This paper reports new analytical formulae for the longitudinal slip lengths for simple shear over a superhydrophobic surface, or bubble mattress, comprising a periodic array of unidirectional circular menisci, or bubbles, protruding into, or out of, the fluid. The accuracy of the formulae is tested against results from full numerical simulations; they are found to give small relative errors even at large no-shear fractions. In the dilute limit the formulae reduce to an earlier result by Crowdy (Phys. Fluids, vol. 22, 2010, 121703). They also extend analytical results of Sbragaglia & Prosperetti (Phys. Fluids, vol. 19, 2007, 043603) beyond the limit of a small protrusion angle.

Among the many aspects of laser ablation, development of conical structures induced by excimer laser radiation on polyimide surfaces has been thoroughly investigated. Because the mechanisms that produce these surface textures are not fully understood, two theories, photochemical bond breaking and thermal reaction, have been introduced. Here we present the first study of ultraviolet laser ablation behavior of thin films made from fluorinated poly(naphthyl-imide)s containing oxadiazole rings and the investigation of the mechanism of cone-like structure formation at two laser fluences, 57 and 240 mJ/cm2. The morphology of thin films before and after laser ablation was studied by using various spectroscopy techniques such as Fourier transform infrared spectroscopy, time-resolved emission and X-ray photoelectron spectroscopy, atomic force microscopy, and contact angle measurements. All of the data suggest impurities shielded at low fluence radiation (57 mJ/cm2) and a radiation hardening process at high value fluence (240 mJ/cm2), which are proposed as the main mechanisms for laser ablation of our polyimide films, and we bring evidence to support them.