Liquid Hertz Contact: softness of weakly deformed drops on non-wetting substrates

The behavior of weakly deformed drops on non wetting surfaces is usually described using linear models. We show that these simple pictures cannot account for measurements of the dynamics of droplets that oscillate or bounce on super-hydrophobic substrates. We demonstrate that several peculiar experimental observations observed in previous works can be understood through a logarithmic correction of the linear model.