arXiv subjects

François Molino

Publications and source records attributed to François Molino.

7 recordsLinked to original sources

arXiv2022

Mapping cell cortex rheology to tissue rheology, and vice-versa

The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behaviour. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid foams as well as of tensegrity structures. A fractional visco-contractile cortex rheology is predicted to yield a high-frequency fractional visco-elastic monolayer rheology, where such a fractional behaviour has been recently observed experimentally at each scale separately. In particular cases, the mapping may be inverted, allowing to derive from a given tissue rheology the underlying cortex rheology. Interestingly, applying the same approach to a 2D hexagonal tiling fails, which suggests that the 2D character of planar cell cortex-based models may be unsuitable to account for realistic monolayer rheologies. We provide quantitative predictions, amenable to experimental tests through standard perturbation assays of cortex constituents, and hope to foster new, challenging mechanical experiments on cell monolayers.

cond-mat.soft↗

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

Non-linear oscillatory rheological properties of a generic continuum foam model: comparison with experiments and shear-banding predictions

The occurence of shear bands in a complex fluid is generally understood as resulting from a structural evolution of the material under shear, which leads (from a theoretical perspective) to a non-monotonic stationnary flow curve related to the coexistence of different states of the material under shear. In this paper we present a scenario for shear-banding in a particular class of complex fluids, namely foams and concentrated emulsions, which differs from other scenarii in two important ways. First, the appearance of shear bands is shown to be possible both without any intrinsic physical evolution of the material (e.g. via a parameter coupled to the flow such as concentration or entanglements) and without any finite critical shear rate below which the flow does not remain stationary and homogeneous. Secondly, the appearance of shear bands depends on the initial conditions, i.e., the preparation of the material. In other words, it is history dependent. This behaviour relies on the tensorial character of the underlying model (2D or 3D) and is triggered by an initially inhomogeneous strain distribution in the material. The shear rate displays a discontinuity at the band boundary, whose amplitude is history dependent and thus depends on the sample preparation.

cond-mat.soft↗

arXiv2010

Note and calculations concerning elastic dilatancy in 2D glass-glass liquid foams

When deformed, liquid foams tend to raise their liquid contents like immersed granular materials, a phenomenon called dilatancy. We have aready described a geometrical interpretation of elastic dilatancy in 3D foams and in very dry foams squeezed between two solid plates (2D GG foams). Here, we complement this work in the regime of less dry 2D GG foams. In particular, we highlight the relatively strong dilatancy effects expected in the regime where we have predicted rapid Plateau border variations.

cond-mat.soft↗

arXiv2009

A tentative geometrical description of static dilatancy in liquid foams: ordered 2D and 3D foams

Liquid foams have been observed to behave like immersed granular materials in at least one respect: deformation tends to raise their liquid contents, a phenomenon called dilatancy. We present a geometrical interpretation thereof in foams squeezed between two solid plates (2D GG foams), which contain pseudo Plateau borders along the plates, and in 3D foams. While experimental observations evidenced the effect of a continuous deformation rate (dynamic dilatancy), the present argument applies primarily to elastic deformation (static dilatancy). We show that the negative dilatancy predicted by Weaire and Hutzler (Phil. Mag. 83 (2003) 2747) at very low liquid fractions is specific to ideal 2D foams and should not be observed in the dry limit of real 2D foams.

cond-mat.soft↗

arXiv2009

Plateau border bulimia transition: discontinuities expected in three simple experiments on 2D liquid foams

We describe the geometry of foams squeezed between two solid plates (2D GG foams) in two main asymptotic regimes: fully dry floor tiles and dry pancakes. We predict an abrupt transition between both regimes, with a substantial change in the Plateau border radius. This should be observable in different types of experiments on such 2D GG foams: when foam is being progressively dried or wetted, when it is being squeezed further or stretched, when it coarsens through film breakage or Oswald ripening.

cond-mat.soft↗

arXiv2007

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.

cond-mat.soft↗