We discuss an evaporation-induced wetting transition on superhydrophobic stripes, and show that depending on the elastic energy of the deformed contact line, which determines the value of an instantaneous effective contact angle, two different scenar
ios occur. For relatively dilute stripes the receding angle is above 90$^circ$, and the sudden impalement transition happens due to an increase of a curvature of an evaporating drop. For dense stripes the slow impregnation transition commences when the effective angle reaches 90$^circ$ and represents the impregnation of the grooves from the triple contact line towards the drop center.
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 d
eformed 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 $phi_Sleq 0.2$.
By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are charac
terized by a texture period L and a fraction of the gas area $phi$. For very large values of h/R we recover the macroscopic formulae for a sphere moving towards a hydrophilic no-slip plane. For h/R=O(1) and smaller the drag force is smaller than predicted by classical theories for hydrophilic no-slip surfaces, but larger than expected for a sphere interacting with a uniform perfectly slipping wall. At a thinner gap, $hll R$ the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing $phi$. In the limit of very small separations our simulation data are in quantitative agreement with an asymptotic equation, which relates a correction to a force for superhydrophobic slip to texture parameters. In addition, we examine the flow and pressure field and observe their oscillatory character in the transverse direction in the vicinity of the wall, which reflects the influence of the heterogeneity and anisotropy of the striped texture. Finally, we investigate the lateral force on the sphere, which is detectable in case of very small separations and is maximized by stripes with $phi=0.5$.
