  When a drop of fluid hits a small solid target of comparable size, it expands
radially until reaching a maximum diameter and subsequently recedes. In this
work, we show that the expansion process of liquid sheets is controlled by a
combination of shear (on the target) and biaxial extensional (in the air)
deformations. We propose an approach toward a rational description of the
phenomenon for Newtonian and viscoelastic fluids by evaluating the viscous
dissipation due to shear and extensional deformations, yielding a prediction of
the maximum expansion factor of the sheet as a function of the relevant
viscosity. For Newtonian systems, biaxial extensional and shear viscous
dissipation are of the same order of magnitude. On the contrary, for thinning
solutions of supramolecular polymers, shear dissipation is negligible compared
to biaxial extensional dissipation and the biaxial thinning extensional
viscosity is the appropriate quantity to describe the maximum expansion of the
sheets. Moreover, we show that the rate-dependent biaxial extensional
viscosities deduced from drop impact experiments are in good quantitative
agreement with previous experimental data and theoretical predictions for
various viscoelastic liquids.
