Flow in linearly sheared two dimensional foams: from bubble to bulk scale

We probe the flow of two dimensional foams, consisting of a monolayer of bubbles sandwiched between a liquid bath and glass plate, as a function of driving rate, packing fraction and degree of disorder. First, we find that bidisperse, disordered foams exhibit strongly rate dependent and inhomogeneous (shear banded) velocity profiles, while monodisperse, ordered foams are also shear banded, but essentially rate independent. Second, we introduce a simple model based on balancing the averaged drag forces between the bubbles and the top plate and the averaged bubble-bubble drag forces. This model captures the observed rate dependent flows, and the rate independent flows. Third, we perform independent rheological measurements, both for ordered and disordered systems, and find these to be fully consistent with the scaling forms of the drag forces assumed in the simple model, and we see that disorder modifies the scaling. Fourth, we vary the packing fraction $\phi$ of the foam over a substantial range, and find that the flow profiles become increasingly shear banded when the foam is made wetter. Surprisingly, our model describes flow profiles and rate dependence over the whole range of packing fractions with the same power law exponents -- only a dimensionless number $k$ which measures the ratio of the pre-factors of the viscous drag laws is seen to vary with packing fraction. We find that $k \sim (\phi-\phi_c)^{-1}$, where $\phi_c \approx 0.84$, corresponding to the 2d jamming density, and suggest that this scaling follows from the geometry of the deformed facets between bubbles in contact. Overall, our work suggests a route to rationalize aspects of the ubiquitous Herschel-Bulkley (power law) rheology observed in a wide range of disordered materials.Comment: 16 pages, 14 figures, submitted to Phys. Rev. E. High quality version available at: http://www.physics.leidenuniv.nl/sections/cm/gr

An elasto-visco-plastic model for immortal foams or emulsions

A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep -- or viscous flow under even higher stresses.Comment: 69 pages, 29 figure

Memory of the Unjamming Transition during Cyclic Tiltings of a Granular Pile

Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phases description -strong and weak contact networks- for a granular system, as soon as it has approached the unjamming transition.Comment: 13 pages, 15 figures, soumis \`{a} Phys. Rev.

Experimental evidence of ageing and slow restoration of the weak-contact configuration in tilted 3D granular packings

Granular packings slowly driven towards their instability threshold are studied using a digital imaging technique as well as a nonlinear acoustic method. The former method allows us to study grain rearrangements on the surface during the tilting and the latter enables to selectively probe the modifications of the weak-contact fraction in the material bulk. Gradual ageing of both the surface activity and the weak-contact reconfigurations is observed as a result of repeated tilt cycles up to a given angle smaller than the angle of avalanche. For an aged configuration reached after several consecutive tilt cycles, abrupt resumption of the on-surface activity and of the weak-contact rearrangements occurs when the packing is subsequently inclined beyond the previous maximal tilting angle. This behavior is compared with literature results from numerical simulations of inclined 2D packings. It is also found that the aged weak-contact configurations exhibit spontaneous restoration towards the initial state if the packing remains at rest for tens of minutes. When the packing is titled forth and back between zero and near-critical angles, instead of ageing, the weak-contact configuration exhibits "internal weak-contact avalanches" in the vicinity of both the near-critical and zero angles. By contrast, the stronger-contact skeleton remains stable

Islands of conformational stability for Filopodia

Filopodia are long, thin protrusions formed when bundles of fibers grow outwardly from a cell surface while remaining closed in a membrane tube. We study the subtle issue of the mechanical stability of such filopodia and how this depends on the deformation of the membrane that arises when the fiber bundle adopts a helical configuration. We calculate the ground state conformation of such filopodia, taking into account the steric interaction between the membrane and the enclosed semiflexible fiber bundle. For typical filopodia we find that a minimum number of fibers is required for filopodium stability. Our calculation elucidates how experimentally observed filopodia can obviate the classical Euler buckling condition and remain stable up to several tens of . We briefly discuss how experimental observation of the results obtained in this work for the helical-like deformations of enclosing membrane tubes in filopodia could possibly be observed in the acrosomal reactions of the sea cucumber Thyone, and the horseshoe crab Limulus. Any realistic future theories for filopodium stability are likely to rely on an accurate treatment of such steric effects, as analysed in this work

Leader Cells Define Directionality of Trunk, but Not Cranial, Neural Crest Cell Migration.

Collective cell migration is fundamental for life and a hallmark of cancer. Neural crest (NC) cells migrate collectively, but the mechanisms governing this process remain controversial. Previous analyses in Xenopus indicate that cranial NC (CNC) cells are a homogeneous population relying on cell-cell interactions for directional migration, while chick embryo analyses suggest a heterogeneous population with leader cells instructing directionality. Our data in chick and zebrafish embryos show that CNC cells do not require leader cells for migration and all cells present similar migratory capacities. In contrast, laser ablation of trunk NC (TNC) cells shows that leader cells direct movement and cell-cell contacts are required for migration. Moreover, leader and follower identities are acquired before the initiation of migration and remain fixed thereafter. Thus, two distinct mechanisms establish the directionality of CNC cells and TNC cells. This implies the existence of multiple molecular mechanisms for collective cell migration.D11I1096 Fondo de Fomento al Desarrollo Científico y TecnológicoThis is the final version of the article. It first appeared from Cell Press via httsp://doi.org/10.1016/j.celrep.2016.04.06

Microscopic elasticity of complex systems

Lecture Notes for the Erice Summer School 2005 Computer Simulations in Condensed Matter: from Materials to Chemical Biology. Perspectives in celebration of the 65th Birthday of Mike Klein organized by Kurt Binder, Giovanni Ciccotti and Mauro Ferrari

Shear-banding in a lyotropic lamellar phase, Part 1: Time-averaged velocity profiles

Using velocity profile measurements based on dynamic light scattering and coupled to structural and rheological measurements in a Couette cell, we present evidences for a shear-banding scenario in the shear flow of the onion texture of a lyotropic lamellar phase. Time-averaged measurements clearly show the presence of structural shear-banding in the vicinity of a shear-induced transition, associated to the nucleation and growth of a highly sheared band in the flow. Our experiments also reveal the presence of slip at the walls of the Couette cell. Using a simple mechanical approach, we demonstrate that our data confirms the classical assumption of the shear-banding picture, in which the interface between bands lies at a given stress $\sigma^\star$. We also outline the presence of large temporal fluctuations of the flow field, which are the subject of the second part of this paper [Salmon {\it et al.}, submitted to Phys. Rev. E]

Dense active matter model of motion patterns in confluent cell monolayers

Epithelial cell monolayers show remarkable displacement and velocity correlations over distances of ten or more cell sizes that are reminiscent of supercooled liquids and active nematics. We show that many observed features can be described within the framework of dense active matter, and argue that persistent uncoordinated cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce swirl-like correlations. We obtain this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based cell models, soft elastic particles and the self-propelled Voronoi model together with in-vitro experiments of confluent corneal epithelial cell sheets. Simulations and normal mode analysis perfectly match when tissue-level reorganisation occurs on times longer than the persistence time of cell motility. Our analytical model quantitatively matches measured velocity correlation functions over more than a decade with a single fitting parameter.Comment: updated version accepted for publication in Nat. Com

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation