## 3 Results and Discussion
Figure 2: (**a**) Optical microscopy images of thin stiff PDMS film resting on a thick soft PDMS foundation, the PDMS foundation is cured with UV/ozone which modifies the elastic properties of its surface; (**b**) The system composed by the stiff film and the soft foundation is compressed uniaxially along the horizontal \(x\)-axis. The wavelength and amplitudes of the wrinkles are measured for successive values of the relative compression \(\delta\); (**c**) amplitudes, \(A_{1}\) and \(A_{2}\), and wavelength, \(\lambda\), as a function of the compression ratio \(\delta\). For small compression (\(\delta=33\%\)), we obtained a wrinkled surface, the apparent contact angle increased to \(135^{\circ}\) and the liquid penetrated into the surface roughness (Figure 3b), corresponding with the Wenzel state. By adding some stress (\(\delta=45\%\)), two peak amplitudes of wrinkle appeared and the contact angle increased to \(\theta_{\rm w}=145^{\circ}\) (Figure 3c), corresponding with the Wenzel state. Increasing the compression ratio (\(\delta=64\%\)), the apparent contact angle strongly increased and reached values close to \(180^{\circ}\), corresponding to the Cassie state (Figure 3d). Figure 4 shows the evolution of \(\cos(\theta)\) as a function of the roughness coefficient (\(\delta+1\)). The observed points (\(\bullet\)) for low/high roughness correspond to both the Wenzel and Cassie models. For low compression (\(\delta<0.4\)), the profile of the surface is sinusoidal. We observe an evolution of \(\cos(\theta)\) with a slope equal to 0.4; these results are in agreement with the Wenzel model (blue line in Figure 4). The theoretical line is obtained from Equation (2), where the roughness factor \(r\approx\delta+1\) and the equilibrium contact angle \(\theta_{\rm e}=110^{\circ}\). When the compression ratio increases (\(0.4<\delta<0.6\)), the profile of wrinkles evolves progressively from sinusoidal morphology to a more complex pattern characterized by a doubled wavelength. The evolution of the apparent angle as a function of the roughness coefficient shows that we reach an intermediate state in between the Wenzel and the Cassie states. This corresponds to a transition regime between these two extreme states. For higher compression ratio (\(\delta>0.6\)), the structure of the surface is characterized by a succession of identical \"pillars\" with a wavelength \(2\lambda\) and a larger amplitude (Figure 4). The ratio between the amplitude and the wavelength becomes larger than \(1/3\). In this case, the droplet of water stays above the surface of wrinkles and pockets of air are easily trapped below it. We thus obtain large contact angles close to \(180^{\circ}\). These results correspond to the theoretical line (red line) of the Cassie model (Figure 4). This theoretical curve is computed from Equation (3), by assuming that the area fraction \(\Phi_{\rm S}=\sigma/\lambda\), where \(\sigma\) is the width of the pillars and \(\lambda\) is the length between two consecutive pillars. In order to confirm superhydrophobicity in this case, we measured the tilt angle (at which the drop of water rolled off) and it was less than \(3^{\circ}\).