Viscoelastic shear banding in foam

Shear banding is an important feature of flow in complex fluids. Essentially, shear bands refer to the coexistence of flowing and non-flowing regions in driven material. Understanding the possible sources of shear banding has important implications for a wide range of flow applications. In this regard, quasi-two dimensional flow offers a unique opportunity to study competing factors that result in shear bands. One proposal is the competition between intrinsic dissipation and an external source of dissipation. In this paper, we report on the experimental observation of the transition between different classes of shear-bands that have been predicted to exist in cylindrical geometry as the result of this competition [R. J. Clancy, E. Janiaud, D. Weaire, and S. Hutzlet, Eur. J. Phys. E, {\bf 21}, 123 (2006)]

Fractional viscoelastic models for power-law materials

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response

Fractional viscoelastic models for power-law materials.

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.Comment: 4 pages, 3 figure

A unified rheological model for cells and cellularised materials.

The mechanical response of single cells and tissues exhibits a broad distribution of time-scales that often gives rise to a distinctive power-law rheology. Such complex behaviour cannot be easily captured by traditional rheological approaches, making material characterisation and predictive modelling very challenging. Here, we present a novel model combining conventional viscoelastic elements with fractional calculus that successfully captures the macroscopic relaxation response of epithelial monolayers. The parameters extracted from the fitting of the relaxation modulus allow prediction of the response of the same material to slow stretch and creep, indicating that the model captured intrinsic material properties. Two characteristic times, derived from the model parameters, delimit different regimes in the materials response. We compared the response of tissues with the behaviour of single cells as well as intra and extra-cellular components, and linked the power-law behaviour of the epithelium to the dynamics of the cell cortex. Such a unified model for the mechanical response of biological materials provides a novel and robust mathematical approach to consistently analyse experimental data and uncover similarities and differences in reported behaviour across experimental methods and research groups. It also sets the foundations for more accurate computational models of tissue mechanics

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

The dynamic mechanical properties of cellularised aggregates.

Cellularised materials are composed of cells interfaced through specialised intercellular junctions that link the cytoskeleton of one cell to that of its neighbours allowing for transmission of forces. Cellularised materials are common in early development and adult tissues where they can be found in the form of cell sheets, cysts, or amorphous aggregates and in pathophysiological conditions such as cancerous tumours. Given the growing realisation that forces can regulate cell physiology and developmental processes, understanding how cellularised materials deform under mechanical stress or dissipate stress appear as key biological questions. In this review, we will discuss the dynamic mechanical properties of cellularised materials devoid of extracellular matrix

On the dependence of the avalanche angle on the granular layer thickness

A layer of sand of thickness h flows down a rough surface if the inclination is larger than some threshold value theta which decreases with h. A tentative microscopic model for the dependence of theta with h is proposed for rigid frictional grains, based on the following hypothesis: (i) a horizontal layer of sand has some coordination z larger than a critical value z_c where mechanical stability is lost (ii) as the tilt angle is increased, the configurations visited present a growing proportion $_s of sliding contacts. Instability with respect to flow occurs when z-z_s=z_c. This criterion leads to a prediction for theta(h) in good agreement with empirical observations.Comment: 6 pages, 2 figure

Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids

With the eventual aim of describing flowing elasto-plastic materials, we focus on the elementary brick of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear strain. We characterize the effect of a nearby wall on this perturbation, and quantify the importance of finite size effects. Although for the sake of simplicity most of our explicit formulae deal with a 2D situation, our statements hold for 3D situations as well.Comment: submitted to EPJ