arXiv subjects

Francois Graner

Publications and source records attributed to Francois Graner.

12 recordsLinked to original sources

arXiv2015

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.

physics.bio-ph↗

arXiv2012

Mechanical state, material properties and continuous description of an epithelial tissue

During development, epithelial tissues undergo extensive morphogenesis based on coordinated changes of cell shape and position over time. Continuum mechanics describes tissue mechanical state and shape changes in terms of strain and stress. It accounts for individual cell properties using only a few spatially averaged material parameters. To determine the mechanical state and parameters in the Drosophila pupa dorsal thorax epithelium, we sever in vivo the adherens junctions around a disk-shaped domain comprising typically hundred cells. This enables a direct measurement of the strain along different orientations at once. The amplitude and anisotropy of the strain increase during development. We also measure the stress to viscosity ratio and similarly find an increase in amplitude and anisotropy. The relaxation time is of order of ten seconds. We propose a space-time, continuous model of the relaxation. Good agreement with experimental data validates the description of the epithelial domain as a continuous, linear, visco-elastic material. We discuss the relevant time and length scales. Another material parameter, the ratio of external friction to internal viscosity, is estimated by fitting the initial velocity profile. Together, our results contribute to quantify forces and displacements, and their time evolution during morphogenesis.

q-bio.CB↗

arXiv2012

Growth laws and self-similar growth regimes of coarsening two-dimensional foams: Transition from dry to wet limits

We study the topology and geometry of two dimensional coarsening foams with arbitrary liquid fraction. To interpolate between the dry limit described by von Neumann's law, and the wet limit described by Marqusee equation, the relevant bubble characteristics are the Plateau border radius and a new variable, the effective number of sides. We propose an equation for the individual bubble growth rate as the weighted sum of the growth through bubble-bubble interfaces and through bubble-Plateau borders interfaces. The resulting prediction is successfully tested, without adjustable parameter, using extensive bidimensional Potts model simulations. Simulations also show that a selfsimilar growth regime is observed at any liquid fraction and determine how the average size growth exponent, side number distribution and relative size distribution interpolate between the extreme limits. Applications include concentrated emulsions, grains in polycrystals and other domains with coarsening driven by curvature.

cond-mat.soft↗

arXiv2006

Two-dimensional flow of foam around a circular obstacle: local measurements of elasticity, plasticity and flow

We investigate the two-dimensional flow of a liquid foam around circular obstacles by measuring all the local fields necessary to describe this flow: velocity, pressure, bubble deformations and rearrangements. We show how our experimental setup, a quasi-2D "liquid pool" system, is adapted to the determination of these fields: the velocity and bubble deformations are easy to measure from 2D movies, and the pressure can be measured by exploiting a specific feature of this system, a 2D effective compressibility. To describe accurately bubble rearrangements, we propose a new, tensorial descriptor. All these quantities are evaluated via an averaging procedure that we justify showing that the fluctuations of the fields are essentially random. The flow is extensively studied in a reference experimental case; the velocity presents an overshoot in the wake of the obstacle, the pressure is maximum at the leading side and minimal at the trailing side. The study of the elastic deformations and of the velocity gradients shows that the transition between plug flow and yielded regions is smooth. Our tensorial description of T1s highlight their correlation both with the bubble deformations and the velocity gradients. A salient feature of the flow, notably on the velocity and T1 repartition, is a marked asymmetry upstream/downstream, signature of the elastic behaviour of the foam. We show that the results do not change qualitatively when various control parameters vary, identifying a robust quasistatic regime. These results are discussed in the frame of the actual foam rheology literature, and we argue that they constitute a severe test for existing rheological models, since they capture both the elastic, plastic and fluid behaviour of the foam.

physics.flu-dyn↗

arXiv2005

Inverse lift: a signature of the elasticity of complex fluids?

