Contact Angle Hysteresis on Superhydrophobic Stripes

We study experimentally and discuss quantitatively the contact angle hysteresis on striped superhydrophobic surfaces as a function of a solid fraction, $phi_S$. It is shown that the receding regime is determined by a longitudinal sliding motion the deformed contact line. Despite an anisotropy of the texture the receding contact angle remains isotropic, i.e. is practically the same in the longitudinal and transverse directions. The cosine of the receding angle grows nonlinearly with $phi_S$, in contrast to predictions of the Cassie equation. To interpret this we develop a simple theoretical model, which shows that the value of the receding angle depends both on weak defects at smooth solid areas and on the elastic energy of strong defects at the borders of stripes, which scales as $phi_S^2 ln phi_S$. The advancing contact angle was found to be anisotropic, except as in a dilute regime, and its value is determined by the rolling motion of the drop. The cosine of the longitudinal advancing angle depends linearly on $phi_S$, but a satisfactory fit to the data can only be provided if we generalize the Cassie equation to account for weak defects. The cosine of the transverse advancing angle is much smaller and is maximized at $phi_Ssimeq 0.5$. An explanation of its value can be obtained if we invoke an additional energy due to strong defects in this direction, which is shown to be proportional to $phi_S^2$. Finally, the contact angle hysteresis is found to be quite large and generally anisotropic, but it becomes isotropic when $phi_Sleq 0.2$.