Résumé
We investigate the dynamics of thin sheets freely expanding in air. The sheets are produced by impacting a drop onto a small target or onto a cushion of liquid nitrogen, in order to suppress any dissipation process. To disentangle the role of capillary, viscous and elastic forces in the dynamics of the sheets several materials are used, whose rheological characteristics are tuned over several orders of magnitude: viscous liquids, viscoelastic Maxwell fluids characterized by an elastic modulus, $G_0$, a relaxation time, $\tau$, and a zero-shear viscosity,$\eta_0=G_0 \tau$, and ultrasoft solids with elastic modulus as low as 10 Pa. For viscoelastic fluids, when$\tau$ is shorter than the typical lifetime of the sheet (~ 10 ms), the dynamics of the sheet is similar to that of Newtonian viscous liquids with equal zero-shear viscosity. In that case, the maximal expansion of the sheet, $d_{\rm{max}}$, decreases with $\eta_0$ and can be quantitatively accounted for by a model based on the viscous dissipation on the target. On the other hand, when $\tau$ is longer than the typical lifetime of the sheet, the behavior drastically differs. The sheet expansion is strongly enhanced as compared to that of viscous samples with comparable zero-shear viscosity, but is heterogeneous with the occurrence of cracks, revealing the elastic nature of the viscoelastic fluid. By contrast, sheets produced with ultrasoft solids expand but never break. Furthermore, we demonstrate that the surface tension of the soft elastic drops must be taken into account in order to successfully model their expansion. Overall, we have rationalized the spreading of sheets for viscous, viscoelastic and elastic materials by taking into account surface tension, elastic deformation and viscous dissipation.