François Graner

Fluid + Fluid = Solid: the strange maths of cellular materials

Liquid foams are made of gas bubbles surrounded by water. Surprisingly, they display elastic and plastic behaviours which are supposed to characterise solid materials. They are model systems to understand complex cellular materials (made of cells tiling the space), which behave simultaneously as solids and liquids. We have established tools to coarse-grain the discrete description, at the bubble scale, to link it with a continuum mechanics description, which encompasses the information useful at the global level.This enabled us to suggest and validate a theoretical model able to predict how a foam flows in general geometries. Such novel and rigorous multi-scale descriptive approach also applies to a large class of disordered systems, irrespective of the underlying physics, including aggregates of living cells or developing tissues. Our model system is the Drosophila metamorphosis, during which the fruit fly changes from larval to adult shape within a few days. We film the flyback (the dorsal thorax, see Figure) and its wingover several orders of magnitude in space and time. We characterize quantitatively, within a unified description, each cell process: cell divisions, cell rearrangements, cell size and shape changes, and programmed cell deaths. We relate them to tissue scale dynamics, namely tissue growth, and morphogenesis. In addition, measuring mechanical stresses in situ in the developing tissues evidences unexpected interplays between patterns of tissue elongation, cell division, and stress.