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Interplay between viscosity and elasticity in freely expanding liquid sheets

We investigate the dynamics of freely expanding liquid sheets prepared with fluids with different rheological properties, (i) viscous fluids with a zero-shear viscosity $η_0$ in the range $(1-1000) \, \mathrm{mPa.s}$ and (ii) viscoelastic Maxwell fluids whose elastic modulus, $G_0$, characteristic relaxation time, $τ$, and zero-shear viscosity, $η_0=G_0 τ$, can be tuned over several orders of magnitude. The sheets are produced by impacting a drop of fluid on a small cylindrical solid target. For viscoelastic fluids, we show that, when $τ$ is shorter than the typical lifetime of the sheet ($\sim 10$ ms), the dynamics of the sheet is similar to that of Newtonian viscous liquids with equal zero-shear viscosity. In that case, for little viscous samples ($η_0 <\sim 30$ mPa.s), the maximal expansion of the sheet, $d_{\rm{max}}$, is independent of $η_0$, whereas for more viscous samples, $d_{\rm{max}}$ decreases as $η_0$ increases. We provide a simple model to account for the dependence of the maximal expansion of the sheet with the viscosity that is based on an energy balance between inertia, surface tension and viscous shear dissipation on the solid target, and which accounts well for our experimental data. By contrast, when $τ$ 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.