominated and dense - and show how these can be distinguished by their rheological fingerprint.