To understand the mechanics of a complex fluid such as a foam we propose a model experiment (a bidimensional flow around an obstacle) for which an external sollicitation is applied, and a local response is measured, simultaneously. We observe that an asymmetric obstacle (cambered airfoil profile) experiences a downards lift, opposite to the lift usually known (in a different context) in aerodynamics. Correlations of velocity, deformations and pressure fields yield a clear explanation of this inverse lift, involving the elasticity of the foam. We argue that such an inverse lift is likely common to complex fluids with elasticity.

cond-mat.soft↗

arXiv2005

Two-dimensional flow of foam around an obstacle: force measurements

A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle, \emph{versus} various separately controlled parameters: flow rate, bubble volume, bulk viscosity, obstacle size, shape and boundary conditions. We separate the drag into two contributions, an elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the bulk viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size, and increases proportionally to the obstacle size. We quantify the effect of shape through a dimensioned drag coefficient, and we show that the effect of boundary conditions is small.

cond-mat.soft↗

arXiv2005

Simulations of viscous shape relaxation in shuffled foam clusters

We simulate the shape relaxation of foam clusters and compare them with the time exponential expected for Newtonian fluid. Using two-dimensional Potts Model simulations, we artificially create holes in a foam cluster and shuffle it by applying shear strain cycles. We reproduce the experimentally observed time exponential relaxation of cavity shapes in the foam as a function of the number of strain steps. The cavity rounding up results from local rearrangement of bubbles, due to the conjunction of both a large applied strain and local bubble wall fluctuations.

cond-mat.soft↗

arXiv2004

Foam in a two-dimensional Couette shear: a local measurement of bubble deformation

We re-analyse experiments on a foam sheared in a two-dimensional Couette geometry [Debregeas et al. , Phys. Rev. Lett. 87 , 178305 (2001)]. We characterise the bubble deformation by a texture tensor. Our measurements are local in time: they show two regimes, one transient and one stationary. They provide both the average and fluctuations of the anisotropy. Measurements are also local in space: they show that both the deformation and the elastic contribution to the stress field do not localise, varying smoothly across the shear gap. We can thus describe the foam as a continuous medium with elastic properties.

cond-mat.soft↗

arXiv2004

Two-dimensional flows of foam: drag exerted on circular obstacles and dissipation

A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle, \emph{versus} various separately controlled parameters: flow rate, bubble volume, solution viscosity, obstacle size and boundary conditions. We separate the drag into two contributions, an elastic one (yield drag) at vanishing flow rate, and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the solution viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size, increases with obstacle size, and that the effect of boundary conditions is small. Measurements of the streamwise pressure gradient, associated to the dissipation along the flow of foam, are also presented: they show no dependence on the presence of an obstacle, and pressure gradient depends on flow rate, bubble volume and solution viscosity with three independent power laws.

cond-mat.soft↗

arXiv2004

Deformation of grain boundaries in polar ice

The ice microstructure (grain boundaries) is a key feature used to study ice evolution and to investigate past climatic changes. We studied a deep ice core, in Dome Concordia, Antarctica, which records past mechanical deformations. We measured a "texture tensor" which characterizes the pattern geometry and reveals local heterogeneities of deformation along the core. These results question key assumptions of the current models used for dating.

cond-mat.mtrl-sci↗

arXiv2004

Regular three-dimensional bubble clusters: shape, packing and growth-rate

We consider three-dimensional clusters of identical bubbles packed around a central bubble and calculate their energy and optimal shape. We obtain the surface area and bubble pressures to improve on existing growth laws for three-dimensional bubble clusters. We discuss the possible number of bubbles that can be packed around a central one: the ``kissing problem'', here adapted to deformable objects.

cond-mat.soft↗

arXiv2003

Swelling of phospholipid floating bilayers: the effect of chain length

The equilibrium distance between two lipid bilayers stable in bulk water and in proximity of a substrate was investigated. Samples consisted of a homogeneous lipid bilayer, floating near an identical bilayer deposited on the hydrophilic surface of a silicon single crystal. Lipids were saturated di-acyl phosphocholines, with the number of carbon atoms per chain, n, varying from 16 to 20. The average and r.m.s. positions of the floating bilayer were determined by means of neutron specular reflectivity. Samples were prepared at room temperature (i.e. with the lipids in the gel phase) and measurements performed at various temperatures so that the whole region of transition from gel to fluid phase was explored. Data have been interpreted in terms of competition between the interbilayer potential and membrane fluctuations and used to estimate the bending rigidity of the bilayer.

cond-mat.soft↗