137 research outputs found
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 ; a floppy network has , while a stiff network
has . 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 , 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
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
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 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 which measures the
ratio of the pre-factors of the viscous drag laws is seen to vary with packing
fraction. We find that , where , 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
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
Tug-of-war between stretching and bending in living cell sheets
The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness
e
of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this paper, we use the framework of non-Euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like
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/
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, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue
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